Answer:
Step-by-step explanation:
Here, we can use an angle rule.
We see that angles ° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.
This means we can use the rule:
Corresponding angles are equal.
This means that:
We can now use this equation we have formed to solve for :
Therefore, our final answer is .
Answer:
68
Step-by-step explanation:
Any function is evaluated by putting the argument value where the variable is, then doing the arithmetic. When the argument is another function value, that function value is evaluated first.
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<h3>f∘g</h3>The "o" in (fog) is a stand-in for the "ring operator" (∘) which is the operator used to signify a composition. A composition is evaluated right-to-left. That means (f∘g)(x) ≡ f(g(x)). The value of g(x) is found first, and is operated on by the function f.
Writing the composition in the form f(g(x)) lets you identify the layers of parentheses. As with any expression evaluation, the Order of Operations applies. It tells you to evaluate the expression in the innermost parentheses and work your way out.
<h3>g(-2)</h3>To evaluate (f∘g)(-2) = f(g(-2)), we must first evaluate g(-2). That is ...
g(x) = 5x +4
g(-2) = 5(-2) +4 = -10 +4 = -6 . . . . . put -2 where x is, do the math
<h3>f(g(-2))</h3>Now that we know g(-2) = -6, we know this expression is ...
f(-6) = 8 -10(-6) = 8 +60 = 68 . . . . . substitute for x in 8-10x
Then the value we're looking for is ...
(f∘g)(-2) = 68
The length of CS is 11.0
Explanation:
Given that the length of the tangent AR is 12
The length of SR is 7.7
To find: The length of CS
The<u> tangent secant theorem</u> states that "if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant’s external part and the entire secant."
Applying the tangent secant theorem, we have,
Rewriting the above equation, we get,
Substituting the values, we get,
Simplifying, we have,
Subtracting both sides by 59.29, we get,
Dividing both sides by 7.7, we have,
Rounding off to the nearest tenth, we get,
Thus, the length of CS is 11.0