Which sentences contain two words that are related in the same way as the underlined words in the paragraph?

What is the equation of the parabola?<br>

Novay_Z [31]

Answer:

The simplest equation for a parabola is y = x^2

3 0

3 years ago

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along

mina [271]

Answer:

The tip of the man shadow moves at the rate of $\frac{20}{3} ft.sec$

Step-by-step explanation:

Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

$\frac{y - x}{y} = \frac{6}{15}$

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

y = $\frac{15x}{9\\} y = \frac{5x}{3}$

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

$\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}$ ----(1)

We are given $\frac{dx}{dt} = 4 ft/sec$ . Plug in the equation (1), we get

$\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec$

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

7 0

3 years ago

Find the coordinates of the missing endpoint if M is the midpoint of DF <br> F(2,9) M(-1,6)

Hunter-Best [27]

Answer:

(-4,3)

Step-by-step explanation:

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%205%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20%3D%207x%20%2B%203x%20%5C%5C%20find%20%5C%3A%20the%20%5C

lana [24]

Answer:

$5 {x}^{2} + 2x = 7x + 3x \\ 5 {x}^{2} + 2x = 10x \\ 5 {x}^{2} = 10x - 2x \\ 5 {x}^{2} = 8x \\ 5x = 8 \\ x = \frac{8}{5} = 1.6 \\ thank \: you$

4 0

2 years ago

A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated fro

Veronika [31]

Answer:

There is no sufficient evidence to reject the company's claim at the significance level of 0.05

Step-by-step explanation:

Let $\mu$ be the true mean weight per apple the company ship. We want to test the next hypothesis

$H_{0}:\mu=120$ vs $H_{1}:\mu\neq 120$ (two-tailed test).

Because we have a large sample of size n = 49 apples randomly selected from a shipment, the test statistic is given by

$Z=\frac{\bar{X}-120}{\sigma/\sqrt{n}}$ which is normally distributed. The observed value is

$z_{0}=\frac{122.5-120}{12/\sqrt{49}}=1.4583$ . The rejection region for $\alpha = 0.05$ is given by RR = {z| z < -1.96 or z > 1.96} where the area below -1.96 and under the standard normal density is 0.025; and the area above 1.96 and under the standard normal density is 0.025 as well. Because the observed value 1.4583 does not fall inside the rejection region RR, we fail to reject the null hypothesis.

5 0

3 years ago