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user100 [1]
3 years ago
13

Please show your work and explain

Mathematics
1 answer:
liberstina [14]3 years ago
4 0
We can use a theorem called Proportional segments in right triangles.

1. How far is library from the park?
<span>The perpendicular is the mean proportional between the segments of the hypotenuse, so:
</span>PL= \sqrt{FL \cdot HL } = \sqrt{8 \cdot 2 } =  \sqrt{16}=4 \ miles

2. How far is the park from the football field?
<span>Each leg of the given triangle is the mean proportional between the hypotenuse and the adjacent segment, so:
</span>PF= \sqrt{FH \cdot FL } = \sqrt{(8+2) \cdot 8 } = \sqrt{80}=4 \sqrt{5}  \ miles

Answer: A.

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Illusion [34]
I'm pretty sure you set them equal to each other. If I'm wrong I'm sorry, I haven't done that in awhile. Just going off memory

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3 years ago
Can someone pls tell me the answer for this question.
n200080 [17]

Answer:

10

Step-by-step explanation:

3000/50 = 60

12/6 = 2(months)

60/6 = 10

6 0
2 years ago
Express your answer in the lowest terms. -1/10-(-8/10)
Zielflug [23.3K]
The exact form is 7/10
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8 0
3 years ago
Line a and b are perpendicular lines.If line a is represented by y=s/t x+10 and line b is represented by y=q/r -4 where s,t,q an
alekssr [168]

Answer:

The options are not shown, so i will answer in a general way.

First, for a line of the form:

y = a*x + b

All the perpendicular lines will have a slope of -(1/a), then we can write a general perpendicular line as:

y = -(1/a)*x + c.

In this problem we have the perpendicular lines:

y=(s/t)*x+10

y = (q/r)*x - 4

Because those lines are perpendicular, we must have that:

(q/r) = -(1/(s/t)) = -(t/s)

q/r = -t/s

and we knew that s, t, q and r are integers (where t and r can not be equal to zero), and because of this relation, where we can see that in the denominator at the right we have the integer s, we can conclude that s can not be zero (we can not divide by zero).

And we know that t and s are both different than zero, then:

-t/s ≠ 0.

This means that:

q/r ≠ 0

And from this, we can conclude that q is different than zero.

7 0
3 years ago
Find a. Write your answer in simplest radical form.
yan [13]

Answer:

a=6mm

<u>Skills needed: Special Right Triangles </u>

Step-by-step explanation:

1) We are given what is known as a right triangle. More specifically, this is a special right triangle. It is a:

30-60-90 triangle, which means it has a:

---> 30-degree angle

---> 60-degree angle

---> 90-degree (right) angle

There is an important property with the side lengths of this special right triangle.

2) The property is the following:

- Let's say the side opposite of the 30-degree angle is b.

- The side opposite the 90-degree angle would be 2b.

- The side opposite the 60-degree angle would be b * \sqrt3

This property is useful for finding side lengths of the triangle.  

3) In this problem, we are given the side opposite the 90-degree angle, which means we can divide by 2 to solve for b (side opposite 30° angle).

4\sqrt{3} = 2b ---> This is the equation

4\sqrt3 \div 2 = b<em> --> </em>We divide by 2 on both sides to isolate the variable.

b = 2\sqrt3 --> We evaluate it out, and get this to be our answer for a

Then, we can solve for the side opposite the 60-degree angle by multiplying b by \sqrt3

---> b*\sqrt3=2\sqrt3*\sqrt3 = 2*\sqrt3*\sqrt3=2*3=6

\sqrt3 times itself would be 3, as multiplying by itself is squaring the square root, and removing it.

---> a=6mm in the diagram.

8 0
2 years ago
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