Set up an equation to model this situation and solve:
2x=56
*Divide both sides by 2*
x=38
Hope this helps!!
I need help please :-)
Answer:
A. 1
B. slope: 1/2 mile/minute; the slope represents the speed of the car
C. correlation
Step-by-step explanation:
A. The points in the table lie on a straight line, so the correlation coefficient is exactly 1.
__
B. The ratio of distance to time is speed. That ratio for this data is 10 miles/20 minutes = 1/2 mile/minute. This is the slope of the graph.
__
C. Passage of time does not cause the car to go any particular distance, nor does the car's traveling cause time to pass. The best that can be said is that the car's distance traveled is strongly correlated with the time it takes. (The reason the car goes some distance is likely due to a cause not mentioned in the problem statement, for example, it was switched on and the motor started.)
Determine whether the relationship between the circumference of a circle and its diameter is a direct variation. If so, identify the constant of proportionality. Justify your response.
Answer:
The relationship between the circumference of a circle and its diameter represent a direct variation
The constant of proportionality is equal to [tex]\pi[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
Let
C=y
D=x
substitute
[tex]y=\pi x[/tex]
therefore
The relationship between the circumference of a circle and its diameter represent a direct variation
The constant of proportionality is equal to [tex]\pi[/tex]
Jenny must peel 300 oranges for kitchen duty. She peeled 30% of them in the morning and 45% of them in the afternoon.How many oranges are left for her to peel in the evening?
Final answer:
To find the number of oranges left for Jenny to peel in the evening, subtract the number of oranges she already peeled from the total number of oranges.
Explanation:
To find the number of oranges left for Jenny to peel in the evening, we need to subtract the number of oranges she already peeled in the morning and afternoon from the total number of oranges.
Jenny peeled 30% of the oranges in the morning, which is (30/100) * 300 = 90 oranges.
Jenny peeled 45% of the oranges in the afternoon, which is (45/100) * 300 = 135 oranges.
Therefore, the number of oranges left for Jenny to peel in the evening is 300 - 90 - 135 = 75 oranges.
Fill in the blank to complete the following sentence.
The two roots a+√b and a-√b are called _______ radicals.
Answer:
Conjugate radicals.
Step-by-step explanation:
The two roots a+√b and a-√b are called Conjugate radicals.
Just like in the complex number system where we have complex conjugates such as of 4+7i and 4 - 7i, the radicals also have their conjugate radicals. The conjugate radical of a+√b is simply obtained by changing the sign of the radical part of the expression to obtain a-√b. Therefore, the two expressions given are conjugate radicals
Answer:
Conjugate.
Step-by-step explanation:
The difference is in the signs. They are conjugate radicals.
4.
Solve the given system, using the substitution method.
y = 4x – 6
8x – 2y = 14
A.
(14, 12)
B.
(12, 14)
C.
There are an infinite number of solutions.
D.
There is no solution.
3.
Solve the given system, using the substitution method.
y = 3x – 7
6x – 2y = 12
A.
There is no solution.
B.
(12, 14)
C.
(14, 12)
D.
There are an infinite number of solutions.
5.
Solve, using the substitution method.
y + 2x = 7
14 – 4x = 2y
A.
The solution is (1, 5)
B.
The solution is (21, 0)
C.
There are an infinite number of solutions.
D.
There is no solution.
Answer:
4. No solution
Step-by-step explanation:
To solve a system of equations, find the (x,y) solution that satisfies both equations. One method that can be used is substitution. It is done by substituting one function into the other function and simplify.
Substitute y = 4x - 6 into 8x - 2y = 14.
8x - 2(4x - 6) = 14
8x - 8x + 12 = 14
12 = 14 FALSE
Since the variable was eliminated and a false statement was found, there is no solution to this system.
Solve 3 and 5 similarly. If the variable is eliminated again, but a true statement is fund then the solution is infinite. If the variable is not eliminated then substitute it back into one equation to find the other.
Final answer:
Using the substitution method, we find that Problem 4 has no solution (D), Problem 3 also has no solution (A), and Problem 5 has an infinite number of solutions (C).
Explanation:
To solve the given systems of equations using the substitution method, we substitute the expression for y from the first equation into the second equation and solve for x. Once x is found, we plug it back into the first equation to find y.
Problem 4:
Starting with the equations:
y = 4x – 6
8x – 2y = 14
We substitute the first equation into the second equation:
8x – 2(4x – 6) = 14
Solving for x:
8x – 8x + 12 = 14
x = 1/2 (not a solution, as the x terms cancel out)
Since the equation simplifies to 12 = 14, which is not true, we conclude that:
Option D. There is no solution.
Problem 3:
The system appears similar:
y = 3x – 7
6x – 2y = 12
Substitution gives:
6x – 2(3x – 7) = 12
And solving for x:
6x – 6x + 14 = 12
Which simplifies to 14 = 12, another impossibility.
So the answer is:
Option A. There is no solution.
Problem 5:
From our system:
y + 2x = 7
14 – 4x = 2y
We express y from the first equation:
y = 7 – 2x
Substitute it into the second one, and solve for x:
14 – 4x = 2(7 – 2x)
14 – 4x = 14 – 4x
This equation is true for all x; hence, y can be found for any corresponding x and the system has infinite solutions:
Option C. There are an infinite number of solutions.
A father who is 42 years old has a son and a daughter. The daughter is three times as old as the son. In 10 years the sum of all their ages will be 100 years. How old are the two siblings at present?
Answer:
The ages at present are:
Age of the son: 7 years oldAge of the daughter: 21 years oldExplanation:
Translate the word language to algebraic expressions.
1) A father who is 42 years old has a son and a daughter.
Age of the father: 422) The daughter is three times as old as the son.
Age of the son: x (this is the variable chosen, x = present age of the son)Age of the dagther: 3x (three times as old as the son, x)3) In 10 years the sum of all their ages will be 100 years
(42 + 10) + (x + 10) + (3x + 10) = 100↑ ↑ ↑ ↑
age of the father age of the son age of the daughter sum
4) How old are the two siblings at present:
Solve the equation
Delete the parenthesis: 42 + 10 + x + 10 + 3x + 10 = 100Combine like terms: 72 + 4x = 100Subtraction property of equalities (subtract 72 from each side)4x = 100 - 72
4x = 28
Division property of equalities (dive both sides by 4)x = 28 / 4
x = 7
5) Answers:
Age of the son: x = 7Age of the daughter: 3x = 3(7) = 216) Verification:
In ten years:age of the son: 7 + 10 = 17
age of the daughter: 21 + 10 = 31
age of the father: 42 + 10 = 52
sum of the ages: 17 + 31 + 52 = 100 ⇒ correct.
Answer: Son’s age:7 Daughter’s age:21
Step-by-step explanation:
1. The daughter is 3 times older than the son. Son will be x. Then the daughter will be 3x
2. In ten years the sum of their ages will be 100. Father+Son+Daughter=(42+10)+(x+10)+(3x+10)=100
3. Solve the equation:
72+4x=100
x=7
4. You have found the age of the son, 7. Now find the daughter. 3*7=21. The daughter is 21.
Success.!
A gym instructer has a total of 60 hand weights in her studio. Some of the hand weights are 3 pound weights and the rest are 5 pound weights. If their are 10 more 5-lb weights , than how many of each kind does she have?
Answer:
Let's imagine that x is the number of 3 pound weights that the gym instructer has.
Since we know that there are 10 more 5 pound weights, which tells us that the number of 5 pound weight is x + 10, and the total amount is 60 hand weights, we have:
x + x + 10 = 60
2x = 60 - 10
2x = 50
x = 50/2 = 25
So there are 25 3 pound weights at the gym.
From the number we have just found, we also know that the number of the 5 pound weights should be:
60 - 25 = 35 (hand weights)
PLEASE HELP! If you apply the changes below to the quadratic parent function, f(x) = x2, what is the equation of the new function?
Shift 1 unit right.
Vertically stretch by a factor of 5
Reflect over the x-axis
Answer:
Step-by-step explanation:
By the way, please use the symbol " ^ " to indicate exponentiation:
f(x) = x^2
Shifted 1 unit to the right, we get g(x) = (x - 1)^2
Vertically stretched by a factor of 5, we get h(x) = 5(x - 1)^2
Reflected over the x-axis: j(x) = -5(x - 1)^2
Answer:
The correct option is A.
Step-by-step explanation:
The quadratic parent function is
[tex]f(x)=x^2[/tex]
The translation is defined as
[tex]g(x)=k(x+a)^2+b[/tex] .... (1)
Where, k is vertical stretch, a is horizontal shift and b is vertical shift.
If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5
Substitute a=-1 and k=5 in equation (1).
[tex]g(x)=-5(x+(-1))^2+(0)[/tex]
[tex]g(x)=-5(x-1)^2[/tex]
Therefore the correct option is A.
A 25-foot ladder leans against a wall. The base of the ladder is 15 feet from the bottom of the wall. How far up the wall does the top of the ladder reach?
Answer: 20 feet.
Step-by-step explanation:
Observe the right triangle attached.
You need to find the value of "x".
Then, you can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.
In this case, you can identify that:
[tex]a=25ft\\b=15ft\\c=x[/tex]
Substitute these values into [tex]a^2=b^2+c^2[/tex]:
[tex](25ft)^2=(15ft)^2+x^2[/tex]
Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:
[tex]x^2=(25ft)^2-(15ft)^2[/tex]
[tex]x=\sqrt{(25ft)^2-(15ft)^2}[/tex]
[tex]x=20ft[/tex]
ANSWER
20ft
EXPLANATION
The ladder, the wall and the ground formed a right triangle.
Let how far up the wall does the top of the ladder reached be x units.
The 25ft ladder is the hypotenuse.
The shorter legs are, 15ft and x ft
Then from Pythagoras Theorem,
[tex] {x}^{2} + {15}^{2} = {25}^{2} [/tex]
[tex] {x}^{2} + 225 = 625[/tex]
[tex] {x}^{2}= 625 - 225[/tex]
[tex]{x}^{2}= 400[/tex]
[tex]x = \sqrt{400} [/tex]
[tex]x = 20ft[/tex]
Therefore the ladder is 20 ft up the wall.
Researchers in a local area found that the population of rabbits with an initial population of 20 grew continuously at the rate of 5% per month the fox population had an initial value of 30 and grew continuously at the rate of 3% per month. Find, to the nearest tenth of a month, how long it takes for these populations to be equal
The answer is:
It will take 20.5 months to the populations to be equal.
Why?Since from the statement we know that both populations are growing, we need to use the formula to calculate the exponential growth.
The exponential growth is defined by the following equation:
[tex]P(t)=StartPopulation*e^{\frac{growthpercent}{100}*t}[/tex]
Now,
Calculating for the rabbits, we have:
[tex]StartPopulation=20\\GrowthPercent=5\\[/tex]
So, writing the equation for the rabbits, we have:
[tex]P(t)=20*e^{\frac{5}{100}*t}[/tex]
[tex]P(t)=20*e{0.05}*t}[/tex]
Calculating for the fox, we have:
[tex]StartPopulation=30\\GrowthPercent=3\\[/tex]
So, writing the equation for the fox, we have:
[tex]P(t)=30*e{\frac{3}{100}*t}[/tex]
[tex]P(t)=30*e^{0.03}*t}[/tex]
Then, if we want to calculate how long does it takes for these populations to be equal, we need to make their equations equal, so:
[tex]20*e^{0.05}*{t}=30*e^{0.03}*{t}\\\\\frac{20}{30}=\frac{e^{0.03}*{t}}{e^{0.05}*t}}\\\\0.66=e^{0.03t-0.05t}=e^{-0.02t}\\\\0.66=e^{-0.02t}\\\\ln(0.66)=ln(e^{-0.02t})\\\\-0.41=-0.02t\\\\t=\frac{-0.41}{-0.02}=20.5[/tex]
Hence, we have that it will take 20.5 months to the populations to be equal.
To find out how long it takes for the populations to be equal, set up and solve an equation using the growth rates of the rabbit and fox populations.
Explanation:To find out how long it takes for the rabbit population and the fox population to be equal, we can set up and solve an equation. Let's start by setting up an equation for each population growth:
Rabbit population: P(t) = 20 * (1 + 0.05)^t
Fox population: P(t) = 30 * (1 + 0.03)^t
We want to find the value of t when the two populations are equal, so we set the equations equal to each other and solve for t:
20 * (1 + 0.05)^t = 30 * (1 + 0.03)^t
Divide both sides by 20:
(1 + 0.05)^t = 1.5 * (1 + 0.03)^t
Now take the natural logarithm of both sides:
t * ln(1 + 0.05) = ln(1.5 * (1 + 0.03)^t)
Divide both sides by ln(1 + 0.05):
t = ln(1.5 * (1 + 0.03)^t) / ln(1 + 0.05)
Using a calculator, we can approximate the value of t to the nearest tenth of a month.
Learn more about Population Growth here:https://brainly.com/question/18415071
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Distribute and combine like terms. Please show all of your work.
-5(3x + 7) - 4(x - 4) + 11
For this case we have the following expression:
[tex]-5 (3x + 7) -4 (x-4) +11[/tex]
For simplicity we follow the steps:
We apply distributive property to the terms within the parenthesis, bearing in mind that:
[tex]- * + = -\\- * - = +\\-15x-35-4x + 16 + 11 =[/tex]
We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.
[tex]-15x-4x-35 + 16 + 11 =\\-19x-8[/tex]
ANswer:
[tex]-19x-8[/tex]
Answer: 19x - 8
Steps-5(3x + 7)
Apply the distributive law: a( b + c ) = ab + ac
a = -5, b = 3x, c = 7
= -5 * 3x + (-5) x 7
Apply minus - plus rules
+(-a) = -a
= -5 * 3x - 5 x 7
Simplify
-5 * 3x - 5 x 7
Multiply the numbers: 5 x 3 = 15
= -15x - 5 x 7
Multiply the numbers: 5 x 7 = 35
= -15x - 35
Plug in the values
-15x - 35 - 4(x - 4) + 11
------------------------------------------------------------------
-4(x - 4)
Apply the distributive law: a( b - c ) = ab - ac
a = -4, b = x, c = 4
= -4x - (-4) * 4
Apply minus - plus rules
-(-a) = a
= -4x + 4 * 4
Multiply the numbers: 4 * 4 = 16
= -4x + 16
Plug in the values
-15x - 35 - 4x + 16 + 11
------------------------------------------------------------------
Simplify
-15x - 35 - 4x + 16 + 11
Group like terms
= -15x - 4x - 35 + 16 + 11
Add similar elements: -15x - 4x = -19x
= -19x - 35 + 16 + 11
Add/Subtract the numbers: -35 + 16 + 11 = -8
= 19x - 8
Which strategy would not correctly solve this story problem? Mellie ran for 30 minutes on Monday, for 45 minutes on Tuesday, and for 25 minutes on Wednesday. How long did Mellie run if she kept up this plan for 8 weeks? A. Translate into an equation. (30 + 45 + 25) × 8 = m B. Use logical reasoning. Add together the number of minutes Mellie exercises each week: 30 + 45 + 25 = 100. Multiply 100 by the number of weeks Mellie keeps up with this plan. C. Draw a diagram. Draw 4 groups of dots to show the 3 types of exercise and the weeks. Write 30, 45, 25, and 8 in each circle. Add the four numbers. D. Make a table. Week 1 2 3 4 5 6 7 8 Total (minutes) 100 200 300 400 500 600 700
Answer:
C. Draw a diagram. Draw 4 groups of dots to show the 3 types of exercise and the weeks. Write 30, 45, 25, and 8 in each circle. Add the four numbers.
Step-by-step explanation:
You might be able to get there starting with strategy C, but it is incomplete as written and will not solve the problem.
Solve the system by using a matrix equation
3x-5y=3
3x-4y=3
Answer:
The correct answer is B. (1,0).
Answer: B. (1,0)
Step-by-step explanation:
1. We will use the matrix method to solve this problem.
3 -5 3
3 -4 3
2. Apply to Row2 : Row2 - Row1.
3 -5 3
0 1 0
3. Simplify rows.
3 -5 3
0 1 0
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
4. Apply to Row1 : Row1 + 5 Row2.
3 0 3
0 1 0
5. Simplify rows.
1 0 1
0 1 0
Note: The matrix is now in reduced row echelon form.
6. Therefore,
x=1
y=0
or (1,0).
On a world globe, the distance between City A and City B, two cities that are actually 10 comma 480 kilometers apart, is 13.9 inches. The actual distance between City C and City D is 1590 kilometers. How far apart are City C and City D on this globe?
City C and City D are
nothing inches apart on this globe.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Answer:
[tex]2.1\ in[/tex]
Step-by-step explanation:
we know that
The scale of the world globe is equal to
[tex]\frac{13.9}{10,480}\frac{in}{km}= 0.0013\frac{in}{km}[/tex]
To find the distance between City C and City D on the globe, multiply the actual distance by the scale
[tex]0.0013\frac{in}{km}*(1,590\ km)=2.1\ in[/tex]
SOMEONE HELP MEEEEEE 75 POINTS TO THE PERSON THAT HELPS
1. Indicate the equation of the given line in standard form.
The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).
2. Indicate the equation of the given line in standard form.
The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).
3. Indicate the equation of the given line in standard form.
The line containing the midpoints of the legs of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.
4. Indicate the equation of the given line in standard form.
The line containing the hypotenuse of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.
5. Indicate the equation of the given line in standard form.
The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
6. Indicate the equation of the given line in standard form.
The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).
7. Indicate the equation of the given line in standard form.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
8. Indicate the equation of the given line in standard form.
The line containing the diagonal of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
Answer:
Part 1) [tex]9x-7y=-25[/tex]
Part 2) [tex]2x-y=2[/tex]
Part 3) [tex]x+8y=22[/tex]
Part 4) [tex]x+8y=35[/tex]
Part 5) [tex]3x-4y=2[/tex]
Part 6) [tex]10x+6y=39[/tex]
Part 7) [tex]x-5y=-6[/tex]
Part 8)
case A) The equation of the diagonal AC is [tex]x+y=0[/tex]
case B) The equation of the diagonal BD is [tex]x-y=0[/tex]
Step-by-step explanation:
Part 1)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{2-6}{2},\frac{-3+5}{2})[/tex]
[tex]M=(-2,1)[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-1=\frac{9}{7}(x+2)\\ \\y=\frac{9}{7}x+\frac{18}{7}+1\\ \\y=\frac{9}{7}x+\frac{25}{7}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=\frac{9}{7}x+\frac{25}{7}[/tex]
Multiply by 7 both sides
[tex]7y=9x+25[/tex]
[tex]9x-7y=-25[/tex]
Part 2)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{1+5}{2},\frac{0-2}{2})[/tex]
[tex]M=(3,-1)[/tex]
step 2
Find the slope
The slope between two points is equal to
[tex]m=\frac{-2-0}{5-1}=-\frac{1}{2}[/tex]
step 3
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
Find the slope of the line perpendicular to the segment joining the given points
[tex]m1=-\frac{1}{2}[/tex]
[tex]m1*m2=-1[/tex]
therefore
[tex]m2=2[/tex]
step 4
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=2[/tex] and point [tex](1,0)[/tex]
[tex]y-0=2(x-1)\\ \\y=2x-2[/tex]
step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=2x-2[/tex]
[tex]2x-y=2[/tex]
Part 3)
In this problem AB and BC are the legs of the right triangle (plot the figure)
step 1
Find the midpoint AB
[tex]M1=(\frac{-5+1}{2},\frac{5+1}{2})[/tex]
[tex]M1=(-2,3)[/tex]
step 2
Find the midpoint BC
[tex]M2=(\frac{1+3}{2},\frac{1+4}{2})[/tex]
[tex]M2=(2,2.5)[/tex]
step 3
Find the slope M1M2
The slope between two points is equal to
[tex]m=\frac{2.5-3}{2+2}=-\frac{1}{8}[/tex]
step 4
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{8}[/tex] and point [tex](-2,3)[/tex]
[tex]y-3=-\frac{1}{8}(x+2)\\ \\y=-\frac{1}{8}x-\frac{1}{4}+3\\ \\y=-\frac{1}{8}x+\frac{11}{4}[/tex]
step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=-\frac{1}{8}x+\frac{11}{4}[/tex]
Multiply by 8 both sides
[tex]8y=-x+22[/tex]
[tex]x+8y=22[/tex]
Part 4)
In this problem the hypotenuse is AC (plot the figure)
step 1
Find the slope AC
The slope between two points is equal to
[tex]m=\frac{4-5}{3+5}=-\frac{1}{8}[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{8}[/tex] and point [tex](3,4)[/tex]
[tex]y-4=-\frac{1}{8}(x-3)[/tex]
[tex]y=-\frac{1}{8}x+\frac{3}{8}+4[/tex]
[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]
Multiply by 8 both sides
[tex]8y=-x+35[/tex]
[tex]x+8y=35[/tex]
Part 5)
The longer diagonal is the segment BD (plot the figure)
step 1
Find the slope BD
The slope between two points is equal to
[tex]m=\frac{4+2}{6+2}=\frac{3}{4}[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex] and point [tex](-2,-2)[/tex]
[tex]y+2=\frac{3}{4}(x+2)[/tex]
[tex]y=\frac{3}{4}x+\frac{6}{4}-2[/tex]
[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]
Multiply by 4 both sides
[tex]4y=3x-2[/tex]
[tex]3x-4y=2[/tex]
Note The complete answers in the attached file
Margaret makes a square frame out of four pieces of wood. Each piece of wood is a rectangular prism with a length of 40 centimeters, a height of 4 centimeters, and a depth of 6 centimeters. What is the total volume of the wood used in the frame?
V= 3,840 cm
Volume is L x W x H
and W is the same as Depth
So you would multiply those and multiply it again by four to make up for the other pieces of wood.
Final answer:
The total volume of wood used in making the square frame is 3840 cubic centimeters, which is calculated by finding the volume of one piece (960 cm³) and multiplying it by the number of pieces (4).
Explanation:
The question concerns the calculation of the total volume of wood used in making a square frame. Each piece of wood is a rectangular prism with given dimensions. To find the total volume, one must multiply the length, height, and depth of a single piece and then multiply the result by the number of pieces.
To calculate the volume of a single piece of wood, we use the formula for the volume of a rectangular prism, which is length × width × height. For one piece of wood:
Length = 40 cm
Width (depth) = 6 cm
Height = 4 cm
The volume of one piece of wood is therefore 40 cm × 6 cm × 4 cm = 960 cm³.
Since there are four pieces that make up the frame, the total volume of wood used is:
960 cm³/piece × 4 pieces = 3840 cm³
Thus, the total volume of the wood used in the frame is 3840 cubic centimeters.
Lily takes a train each day to work that averages 35 miles per hour . On her way home her train ride follows the same path and averages 45 miles per hour . If the total trip takes 2.5 hours , what equation can be used to find n, the number of miles Lilly's homes is for work
Answer:
49.2 miles
Step-by-step explanation:
The distance remains the same. d
The time spent on the outbound trip is t1 = -------------
35 mph
and that on the inbound (return) trip is
d
t2 = -------------
45 mph
We combine these two fractions and set the sum = to 2.5 hours:
d(1/35 + 1/45) = 5/2
We wish to solve for d, the distance between home and work.
The LCD of 35, 45 and 2 is 630.
1/35 becomes 18/630; 1/45 becomes 14/630, and 5/2 becomes 1575/630. Then we have the simpler equation d(18 + 14) = 1575, or
d(32) = 1575, and d is then
d = 1575/32 = 49.2 miles
A department store is haveing 30% off sale on all pair of jeans. If you have an coupon for an additional 15% off any items price, how much will a $60.00 pair of Jeans cost? (hint: first find the scale price of the jeans and then take the coupon discount off the sale price)
then jeans will cost $38.25
Answer:
the answer would be $35.70
Step-by-step explanation:
0.70 x $60 = $42
0.85 x $42 = $35.70
This is using multipliers so the amount off will be taken away from 1 and that answer times amount needed to found from will give the answer you are looking for
which of the following formulas would find the lateral area of a right cylinder where h is the height and r is the radius
Answer:
B. [tex]LA=2\pi rh[/tex]
Step-by-step explanation:
The lateral area of the right cylinder refers to the curved surface area.
The lateral area of the right cylinder does not include the two circular bases.
The lateral area is given by the formula;
[tex]LA=2\pi rh[/tex]
The correct choice is B.
Answer:
thats the correct answer =B
Step-by-step explanation:
Which of these statements are true?
A. Both graphs have exactly one asymptote
B. Both graphs have been shifted and flipped.
C. Both graphs are logarithmic functions.
D. Both graphs are exponential functions.
Answer:
Step-by-step explanation:
Given are two graphs. f(x) will have x axis as asymptote while x=2 is asymptote for g(x).
Hence both graphs have exactly one asymptote
First graph passes through (0,2)
f(x) is exponential while g(x) is log.
Both graphs are shifted because f(x) is vertically shifted by 1, while g(x) is horizontally shifted by 3 units to left
What is the length of the conjugate axis?
[tex]\frac{(x-2)^2}{36} - \frac{(y+1)^2}{64} =1[/tex]
Answer:
the length of the conjugate axis is 16
Step-by-step explanation:
We know that the general equation of a hyperbola with transverse horizontal axis has the form:
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]
Where the point (h, k) are the coordinates of the center of the ellipse
2a is the length of the transverse horizontal axis
2b is the length of the conjugate axis
In this case the equation of the ellipse is:
[tex]\frac{(x-2)^2}{36} + \frac{(y+1)^2}{64} = 1[/tex]
Then
[tex]b^2 = 64\\\\b = \sqrt{64}\\\\b = 8\\\\2b = 16[/tex]
Finally the length of the conjugate axis is 16
Final answer:
The length of the conjugate axis of the given hyperbola \(\frac{(x-2)²}{36} - \frac{(y+1)²}{64} =1\) is 16 units.
Explanation:
The question asks to find the length of the conjugate axis of a hyperbola given by the equation:
\(\frac{(x-2)²}{36} - \frac{(y+1)²}{64} =1\)
In the equation of a hyperbola of the form \(\frac{(x-h)²}{a²} - \frac{(y-k)²}{b²} = 1\), where \((h,k)\) is the center of the hyperbola, \(a²\) is the denominator under the \(x\)-term, and \(b^2\) is the denominator under the \(y\)-term, the length of the transverse axis is \(2a\) and the length of the conjugate axis is \(2b\).
For the given hyperbola:
a² = 36, so \(a = 6\)
b² = 64, so \(b = 8\)
Therefore, the length of the conjugate axis is \(2 \times 8 = 16\) units.
the variable used to show correlation is r, which is also known as the correlation constant?
A. True
B. False
Answer:
FALSE
Correlations tell us the strength and the direction of the relationship between two variables. The main result of a correlation is called the correlation coefficient (or "r").
Hope this helps and have a great day!!
[tex]Sofia[/tex]
Answer:false
Step-by-step explanation:
Which of the following points is not on the graph of y=-3x^2+6x-4 ?
(6, -70)
(4, -28)
(-8, -244)
(12, -364)
Answer:
(6, -70) is not on the graph
Step-by-step explanation:
we have
[tex]y=-3x^{2}+6x-4[/tex]
we know that
If a ordered pair is on the graph of the quadratic equation, then the ordered pair must satisfy the quadratic equation
Verify each case
Substitute the x-coordinate of the ordered pair in the quadratic equation to find the value of y and then compare the results
case 1) (6, -70)
For x=-6
[tex]y=-3(-6)^{2}+6(-6)-4=-148[/tex]
[tex]-148\neq-70[/tex]
therefore
the ordered pair is not on the graph
case 2) (4, -28)
For x=4
[tex]y=-3(4)^{2}+6(4)-4=-28[/tex]
[tex]-28=-28[/tex]
therefore
the ordered pair is on the graph
case 3) (-8,-244)
For x=-8
[tex]y=-3(-8)^{2}+6(-8)-4=-148[/tex]
[tex]-244=-244[/tex]
therefore
the ordered pair is on the graph
case 4) (12,-364)
For x=12
[tex]y=-3(12)^{2}+6(12)-4=-148[/tex]
[tex]-364=-364[/tex]
therefore
the ordered pair is on the graph
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
-4a^2 -7a^2 - 2ab +3ab +9b^2 -5b^2
11a^2 + ab +4b^2
Step-by-step explanation:
Answer:
-11a^2+ab+4ab^2
Step-by-step explanation:
The expression f(x) = 12(1.035)x models the monthly growth of membership in the new drama club at a school. According to the function, what is the monthly growth rate?
A.
0.35%
B.
1.035%
C.
3.5%
D.
12%
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
The expression is defined as
[tex]f(x)=12(1.035)^x------------------------(1)[/tex]
As we know the general form of exponential function:
[tex]f(x)=a(1+r)^x--------------------------(2)[/tex]
Here, a denotes the initial amount.
r denotes the growth rate.
On comparing, we get that
[tex]1+r=1.035\\\\r=1.035-1\\\\r=0.035\\\\r=0.035\times 100\%\\\\r=3.5\%[/tex]
Hence, option 'C' is correct.
Answer:
C) 3.5%
Step-by-step explanation:
how to find the derivative of x + y2 = ln(x/y) ? please show all workings and simplify!
the answer is supposed to be y^2-x/xy
Answer:
Step-by-step explanation:
If your function is
[tex]x+y^2=ln(\frac{x}{y} )[/tex], that is definitely not the answer you should get after taking the derivative implicitely. Rewrite your function to simplify a bit:
[tex]x+y^2=ln(x)-ln(y)[/tex]
Take the derivative of x terms like "normal", but taking the derivative of y with respect to x has to be offset by dy/dx. Doing that gives you:
[tex]1+2y\frac{dy}{dx}=\frac{1}{x}-\frac{1}{y}\frac{dy}{dx}[/tex]
Collect the terms with dy/dx on one side and everything else on the other side:
[tex]2y\frac{dy}{dx}+\frac{1}{y}\frac{dy}{dx}=\frac{1}{x}-1[/tex]
Now factor out the common dy/dx term, leaving this:
[tex]\frac{dy}{dx}(2y+\frac{1}{y})=\frac{1}{x}-1[/tex]Now divide on the left to get dy/dx alone:
[tex]\frac{dy}{dx}=\frac{\frac{1}{x}-1 }{2y+\frac{1}{y} }[/tex]
Simplify each set of fractions to get:
[tex]\frac{dy}{dx}=\frac{\frac{1-x}{x} }{\frac{2y^2+1}{y} }[/tex]
Bring the lower fraction up next to the top one and flip it upside down to multiply:
[tex]\frac{dy}{dx}=\frac{1-x}{x}[/tex]×[tex]\frac{y}{2y^2+1}[/tex]
Simplifying that gives you the final result:
[tex]\frac{dy}{dx}=\frac{y-xy}{x(2y^2+1)}[/tex]
or you could multiply in the x on the bottom, as well. Same difference as far as the solution goes. You'd use this formula to find the slope of a function at a point by subbing in both the x and the y coordinates so it doesn't matter if you do the distribution at the very end or not. You'll still get the same value for the slope.
Using the quadratic formula to solve 2x^2 = 4x - 7, what are the values of x?
Explaining the quadratic formula application in solving an equation.
The quadratic formula:
Given equation: [tex]2x^2 = 4x - 7[/tex]Rearrange into a quadratic equation: [tex]2x^2 - 4x + 7 = 0[/tex]Using the quadratic formula, a=2, b=-4, c=7Substitute into the formula to get x = 1 or x = -3/2AP CALC HELP!!! Worth 38 points. AP Calc AB differental FRQ
Answer:
5a. approximately 6 grams remain after 2 seconds
5b. The graph shown cannot be a solution. The solution has negative slope everywhere.
5c. y = 50/(t+5)
5d. The amount is changing at a decreasing rate. (As y gets smaller, so does the magnitude of dy/dt.)
Step-by-step explanation:
5a. The tangent line has the equation ...
y = f'(0)t +f(0)
Here, that is
y = -0.02·10²·t +10 = 10 -2t
Then at t=2, the value is ...
y = 10 -2·2 = 6 . . . . grams remaining
__
5b. y² is always positive (or zero), so -0.02y² will be negative. This is dy/dt, the slope of the curve with respect to time, so any curve with positive slope somewhere cannot be a solution.
__
5c. The equation is separable so can be solved by integrating ...
∫y^-2·dy = -0.02∫dt
-y^-1 = -0.02t +c . . . . for some arbitrary constant c
Multiplying by -50 gives ...
50/y = t + c . . . . for some constant c
We can find the value of c by invoking the initial condition. At t=0, y=10, so we have ...
50/10 = 0 +c = 5
Then, solving for y, we get ...
y = 50/(t+5)
__
5d. As noted above (and as described by the differential equation), the magnitude of the rate of change is proportional to the square of y. As y decreases, its rate of change will also decrease (faster). You can see that the curve for y flattens out as t increases. The amount of the substance is changing at a decreasing rate.
Jina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Jina drove home, there was no traffic and the trip only took
4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Jina live from the mountains?
Do not do any rounding.
Answer:
264 miles
Step-by-step explanation:
Using the relation ...
distance = speed · time
we can rearrange to get ...
speed = distance/time
We can choose to let d represent the distance we want to find. Then Jina's speed going to the mountains is d/6. Her speed coming home is then d/6+22. It takes Jina 4 hours at that speed to cover the same distance, so we have ...
d = 4(d/6 +22)
d = 2/3d +88 . . . . eliminate parentheses
1/3d = 88 . . . . . . . subtract 2/3d
d = 264 . . . . . . . . . multiply by 3
Jina lives 264 miles from the mountains.
I need a clear understanding....
You have no more than $65 to spend after paying your bills. You want a drink that costs
$2.25 including tax, and you want to buy a pair of shoes, which will have 7% sales tax.
What is the inequality that represents the amount of money you have to spend?
a. x + 0.07x + 2.25 > 65
b. x + 0.07x + 2.25 ≤ 65
c. x + 0.07x + 2.25 < 65
d. x + 0.07x + 2.25 ≥ 65
Answer: B
Step-by-step explanation: You have no more than $65 which means you will want to spend equal to or less. Since you have $65, you will be able to spend up to that amount but you will not be able to spend any more than that. So, you will need to make sure the final price remains under or equal to your amount.