The given triangle UVW is a right angle triangle. This is because one of its angles is 90 degrees. The sum of the two other angles is 180. To determine Cos U, we will apply trigonometric ratio.

Cos U = adjacent side/ hypotenuse.

Looking at the triangle with C as the reference angle,

Adjacent side = 12

Hypotenuse( always the longest side of the triangle) = 13

Therefore,

Cos U = 12/13

6 0

3 years ago

A gas tank contains 5.3 gallons.the capacity of the tank is 12.5 gallons.how much will it cost to fill the tank at $1.30 per gal

fredd [130]

Answer:

$9.36

Step-by-step explanation:

First 12.5 - 5.3 = 7.2

7.2 x 1.30 = 9.36

3 0

4 years ago

Diane is participating in a 4-day cross-country biking challenge. She biked for 57, 67, and 45 miles on the first three days. Ho

ella [17]

Answer:

139

Step-by-step explanation:

57+67+45=169÷3=139

6 0

3 years ago

What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

<u>Range:</u>

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

4 years ago