Answer:
slope=5/4
slope=-4/5
Step-by-step explanation:
Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other.
Answer:
9.42
Step-by-step explanation:
Hey There!
The first step of this problem is to find the formula for arc length
![arc-length=2\pi r(\frac{0}{360} )](https://tex.z-dn.net/?f=arc-length%3D2%5Cpi%20r%28%5Cfrac%7B0%7D%7B360%7D%20%29)
r=raduis
0 = angle
now we just plug in the values
![arc-length=2\pi 10\frac{54}{360} \\2\pi =6.283185307\\6.283185307x10=62.83185307\\62.83185307\frac{54}{360}=9.424777961](https://tex.z-dn.net/?f=arc-length%3D2%5Cpi%2010%5Cfrac%7B54%7D%7B360%7D%20%5C%5C2%5Cpi%20%3D6.283185307%5C%5C6.283185307x10%3D62.83185307%5C%5C62.83185307%5Cfrac%7B54%7D%7B360%7D%3D9.424777961)
so the arc length equals 9.424777961
the last step is to round to the nearest hundreth
so your final answer is 9.42
Answer:
118.3 m²
Step-by-step explanation:
Step 1. Calculate the <em>semiperimeter</em> (s).
s = (p + q + r)/2
s = (17 + 18+ 15)/2
s = 50/2
s = 25 m
===============
Step 2. Calculate the <em>area</em> (A).
Use <em>Heron’s formula</em>:
![A = \sqrt{s(s-p)(s-q)(s-r)}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7Bs%28s-p%29%28s-q%29%28s-r%29%7D)
![A = \sqrt{25(25-17)(25-18)(25-15)}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B25%2825-17%29%2825-18%29%2825-15%29%7D)
![A = \sqrt{25\times8\times7\times10}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B25%5Ctimes8%5Ctimes7%5Ctimes10%7D)
![A = \sqrt{14 000}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B14%20000%7D)
![A = 20\sqrt{35}](https://tex.z-dn.net/?f=A%20%3D%2020%5Csqrt%7B35%7D)
A = 118.3 m²
Answer:
0.5
Step-by-step explanation:
Total space in the parking lot = 10
number of cars parked = p
number of empty parking spaces = e
There are the same number of cars parked in the parking lot as there are empty parking spaces.
This means,
Number of parked cars = number of empty parking spaces
p = e
If the number of parked cars and number of empty parking spaces = 10
p + e = 10
If p = 5
Then,
p + e = 10
5 + 5 = 10
Write a decimal to show the part of the parking lot that has empty parking spaces.
Empty parking space/total parking space
= 5/10
= 1/2
= 0.5
part of the parking lot that has empty parking spaces = 0.5
Answer:
The value of x is 5
Step-by-step explanation:
<em>The measure of the </em><em>exterior angle</em><em> at one vertex of a triangle equals the </em><em>sum of the measures of the two opposite interior angles</em><em> to this vertex</em>
In ΔQRS
∵ ∠QRS is an exterior angle of the triangle at vertex R
∵ ∠PQR and ∠RPQ are the opposite interior angles of vertex R
→ By using the rule above
∴ m∠QRS = m∠PQR + m∠RPQ
∵ m∠QRS = (10x - 10)°
∵ m∠PQR = (2x + 1)°
∵ m∠RPQ = (3x + 14)°
→ Substitute them in the equation above
∴ 10x - 10 = 2x + 1 + 3x + 14
→ Add the like terms in the right side
∵ 10x - 10 = (2x + 3x) + (1 + 14)
∴ 10x - 10 = 5x + 15
→ Subtract 5x from both sides
∵ 10x - 5x - 10 = 5x - 5x + 15
∴ 5x - 10 = 15
→ Add 10 to both sides
∵ 5x - 10 + 10 = 15 + 10
∴ 5x = 25
→ Divide both sides by 5 to find x
∴ x = 5
∴ The value of x is 5