Answer:
Angle 1 = 40
Step-by-step explanation:
Angle 1 and Angle 2 are alternate angles. So,
2x + 20 = 3x + 10
3x - 2x = 20 - 10
x = 10
Angle 1 = 2x + 20 = 2 x 10 + 20 = 40
The given function are
r(x) = 2 - x² and w(x) = x - 2
<span>(w*r)(x) can be obtained by multiplying the both function together
</span>
So, <span>(w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)</span>
<span>(w*r)(x) = x (2-x²) - 2(2-x²)</span>
= 2x - x³ - 4 + 2x²
∴ <span>
(w*r)(x) = -x³ + 2x² + 2x - 4</span>
<span>It is a polynomial function with a domain equal to R
</span>
The range of <span>(w*r)(x) can be obtained by graphing the function
</span>
To graph (w*r)(x), we need to make a table between x and (w*r)(x)
See the attached figure which represents the table and the graph of <span>(w*r)(x)
</span>
As shown in the graph the range of <span>
(w*r)(x) is (-∞,∞)</span>
We have the formula A = (h x b) / 2, where A is the area of the triangle, h is the height of the triangle, b is the base of the triangle;
So, 32 =(8 x b) / 2;
Then, 64 = 8 x b;
b = 64 ÷ 8;
b = 8 inches;
The length of extra cable that is required to connect the two pieces of existing cable is equal to 182 meters.
<h3>How to determine the length of extra cable?</h3>
In order to determine the length of extra cable that is required to connect the two pieces of existing cable, we would apply the law of cosine as follows:
B² = A² + C² - 2(A)(C)cosB
Substituting the given parameters into the formula, we have;
B² = 325.0² + 430.0² - 2(325.0)(430.0)cos23
B² = 105,625 + 184,900 - 279,500(0.9205)
B² = 290,525 - 257,279.75
B² = 33,245.25
B = √33,245.25
B = 182.33 ≈ 182 meters.
Read more on cosine law here: brainly.com/question/11000638
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N = number of hours.
$5 per hour, total = 5*n = $5n
Since $35 has been saved.
The amount saved plus the amount got from baby sitting should be greater or equal to the $90 cost.
5n + 35 ≥ 90
5n ≥ 90 -35
5n ≥ 55
n ≥ 55/5
n ≥ 11
So Rodney should baby sit for at least 11 hours, that is 11 and above.