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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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(08.07 HC)
andreev551 [17]

Answer:

\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}

\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

C)  See attachment.

Step-by-step explanation:

Given function:

f(x)=2x^2-x-10

<h3><u>Part A</u></h3>

To factor a <u>quadratic</u> in the form  ax^2+bx+c<em> , </em>find two numbers that multiply to ac and sum to b :

\implies ac=2 \cdot -10=-20

\implies b=-1

Therefore, the two numbers are -5 and 4.

Rewrite b as the sum of these two numbers:

\implies f(x)=2x^2-5x+4x-10

Factor the first two terms and the last two terms separately:

\implies f(x)=x(2x-5)+2(2x-5)

Factor out the common term  (2x - 5):

\implies f(x)=(x+2)(2x-5)

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

\implies (x+2)(2x-5)=0

Therefore:

\implies (x+2)=0 \implies x=-2

\implies (2x-5)=0 \implies x=\dfrac{5}{2}

So the x-intercepts are:

x=-2, \:\:x=\dfrac{5}{2}

<h3><u>Part B</u></h3>

The x-value of the vertex is:

\implies x=\dfrac{-b}{2a}

Therefore, the x-value of the vertex of the given function is:

\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}

To find the y-value of the vertex, substitute the found value of x into the function:

\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}

Therefore, the vertex of the function is:

\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

<h3><u>Part C</u></h3>

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards.  This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>.  Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0
2 years ago
Solve
grin007 [14]
Answer would be a (-1, ten-thirds) :)
8 0
3 years ago
Choose the correct simplification of the expression f4 • f8.
hammer [34]

Answer:

f^12

Step-by-step explanation:

In this equation, you need to add the two exponents so this would make f^12

hope this helps!

8 0
3 years ago
Read 2 more answers
What is the square root of 100?
natulia [17]

Answer:

10

Step-by-step explanation:

the answer is 10 because 100 divided by 10 is 10

Please mark Brainliest

3 0
2 years ago
Read 2 more answers
If f (x) = 4x - 11 , What is the value of f(5)<br> a. 20x - 55<br> b. 34<br> c. 9<br> d. 4
kramer

Answer:C

Step-by-step explanation:

C

5 0
3 years ago
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