The scale on a map is 1/2 inch = 80 miles. how far apart are two cities that at 4 3/4 inches apart on the map?

Neporo4naja [7]

First Problem:

angle R and angle S are complementary which means they add to 90 degrees. Think "C" for "Complementary" and "Corner" as in a sharp 90 degree corner. That's how I remember it.

Let's solve for x
(angle R) + (angle S) = 90
(12x-3) + (7x-2) = 90
12x-3 + 7x-2 = 90
(12x+7x)+(-3-2) = 90
19x-5 = 90
19x-5+5 = 90+5
19x = 95
19x/19 = 95/19
x = 5

Since x = 5, we can say
angle R = 12x - 3
angle R = 12*5 - 3
angle R = 60 - 3
angle R = 57 degrees

Final Answer: 57 degrees

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Second Problem:

Angle 1 and angle 2 "form a linear pair". This means they are adjacent and supplementary (add to 180 degrees). Put another way, they combine to form a single straight angle or line.

Let's make
x = measure of angle 1
y = measure of angle 2

We're also told that "the measure of angle 2 is six more than twice the measure of angle 1", which basically translates to
y = 2*x + 6

Because the angles (x and y) are supplementary, we can also say
x+y = 180

So we have this system of equations
y = 2x+6
x+y = 180

Start with equation (2). Plug in the equation (1) and solve for x
x+y = 180
x+2x+6 = 180 ... note how y has been replaced with 2x+6
3x+6 = 180
3x+6-6 = 180-6
3x = 174
3x/3 = 174/3
x = 58

Now that we know x, we can find y
y = 2x+6
y = 2*58+6
y = 116+6
y = 122

Final Answer: 122 degrees

8 0

3 years ago

Your budget is to spend no more than $450 on frozen treats.

ikadub [295]

The inequality that shows no more than $450 is to be spent on frozen treats is 0.75C + 0.85I + 0.5F ≤ 450

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Let C represent the number of chocolate fudge bars, F represent the number of frozen fruit bars and I represent the number of ice-cream sandwiches

Hence:

0.75C + 0.85I + 0.5F ≤ 450

The inequality that shows no more than $450 is to be spent on frozen treats is 0.75C + 0.85I + 0.5F ≤ 450

Find out more on equation at: brainly.com/question/2972832

#SPJ1

4 0

2 years ago

A sailboat with a sick passenger abroad is following a parabolic path given by the equation y=-x^{2}+4x+5. The boat's captain se

max2010maxim [7]

Answer: can u add a link of the question i kno it jus need a link to make sure

Step-by-step explanation:

3 0

3 years ago

A top-loading washing machine has a cylindrical basket that rotates about a vertical axis. The basket of one such machine starts

damaskus [11]

Answer:

$n_{tot}=44rev$

Step-by-step explanation:

In order to solve this problem we can make use of the following formula:

$\theta=(\frac{\omega_{f}+\omega_{0}}{2})t$

where θ is the total angle the basket has turned, ω is the angular velocity and t is the time.

Generally theta is written in radians and omega is written in radians per second. Now, since the revolutions are directly related to the radians and they want us to write our answer in revolutions, we can directly use the provided speeds in the formula, so we can rewrite it as:

$n=(\frac{f_{f}+f_{0}}{2})t$

where n represents the number of revolutions and f is the frequency at which the basket is turning.

The movement of the cylindrial basket can be split in two stages, when it accelerates and when it decelerates. So let's analye the first stage:

$n=(\frac{4rev/s+0}{2})(9s)=18rev$

and now let's analyze the second stage, where it decelerates, so we get:

$n=(\frac{0rev/s+4rev/s}{2})(13s)=26rev$

So now that we know how many revolutions the cylindrical basket will take as it accelerates and as it decelerates we can add them to get:

n=18rev+26rev=44rev

So the basket will turn a total of 44 revolutions during this 22s interval.

3 0

3 years ago

7.8x = 32.76<br><br><br> Show your work

castortr0y [4]

Answer:

x=4.2

Step-by-step explanation:

7.8x = 32.76

/7.8 /7.8

x=4.2

6 0

3 years ago