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 recipe calls for 1/6 of a cup of white sugar and 3/6 of a cup of brown sugar. What is the total amount of sugar in the recipe?
Answer:
2/3 cup
Step-by-step explanation:
Add 1/6 cup and 3/6 cup, obtaining 4/6 cup of sugar, total.
4/6 reduces to 2/3.
The total amt of sugar in the recipe is 2/3 cup.
For questions 4-5, find the volume of the cylinder in terms of pi.
4. height 8, radius 3.8
5. height 14, radius 5
Answer:
hope it helps you!!!!!!!!
The volume of a cylinder with a height of 8 and a radius of 3.8 is 115.52π cubic units, and with a height of 14 and a radius of 5, it is 350π cubic units.
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height of the cylinder.
For question 4 with a height of 8 and a radius of 3.8, the volume would be: V = π(3.8)²(8) = 115.52π cubic units.
For question 5 with a height of 14 and a radius of 5, the volume would be: V = π(5)²(14) = 350π cubic units.
These calculations illustrate how to determine the volume of cylinders using their respective dimensions, providing a fundamental understanding of geometric principles and applications.
Derrick needs to figure out how he’s doing on his test scores so far this year. You can help by calculating the mean and the median to get an overall picture of his scores. Below are all of his scores: 25, 40, 68, 85, 95, 98, 70, 78, 85, 100 What is Derrick’s mean test score so far? What is Derrick’s median test score so far? Which gives a better picture of his scores?
Answer: Derrick’s mean test score= 74.4
Derrick’s median test score = 81.5
Better picture of his scores is given by Median.
Step-by-step explanation:
The given data : 25, 40, 68, 85, 95, 98, 70, 78, 85, 100
[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}\\\\\Rightarrow\ \text{Mean}=\dfrac{744}{10}=74.4[/tex]
For Median , Arrange the data in order
25, 40, 68, 70, 78, 85, 85, 95, 98, 100
Median = Mean of two middle most value
[tex]\text{Median}=\dfrac{78+85}{2}=81.5[/tex]
Since the data set has outlier (25) and mean is affected by outlier.
So the better picture of his scores given by median value.
Answer:
(A) 74.4 (B) 81.5 (C) Median (Look below or dont)
Step-by-step explanation:
Use the following half-life graph to answer the following question:
A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.5625.
The graph is attached.
What is the mass of the radioactive isotope remaining at 2.0 minutes? (5 points)
A. 25.0 mg
B. 12.5 mg
C. 6.25 mg
D. 3.13 mg
Answer:
The correct answer is 12.5.
Step-by-step explanation:
When looking at the x axis, you locate the 2. After 2 minutes, the point connects at (2,12.5). Therefore, the correct answer is 12.5.
Answer:
At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.
Step-by-step explanation:
To get the answer of this question we will solve this further with the help of the equation [tex]A_{t}=A_{0}e^{-kt}[/tex]
where k = decay constant
t = time for decay
[tex]A_{0}[/tex] = Initial quantity taken
From the graph attached we can say that 50 mg of a radioactive element remained half in 1 minute.
So the equation becomes
[tex]50=25e^{-k(1)}[/tex]
Now we take natural log on both the sides of the equation
ln50 = ln[25.[tex]e^{-k}[/tex]
3.912 = ln25 + [tex]ln(e^{-k})[/tex]
3.912 = 3.219 + (-k)lne
3.912 - 3.219 = -k [since lne = 1]
0.693 = -k
k = -0.693
Now we will calculate the remaining quantity of the element after 2 minutes
[tex]A_{t}=50.e^{-(0.693)(2)}[/tex]
= [tex]50.e^{-1.386}[/tex]
= [tex]\frac{50}{e^{1.386}}[/tex]
= [tex]\frac{50}{3.9988}[/tex]
= 12.50 mg
Now we confirm this value from the graph.
At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.
Please simplify, 50 points.
(sin Θ - cos Θ) - (sin Θ + cos Θ)^2
Answer choices are attached.
Answer:
The trigonometric equation (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:Using x for Θ: (sinx - cosx)^2 - (sinx + cosx)^2 = (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) = - 2 sinx cosx - 2 sinx cosx = - 4 sinx cosx = - 2sin(2x)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Expand (sinΘ + cosΘ)²
= sinΘ - cosΘ - (sin²Θ + 2 sinΘcosΘ + cos²Θ)
= sinΘ - cosΘ - sin²Θ - 2sinΘcosΘ - cos²Θ
= sinΘ - cosΘ - 2sinΘcosΘ - (sin²Θ + cos²Θ)
= - 2sinΘcosΘ - cosΘ + sinΘ - 1 → D
Complete the square to determine the minimum or maximum value of the function defined by the expression. ?x2 + 10x + 5 )
Answer:
(x+5)^2-20
(-5,-20)
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term to complete the square.
A triangle with a base of 1/4 meter has an area of 8 square meters. What is the height, in meters, of the triangle? A. 1 B. 12 C. 32 D. 64
Answer:
D.64
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Givens
A = 8 square meters.
B = 1/4 meter
h = ?
Formula
A = 1/2 B * h
Solution
8 = 1/2 1/4 * h Combine
8 = 1/8 * h Multiply by 8
8*8 = 1/8 * 8 * h
h =64 m
D answer
==============
I had to edit this to get it. Give the brainliest to the other responder.
Simplify negative 5 minus the square root of negative 44 negative 5 minus 4 times the square root of 11 i negative 5 minus 4 i times the square root of 11 negative 5 minus 2 i times the square root of 11 negative 5 minus 2 times the square root of 11 i
To simplify negative 5 minus the square root of negative 44, you need to use imaginary numbers. The expression simplifies to -5 minus 2i√11. Hence, the correct answer is Option B.
To simplify
negative 5 minus the square root of negative 44, we need to work with imaginary numbers. Recall that the square root of -1 is defined as i, which is the imaginary unit. Using this, we can simplify the given expression step-by-step:
Recognize that
√-44 can be written as
√(-1 × 44).
Since
√(-1 × 44) = √(-1) × √44, and
√(-1) = i, we get
i × √44.
Now, we simplify
√44:
√44 = √(4×11) = 2√11.
Therefore,
i × √44 = 2i√11.
Putting it all together,
-5 - √-44 becomes
-5 - 2i√11.
Hence, the correct answer is
Option B. negative 5 minus 2 i times the square root of 11.
The fully simplified form of the expression is [tex]-25 - 14i \sqrt{11}[/tex]
To simplify the expression [tex]-5 - \sqrt{-44} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \cdot \sqrt{11} - 5 - 2 \cdot \sqrt{11} i[/tex], we will follow these steps:
Understanding Square Roots of Negative Numbers:
The square root of a negative number can be written using the imaginary unit [tex]i[/tex], where [tex]i = \sqrt{-1}[/tex].
Thus, we can rewrite [tex]\sqrt{-44}[/tex] as follows:
[tex]\sqrt{-44} = \sqrt{-1 \cdot 44} = \sqrt{-1} \cdot \sqrt{44} = i \cdot \sqrt{44}[/tex]
Note that [tex]\sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11}[/tex].
Thus,
[tex]\sqrt{-44} = 2i \sqrt{11}[/tex]
Now substituting this into the expression gives us:
[tex]-5 - 2i \sqrt{11} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \sqrt{11} - 5 - 2\sqrt{11} i[/tex]
Combining Like Terms:
Now combine all the real parts and the imaginary parts separately in the expression:
Real Part:
[tex]-5 - 5 - 5 - 5 - 5 = -25[/tex]
Imaginary Part:
[tex]-2i\sqrt{11} - 4i\sqrt{11} - 4i\sqrt{11} - 2i\sqrt{11} - 2i\sqrt{11}[/tex]
Combining these gives:
[tex]-2i \sqrt{11} - 4i \sqrt{11} - 4i \sqrt{11} - 2i \sqrt{11} - 2i \sqrt{11} = -14i\sqrt{11}[/tex]
Final Result:
Combining the real and imaginary parts, we get:
[tex]-25 - 14i \sqrt{11}[/tex]
A company will make a cereal box with whole number dimensions and a volume of 100 cubic centimeters. if cardboard costs $0.05 per 100 square centimeters, what is the least cost to make 100 boxs
Answer:
The best dimension to use to have the least cost to make 100 boxes is 5 x 5 x 4. It only costs $6.50 to make 100 boxes.
Step-by-step explanation:
The area of the circular base of a cylinder is 36 square units. The height is 2
Answer:
24 π
Step-by-step explanation:
First step is to determine the radius of the base. We have the area, so we can easily determine the radius. The base is a circle, and the area of a circle is given by A = π * r² , so r² = A / π
r² = (36 π) / π = 36
So, r = 6
The lateral surface of a cylinder is given by the following:
L = 2* π * r * 2
Now that we have r, we can easily calculate it:
L = 2 * π * 6 * 2 = 24π, second choice listed
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The bar graph shows the z-score results of four contestants in a bowling contest.
The contestants bowled Round 1 and bowled Round 2 two months later.
Which contestant had the worst score for Round 1?
Answer: d) Easton
Step-by-step explanation:
Let's evaluate Round 1 (blue) for each bowler:
Jimmy --> the lowest score is 0.5 SD below the mean
Claudia --> the lowest score was the mean
Easton --> the lowest score is 0.75 SD below the mean
Cynthia --> the lowest score was the mean
The person that had the worst game is: Easton
Answer:
easton
Step-by-step explanation:
I did the test
A circular pizza that is 18 inches in diameter is cut into 8 equal slices. What is the area of a single slice?
Answer:
31.8 in^2
Step-by-step explanation:
The area of a circle is pi×radius^2.
r=.5d=18/2=9
A=(3.14159)(9^2)=(3.14159)(81)=254.5
And if each peice is of equal area, the area of one peice will equal:
254.5/8=31.8
The area of single slice is 31.7925 inch².
What is area of circle?The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.
Given:
diameter= 18 inches
radius= 9 inches
Area of pizza
=πr²
=3.14*9*9
=254.34 inch²
Now, area of 8 equal slices=254.34 inch²
area of 1 equal slices=254.34 /8
= 31.7925 inch²
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What is an attribute of a fractional equation?
there are multiple variables.
there are variables in the denominator of all involved fractions
there is a variable in the denominator of at least one involved fraction.
there are variables in the numerator of at least one involved fraction?
its either a half or part of what its worth
Answer:
There is a variable in the denominator of at least one involved fraction.Step-by-step explanation:
The actual definition of a fractional equation could be:
[tex]\frac{a}{x}+\frac{b}{x+1}=c[/tex]
In words, fractional equations are those which has variables in the denominator of a fractional term, that doesn't mean that all fractions must have a unknown denominator, but at least one of the denominators should have a variable.
Therefore, according to its definition, the right answer is third option.
In addition, other options don't make sense, multiple variables is not necessarily the case for fractional equations. Similarly, not all denominators must have variables. And, having variable only in the numerators don't define the equation as fractional.
What is the exact area of a circle with radius 5?
10
25
25π
10π
How do you solve the inequality -2x > -10
Divide both sides by -2.
Add 10 to both sides
Add 2 to both sides.
Divide both sides by -2 and reverse the inequality.
the radius of this question 25pi
Answer:
Step-by-step explanation:
(1) The formula for the area of a circle of radius r is A = πr².
If the radius is 5 units, then the exact area of the circle is A = π(5 units)², or A = 25π units².
The third possible answer is the correct one.
(2) To solve -2x > -10, we must isolate x.
Divide both sides by -2, remembering that if we divide an inequality by a negative number, we must reverse the direction of the inequality sign:
-2x > -10
----- ------- → x < 5
-2 -2
The first possible answer is the correct one: Divide both sides by -2.
(WORTH 30 POINTS PLS HELP LAST DAY OF ONLINE SCHOOL) !!!! The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
Answer:what is the table
Step-by-step explanation:
The volume inside a rectangular storage room is 2,088 cubic feet. The room is 3 feet high. Find the area of the floor.
ANSWER
The area of the floor is 696 square feet.
EXPLANATION
It was given that, the volume inside a rectangular storage room is 2,088 cubic feet.
The rectangular room is a rectangular prism.
The volume of a rectangular prism is
[tex]V = floor \: area \times height[/tex]
The height of the room is 3 ft.
This implies that,
[tex]2088= floor \: area \times3[/tex]
Divide both sides by 3.
[tex] \frac{2088}{3} = floor \: area [/tex]
[tex]floor \: area = 696 {ft}^{2} [/tex]
The area of the floor is 696 square feet.
In the synthetic division problem shown below, what number belongs in the place of the question mark?
Answer:
7
Step-by-step explanation:
The full solution is:
1 |...1.....3.....-5.....7
.............-1....-2......7
__________________
.......1.....2.....-7.....14
So the answer is 7
The question doesn't provide enough information to answer it properly, as it doesn't specify the polynomial or the divisor necessary for synthetic division. Synthetic division involves dividing a polynomial by a linear divisor, but without the set polynomial and divisor, the number that would belong in the place of the question mark can't be determined.
Explanation:Unfortunately, the information provided doesn't clearly indicate the format or context of a synthetic division problem. Synthetic division typically involves dividing a polynomial by a linear divisor. The elements of the polynomials are numbers, specifically the coefficients of the polynomial terms. The repetition in your question about various Car X, Car Y and dots at various hash marks appears to be irrelevant data as it does not correlate with the synthetic division problem.
However, to apply synthetic division, we would need a specific polynomial to carry out the process. In synthetic division, a box is drawn, the coefficients of the polynomial are written in that box, and then the divisor is placed outside the box. From there, the numbers inside the box are manipulated, in a step-by-step manner, based on the divisor. The numbers derived from this process are the coefficients of the answer. Without this specific data, we cannot accurately determine what number belongs in the place of the question mark.
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Problem situation: Anna is at the movie theater and has $35 to spend. She spends $9.50 on a ticket and wants to buy some snacks. Each snack costs $3.50. How many snacks, x, can Anna buy? Inequality that represents this situation: 9.50+3.50x?35 Drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution. 4 314 912 4.25 ?2 2 Solution to BOTH the inequality and the situation Solution to the inequality ONLY NOT a solution
Answer:
The answer in the procedure
Step-by-step explanation:
Let
x-----> the number of snacks
we know that
The inequality that represent this situation is
[tex]9.50+3.50x\leq 35[/tex]
Solve for x
[tex]3.50x\leq 35-9.50[/tex]
[tex]3.50x\leq 25.50[/tex]
[tex]x\leq 7.3\ snacks[/tex]
The maximum number of snacks is 7
The solution for the inequality is all real numbers less than or equal to 7.3 snacks
The solution for the problem situation is all whole positive numbers less than or equal to 7 snacks
Verify each case
case 1) 4 snacks
Is a solution to both the inequality and the problem situation
case 2) 314 snacks
Is not a solution
case 3) 912 snacks
Is not a solution
case 4) 4.25 snacks
Solution to the inequality ONLY
Answer:
solution to both: 2,4
solution to inequality ONLY: -2,4.25,3 1/4
NOT a solution: 9 1/2
Step-by-step explanation:
yw ;)
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
ANSWER
Step 3
EXPLANATION
The given polynomial expression is:
[tex]2 {p}^{2} - 3p - 7 - (3 {p}^{2} + p - 5)[/tex]
Fatau correctly expanded the parenthesis in the first step.
[tex]2 {p}^{2} - 3p - 7 - 3 {p}^{2} - p + 5[/tex]
Fatau also correctly grouped the like terms to obtain:
[tex](2- 3) {p}^{2} + (- 3 - 1)p + (- 7 + 5)[/tex]
Fatau committed a mistake at the third step.
Instead of obtaining,
[tex] - {p}^{2} - 4p - 2[/tex]
He mistakenly got:
[tex]{p}^{2} - 2p +2[/tex]
Find the location of Point F which is 3/4 of the way between points E and G. Point G is located at (-8,-2). Point E is located at (-4,14).
Answer:
(-7 , 7/2)
Step-by-step explanation:
Given in the question,
point E(-4,14)
x1 = -4
y1 = 14
point G(-8,-2)
x2 = -8
y2 = -2
Location of point F which is 3/4 of the way from E to G
which means ratio of point F from E to G is 3 : 1
a : b
3 : 1
xF = [tex]x1+\frac{a}{a+b}(x2-x1)[/tex]
yF = [tex]y1+\frac{a}{a+b}(y2-y1)[/tex]
Plug values in the equation
xF = -4 + (3)/(3+1) (-8+4)
xF = -7
yF = 14 + (3)/(3+1)(-2-14)
yf = 7/2
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
2 a^4 -2a^2b^2 -6b^4
Step-by-step explanation:
C = 7a^4 + 5a^2b^2 -3b^4
D = 5a^4 +7a^2b^2 +3b^4
C-D = 7a^4 + 5a^2b^2 -3b^4 - ( 5a^4 +7a^2b^2 +3b^4)
Distribute the minus sign
7a^4 + 5a^2b^2 -3b^4 - 5a^4 -7a^2b^2 -3b^4
I like to line them up vertically
7a^4 + 5a^2b^2 -3b^4
- 5a^4 -7a^2b^2 -3b^4
--------------------------------------
2 a^4 -2a^2b^2 -6b^4
What is the probability of rolling a 6 on a die?
1/5
1/6
5/6
1/4
What is the probability of not rolling a 6 on a die?
Answer:
Step-by-step explanation:
There's only 1 '6' on an ordinary die with 6 sides, so the probability of rolling a 6 is 1/6.
That of NOT rolling a 6 is the complementary probability: 1 - 1/6 = 5/6.
A park has a large circle painted in the middle of the playground area. The circle is divided into 444 equal sections, and each section is painted a different color. The radius of the circle is 10 \text{ meters}10 meters10, space, m, e, t, e, r, s. What is the area AAA of each section of the circle? Give your answer in terms of pi. A=A=A, equals \text{m}^2m 2 m, start superscript, 2, end superscript
Answer:
The area of each section of the circle is [tex]A=25\pi\ m^{2}[/tex]
Step-by-step explanation:
we know that
Each section represent a quarter of circle
The area of a quarter of circle is equal to
[tex]A=\frac{1}{4}\pi r^{2}[/tex]
we have
[tex]r=10\ m[/tex]
substitute
[tex]A=\frac{1}{4}\pi (10)^{2}[/tex]
[tex]A=25\pi\ m^{2}[/tex]
Is this graph continuous at x=1?
Answer:
Step-by-step explanation:
By my definition, no. There's a continuity up to and including just before 1 approaching from the left, and there's a continuity just after 1 going to the right. But 1 itself has a special definition h(x) = 4 when x = 1 and that makes it discontinuous.
3. A jewelry store buys small boxes in which to wrap the items that it sells. The diagram below shows one of the boxes. The diagram is not drawn to scale.
What are the lateral area and the surface area of the box to the nearest whole number? Use the large 15cm x 6cm rectangles on the top and bottom as the bases.
A) 47 cm² ; 275 cm²
B) 95 cm² ; 365 cm²
C) 47 cm² ; 365 cm²
D) 95 cm² ; 275 cm²
Answer:
1) The lateral area is LA=95 cm²
2) The surface area is SA=275 cm²
The answer is the option D) 95 cm² ; 275 cm²
Step-by-step explanation:
we know that
The surface area of the box (rectangular prism) is equal to
SA=2B+LA
where
B is the area of the base
LA is the lateral area of the box
Find the lateral area
LA=PH
where
P is the perimeter of the base
H is the height of the box
substitute
LA=2[15+6](2.26)=94.92 cm²
Round to the nearest whole number
LA=95 cm²
Find the area of the base B
B=(15)(6)=90 cm²
Find the surface area of the box
SA=2B+LA
substitute the values
SA=2(90)+95=275 cm²
This parabola opens to the left.
x=1/4y^2
A. True
B. False
Answer:
B. False
Step-by-step explanation:
Given an equation of the type x = a(y-x)^2 + h, We know that If the "y" is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.
Like the y is squared and the "a" is positive then it opens to the right, so it's false
What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?
Answer:
The graph of [tex]y=cos(x)[/tex] is:
*Stretched vertically by a factor of 3
*Compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
*Moves horizontally [tex]\pi[/tex] units to the rigth
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Step-by-step explanation:
If the function [tex]y=cf(h(x+b))[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] The graph moves horizontally b units to the left
If [tex]b <0[/tex] The graph moves horizontally b units to the rigth
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this problem we have the function [tex]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Then [tex]c =3>1[/tex] and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]
Therefore the graph of [tex]y=cos(x)[/tex] is:
Stretched vertically by a factor of 3.
Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth
Solve the inequalities by graphing. Select the correct graph.
5 x + 2 y 3
y x
To solve the inequalities by graphing, transform each inequality into an equation form, plot the lines on the graph, and identify the overlapping region that satisfies both inequalities. The lines are 5x + 2y ≥ 3 and y ≥ x, with appropriate slopes and y-intercepts.
Explanation:To solve the inequalities by graphing, we need to transform each inequality into a graphable equation form and then use the properties of the lines to find the solution set. The inequalities in question are:
Let's graph each inequality one by one:
For the inequality 5x + 2y ≥ 3, convert it to y-intercept form (y = mx + b) by isolating y: 2y ≥ -5x + 3, y ≥ -2.5x + 1.5. This line has a slope (m) of -2.5 and a y-intercept (b) of 1.5.To graph y ≥ x, simply draw a line with a slope of 1 and a y-intercept of 0, which is the identity line where y equals x.The solution to the system of inequalities will be the region on the graph where both conditions are satisfied, typically above the lines in this case because both inequalities are greater than or equal to.
Always label your graph with f(x) and x, and select an appropriate scale for the x and y axes to ensure all important points and lines are visible on the graph.
The provided figures and instructions on slope and graphing help us understand how to plot each line based on their equations. Using the slope-intercept form, we graph the lines and identify the intersection or overlapping regions that satisfy both inequalities.
PLEASE HELP!!!
How is [tex] \sqrt[7]{x^5} *\sqrt[7]{x^5} [/tex] equal too [tex] x\sqrt[7]{x^3} [/tex] ? Please write the steps and properties of how you obtain [tex] x\sqrt[7]{x^3} [/tex] as a result of the equation.
First combine the roots:
[tex]\sqrt[7]{x^5}\cdot\sqrt[7]{x^5}=\sqrt[7]{x^5\cdot x^5}=\sqrt[7]{x^{10}}[/tex]
Now use the fact that [tex]\sqrt[n]{x^n}=x[/tex] (for odd [tex]n[/tex]):
[tex]\sqrt[7]{x^{10}}=\sqrt[7]{x^7\cdot x^3}=\sqrt[7]{x^7}\cdot\sqrt[7]{x^3}=x\sqrt[7]{x^3}[/tex]
Which statement justifies that 3x2 − 2x − 4 multiplied by 2x2 + x − 3 obeys the closure property of multiplication? The result 6x4 − 2x2 + 12 has a degree of 4. The result 6x4 − 2x2 + 12 is a trinomial. The result 6x4 − x3 − 19x2 + 2x + 12 is a polynomial. The result 6x4 − x3 − 19x2 + 2x + 12 has a degree of 4.
Answer:
The result [tex]6x^4-x^3-19x^2+2x+12[/tex].
is a polynomial.
Step-by-step explanation:
The first polynomial is [tex]3x^2-2x-4[/tex].
The second polynomial is [tex]2x^2+x-3[/tex]
The closure property of multiplication states that if we multiply two polynomials the result must be a polynomial.
The product of these two polynomials is :
[tex](3x^2-2x-4)(2x^2+x-3)=6x^4-x^3-19x^2+2x+12[/tex].
We can see that the result is still a polynomial.
Answer: I believe the answer is C) The result 6x4 − x3 − 19x2 + 2x + 12 is a polynomial. !!!!!!!!