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2 years ago

Solve for X. Please solve this.

Mathematics

1 answer:

Alika [10]2 years ago

3 0

Answer:

Step-by-step explanation:

Opposite angles are congruent, so Angle BAC is 58 degrees.

Line KL and FG are perpendicular (forms a 90 degree angle), so Angle ABC is 90 degrees.

Points ABC form a triangle, and the interior angles of a triangle must add up to 180 degrees.

Thus, 58 + 90 + Angle BCA = 180. Solving for BCA, we get 32 degrees. Since Angle GCJ is opposite to BCA, x is 32 degrees.

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3 years ago

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3 years ago

To two decimal places, find the value of k that will make the function f(x) continuous everywhere. f of x equals the quantity 3x

Fiesta28 [93]

Given function is

$f(x)=\left\{\begin{matrix}3x+k & x\leq -4 \\ kx^2-5 & x> -4\end{matrix}\right.$

now we need to find the value of k such that function f(x) continuous everywhere.

We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.

So we just need to find both left and right hand limits then set equal to each other to find the value of k

To find the left hand limit (LHD) we plug x=-4 into 3x+k

so LHD= 3(-4)+k

To find the Right hand limit (RHD) we plug x=-4 into

$kx^2-5$

so RHD= $k(-4)^2-5$

Now set both equal

$k(-4)^2-5=3(-4)+k$

$16k-5=-12+k$

$16k-k=-12+5$

$15k=-7$

$k=-\frac{7}{15}$

k=-0.47

Hence final answer is -0.47.

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3 years ago