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saul85 [17]
3 years ago
15

Simplify and write the trigonometric expression in terms of sine and cosine:

Mathematics
1 answer:
kicyunya [14]3 years ago
6 0

Answer:

f(x) = + cosx or - cosx

Step-by-step explanation:

(2+tan^2x/sec^2x) -1 =(f(x))^2​

=(( 1 + sec^2x)/sec^2x) -1

= 1 / sec^2x + 1 - 1

=  1 / sec^2x

= cos^2x

(f(x))^2​ = cos^2x

f(x) = + cosx or - cosx

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Y=-x^2+2x+10<br> y=x+2<br><br> Substitution<br> Need ASAP
aniked [119]

Answer:

x_1=\frac{1+\sqrt{33} }{2},y_1=\frac{5+\sqrt{33} }{2}\\ \\ x_2=\frac{1-\sqrt{33} }{2},y_2=\frac{5-\sqrt{33} }{2}

Explanation:

You must find the solution of the system using the substitution method.

System:

y=-x^2+2x+10\\\\ y=x+2

Substitute x+2 for y:

x+2=y=-x^2+2x+10

Pass all the terms to one side:

x^2-2x+x+2-10\\ \\ x^2-x-8=0

Use the quadratic formula to solve:

x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\ \\ x=\frac{-(-1)+/-\sqrt{(-1)^2-4(1)(-8)} }{2(1)}\\ \\ x=\frac{1+/-\sqrt{1+32} }{2}

x_1=\frac{1+\sqrt{33} }{2}\\ \\x_2=\frac{1-\sqrt{33} }{2}

Use y = x  + 2 to find the value of y:

y_1=2+x_1=2+\frac{1+\sqrt{33} }{2}\\ \\y_1=\frac{5+\sqrt{33} }{2} \\\\y_2=2+x_2=2+\frac{1-\sqrt{33} }{2}\\ \\ y_2=\frac{5-\sqrt{33} }{2}

6 0
3 years ago
Are the ratios 13:14 and 1:2 equivalent?
eduard

Answer:

NO!

Step-by-step explanation:

They are not equivalent. We can check this. If you rewrite them as fractions 13/14 and 1/2, you can cross multiply and see if they are equal. Which they are not. Also, you could just guess.... think of 13:14 as 13 out of 14. And 1:2 as 1 out of 2. You can tell that 13/14 is much greater than 1/2.

6 0
3 years ago
Pentagon ABCDE is shown on the coordinate plane below​
77julia77 [94]

Answer:  c) B' = (6, -3)

<u>Step-by-step explanation:</u>

The simplest way is to rotate the graph.

Rotating the graph 1 time to the left (counterclockwise) = 90°

Rotating the graph 2 times to the left (counterclockwise) = 180°

Rotating the graph 3 times to the left (counterclockwise) = 270°

The longer way is to reflect over the x-axis and over the y-axis, which is the same as a rotation of 180°

Z = (x, y)    →     Z' = (-x, -y)

<em>the image below shows the graph rotated 2 times = 180°</em>

<em />

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5 0
4 years ago
Read 2 more answers
What is the inverse of the function f(x)=1/9x+2
Anna35 [415]

Answer:

f^{-1}(x)=9x-18

Step-by-step explanation:

we have

f(x)=\frac{1}{9}x+2

Let

y=f(x)

y=\frac{1}{9}x+2

Exchange variables x for y and y for x

x=\frac{1}{9}y+2

Isolate the variable y

x-2=\frac{1}{9}y

y=9(x-2)

y=9x-18

Let

f^{-1}(x)=y

f^{-1}(x)=9x-18 -------> inverse function

7 0
4 years ago
Read 2 more answers
An ellipse has a co-vertex at (–8, 9) and a foci at (4, 4). If the center of the ellipse is located below the given co-vertex, t
vovikov84 [41]

Answer:

Step-by-step explanation:

“the center of the ellipse is located below the given co-vertex”

Co-vertex and center are vertically aligned, so the ellipse is horizontal.

Equation for horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

with

a² ≥ b²

center (h,k)

vertices (h±a, k)

co-vertices (h, k±b)

foci (h±c,k), c² = a² -b²

One co-vertex is (-8,9), so h = -8.

One focus is (4,4), so k = 4.

Center (h,k) = (-8,4)

c = distance between center and focus = |-8 - 4| = 12

b = |9-k| = 5

a² = c² + b² = 169

(x+8)²/169 + (y-4)²/25 = 1

7 0
3 years ago
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