Help please!you’ll get 15 points.

Joe worked 12 hours and packed 32 cartons. Bob worked 25 hours and packed 64 cartons. Did Joe and Bobwork at the same rate?O YES

Bas_tet [7]

To be able to compare the rates, we will write them in fraction form.

The fraction that represents Joe's rate is:

$\frac{32}{12},$

and the fraction that represents Bob's rate is:

$\frac{64}{25}\text{.}$

Simplifying the above fractions, we get:

$\begin{gathered} \frac{32}{12}=\frac{8}{3}, \\ \frac{64}{25}=\frac{64}{25}\text{.} \end{gathered}$

Since:

$\frac{8}{3}\ne\frac{64}{25}$

then Bob and Joe did not work at the same rate.

Answer:

No, Bob and Joe did not work at the same rate.

4 0

1 year ago

Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”

Leviafan [203]

Answer:

The equation determine a relation between x and y

x = ± $\sqrt{1-(y-2)^{2}}$

y = ± $\sqrt{1-x^{2}}+2$

The domain is 1 ≤ y ≤ 3

The domain is -1 ≤ x ≤ 1

The graphs of these two function are half circle with center (0 , 2)

All of the points on the circle that have distance 1 from point (0 , 2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation x² + (y - 2)² and the relation "(x , y) R (0, 2)", where

R is read as "has distance 1 of"

- This relation can also be read as “the point (x, y) is on the circle

of radius 1 with center (0, 2)”

- “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”

* <em>Lets solve the problem</em>

- The equation of a circle of center (h , k) and radius r is

(x - h)² + (y - k)² = r²

∵ The center of the circle is (0 , 2)

∴ h = 0 and k = 2

∵ The radius is 1

∴ r = 1

∴ The equation is ⇒ (x - 0)² + (y - 2)² = 1²

∴ The equation is ⇒ x² + (y - 2)² = 1

∵ A circle represents the graph of a relation

∴ The equation determine a relation between x and y

* Lets prove that x=g(y)

- To do that find x in terms of y by separate x in side and all other

in the other side

∵ x² + (y - 2)² = 1

- Subtract (y - 2)² from both sides

∴ x² = 1 - (y - 2)²

- Take square root for both sides

∴ x = ± $\sqrt{1-(y-2)^{2}}$

∴ x = g(y)

* Lets prove that y=h(x)

- To do that find y in terms of x by separate y in side and all other

in the other side

∵ x² + (y - 2)² = 1

- Subtract x² from both sides

∴ (y - 2)² = 1 - x²

- Take square root for both sides

∴ y - 2 = ± $\sqrt{1-x^{2}}$

- Add 2 for both sides

∴ y = ± $\sqrt{1-x^{2}}+2$

∴ y = h(x)

- In the function x = ± $\sqrt{1-(y-2)^{2}}$

∵ $\sqrt{1-(y-2)^{2}}$ ≥ 0

∴ 1 - (y - 2)² ≥ 0

- Add (y - 2)² to both sides

∴ 1 ≥ (y - 2)²

- Take √ for both sides

∴ 1 ≥ y - 2 ≥ -1

- Add 2 for both sides

∴ 3 ≥ y ≥ 1

∴ The domain is 1 ≤ y ≤ 3

- In the function y = ± $\sqrt{1-x^{2}}+2$

∵ $\sqrt{1-x^{2}}$ ≥ 0

∴ 1 - x² ≥ 0

- Add x² for both sides

∴ 1 ≥ x²

- Take √ for both sides

∴ 1 ≥ x ≥ -1

∴ The domain is -1 ≤ x ≤ 1

* The graphs of these two function are half circle with center (0 , 2)

* All of the points on the circle that have distance 1 from point (0 , 2)

8 0

3 years ago

Are all trapezoids quadrilaterals

zysi [14]

Yes all trapezoids are quadrilaterals

7 0

3 years ago

A certain star is 2.6×102 light years from the Earth. One light year is about 5.9×1012 miles. How far from the earth (in miles)

navik [9.2K]

Answer:

2.5 x $10^{15}$ miles

3 0

3 years ago

Read 2 more answers

The table shows some

valentinak56 [21]

Answer:

<u>For 1 quart of orange juice:</u>

Calories = 448

Vitamin C = 387.6 mg

Carbohydrates = 107.56 mg

Step-by-step explanation:

The following information is given about 1 CUP of orange juice:

<h2>Calories</h2><h3>112</h3><h2>Vitamin C</h2><h3>96.9 mg</h3><h2>Carbohydrates</h2><h3>26.89 mg</h3>

Now, we have to estimate the 3 values for 1 quart of orange juice. Remember, 4 cups is 1 quart, so we need to multiply each value by 4 to get the values for 1 quart.

Calories = 112 * 4 = 448

Vitamin C = 96.9 * 4 = 387.6 mg

Carbohydrates = 26.89 * 4 = 107.56 mg

6 0

3 years ago