You want to paint a piece of pottery at an art studio. The total cost is the cost of the piece plus an hourly studio fee. There are two studios to choose from. For studio a: The vase is $10 and the studio fee is $8 per hour. For studio b: The vase is $16 and the studio fee is $6 per hour. After how many hours of painting are the total costs the same at both studios?

Answer:

1. Commutative Property of Addition

2. Distributive property

Step-by-step explanation:

Given

[tex]Line 1: 4(8+9x)[/tex]

[tex]Line 2: 4(9x+8)[/tex]

[tex]Line 3: 36x+32[/tex]

Required

Justify each step

From Line 1 to 2:

The property from Line 1 to 2 depicts [tex]a + b = b + a[/tex];

i.e.

[tex]4(8 + 9x) = 4(9x + 8)[/tex]

This is referred to as Commutative Property of Addition

From Line 2 to 3:

The property here depicts [tex]a(b + c) = a * b + b * c[/tex]

i.e.

[tex]4(9x + 8) = 4 * 9x + 4 * 8[/tex]

[tex]4(9x + 8) = 36x + 32[/tex]

This is referred to as Distributive property

Answer:

Line 1 to Line 2: Commutative Property of Addition

Line 2 to Line 3: Associative Property of Addition

Step-by-step explanation:

does that answer anything

Answer:

24

Step-by-step explanation:

if u subrtact 207-15 u will have 192 i divided that by 8 and got 24

Answer:

3

Step-by-step explanation:

j/4

Let j = 12

12/4

3

Answer:

m=3

Step-by-step explanation:

:D

Answer:

m ≈ 3

Step-by-step explanation:

hope this helps!

~mina

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

Solve for [tex]x[/tex] :

[tex]2x - 1 = 7[/tex]

-Add both sides by [tex]1[/tex] :

[tex]2x - 1 + 1 = 7 + 1[/tex]

[tex]2x = 8[/tex]

-Take [tex]2x[/tex] and divide it on both side of the equation:

[tex]\frac{2x}{2} = \frac{8}{2}[/tex]

[tex]x = 4[/tex]

So, the value of [tex]x[/tex] is [tex]4[/tex].

Answer:

you are trying to get up to 180 ( a straight line is 180 degrees).

So 26+32 =58 and go through your answer choices to see which one adds up to 180

and it that case your answer would be A 122+58=180

Step-by-step explanation:

Answer:

d > 0

Step-by-step explanation:

Answer:

the answer would be line AC

Step-by-step explanation:

the reason. for this is because a segment is a line with two endpoints, and line AC fits that description.

Answer:

A quadratic polynomial is a type of polynomial that cannot be factored

Examples are;

x^2 + 3x + 5

x^2 + 5x + 7

Step-by-step explanation:

A quadratic polynomial is a type of polynomial which cannot be factored. Just like prime numbers, it only has two factors, 1 and itself.

Hence, a quadratic polynomial does not have rational roots. Its roots are complex and not real

Example are as follows;

(i) x^2 + 3x + 5

(ii) x^2 + 5x + 7

[tex]\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}[/tex]

# What does it mean if a quadratic polynomial

is prime? Give two examples of quadratic

polynomials that are prime. Now, find a quadratic

polynomial that is prime.

[tex]\huge\sf\underline{\purple{❥}\pink{A}\orange {N}\blue{S}\red{W}\green{E}\purple{R}}[/tex]

[tex]\color{red}{About \:Quadratic \: polynomials\: :-}[/tex]

➯ A polynomial having degree 2 is called a quadratic polynomial.

➯ The form of quadratic polynomial is

[tex]p(x) = a {x}^{2} + bx + c[/tex]

➯ Degree of the quadratic polynomial will be 2.

➯ Variable of the quadratic polynomial will be 1.

[tex]\color{red}{For \:example :-}[/tex]

[tex]p(x) = 2 {x}^{2} + 5x + 3 \\ 3 \:➝ \: constant \\ 2 \: and \: 5 \: ➝ \: coefficient \\ {}^{2} \: ➝ \: degree \\ x \:➝ \: variable \:[/tex]

➯ In a quadratic polynomial there are 2 zeros because it has degree 2.

[tex]\color{red}{➯ The \: 2\: zeros \:are :-}[/tex]

[tex]i) \: \: alpha( \alpha ) \: \\ ii) \: beta \: ( \beta )[/tex]

[tex]\color{red}{For \:example :-}[/tex]

[tex]p(x) = 2 {x}^{2} + 5 + 3 \\ = 2 {x}^{2} + 2x + 3x + 3 \\ = 2x(x + 1) + 3(x + 1) \\ = (x + 1)(2x + 3) \\ \\ As, \: \: p(x) = 0 \\ \\ ❥∴ \: (x + 1)(2x + 3) = 0 \\ x + 1 = 0 \\ x = - 1 \\ \\ ❥ \: 2x + 3 = 0 \\ 2x = - 3 \\ x = \frac{ - 3}{2} \\ \\ Here, \: \alpha = - 1 \\ \beta = \frac{ - 3}{2} [/tex]

Answer:

-5

Step-by-step explanation:

Your basic equation if y = mx + b

Convert your equation to the above format: y = -5x -2/3

Now you can see that your slope is -5

Answer:

- 5

Step-by-step explanation:

[tex]y = - \frac{2}{3} - 5x \\ y = - 5x - \frac{2}{3} ..(1) \\ equating \:equation \: by (1) \: \\ y = mx + b \\ slope \: (m) = - 5[/tex]

Answer: y= -5/7 x + 1/7

Step-by-step explanation:

Answer:

[tex]y=-\frac{5}{7} x+\frac{1}{7}[/tex]

Step-by-step explanation:

Equation of a line: [tex]y = mx+b[/tex]

m is the slope, and b is the y-intercept.

m = [tex]\frac{rise}{run} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{-2-3}{3-(-4)} =-\frac{5}{7}[/tex]

Now, we have [tex]y=-\frac{5}{7} x+b[/tex]

We can insert one set of points in to solve for b.

We will use the first point (-4, 3):

[tex]3=-\frac{5}{7} (-4)+b[/tex]

[tex]\frac{5}{7}* \:4+b=3[/tex]

[tex]\frac{20}{7}+b=3[/tex]

[tex]b=\frac{1}{7}[/tex].

Equation:[tex]y=-\frac{5}{7} x+\frac{1}{7}[/tex]

Answer:

45

Step-by-step explanation:

13 x 4 = 52

13 represents # of cars

4 represents tires per car

52 represents total tires

52 tires - 7 damaged tires = 45 undamaged tires

Answer:

45

Step-by-step explanation:

13 * 4=52

52-7=45

45 tires not damaged

Answer:

k=-2

Step-by-step explanation:

Answer:

[tex]\boxed {\tt 23}[/tex]

Step-by-step explanation:

In order to find the mean, we must add all the values together, then divide by the number of values.

1. Add the values together

2. Divide by the number of values.

Count how many values are in the set of data. There are 5 values. Divide by 5.

The mean is 23.

Answer:

to find c you divide 18 by 3 to find that c = 6

Answer:

c would equal 6

Step-by-step explanation:

3(6) = 18

Answer:

60 ft tall

Step-by-step explanation:

tall          |     6       |      x  

shadow  |     4       |    40  

4 times 10 = 40

6 times 10 = 60

Answer:

60 ft tall

Step-by-step explanation:

(1) [tex]50y^3=5y\cdot 10y^2[/tex], and

[tex]10y^2\cdot(5y-4)=50y^3-40y^2[/tex]

Subtract this from [tex]50y^3+10y^2-35y-7[/tex] to get a remainder of

[tex](50y^3+10y^2-35y-7)-(50y^3-40y^2)=50y^2-35y-7[/tex]

What we've done here is show that

[tex]\dfrac{50y^3+10y^2-35y-7}{5y-4}=10y^2+\dfrac{50y^2-35y-7}{5y-4}[/tex]

We can keep going as long as the degree of the remainder's numerator is at least the same as the degree of its denominator.

Next, [tex]50y^2=5y\cdot 10y[/tex], and

[tex]10y\cdot(5y-4)=50y^2-40y[/tex]

Subtract this from the previous remainder to get a new remainder of

[tex](50y^2-35y-7)-(50y^2-40y)=5y-7[/tex]

which means

[tex]\dfrac{50y^3+10y^2-35y-7}{5y-4}=10y^2+10y+\dfrac{5y-7}{5y-4}[/tex]

Finally, [tex]5y=5y\cdot1[/tex], and

[tex]1\cdot(5y-4)=5y-4[/tex]

Subtract this from the previous remainder to get

[tex](5y-7)-(5y-4)=-3[/tex]

So we end up with

[tex]\dfrac{50y^3+10y^2-35y-7}{5y-4}=\boxed{10y^2+10y+1}-\dfrac3{5y-4}[/tex]

(the quotient is the expression in the box)

(2) Using the same process as before:

[tex]8m^4=2m\cdot4m^3[/tex]

[tex]4m^3\cdot(2m+1)=8m^4+4m^3[/tex]

[tex](8m^4-4m^2+m+4)-(8m^4+4m^3)=-4m^3-4m^2+m+4[/tex]

[tex]\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=4m^3-\dfrac{4m^3+4m^2+m+4}{2m+1}[/tex]

[tex]-4m^3=2m\cdot(-2m^2)[/tex]

[tex]-2m^2\cdot(2m+1)=-4m^3-2m^2[/tex]

[tex](-4m^3-4m^2+m+4)-(-4m^3-2m^2)=-2m^2+m+4[/tex]

[tex]\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=4m^3-2m^2-\dfrac{2m^2-m-4}{2m+1}[/tex]

[tex]-2m^2=2m\cdot(-m)[/tex]

[tex]-m\cdot(2m+1)=-2m^2-m[/tex]

[tex](-2m^2+m+4)-(-2m^2-m)=2m+4[/tex]

[tex]\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=4m^3-2m^2-m+\dfrac{2m+4}{2m+1}[/tex]

[tex]2m=2m\cdot1[/tex]

[tex]1\cdot(2m+1)=2m+1[/tex]

[tex](2m+4)-(2m+1)=3[/tex]

[tex]\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=\boxed{4m^3-2m^2-m+1}+\dfrac3{2m+1}[/tex]

Answer:

x=-2.5

Step-by-step explanation:

Answer:

x=  -5/2

Step-by-step explanation:

i just did scratch work an figured it out.. Lemme kno if u need ore help-..:):)

Answer:

Since x=3 and y=2, plug into the equation.

4(3)²-2(2)

= 4(9)-4

= 36-4

= 32

Answer:

67, no remainder.

Step-by-step explanation:

Answer:

67, no remainder.

Step-by-step explanation:

Answer: 60 yd

Step-by-step explanation:

Here: subdivided into 3 smaller pens (2w + w + w) extra widths for separation purposes (3 smaller pens)

180 yards of fencing material

180yd = 2L + 4w

180dy = 2*60 + 4w

60dy = 4w

w = 15yd, how wide can the rectangle can  be with L = 60yd

Answer: 30

Step-by-step explanation:

Answer:

10.

Step-by-step explanation:

First of all, the little 2 stands for multiply by 2 so multiply 5 by 2 then you will get 10. Add 10 and 10 so you will get 20. Then divide 20 by 2 and you will get 10!

Hope it helps!

OwO

Answer:

well the square root of 49 is 7 . so maybe this will help you.

Answer:

171 degrees (C)

Step-by-step explanation:

Because you have to find the overall angle you add both angles together, hence giving you 171 (C)

Answer:

171°

Step-by-step explanation:

Angle KJU = 67°     Angle UJI = 104°

By adding 67 and 104, you would get 171, which is the angle of KJI.

Answer and explanation:

The domain would be [-9,3]. A closed circle lets you know if you will have to put parenthesis or a bracket when writing the domain. You can use every number between -9 and 3, including -9 and 3.

The domain of the given graph is  -9 ≤ x ≤ 3.

The domain of a function f is the set of all values of x for which f(x) is defined and real.

Now from the given graph it is seen that the graph runs from -9 to 3 on x-axis.

and it is known that the domain of the graph is the set of all possible values of x.

Hence the required domain the given graph is written as,

-9 ≤ x ≤ 3

Thus, the domain of the given graph is  -9 ≤ x ≤ 3.

To learn more about domain of the graph :

https://brainly.com/question/20035161

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