Solve the equation for the specified variable
Y=cd-8, for c

Answer:

[tex]\frac{3}{2}[/tex] c

Step-by-step explanation:

Given

[tex]\frac{3a+3b}{2a-2b}[/tex] ← factor numerator and denominator

= [tex]\frac{3(a+b)}{2(a-b)}[/tex]

= [tex]\frac{3}{2}[/tex] × [tex]\frac{a+b}{a-b}[/tex] ← this = c

= [tex]\frac{3}{2}[/tex] × c = [tex]\frac{3}{2}[/tex] c

Answer:

Please read the answer to Parts A and B below.

Correct statement, question and data:

Lucas and Brianna read three books each last month. The table shows the number of pages in each book and the length of time it took to read the entire book.

Pages Lucas Read 208 156 234  

Time (hours)          8      6     9

Pages Brianna Read 168 120 348  

Time (hours)               6     4      12

a. How many observations can you make about any similarities or difference that exist between the reading rates  of the two students.

b. Both Lucas and Brianna had specific reading goals they needed to accomplish. What different strategies did  each person employ in reaching those goals?

Source:

Grade 7, Module 1 - Student material of New York State

Step-by-step explanation:

Part A.

We notice that Lucas read at a constant reading rate of 26 pages per hour and he read for a total of 23 hours. On the other hand, Brianna, does not follow a constant reading rate, she read the first book at a rate of 28 pages per hour, the second at a rate of 30 pages per hour and the third book at a rate of 29 pages per hour, adding up to 22 hours.

Part B.

Lucas followed at a constant rate of 26 pages per hour and Brianna was not constant but she reads faster than Lucas with an average rate of 29 pages per hour (636 pages in 22 hours).

Answer:

=4(x−3)(x+6)

Step-by-step explanation:

4x^2+12x-72

=4(x−3)(x+6)

The factorized form of the equation 4x² + 12x - 72 is

A = 4 ( x + 6 ) ( x - 3 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A = 4x² + 12x - 72

Now , the equation can be simplified by

A = 4 ( x² + 3x - 18 )

Now , on simplifying the equation , we get

A = 4 ( x² - 3x + 6x - 18 )

Now , on grouping the similar terms in the equation , we get

A = 4 ( x ( x - 3 ) + 6 ( x - 3 ) )

A = 4 ( x + 6 ) ( x - 3 )

So , the factorized form of the equation is

A = 4 ( x + 6 ) ( x - 3 )

Hence , The factorized form of the equation 4x² + 12x - 72 is

A = 4 ( x + 6 ) ( x - 3 )

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Answer:

21

Step-by-step explanation:

x-4=17

x=17+4

x=21

that's the solution

Answer:

D.a relation only

Step-by-step explanation:

Relation: It is mapping between two non empty set A and B.

In relation any input value can have two or more than two output values.

Function: It is that relation in which every input value has only one output .

All function are relations but all relations are not function.

In given data

Image of 3 =4

Image of 3=3

By definition of function

It is not a function.

By definition of relation

It is a relation.

Hence, option D is true.

Answer: D

RELATION ONLY//PLATO//EDMENTUM

Answer:

f= .75 or 3/4

Step-by-step explanation:

13/4 = 3 1/4 or 3.25

4-3.25= .75

Or

3/4

Answer:

f = 3/4

Step-by-step explanation:

f+(13/4)= 4

subtract (13/4) from both sides

⇒f + (13/4)- (13/4) = 4 -(13/4)        

⇒f =(16-13) /4

∴f = 3/4

let's bear in mind that we have two fractions whose denominators are 2 and 4, thus their LCD will be 4, now let's multiply both side by that LCD to do away with the fractions, but let's add some first.

[tex]\bf 2-\left( 4-\cfrac{1}{2}x \right)=6\left( \cfrac{1}{4}x-1 \right)\implies 2- 4-\cfrac{x}{2} =\cfrac{6x}{4}-6 \\\\\\ -2-\cfrac{x}{2} =\cfrac{6x}{4}-6\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( -2-\cfrac{x}{2} \right)=4\left( \cfrac{6x}{4}-6 \right)}\implies -8-2x=6x-24 \\\\\\ 16-2x=6x\implies 16=8x\implies \cfrac{16}{8}=x\implies 2=x[/tex]

Answer:

Step-by-step explanation:

You first rearrangel all of numbers from least to greatest, then you cross out the smallest and bigest number untill you meet in the middle. If you there two numbers in the middle then you find the average of those numbers.

97

10 times 4 is 40 40 plus 57 is 97

Answer: 97

Step-by-step explanation:

1. Take your $10 and multiply it by the four hours she babysits. --> 10•4=40

2. Take the answer you just received from the multiplication problem, 40, and add it by the amount of money she had in her account, $57.    -->40+57=97

I hope this helps you!

Answer:

1/24

Step-by-step explanation:

First, multiply the two fractions together.

3/8 * 1/9

Multiply the numerators:

3*1=3

And the denominators:

8*9=72

So, the fraction ends up being 3/72.

I need simplify the fraction by dividing both the numerator and the denominator by 3:

3/3=1

72/3=24

Simplified fraction is 1/24.

Answer: [tex]\frac{1}{24}[/tex]

Step-by-step explanation: To multiply fractions, first multiply across the numerators and then multiply across the denominators.

[tex](\frac{3}{8}) (\frac{1}{9}) = \frac{3}{72}[/tex]

[tex]\frac{3}{72} = \frac{1}{24}[/tex]

Answer: 4/12 is 0.3333333333333333 so it would be repeating decimal

Step-by-step explanation: divide 4 by 12 and get 0.333

Answer:

7a - 2

Step-by-step explanation:

A perimeter is just the sum of all sides added together, so just put all the expressions together into a big equation.

2a - 3 + 2a + 3a + 1

Combine like terms

7a - 2

Answer:

4. Tell your interviewer what you do know.

If you do have some knowledge of the question, then take the time to tell your interviewer what you do know of the situation. Saying everything out loud can start you on the process of figuring out the problem.

Step-by-step explanation:

Answer:

[tex] u = -\dfrac{vx}{w} [/tex]

Step-by-step explanation:

You are allowed to multiply and divide both sides of an equation by the same non-zero number or non-zero variable. Do the appropriate operations to isolate the u.

[tex] x = -\dfrac{1}{v}uw [/tex]

We are solving for u, so first, switch sides.

[tex] -\dfrac{1}{v}uw = x [/tex]

Multiply both sides by v.

[tex] -\dfrac{1}{v}uw \times v = x \times v [/tex]

[tex] -uw = x \times v [/tex]

Divide both sides by -w.

[tex] \dfrac{-uw}{-w} = \dfrac{xv}{-w} [/tex]

[tex] u = -\dfrac{vx}{w} [/tex]

Answer: 1760

Step-by-step explanation:

[tex]\dfrac{5280\ feet}{1\ mile}\times \dfrac{1\ yard}{3\ feet}\quad =\dfrac{5280\ yard}{3\ feet}\quad =\large\boxed{1760\ yard\ per\ mile}[/tex]

Answer:The number should be 123456789.

Step-by-step explanation:

The total digits should be 9 i.e. 1, 2, 3, 4,5, 6,7, 8, and 9.

The largest number should be at the unit place, the 2nd largest number should be at the tenth place, and the  3rd largest number should be at the 100th place, and so on.

So in this way, the 1 number should be written at the left-most position.

Therefore we can conclude that The number should be 123456789.

Answer: 2/3^3

Step-by-step explanation:

To find the volume of a box, you use the formula, Lenth*Width*Height=Volume

The Lenth is 3 1/2. The width is 1 1/3 and the height is 2/14

Plug the values in formula

3 1/2*1 1/3*2/14

Covert the mixed numbers into imporper fractions so it is easier to solve

3 1/2=7/2

1 1/3=4/3

7/2*4/3*2/14

Reduce 2/14

2/14=1/7

7/2*4/3*1/7=7*4*1/(2*3*7)=28/42

Reduce 28/42=14/21=2/3

2/3 ft^3

Answer:

y intercept (0,490)

I would use (Graphing equation standard form) to identify x and y intercepts. I will Plot the y intercept (0,490) and the x intercept (735,0)

,It will Connect the two intercepts with a straight line

2x + 3y = 1,470

3y = -2x + 1470

y = (-2x + 1470 ) / 3

y = -2/3 * x + 1470/3

y = -2/3 * x + 490

slope is -2/3

y intercept is 490

x intercept (735,0)

Step-by-step explanation:

Answer:

[tex]2x+3y=1470[/tex]

Step-by-step explanation:

Givens

So, [tex]x[/tex] represents the number of sandwiches and [tex]y[/tex] represents the number of wraps, so the profit on each food is

[tex]2x[/tex] and [tex]3y[/tex], so the sum of them must be equal to $1470, as follows

[tex]2x+3y=1470[/tex]

Which is a linear equation, that means if we graph, it would be a line.

To graph this, we just need to find two points.

For [tex]x=0[/tex], let's find [tex]y[/tex]

[tex]2x+3y=1470\\2(0)+3y=1470\\y=\frac{1470}{3}=490[/tex]

For [tex]y=0[/tex]. let's find [tex]x[/tex]

[tex]2x+3y=1470\\2x+3(0)=1470\\x=\frac{1470}{2}=735[/tex]

Therefore, the two points to graph the line are [tex](0,490)[/tex] and [tex](735, 0)[/tex]. Now, we graph these coordinates and draw a line that must cross them

The resulting graph should be like the image attached.

Step-by-step explanation:

5(x+2)-7=5(x-3)

5x + 10 -7 = 5x -15

5x - 5x ..... this question must have an error

Answer:

Undefined

Step-by-step explanation:

5(x+2)-7=5x-3

5x+10-7=5x-3

5x+3=5x-3

5x=5x

can't solve, so it is undefined.

The offered overtime hourly rate is 1.5 times the given hourly rate.

The amount Colin Katz earns per hour = $10.75

The number of additional hours Colin Katz is asked to work = 2 hours

Rate at which the additional hours will be paid = Hourly rate and half = 1.5 hourly rate

The amount he will earn for the additional hours.

The hourly rate for the additional hours = 1.5 × $10.75 = $16.125

Amount Colin Katz earns working 2 additional hours = 2 × $16.125 = $32.25

The amount he will earn for the two hours overtime = $32.25

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Answer:

The subtraction property of equality

Step-by-step explanation:

it just is

The justification for the step taken from line 2 to line 3 is the subtraction property of equality

Equations are expressions that have equal values when compared using the "=" sign

The equation on line 2 is given as:

[tex]-4x + 9 = 2x + 10[/tex]

The equation on line 3 is given as:

[tex]-6x + 9 = 10[/tex]

2x is subtracted from both sides of the equation in step 2 to get the equation in step 3

Hence, the justification for the step taken from line 2 to line 3 is the subtraction property of equality

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Given ST = 12 and RT = 49, we apply the basic principle of part-whole relationships in a line to find RS. By subtracting the length of ST from RT, we determine that RS equals 37.

The question asks to find the length of RS given that ST = 12 and RT = 49. To find the length of RS, we can apply the concept that in a linear situation, if S is a point between R and T, then RS + ST = RT. This concept is based on the principle of the sum of parts of a whole.

Given:

To find RS, we use the equation:

RS + ST = RT

Plugging in the given values:

RS + 12 = 49

Solving for RS, we subtract 12 from both sides:

RS = 49 - 12

RS = 37

Therefore, the length of RS is 37.

Answer:

n = 5

Step-by-step explanation:

5 * (n/5) = 5 / (n/5)

(5 * n) /5  = 5 * (5/n)          

n   = ( 5*5) / n

n = 25/n

n² = 25

n = 5

To calculate the change in volume of a box when cutout length increases from 0.3 inches to 1.2 inches using function notation, use the formula ΔV=f(l2)-f(l1), where f(l) represents the volume of the box given the length of the edge.

The change in volume when the cutout length increases from 0.3 inches to 1.2 inches can be represented in function notation as ΔV=f(l2)-f(l1), where f(l) represents the volume of the box as a function of the length (l) of the edge. Here, l1=0.3 and l2=1.2.

Given the formula for the volume of the box V = Length x Width x Height. Let's assume Width and Height remain constant. If initially the volume was V1=f(l1) and finally it became V2=f(l2), the change in volume will be ΔV=V2-V1 which equals f(l2)-f(l1).

For example, if the width and height of the box are 6 inches and 3 inches respectively, then the initial volume is V1 = 0.3 x 6 x 3 cubic inches and the final volume is V2 = 1.2 x 6 x 3 cubic inches. Therefore, ΔV = (1.2 x 6 x 3) - (0.3 x 6 x 3) cubic inches.

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The change in the volume of the box when the cutout length increases from 0.3 inches to 1.2 inches can be calculated using the function ΔV = V(1.2) - V(0.3). Assuming the rest of the box's dimensions are constant, this results in a change in volume of 16.2 cubic inches.

To use function notation to represent how the volume of the box changes by if the cutout length increases from 0.3 inches to 1.2 inches, let us first define a function V(l) that represents the volume of the box as a function of the cutout length 'l'. If the initial cutout length is 0.3 inches and the final cutout is 1.2 inches, the change in length Δl would be 1.2 inches - 0.3 inches = 0.9 inches. We can express the change in volume, ΔV, as the function of the change in cutout length as follows: ΔV = V(1.2) - V(0.3).

Given that the volume of a rectangular box can be calculated by the formula volume = length × width × height, and assuming other dimensions of the box do not change, the function V(l) becomes:

V(l) = length × width × l

Let's consider an example where the dimensions of the box remain constant at 6 inches by 3 inches. The volume function would then be:

V(l) = 6 in. × 3 in. × l in.

The change in volume for an increase in cutout from 0.3 to 1.2 inches is then:

ΔV = V(1.2) - V(0.3) = (6 × 3 × 1.2) - (6 × 3 × 0.3) = 21.6 in.³ - 5.4 in.³ = 16.2 in.³.

Answer:

whats equivelent to 6x4?

Step-by-step explanation:

6 x 4 = 24

8 x 2 = 16 so 8 x 3 = 24 because 8 x 4 would be

8 x 2 = 16

16 x 2 =

6 + 6 = 12

carry the one.

2

1 + 1 + 1 (We now have three ones from carrying that 1) and our answer is

32.

So N = 3

Answer:

6x4=8xN N=8x3

Step-by-step explanation: N=8x3 because 6x4=24 so if you multiply 8x3 it =  

24

Answer:

[tex]v = 3[/tex]

Step-by-step explanation:

-(v-1)=-6v+16

-v+1=-6v+16

grouping like terms

-v+6v=16-1

5v=15

dividing through by 5

[tex] \frac{5v}{5} = \frac{15}{5} [/tex]

[tex]v = \frac{15}{5} [/tex]

[tex]v = 3[/tex]

Expressions can be split into equivalent expressions by factoring them.

The expression equivalent to [tex]\mathbf{9b + 21}[/tex] is [tex]\mathbf{3 (3b + 7)}[/tex]

The expression is given as:

[tex]\mathbf{9b + 21}[/tex]

Express each term as a product of 3 (the GCF)

[tex]\mathbf{9b + 21 = 3 \times 3b + 3 \times 7}[/tex]

Factor out 3

[tex]\mathbf{9b + 21 = 3 (3b + 7)}[/tex]

Hence, the expression equivalent to [tex]\mathbf{9b + 21}[/tex] is [tex]\mathbf{3 (3b + 7)}[/tex]

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Answer:

[tex]-0.45[/tex]

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors. you'll get your answer as [tex]-\frac{9}{20}=-0.45[/tex]

Answer:

solving

Step-by-step explanation:

Answer:

52.50/5.8= $9 per hour