Rachel earns $67.50 for working 9 hours at the dairy farm. How much does Rachel make per hour? How much would Rachel make if she works 5 hours a day for 6 days?

Answer:

13

Step-by-step explanation:

Let PS = x and RP = x-5

Using Pythagorean theorem on the two smaller rt triangles formed,

6^2 + x^2 = (ST)^2

6^2 + (x-5)^2 = (RT)^2

Now use Pythag on big triangle and sub in above values:

(2x-5)^2 = 6^2 + x^2 + 6^2 + (x-5)^2

Multiply out and simplify to

x^2 - 5x -36 = 0

Factor the quadratic: ((x-9)(x+4)=0  Therefore x=9 or x=-4.  We may disregard the negative answer so x = 9.  So PS is 9 and RP is 4.

Therefore entire hypotenuse is 4 + 9 or 13.

Answer:

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]

Step-by-step explanation:

The question is poorly formatted.

Given

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y}[/tex]

Required

Derive an equivalent expression

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y}[/tex]

Express 18 as 9 * 2

[tex]\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}[/tex]

Split the expression as follows:

[tex]\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}[/tex]

Take positive square root of 9

[tex]\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}[/tex]

[tex]\sqrt[3]{2y^3} * 21 * \sqrt{2y}[/tex]

[tex]21*\sqrt[3]{2y^3} * \sqrt{2y}[/tex]

The cube root can be rewritten to give:

[tex]21*\sqrt[3]{2}*\sqrt[3]{y^3} * \sqrt{2y}[/tex]

[tex]\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y[/tex]

So, we have:

[tex]21*\sqrt[3]{2} * y * \sqrt{2y}[/tex]

Rewrite as:

[tex]21y *\sqrt[3]{2} * \sqrt{2y}[/tex]

Split [tex]\sqrt{2y[/tex]

[tex]21y *\sqrt[3]{2} * \sqrt{2} * \sqrt{y}[/tex]

Collect Like Terms

[tex]21y*\sqrt{y} *\sqrt[3]{2} * \sqrt{2}[/tex]

Represent in index form

[tex]21y*y^{\frac{1}{2}} *2^\frac{1}{3} *2^\frac{1}{2}[/tex]

Apply law of indices

[tex]21*y^{1+\frac{1}{2}} *2^{\frac{1}{3} +\frac{1}{2} }[/tex]

[tex]21*y^{\frac{2+1}{2}} *2^{\frac{2+3}{6}}[/tex]

[tex]21*y^{\frac{3}{2}} *2^{\frac{5}{6}}[/tex]

[tex]21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]

Hence:

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]

Answer:

aww I find this so cutee

Step-by-step explanation:

Merry Christmas :) :) ^ ^

Answer:

its past t but it never too late to celebrate christmas happy christmas past and future

Step-by-step explanation:

Answer/Step-by-step explanation:

5. 21x + 4 = 22x - 2 (corresponding angles)

Collect like terms

21x - 22x = -4 - 2

-x = -6

divide both sides by -1

x = 6

6. (x + 72) + (x + 132) = 180 (linear pair)

x + 72 + x + 132 = 180

Add like terms

2x + 204 = 180

2x = 180 - 204

2x = -24

x = -12

7. 90 = 22x + 2 (vertical angles)

90 - 2 = 22x

88 = 22x

Divide both sides by 22

4 = x

x = 4

8. 12x + 10 = 13x + 3 (vertical angles)

Collect like terms

12x - 13x = -10 + 3

-x = -7

Divide both sides by -1

x = 7

9. 17x = 16x + 5 (alternate exterior angles)

17x - 16x = 5

x = 5

✔️17x

Plug in the value of x

17(5) = 85°

10. 21x - 6 = 20x (corresponding angles)

Add like terms

21x - 20x = 6

x = 6

✔️20x

20(6) = 120°

Answer:

D.$79.89

Step-by-step explanation:

Cost of one yard of fabric = $6.99

Length of fabric bought = 8 yards

Cost of one bag of polyester filling = $7.99

Number of bags of polyester filling bought = 3

Total cost of fabric = [tex]6.99\times 8=\$55.92[/tex]

Total cost of polyester filling = [tex]7.99\times 3=\$23.97[/tex]

Total cost of materials bought = Total cost of fabric + Total cost of polyester filling

[tex]=55.92+23.97=\$79.89[/tex]

Total cost of materials bought is [tex]\$79.89[/tex].

Answer:

4:3 or 4 to 3

Step-by-step explanation:

Answer:

e. 2

Step-by-step explanation:

Answer:

Slope=2

y intercept= Length of spring without any weight

15 lbs= 38 inches

Step-by-step explanation:

slope=

18-12/5-2= 6/3 = 2

y intercept= 0=x and x=amount of weight

equation= 2x+8=y

2(15)+8=38

Answer:

the length of the diagonal BD is 8 cm

Step-by-step explanation:

The computation of the length of diagonal BD is as follows

Here the trapezoid diagonals divides each other in an equivalent ratio

So, equation would be

AO ÷ OC = OB ÷ OD

Now put there values to the above equation

3 ÷ 1 = 6 ÷ OD

3OD = 6

Now divided it by 3 in both the sides

OD = 2

Now the BD would be

= BO + OD

= 6 +  2

= 8 cm

hence, the length of the diagonal BD is 8 cm

Answer:

72

Step-by-step explanation:

Based on the table, the left and the right side have a pattern. When 3 is added to the left side, the right side is multiplied by 6. Since 12 multiplied by 6 is 72, the missing number is 72.

Answer:

The maximum height it reaches is 20 meters

The time taken by it to reach the height is 2 seconds

Step-by-step explanation:

The formula of the height of the stone is h = u t - [tex]\frac{1}{2}[/tex] g t², where

∵ A stone is thrown vertically upwards with an initial velocity of 20 m/s

∴ u = 20 m/s

∵ g = 10 m/s²

→ Substitute them in the equation above

∴ h(t) = 20t - [tex]\frac{1}{2}[/tex] (10) t²

∴ h(t) = 20t - 5t²

→ Arrange the terms of the right side according to the greatest power of t

∴ h(t) = -5t² + 20t

To find the maximum height and the time of it find the vertex of the quadratic function (m, k), where m = [tex]\frac{-b}{2a}[/tex] and k is the value of h at t = m, a is the coefficient of t² and b is the coefficient of t

∵ The coefficient of t² is -5

∴ a = -5

∵ The coefficient of t is 20

∴ b = 20

→ Use them to find h

∵ m = [tex]\frac{-20}{2(-5)}[/tex] = [tex]\frac{-20}{-10}[/tex] = h

∴ m = 2

→ Substitute it in the equation above to find k

∵ h(m) = k

∵ k = -5(2)² + 20(2)

∴ k = -5(4) + 40

∴ k = -20 + 40

∴ k = 20

∴ The coordinate of the vertex of the function are (2, 20)

→ m represents the time of the maximum height and k represents

  the maximum height

∴ The maximum height it reaches is 20 meters

∴ The time taken by it to reach the height is 2 seconds

Step-by-step explanation:

The equation of the line is y = 279.

Answer:

You need to insert different x values and plot the point. So let's say x=1 the answer would be 10 and for 2 it would be 17

x= 6.32

y= 12

z= 18.97

I got my answer by; using the MCF and multiplying to see how many times 6/2 will go into x,y,z!

Hope this helps:)!

Answer:

x= 6.32

y= 12

z= 18.97

Answer:

A. Increasing

Step-by-step explanation:

According to the graph, we see that as the x-values increase, the y-values also increase. Therefore, the entire graph is increasing.

Answer:

21.74 But if it tells you to round I would round to 21 lbs

Step-by-step explanation:

its basically just a ratio of 92 to 20

92/20=4.6

92-20=72% the amount that is lost

so given that the plum is 100 lbs we know that 72% is depleted

(72/92 = .78)X100= 78 lbs depleted

Lastly 100-78 =22 for the remaining weight of the prunes.

Answer:

The scale factor is 18 to 1 for the painting

Step-by-step explanation:

Here we want to get the scale factor of the original to what is reproduced

Let us have same units first

Mathematically;

1 foot = 12 inches

3 feet = 36 inches

2 feet = 24 inches

So 36 to 2 and 24 to 1 1/3

That will be ratio 36/2 = 18 to 1

same as 25 divided by 1 1/3 = 18 to 1

Answer:

The probability that five of the eight students exhibit an higher IQ than the median of the general population is 0.21875

Step-by-step explanation:

The given parameters are;

The number of students in the sample, n = 8

The number of the students, x, that exhibit higher IQ's than the median = 5

The probability of obtaining the given result by chance is given as follows;

P(x) = n!/((n - x)!x!) × pˣ × qⁿ⁻ˣ

The probability that a student exhibit higher IQ's than the median = 0.5 = p

Similarly, we have, the probability that a student exhibit lower IQ's than the median = 0.5 = q

Substituting the known values, gives;

P(5) = (8!/((8 - 5)!×5!)) × 0.5^(5) × 0.5^(8 - 5) = 0.21875

Therefor, the probability that 5 of the 8 students exhibit an higher IQ than the median of the general population, P(5) = 0.21875.

A

Step-by-step explanation:

sale price of the television is c

no number line is shown so this answer is improvible

Answer:

The maximum price per share is $250 and it happens after 10 days of trading.

Step-by-step explanation:

The performance of a stock is modeled by the function:

[tex]P(d)=-2.5d^2+50d[/tex]

Where d is the number of days of trading and P is the price per share.

To find the maximum price, we use the first derivative:

[tex]P'(d)=-5d+50[/tex]

Equating to zero:

-5d+50=0

Solving for d:

-5d = -50

d = -50/(-5) = 10

d = 10

The price for d=10 is:

[tex]P(10)=-2.5*10^2+50*10[/tex]

[tex]P(10)=-2.5*100+500= 250[/tex]

The maximum price per share is $250 and it happens after 10 days of trading.

Answer:

slope = - [tex]\frac{3}{11}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 7) and (x₂, y₂ ) = (6, 4)

m = [tex]\frac{4-7}{6+5}[/tex] = [tex]\frac{-3}{11}[/tex] = - [tex]\frac{3}{11}[/tex]

Answer:

x = -1

Step-by-step explanation:

The axis of symmetry of the graph [tex]y=(x-3)^2[/tex] is  x=3 but,

If shift the graph 4 units to the left it would mean the new value of x would be -1 as shown here:

[tex]x=3-4\\x=-1[/tex]

-4 because it shifted 4 units to the left so the axis of symmetry of the transformed graph would be x = -1 and since it shifted 2 units down the y-coordinate of the turning point would be -2 so the turning point of the original graph is (3 , 0) and the turning point of the transformed graph is

(-1 , -2) I attached an image so you can visualize clearly

Answer:

I’m guessing D

Step-by-step explanation:

As the perpendicular would be -4 the negative reciprocal. I just worked out the whole equation including the point it passes.

Answer:

-6

Step-by-step explanation:

Answer:

Wind speed = 30 mph

Plane speed = 270 mph

Step-by-step explanation:

Given that :

Distance = 600 miles

Let speed of airplane = a ; speed of wind = b

Net speed ; with wind = a + b

Net speed against wind = a - b

Time taken with wind = 2 hours

Time taken against wind = 2.5 hours

Recall :

Speed = distance / time ; distance = speed * time

(a + b) * 2 = (a - b) * 2.5

2a + 2b = 600

a + b = 300 - - - (1)

a = 300 - b

2.5a - 2.5b = 600

a - b = 240 - - - (2)

300 - b - b = 240

300 - 2b = 240

-2b = - 60

b = 30

a = 300 - 30

a = 270

Wind speed = 30 mph

Plane speed = 270 mph

Answer:

the second graph

Step-by-step explanation:

Answer:

63/88

any more help just ask

Answer:

c

Step-by-step explanation:

bc it is