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kogti [31]
2 years ago
9

In Greenville, the library is due south of the courthouse and due west of the community swimming pool. If the distance between t

he library and the courthouse is 7 kilometers and the distance between the courthouse and the city pool is 25 kilometers, how far is the library from the community pool?
Mathematics
1 answer:
Otrada [13]2 years ago
3 0

Answer:

24 km

Step-by-step explanation:

this is a right triangle

use the pythagorean theorem

a² + b² = c²

a² + 7² = 25²

a² + 49 = 625

Subtract 49 from both sides

a² = 576

Take the square root of oth sides

a = 24

24 km

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Which equation best represents the line? (10 Points)
son4ous [18]

Answer: D. y = 3x − 1

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the graph,

y2 = 2

y1 = - 1

x2 = 1

x1 = 0

Slope,m = (2 - - 1)/(1 - 0) = 3/1 = 3

To determine the intercept, we would substitute x = 1, y = 2 and m= 3 into y = mx + c

y = mx + c. It becomes

2 = 3 × 1 + c = 3 + c

c = 2 - 3 = - 1

The equation becomes

y = 3x - 1

7 0
3 years ago
(pls help quick and explain how you got the answers for brainliest)
scoray [572]

You only have to apply the theorem of Pythagoras here. Remember the square on the hypotenuse (the longest side) is equal to the sum of the squares on the other two sides :

1. AB is the hypotenuse, so, according to the theorem we can write :

AB² = AC² + CB²

c² = 5² + 4²

c²= 25 + 16

c² = 41

applying the square root of 41 we get :

c ≈ 6.40 rounded to the hundred

The next cases are exactly the same thing so there is no need for explanation :

2.

AB is the hypotenuse here because it is the biggest side clearl :

AB² = AC² + CB²

25² = 15² + b²

Thus

b² = 25² - 15²

we just subtracted 15² on each side of the equation

b² = 625 - 225

b² = 400

applying the square root of 400 we get

b = √400 = 20

So AC = 20

3. The longest side is clearly AB = 60

So

AB² = AC² + CB²

60² = 40² + a²

subtracting 40² on each side of the equation we get :

a² = 60² - 40²

I let you finish this using your calculator and doing exactly like the previous cases

4.

AB is the hypotenuse,

AB² = AC² + CB²

23² = b² + 14²

Subtracting 14² from each side of the equation we get

b² = 23² - 14²

5.

AB is the biggest side :

AB² = AC² + CB²

29² = 23² + a²

We subtract 23² on each sides of the equation :

a² = 29² - 23²

You can finish with your calculator

6.

AB² = AC² + BC²

78² = b² + 30²

subtraction...

b² = 78² - 30²

Good luck :)

7 0
2 years ago
What is the coefficient of q in the sum of these two expressions?
a_sh-v [17]

Answer: 1/2

Step-by-step explanation:

3 0
3 years ago
Giving brainliest :)
Verizon [17]

Answer:

f^{-1}(x)=x^2+1

Step-by-step explanation:

The inverse of a function is when the x and y are swapped. So the first step is to write f(x) as y and then swap the x and y

Original Equation:

f(x)=\sqrt{x-1}\\

write f(x) as y (since that's what it represents)

y=\sqrt{x-1}

Swap x and y

x=\sqrt{y-1}

Square both sides

x^2=y-1

Add 1 to both sides

x^2+1=y

So this gives you the equation:

f^{-1}(x)=x^2+1

8 0
2 years ago
A school is organizing a cookout where hotdogs will be served. The hotdogs come in small packs and large packs. Each small pack
Bas_tet [7]
6 x 18
7 x 8
6 x 18 = 108
7 x 8 = 56
108 + 56 = 164
6 0
2 years ago
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