A certain stylist charges $15 for a haircut and $30 for hair coloring. A haircut takes on average 30 minutes, while coloring takes 2 hours. The stylist works up to 8 hours in a day, and she needs to make a minimum of $150 a day to pay for her expenses.

a. Create a system of inequalities that describes the constraints in this situation. Be sure to specify what each variable represents.

b. Graph the inequalities and show the solution set.

c. Identify a point that represents a combination of haircuts and and hair-coloring jobs that meets the stylist's requirements.

Equivalent expressions are expressions that have the same value, and can be used interchangeably.

The result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]

The expression is given as:

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex]

Rewrite the expression as:

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y}) + 4 (\sqrt[3]{3^3 \times 2x^6y^5})[/tex]

Evaluate the roots

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y}) + 4 (3x^2y\sqrt[3]{2y^2})[/tex]

Open the brackets

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y} + 12x^2y\sqrt[3]{2y^2})[/tex]

The above expression cannot be further simplified.

Hence, the result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]

Read more about equivalent expressions at:

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The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].

We have to determine, the sum of the given expression.

According to the question,

Expression; [tex]2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})[/tex]

To determine the sum of the given expression following all the steps given below.

Rewrite the expression term in the form of their cubes,

[tex]\rm = 2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})\\\\ = 2(\sqrt[3]{2^4x^3y} +4(\sqrt[3]{3^3 \times 2 \times x^6y^5})\\\\= 2\times 2(\sqrt[3]{x^3y} +4\times 3(\sqrt[3]{ 2 \times x^6y^5})\\\\= 4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\\\=4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex]

Hence, The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].

For more details refer to the link given below.

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Answer:

135%

Step-by-step explanation:

Answer:

105°.

Step-by-step explanation:

1) to calculate m(∠ABC): m(∠ABC)=180-m(∠BAC)-m(∠(ACB)=180-90-65=25°;

2) note, m(∠ABC)=m∠(ABD)=25°, then it is possible

3) to calculate m(∠BAD): m(∠BAD)=180-m(∠ABD)-m(∠ADB)=180-25-50=105°.

Answer:

x = 7

Step-by-step explanation:

you can create a proportion:

PT / ST =  PQ / RQ

36 / 30 = (5x+13) / (6x-2)

cross-multiply:

36(6x-2) = 30(5x+13)

distribute:

216x - 72 = 150x + 390

216x = 150x + 462

66x = 462

x = 7

The value of x for the given triangle sides is x = 7.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position. A geometer is a mathematician who works in the field of geometry.

Given that the side PQ = 5x + 13 and the QR is 6x- 2. The value of x will be calculated by the concept of similarity.

PT / ST =  PQ / RQ

36 / 30 = (5x+13) / (6x-2)

Cross-multiply the equations,

36(6x-2) = 30(5x+13)

Distribute:

216x - 72 = 150x + 390

216x = 150x + 462

66x = 462

x = 7

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The answer is 4+5+6=15.Hope that helps. :)

Answer:

Step-by-step explanation:

Let the first number be x,

The second number (since it is consecutive) will be = x + 1

The third number (since it is right after the second) = (x+1) + 1 = x + 2

x + x + 1 + x + 2 = 15

3x + 3 = 15

3x = 15 - 3

3x = 12

x = 12/3 = 4

If the first number = 4,

Second number will be = 5 [(x+1) = 4+1]

Third number will be = 6 [(x+2) = 4 + 2]

Step-by-step explanation:The second way of approximating a square root is to use a calculator. Most calculators have a radical sign on them. To find the square root of a number, we enter the radical sign, then the value and press enter. This will give us a decimal approximation of the square root.

[tex]f(x) =-3\\\\\implies 3x^3= -3\\\\\implies x^3 = -1\\\\\implies x = \sqrt[3]{-1} ~~\text{or}~~ x= \sqrt[3]{-1} \left(\dfrac{-1 \pm i\sqrt 3}2\right)\\[/tex]

[tex]\text{For x} \in \mathbb{R}, ~\text{the answer is x} = \sqrt[3]{-1} = -1[/tex]

Answer:

2/9

Step-by-step explanation:

Answer:

[tex]w_1=-\frac{1}{4},w_2=-2}[/tex]

Step-by-step explanation:

[tex]4w^2+9w=-2[/tex]

[tex]4w^2+9w+2=0[/tex]

[tex]w^2+9w+8=0[/tex]

[tex](w+1)(w+8)=0[/tex]

[tex](4w+1)(w+2)=0[/tex]

[tex]w_1=-\frac{1}{4},w_2=-2}[/tex]

Answer:

Cost of each share is [tex]6Rs[/tex]

Step-by-step explanation:

Let the cost be [tex]5x,7x,4x[/tex]

We have

[tex]5x+7x+4x=96\\\\16x=96\\\\x=6[/tex]

Cost of each share is [tex]6Rs[/tex]

Answer:

The answer is 3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{8+3}{12}[/tex] = [tex]\frac{11}{12}[/tex] ≈ 1

The correct answer is the last one (C)

Answer:

1) the baseball will take approx 0.514 seconds to move 18 meters.

35/1 = 18/x

x = 0.514s

2)  the car's average speed is 60 km per hour.

870/14.5 = x/1

x = 60h

Answer:

$31.68

Step-by-step explanation:

Multiply each by the correct number

almond= 1.4*9.15= 12.81

cashews= 10.75* 0.8= 8.6

Peanuts= 3.95 * 2.6= 10.27

Add them all up

12.81+8.6+10.27

you’ll get 31.68

Answer:

He earn approximately $2.14 everyday

Step-by-step explanation:

hope this helps :3

Answer:

Circumference of a circle

[tex] =( \frac{1}{2} \times 10.4 \times 16.9) {ft}^{2} \\ = (5.2 \times 16.9) {ft}^{2} \\ = 87.88 {ft}^{2} [/tex]

Answer:

The area of the triangle is 87.88 square feet.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

The value of n is 5.

Step-by-step explanation:

Concept :

Here, we will use the below following steps to find a solution using the transposition method:

Solution :

By using the transposition method. we get,

[tex]{\dashrightarrow{\tt{3n + 2 = 17}}}[/tex]

[tex]{\dashrightarrow{\tt{3n= 17 - 2}}}[/tex]

[tex]{\dashrightarrow{\tt{3n= 15}}}[/tex]

[tex]{\dashrightarrow{\tt{n= 15 \div 3}}}[/tex]

[tex]{\dashrightarrow{\tt{n= \dfrac{15}{3}}}}[/tex]

[tex]{\dashrightarrow{\tt{n= \cancel{\dfrac{15}{3}}}}}[/tex]

[tex]{\dashrightarrow{\underline{\boxed{\tt{\red{n= 5}}}}}}[/tex]

Hence, the value of n is 5.

[tex]\rule{300}{1.5}[/tex]

Solve : 3n + 2 = 17

n = 5

=> 3n + 2 = 17

=> 3n = 17-2

=> 3n = 15

=> n = 15/3

=> n = 5

Answer:

is this a questions or no?

Step-by-step explanation:

Step-by-step explanation:

Simply divide the percent by 100 and multiply by the number. For example, 48.9 /100 x 264 = 129.096 or 0.489 x 264 = 129.096

Rounded to nearest hundredth

= 129.10

Answer:129.10

Step-by-step explanation:

Simply, the equation for the percentage value of a number is:

x*(z%/100%)=y

where x is your initial value, z is your percentage value, and y is the resultant value

for this question, the equations gives us as follows

264*(48.9%/100%)=129.096=129.10

Answer:

$0.73

Step-by-step explanation:

Let's say an orange costs O dollars and a grapefuit costs G dollars.

We add G dollars for each grapefuit and O dollars for each orange, so, for example, 12 grapefuit = G added 12 times = 12 *G = 12G

a.

6G = 10O

12G + 24O = 12

6 grapefuit = 6G = 10 oranges = 10O

b.

6G = 10O

12G + 24O = 12

We can solve this using substitution. First, we can solve the first equation for G. After that, we can plug that into the second to find O and go from there.

6G = 10O

divide both sides by 6 to remove the coefficient for G

G = (10/6)O

plug that into the second equation

12*(10/6)O + 24O = 12

20O + 24O = 12

44O = 12

divide both sides by 44 to solve for O

O=12/44 = 6/22

6G = 10O

6G = 60/22

divide both sides by 6 to solve for G

10/22 = G

c.

These solutions mean that an orange (O) costs 6/22 dollars and a grapefuit (G) costs 10/22, so 1O + 1G = 16/22 dollars ≈ $0.73. Note that O and G are kept as fractions because they are not exact dollar amounts, e.g. 0.27 repreating

Answer:

Step-by-step explanation:

5

+

1

=

3

+

7

5x+1=3x+7

Solve

1

Subtract  

1

1

from both sides of the equation

5

+

1

=

3

+

7

5x+1=3x+7

5

+

1

−

1

=

3

+

7

−

1

5x+1{\color{#c92786}{-1}}=3x+7{\color{#c92786}{-1}}

2

Simplify

Subtract the numbers

Subtract the numbers

5

=

3

+

6

5x=3x+6

3

Subtract  

3

3x

from both sides of the equation

5

=

3

+

6

5x=3x+6

5

−

3

=

3

+

6

−

3

5x{\color{#c92786}{-3x}}=3x+6{\color{#c92786}{-3x}}

4

Simplify

Combine like terms

Combine like terms

2

=

6

2x=6

5

Divide both sides of the equation by the same term

2

=

6

2x=6

2

2

=

6

2

\frac{2x}{{\color{#c92786}{2}}}=\frac{6}{{\color{#c92786}{2}}}

6

Simplify

Cancel terms that are in both the numerator and denominator

Solution

=

3

Answer:

[tex]\frac{\frac{1}{4}}{1}=\frac{\frac{5}{6}}{x}[/tex]

Step-by-step explanation:

Per = 1

[tex]\frac{1}{4}[/tex]

So, if we were to solve:

[tex]\frac{1}{4}=\frac{5}{6x}[/tex]

[tex]\frac{1}{4}\cdot \:6x=1\cdot \:5[/tex]

[tex]\frac{3}{2}x=5[/tex]

[tex]\frac{3}{2}x\cdot \:2=5\cdot \:2[/tex]

[tex]3x=10[/tex]

[tex]\frac{3x}{3}=\frac{10}{3}[/tex]

[tex]x=\frac{10}{3}[/tex]

Troy can make [tex]\frac{10}{3}[/tex] dozen of cupcakes.

Answer:

18x² - 24x + 9

Step-by-step explanation:

To find f(g(x)), substitute x = g(x) into f(x) , that is

f3x - 2)

= 2(3x - 2)²+ 1 ← expand factor using FOIL

= 2(9x² - 12x + 4) + 1 ← distribute parenthesis by 2

= 18x² - 24x + 8 + 1

= 18x² - 24x + 9

Answer:

i think B is answer

Step-by-step explanation:

0.5x+9 = -3x+2

x = -2

y = -3x+2

y = -3(-2) +2

y = 6+2

y = 8

(x,y) = (-2,8)

Answer:

(100-12) - 3

Step-by-step explanation:

we dont know what the cost of the shirts are so that one should be it.

Answer:

parallelogram is the answer

Answer:

Step-by-step explanation:

The quadrilateral is a parallelogram ( more precisely is the rhombus )

the answer is 4

The store owner is adding cost, so we will use addition. The answers should be as follows:

[] c + $3.49 = $9.84

[] c = $6.35 <- subtract $3.49 from both sides of the equation

[] Solution of answer represents the old cost of the toy.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather