Multiply r^2+7r+10/3 by 3r-30/r^2-5r-50
<span>=( r^2+7r+10)/3 (3r-30)/(r^2-5r-50) </span>
<span>=(r+2)(r+5)/3 3(r+10)/ (r-10)(r+5) </span>
<span>=3 (r+2)(r+5)(r+10)/3(r-10)(r+5) </span>
<span>=(r+2)(r+10)/(r-10)</span>
The answer is √91 feet (which is the same as 9.54 feet).
Imagine this as a right triangle. A length of the foot is actually a hypotenuse (c). The distance from wall's base to the ladder foot is one of the sides of the triangle (let it be a).
So, using the Pythagorean theorem:
c² = a² + b²
It is given:
c = 10 feet
a = 3 feet
b = ?
c² = a² + b²
⇒ 10² = 3² + b²
100 = 9 + b²
b² = 100 - 9 = 91
⇒ b = √b² = √91 ≈ 9.54 feet
Answers
b = 2.77 m
A = 43.0°
C = 111.1°
cosine law to find b
b = 2.7708\ m
Find angle A with sine law
![\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} \\ \\ \sin A = \frac{a \sin B}{b} \\ \\ A = \sin^{-1} \left[ \frac{a \sin B}{b} \right] \\ \\ A = \sin^{-1} \left[ \frac{4.33 \sin 25.9}{2.7708} \right] \\ \\ A = 43.0467020](https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%20%3D%20%5Cfrac%7B%5Csin%20B%7D%7Bb%7D%20%5C%5C%20%5C%5C%0A%5Csin%20A%20%3D%20%5Cfrac%7Ba%20%5Csin%20B%7D%7Bb%7D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7Ba%20%5Csin%20B%7D%7Bb%7D%20%20%5Cright%5D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7B4.33%20%5Csin%2025.9%7D%7B2.7708%7D%20%20%5Cright%5D%20%20%5C%5C%20%5C%5C%0AA%20%3D%2043.0467020)
Find C with angles in triangle sum to 180
A + B + C = 180
C = 180 - A - B
C = 180 - 43.0467020 - 25.9
C = 111.1
Simplify both sides of the equation.
<span><span><span><span>3/5</span>n </span>+ 15 </span>= <span><span><span>2/5</span>n </span>+ 10
</span></span>Subtract 2/5n from both sides.
<span><span><span><span><span>3/5</span>n </span>+ 15 - </span><span><span>2/5</span>n </span></span>= <span><span><span><span>2/5</span>n </span>+ 10 - </span><span><span>2/5</span>n</span></span></span><span><span><span><span>15</span>n </span>+ 15 </span>= 10
</span>Subtract 15 from both sides.
<span><span><span><span><span>1/5</span>n </span>+ 15 - </span>15 </span>= <span>10 - 15</span></span><span><span><span>1/5</span>n </span>= -<span>5
</span></span>Multiply both sides by 5.
<span><span>5 </span></span>× (1/5n) = (5) × (−5)<span>n = -<span><span>25
Answer: n is -25.</span></span></span>
Answer:
8x + 2y.
Step-by-step explanation:
8 . x . 2 . y = 16xy = 16yx
