Since the difference between steps 1 and 2 is that 2x was subtracted from both sides, i'm pretty sure the answer is B, the Subtraction property of equality. Hope this helps you!
Answer:
B) Subtraction property of equality
Step-by-step explanation:
4x - 7 = 2x + 9
Subtract 2x from each side using the subtraction property of equality
4x -2x - 7 = 2x-2x + 9
2x -7 = 9
Dinner at your favorite restaurant cost $64.50 with tax for you and your family. You give the waiter $75 to pay the bill and a tip. What is the approximate percentage of the tip?
Answer:16
Step-by-step explanation:
original price
100
=
new price
new percent
;
64.5
100
=
75
x
64.5x = 7500 → x ≈ 116.3
Subtract 100 from the new percent (116.3 − 100 = 16.3) → 16%
The approximate percentage of the tip is 14%.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Dinner at your favorite restaurant cost $64.50 with tax for you and your family.
You give the waiter $75 to pay the bill and a tip.
That means,
the tip amount = 75 - 64.50
= 10.50
The tip percentage,
= 10.50 x 100 / 75
= 14%
Therefore, 14% is the required percentage.
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The area of the conference table in Mr. Nathan’s office must be no more that 175 ft^2. If the length of the table is 18 ft more that the width, x, which interval can be the possible widths ?
Answer:
(0, 7]
Step-by-step explanation:
Let's call the width W and the length L. The length is 18 feet more than the width, so:
L = W + 18
The area can be no more than 175, so:
A ≤ 175
LW ≤ 175
Since L = W + 18:
(W + 18) W ≤ 175
W² + 18W ≤ 175
W² + 18W - 175 ≤ 0
(W - 7) (W + 25) ≤ 0
-25 ≤ W ≤ 7
However, the width of the table can't be nonpositive, so:
0 < W ≤ 7
Or in interval notation, (0, 7].
What is the standard form of the equation of a parabola that opens up or down
the standard form of the equation of a parabola that opens up or down is (x - h)^2 = 4p(y - k)
Answer: y=ax^2+bx+c
Step-by-step explanation:
Consider the following graph of a piecewise-defined function.
Choose the correct expression to represent the piecewise-defined function.
Answer:
Step-by-step explanation:
When x<-2, f(x)=5
When -2<x<3, f(x)=2x+2
When x>3, f(x)=-3
Answer:
Step-by-step explanation:
Given is a graph of piecewise function.
We are given a horizontal line for
[tex]x<-2[/tex]
Hence [tex]f(x) = 5, x<-2[/tex] ... I
Whenever
[tex]-2\leq x<3[/tex], the graph is a line passing through (-2,-2) and (3,8)
Hence using two point equation we get
[tex]\frac{y+2}{8+2} =\frac{x+2}{3+2}\\5(y+2)=10(x+2)\\y=2x+2[/tex]...II
Again for
[tex]x>3\\y=-3[/tex]... III
I,II and III together give the piecewise funciton
lauri's cat had a litter of 4 kittens. What is the probability that there were 3 males
Answer:
The probability that there were 3 males is 1/4.
Step-by-step explanation:
Total Number of kitten = 4
Probability of a kitten to be male = 1/2
Probability of a kitten to be female = 1/2
Probability that out of 3 were male = 4 × 1/2 × 1/2 × 1/2 × 1/2
= 1/4
Therefore, The probability that there were 3 males is 1/4.
Lizzie has 12 pounds of clay and wants to use all of it. She does not need to make all of the projects, and may make more than one of any project. Describe a plan for Lizzie to use 12 pounds of clay making projects from the chart. Show how you know she will use exactly 12 pounds of clay with this plan, with no clay left over.
Answer:
many answers,
Step-by-step explanation:
she could make 9 mugs, (3/4 x 9 = 12)
she could make 1 small bowl, 1 small plate, 2 large bowls and 2 mugs. (2.5 + 1.5 = 4, 3.25 x2 = 6.5 .75 x 2 = 1.5; 4+ 6.5= 10.5 10.5 + 1.5 = 12) etc
Please help! Determine where f(x) = g(x) by graphing.
A. x = 3
B. x = 2
C. x = 4
D. x = 1
Answer:
C
Step-by-step explanation:
We can point plot to get graph of both the functions.
** Attached is the graph of both the functions. f(x) is in RED & g(x) is in BLUE.
From the graph shown, it is clear that the point of intersection is x = 4, y = 2
So f(x) = g(x) at the point x = 4
Answer choice C is right.
PLZ Help. It will be very appreciated.
when the two books were published
Answer: It would be (B) because you don't actually have to know the date unless it is a part of the equation which you dont have to know in this question :)
Hope this will help you out :)
What’s is the answer?
Answer:
Option D)
Step-by-step explanation:
Given:
x= {2,3,4}
y={49,343,2401}
Points with coordinates (x,log(y)) are required to be plotted
Finding (x,log(y)):
log(y)= {log(49),log(343),log(2401)}
Log(49)=1.69020
log(343)=2.53529
log(2401)=3.38039
Now the transformed data set will be written in coordinates form:
(2,1.690),(3,2.535),(4,3.380)
Which is option D !
Can anyone help me with the answer for number 4
Answer:
b
Step-by-step explanation:
Given K is the midpoint of JL, then
JK = KL ← substitute values
6x = 3x + 3 ( subtract 3x from both sides )
3x = 3 ( divide both sides by 3 )
x = 1
Hence
JK = 6x = 6 × 1 = 6
KL = 3x + 3 = (3 × 1) + 3 = 3 + 3 = 6
JL = 6 + 6 = 12
An ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin. Which is the equation of the ellipse in standard form?
ANSWER
[tex]\frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]
EXPLANATION
The given ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin.
The equation of an ellipse with vertices on the x-axis and center at the origin is:
[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
The ellipse has vertex at (4,0) , hence a=4.
Also the co-vertex is at (0,3) , b=3
We substitute the values into the equation to get:
[tex] \frac{ {x}^{2} }{ {4}^{2} } + \frac{ {y}^{2} }{ {3}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]
The equation of the ellipse centered at the origin with a vertex at (4,0) and a co-vertex at (0,3) is (x/4)² + (y/3)² = 1.
Explanation:The ellipse in question has a vertex at (4,0) and a co-vertex at (0,3), with a center at the origin. The standard form equation for an ellipse with a center at the origin is given by (x/a)² + (y/b)² = 1. In this case, 'a' represents the distance from the center to a vertex, and 'b' represents the distance from the center to a co-vertex. Since our vertex is at (4,0), 'a' equals 4, and since our co-vertex is at (0,3), 'b' equals 3.
So in this case the standard form equation of the ellipse would be (x/4)² + (y/3)² = 1.
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1. Jill had the following scores on her math quizzes 20, 40, 40, 40, 60, 60, 60, 60, 80, 80, 80, 80, 100.
What is the mean score for Jill’s quizzes? Show your work.
a. What is the total of her quiz scores?
b. How many quizzes did she take?
c. What is the average Jill scored on her quizzes?
Answer:
a is 800
b is 13
c is 61.5
Step-by-step explanation:
for a you add all of the given data together
b you count how many data points there are
c you get the answer from the a and divided by 13
By adding all of Jill's quiz scores (totaling 800) and dividing by the number of quizzes (13), we find that Jill's average score is approximately 61.54.
To determine the mean score for Jill's quizzes, we will follow these steps:
Total the quiz scores: Add all individual scores together.
Count the number of quizzes: Determine how many quizzes Jill took.
Calculate the average score: Divide the total score by the number of quizzes.
A. Total of Quiz Scores
20 + 40 + 40 + 40 + 60 + 60 + 60 + 60 + 80 + 80 + 80 + 80 + 100 = 800
B. Number of Quizzes
Jill took 13 quizzes.
C. Average Score
The mean score is calculated by dividing the total score by the number of quizzes:
Mean Score = Total Score / Number of Quizzes = 800 / 13 ≈ 61.54
Part 1
The ratio table shows the amounts of sand and water in a concrete mixture. Which fraction represents the ratio for the gallons of water to bags of sand?
A)3/6
B)3/7
C)5/3
D)7/3
Part 2
How many bags of sand should be mixed with 12 gallons of water?
A)22 bags
B)24 bags
C)28 bags
D)30 bags
Please help
Divide bags of sand by gallons of water:
14 /6 = 2.33
21/9 = 2.33
The ratio is the same, so this means for every gallon of water you need 2.33 bags of sand.
Convert the fractions into decimals and you will get 7/3 = 2.33
The answer for Part 1 is D) 7/3
For part 2, multiply the gallons of water by 2.33 to get the number of sand bags needed:
12 x 2.33 = 27.99, which rounds to 28.
The answer is C) 28 bags.
Answer:
A) [tex]\frac{3}{7}[/tex]
C) 28 bags
Step-by-step explanation:
Part 1 :
By the given table,
[tex]\frac{\text{Gallon of water}}{\text{bags of sand}}=\frac{6}{14}=\frac{9}{21}=\frac{15}{35}=\frac{3}{7}[/tex]
Hence, the proportion of gallons of water to bags of sand is same,
Which is [tex]\frac{3}{7}[/tex]
OPTION A) is correct.
Part 2 : Let x bags of sand should be mixed with 12 gallon of water,
Then the ratio of gallon of water and number of bags of sand = [tex]\frac{12}{x}[/tex]
By part 1,
[tex]\frac{12}{x}=\frac{3}{7}[/tex]
[tex]84 = 3x[/tex] ( by cross multiplication )
[tex]\implies x = \frac{84}{3}=28[/tex]
Hence, 28 bags of sand should be mixed.
OPTION C) is correct.
Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
0.901 recurring
Answer:
[tex]\frac{901}{999}[/tex]
Step-by-step explanation:
we know that
A Recurring Decimal, is a decimal number with a digit (or group of digits) that repeats forever.
In this problem we have
0.901 recurring
that means
0.901901901..
Let
[tex]x=0.901901901..[/tex]
Multiply x by a power of [tex]10[/tex], one that keeps the decimal part of the number the same:
[tex]1,000x=901.901901..[/tex]
Subtract [tex]x[/tex] from [tex]\\1000x[/tex]
[tex]1,000x-x=901.901901..-0.901901..=901[/tex]
The repeating decimals should cancel out
[tex]\\999x=901[/tex]
solve for x
Divide by [tex]999[/tex] both sides
[tex]990x/990=135/990[/tex]
[tex]x=\frac{901}{999}[/tex]
A class student council election was held on Monday and 15 of the 20 students decided to vote. On Tuesday, another election was held, but only 16 students were in the class that day. Use the ratio of students who voted in Monday's election to the total number of students in class on Monday to predict the number of students who voted in Tuesday's election.
Answer:
12
Step-by-step explanation:
We know that 15/20 students voted in the StuCo election on the first go around.
Using this ratio for 16 student is as simple as multiplying 15/20 by 16
(15/20)*16=12
Based on the voting ratio of 3:4 from Monday's election, we predict that 12 out of the 16 students present on Tuesday voted.
The question asks to predict the number of students who voted in Tuesday's election based on the ratio of students who voted on Monday. On Monday, 15 out of 20 students voted, which establishes a voting ratio of 15:20, or 3:4 when simplified. To predict Tuesday's voter turnout, we apply this ratio to the 16 students present on Tuesday.
Using the simplified ratio of 3:4, for every 4 students, 3 vote. Since 16 students were in class on Tuesday:
Divide 16 by 4 to find how many groups of 4 there are, which is 4.Multiply the number of groups (4) by the number of voters per group (3), which equals 12.Therefore, we predict that 12 students voted in Tuesday's election.
The point (-2,11) is on the graph of y=4x^2+2x-1
True
False
Nope, it aint there. False
35. A 60° angle is complementary to an ang
that measures xº. Which of the following
equations represents this situation?
A 60 + X = 90
B 60 = x + 90
C 60+ x = 180
D. 60 = x + 180
Answer:
A. 60+x°=90
Step-by-step explanation:
Complementary angles add up to 90°.
Convert 150 pounds into kg.
Answer:
About 68 or 68.03
Step-by-step explanation:
Answer:
it is 68.0388555 Kg when you convert it to Kg.
Step-by-step explanation:
1 pound is 0.45359237 Kg
The equation of line AB is (y-3) = 5(x-4) what is the slope
Answer:
slope = 5
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 3 = 5(x - 4) ← is in point- slope form
with slope m = 5
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answer:
y = - 6x - 57
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 6, thus
y = - 6x + c ← is the partial equation
To find c substitute (- 9, - 3) into the partial equation
- 3 = 54 + c ⇒ c = - 3 - 54 = - 57
y = - 6x - 57 ← equation of line
Answer:
y + 3 = –6(x + 9)
Step-by-step explanation:
6r+7=13+7r help me asap
Answer:
r = - 6
Step-by-step explanation:
Given
6r + 7 = 13 + 7r ( collect terms in r on the left and numbers on the right )
Subtract 7r from both sides
- r + 7 = 13 ( subtract 7 from both sides )
- r = 6 ( multiply both sides by - 1 )
r = - 6
6r+7=13+7r
-6r -6r
------------
7=13+1r
flip the equasin to make it easier
13+1r= 7
-13 -13
---------
1r= -6
The gradient of the curve is given by the equation and a point on the curve is also given. Find the equation of the curve with working
Answer:
4 x^(3/2) + 5x -32
Step-by-step explanation:
This problem involves definite integration (anti-derivatives).
If dy/dx = 6x^(1/2) - 5, then dy = 6x^(1/2)dx - 5dx.
(1/2) + 1
This integrates to y = 6x
----------------
(1/2) + 1 x^(3/2)
= 6 ------------ + C
3/2
or: 4 x^(3/2) + C
and the ∫5dx term integrates to 5x + C.
The overall integral is:
4 x^(3/2) + C + 5x + C. better expressed with just one C:
4 x^(3/2) + 5x + C
We are told that the curve represented by this function goes thru (4, 20).
This means that when x = 4, y = 20, and this info enables us to find the value of the constant of integration C:
20 = 4 · 4^(3/2) + 5·4 + C, or:
20 = 4 (8) + 20 + C
Then 0 = 32 + C, and so C = -32.
The equation of the curve is thus 4 x^(3/2) + 5x -32
(1/2 + 1)
The equation of the curve is [tex]y=6x^2-5x+7$.[/tex]
From the given information, we know that the gradient of the curve is [tex]$dy/dx=6x-5[/tex]
This means that the equation of the curve is of the form [tex]$y=6x^2-5x+C$[/tex] for some constant C.
We can find the value of C by substituting the point (4,20) into the equation of the curve.
This gives us [tex]20=6\cdot4^2-5\cdot4+C[/tex] so C=7.
Therefore, the equation of the curve is [tex]y=6x^2-5x+7$.[/tex]
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HELP!
In the triangle below, b = ___. If necessary, round your answer to two decimal places.
Answer:
[tex]b=40.01\ units[/tex]
Step-by-step explanation:
we know that
Applying the law of sines
[tex]\frac{b}{sin(B)}=\frac{a}{sin(A)}[/tex]
[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]
we have
[tex]a=25\ units[/tex]
[tex]A=32.5\°[/tex]
Find the measure of angle B
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
[tex]A+B+C=180\°[/tex]
substitute the given values
[tex]32.5\°+B+26.8\°=180\°[/tex]
[tex]B=180\°-59.3\°=120.7\°[/tex]
Find the length side b
[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]
substitute the values
[tex]b=\frac{25}{sin(32.5\°)}(sin(120.7\°))[/tex]
[tex]b=40.01\ units[/tex]
Help !!
Which transformation can not be used to prove that ABC is congruent to DEF ?
D
the answer is D. dilation cannot be used to prove this
The answer is D since dialation only beating to increase in size
Determine whether y varies directly with x. If so, find the constant of variation and write the equation.
Answer:
The answer is yes , k = -2 and y = -2x ⇒ first answer
Step-by-step explanation:
* To prove the variation
- Check the constant change in the values of x and y
- Lets check that from the table
# At x = 1 ⇒ y = -2
# At x = 3 ⇒ y = -6
# At x = 5 ⇒ y = -10
* -6 - -2 = -6 + 2 = -4 ⇒ 3 -1 = 2
-10 - -6 = -10 + 6 = -4 ⇒ 5 - 3 = 2
∴ y decreased by 4 when x increased by 2
* This is a constant change
∴ y is varies directly with x
∴ y ∝ x
∴ y = k x ⇒ where k is the constant of the variation
* Lets find the value of k
- You can use one value of x and y from the table
∵ x = 3 and y = -6
∴ -6 = k (3) ⇒ divide two sides by 3
∴ k = -2
∴ The equation of the variation is = y = -2x
* The answer is yes , k = -2 and y = -2x
Answer:
Yes, k=-2 and y=-2x
Step-by-step explanation:
Using (1,-2) and (3,-6)
[tex]k=\frac{-6--2}{3-1}=-2[/tex]
This implies that
y=-2x
check for the 3rd point;
When x=5,
y=-2(5)=-10
Hence y varies directly as x. The constant of variation is k=-2
I need help with 4,8,12,16,18 I missed school so much last week and an am behind.
Answer:
4: 376 8: -708 12: -59 16: 0 18: -1,884
Step-by-step explanation:
I have really bad eyesight so, I hope I read all the numbers correctly. I hope you get caught up, it sucks to be behind in class.
Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The answer is follows:
4) -2632/-7 = 3768) -7080/10 = - 70812) 4956/-84 = -5916) 0/-600 = 018) (-3768/-6) (-3) = 18What exactly is the division formula?Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The dividend is the number that is being divided in this case. The divisor is the number that divides the dividend (number) into equal parts. Divisibility tests or division rules in Math, as the name implies, assist in determining whether a number is divisible by another number without using the actual method of division.If one number is completely divisible by another, the quotient is a whole number and the remainder is zero.Therefore,
4) -2632/-7 = 376
Use the fraction rule.: [tex]$\frac{-a}{-b}=\frac{a}{b}$[/tex]
-2632/-7
Divide the numbers as follows:
2632/7 = 376
8) -7080/10 = - 708
12) 4956/-84 = -59
16) 0/-600 = 0
18) (-3768/-6) (-3) = 18
Within parentheses, compute (-3768 /-6) : -6
= -6(-3)
Divide and multiply (left to right) -6(-3 ) : 18
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If M=5x^2 and N=-3x^2-4x+5,then M-N equals
Answer:
8x² + 4x - 5
Step-by-step explanation:
M - N
= 5x² - (- 3x² - 4x + 5) ← distribute parenthesis by - 1
= 5x² + 3x² + 4x - 5 ← collect like terms
= 8x² + 4x - 5
Two vertices of a right triangle have the coordinates (-2, 5) and (9,5)
What is the length of the side formed by these vertices?
Answer:
The length of the formed by these vertices is 11 units.
Step-by-step explanation:
We are given the following coordinates of two vertices of a right angled triangle and we are to find the length of the side formed by these vertices:
[tex](-2, 5)[/tex] and [tex](9,5)[/tex]
Using the distance formula to find the side length:
Side length = [tex] \sqrt { ( 9 - ( - 2 ) ) ^ 2 + ( 5 - 5 ) ^ 2 } [/tex] = [tex]\sqrt{121}[/tex] = 11 units
Answer:
11
Step-by-step explanation:
Note that the horizontal line y = 5 goes through both vertices, and that the length of the side formed by those vertices is the distance between the vertices in this case. That distance would be 9 - (-2), or 11.
165 is what percent of 375
44%
1. We assume, that the number 375 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 375, so we can write it down as 100%=375.
4. We know, that x% equals 165 of the output value, so we can write it down as x%=165.
5. Now we have two simple equations:
1) 100%=375
2) x%=165
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=375/165
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 165 is what percent of 375
100%/x%=375/165
(100/x)*x=(375/165)*x - we multiply both sides of the equation by x
100=2.27272727273*x - we divide both sides of the equation by (2.27272727273) to get x
100/2.27272727273=x
44=x
x=44
Machine A produces 75 fishing lures per minute. Machine B produces 50 of the same lure per minute. How long will it take both machines running to produce 2100 fishing lures? A.14.4 minutes B.16.8 minutes C.18.2 minutes D.20.7 minutes
Answer: Option B
16.8 minutes
Step-by-step explanation:
Machine A produces 75 fishing lures per minute.
Machine B produces 50 fishing lures per minute.
Let's call t time in minutes.
So we want to know how long it will take to produce 2100 fishing lures
We propose the following equation
[tex]75t + 50t = 2100[/tex]
Now we solve for t
[tex]125t = 2100[/tex]
[tex]t = 16.8\ min[/tex]
The answer is Option B