Angles α and β are the two acute angles in a right triangle. use the relationship between sine and cosine to find the value of β if β < α.

sin(2x + 2) = cos(3x + 8)
a) 16°
b) 34°
c) 56°
d) 74°

Step-by-step explanation:

we know that

in a right triangle

if sin A= cos B

then

angle A and angle B are complementary angles

so A+B=90

therefore

(7x-15)+(3x+5)=90> 10x-10=90> 10x=100> x=10°

so

7x-15> 7*10-15> 55°

3x+5> 3*10+5> 35°

we know that

β < α

therefore

the answer is

β =35°

α=55°

34

Step-by-step explanation:

Thats the answer o usatest prep

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.