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motikmotik
3 years ago
9

Find AC What Is The Equation To AC?

Mathematics
1 answer:
In-s [12.5K]3 years ago
6 0

<u>Given</u>:

Given that ABC is a right triangle.

The length of AB is 7 units.

The measure of ∠A is 65°

We need to determine the length of AC

<u>Length of AC:</u>

The length of AC can be determined using the trigonometric ratio.

Thus, we have;

cos \ \theta=\frac{adj}{hyp}

Where the value of \theta is 65° and the side adjacent to the angle is AC and the side hypotenuse to the angle is AB.

Substituting the values, we have;

cos \ 65^{\circ}=\frac{AC}{AB}

Substituting AB = 7, we have;

cos \ 65^{\circ}=\frac{AC}{7}

Multiplying both sides by 7, we get;

cos \ 65^{\circ} \times 7=AC

  0.423 \times 7=AC

        2.961=AC

Rounding off to the nearest hundredth, we get;

2.96=AC

Thus, the length of AC is 2.96 units.

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Given f(x) = x2 + 4x − 1 and g(x) = 5x − 7, identify (fg)(x).
8_murik_8 [283]
<span> f(x) = x^2 + 4x − 1 and g(x) = 5x − 7
</span>(fg)(x) =  (x^2 + 4x − 1)(5x − 7)
(fg)(x) = 5x^3 + 20x^2 - 5x - 7x^2 - 28x + 7
(fg)(x) =  5x^3 + 13x^2 - 33x + 7

answer is C. third choice

(fg)(x) =  5x^3 + 13x^2 - 33x + 7

4 0
3 years ago
The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in
Anon25 [30]

We have been given a quadratic function f(x)=(x-5)^{2} +2 and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is [2,\infty).

If we restrict the domain of this function to either (-\infty,5] or [5,\infty), it will become one to one function.

Let us know find its inverse.

y=(x-5)^{2}+2

Upon interchanging x and y, we get:

x=(y-5)^{2}+2

Let us now solve this function for y.

(y-5)^{2}=x-2\\&#10;y-5=\pm \sqrt{x-2}\\&#10;y=5\pm \sqrt{x-2}\\

Hence, the inverse function would be f^{-1}(x)=5+\sqrt{x-2} if we restrict the domain of original function to [5,\infty) and the inverse function would be f^{-1}(x)=5-\sqrt{x-2} if we restrict the domain to (-\infty,5].

8 0
2 years ago
Consider that ΔQRS is similar to ΔLMN and the measure of ∠N is 42°. What is the measure of ∠S? A) 42° B) 48° C) 56° D) 58°
Veseljchak [2.6K]

Answer:

The answer is A) 42°

plz mark me as brainliest :)

7 0
3 years ago
Read 2 more answers
N the recursive formula f(n) = f(n - 1) + 5, the value of the previous term is represented by
eimsori [14]
F(n-1) = f(n) - 5, based off of the first one
3 0
3 years ago
A gardener makes a new circular flower bed. The bed is teen feet in diameter. Calculate the circumference and the area of the ci
KATRIN_1 [288]

Answer:

I. Circumference of circular flower bed = 31.42 ft.

II. Area of circular flower bed = 78.55 ft²

Step-by-step explanation:

Given the following data;

Diameter = 10 ft

Radius = diameter/2

Radius = 10/2

Radius, r = 5 ft

I. To find the circumference of the circular flower bed;

Circumference of circle = 2πr

Substituting into the formula, we have

Circumference of circular flower bed = 2*3.142*5

Circumference of circular flower bed = 31.42 ft

II. To find the area;

Area of circle = πr²

Substituting into the formula, we have;

Area of circular flower bed = 3.142*5²

Area of circular flower bed = 3.142*25

Area of circular flower bed = 78.55 ft²

8 0
3 years ago
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