Chicago ave is parallel to Ontario Street. What is the relationship between angles 2 and 3?

write the equation that describes the line in slope-intercept form. slope = 4, point (3, −2) is on the line y = 4x 14 y = 4x − 2

amid [387]

Equation of a line is given by y - y1 = m(x - x1) where m is the slope and (x1, y1) is any point on the line.

y - (-2) = 4(x - 3)
y + 2 = 4x - 12
y = 4x - 12 - 2
y = 4x - 14

5 0

3 years ago

Please help me <br> Show your work <br> 10 points

Svet_ta [14]

<h2>Answer</h2>

After the dilation $\frac{5}{3}$ around the center of dilation (2, -2), our triangle will have coordinates:

$R'=(2,3)$

$S'=(2,-2)$

$T'=(-3,-2)$

<h2>Explanation</h2>

First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:

$(x,y)$ → $(x-2, y+2)$

Next, we are going to perform our dilation, so we are going to multiply our resulting point by the dilation factor $\frac{5}{3}$ . Therefore our second partial rule will be:

$(x,y)$ → $\frac{5}{3} (x-2,y+2)$

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3} ,\frac{5}{3} y+\frac{10}{3} )$

Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3}+2,\frac{5}{3} y+\frac{10}{3}-2)$

$(x,y)$ → $(\frac{5}{3} x-\frac{4}{3} ,\frac{5}{3}y+ \frac{4}{3})$

Now that we have our rule, we just need to apply it to each point of our triangle to perform the required dilation:

$R=(2,1)$

$R'=(\frac{5}{3} x-\frac{4}{3} ,\frac{5}{3}y+ \frac{4}{3})$

$R'=(\frac{5}{3} (2)-\frac{4}{3} ,\frac{5}{3}(1)+ \frac{4}{3})$

$R'=(\frac{10}{3} -\frac{4}{3} ,\frac{5}{3}+ \frac{4}{3})$

$R'=(2,3)$

$S=(2,-2)$

$S'=(\frac{5}{3} (2)-\frac{4}{3} ,\frac{5}{3}(-2)+ \frac{4}{3})$

$S'=(\frac{10}{3} -\frac{4}{3} ,-\frac{10}{3}+ \frac{4}{3})$

$S'=(2,-2)$

$T=(-1,-2)$

$T'=(\frac{5}{3} (-1)-\frac{4}{3} ,\frac{5}{3}(-2)+ \frac{4}{3})$

$T'=(-\frac{5}{3} -\frac{4}{3} ,-\frac{10}{3}+ \frac{4}{3})$

$T'=(-3,-2)$

Now we can finally draw our triangle:

8 0

3 years ago

Find the volume of each ball. use the formula. where v is the volume and r is the radius. record the volume in table A of your s

pochemuha

Answer:

The volume of tennis ball = 38.808 $cm^{3}$ .

Volume of golf ball = 33.523 $cm^{3}$ .

Step-by-step explanation:

Given: The radius of the tennis ball is 2.1cm and the radius of thr golf ball is 2.0cm. the formula is V=4πr(to the 3rd power) /3 .

To find: Volume of tennis ball and golf ball .

Formula used: Volume = $\frac{4 π r^{3} }{3}$ .

pi(π) = $\frac{22}{7}$ .

Explanation : We are given that

Radius of the tennis ball = 2.1 cm

radius of the golf ball =2.0 cm.

We need to find the volume of each ball

So , plugging the given values of radius in above formula

Volume of the tennis = $\frac{4*22(2.1)^{3} }{3*7}$

On simplification we get, volume of tennis ball = 38.808 $cm^{3}$

Volume of the golf ball= $\frac{4*22(2.0)^{3} }{3*7}$

On simplification we get, volume of golf ball = 33.523 $cm^{3}$

Therefore , The volume of tennis ball = 38.808 $cm^{3}$ .

Volume of golf ball = 33.523 $cm^{3}$ .

7 0

3 years ago

Read 2 more answers

(02.01MC)The Department of Health in the Germany wants to know whether the national healthcare system is achieving its goals in

solniwko [45]

It should be noted that a population means the entire group that a researcher wants to draw conclusions about.

<h3>What is a population?</h3>

Your information is incomplete s the data is not provided. Therefore, an overview will be given.

In statistics, a population refers to a set of similar items which is of interest for an experiment.

On the other hand, a sample is a set of individuals or objects that are selected from a statistical population through a defined procedure.

In this case, it is important to deduce if the sample represents the population.

Learn more about population on:

brainly.com/question/25896797

6 0

2 years ago

Round 0.00076511 to one significant figure

FrozenT [24]

Answer: 0.0008

Step-by-step explanation: Hope this helps :)

6 0

3 years ago