Using the image below, determine the measure of angle RTQ.

A group of church members chartered a bus for $832. After making the arrangements, 6 more members decided to join the excursion

g100num [7]

Let x = # of original members
Cost per person (originally) = 832/x
Cost per person after 6 more people = 832/(x+6)
Solve 832/x=832/(x+6) +6 (because the cost was reduced by 6
Solve for x.
x = 26 or -32 (but x is number of members, so it can't be negative)
# of original members is 26.
Original cost is 832/26 = $32 per person.

3 0

3 years ago

Pam’s monthly food budget is equal to 40% of her monthly rent payment. If her food budget is $200 a month, how much is her rent

Alika [10]

200 dollars is equivalent to 40%
So what is 100% equivalent to;
Rent payment= $\frac{100*200}{40}$
= 500 dollars

3 0

3 years ago

1/4(-8x - 12) + -4 = 3/4(-8x - 12)

nekit [7.7K]

Here's our equation:

$\frac{1}{4} (-8x-12)-4=\frac{3}{4} (-8x-12)$

Factor out the left side

(-2x - 3) - 4 = 3/4 (-8x - 12)

Simplify

-2x - 7 = 3/4 (-8x - 12)

Factor out the right side

-2x - 7 = -6x - 9

Add 7

-2x = 6x - 2

Add 6x to isolate the variable

4x = -2

Divide by 4

x = - 1/2

Here is how I simplified both sides initially. I'll only be showing the right side because this is a LOT of typing.

Begin with 3/4 (-8x - 12)

Use rule $a*\frac{b}{c} = \frac{a * b}{c}$ to multiply

3(-8x-12)/4

Factor 3(-8x-12)

(-8x - 12) = (-4 * 2x - 4 * 3)

Simplify (-4 * 2x - 4 * 3)

-3 * 4 (2x+3)

- 12 (2x + 3)

Now that we've factored 3/4 (-8x - 12), we're left with- 12 (2x + 3)/4.

12/4 =3, giving us -3(2x + 3)

Distribute and simplify, then you're done.

8 0

3 years ago

Help me do this …math

Daniel [21]

Step-by-step explanation:

How to find inverse function:

Step 1: Write down equation.

$f(x) = 4 \sin(x) + 3$

Remeber Ruler notation that

f(x)=y so we replace y with f(x).

$y = 4 \sin(x) + 3$

Next, we must isolate x so first we subtract 3.

$y - 3 = 4 \sin(x)$

Divide both sides by 4.

$\frac{y - 3}{4} = \sin(x)$

$\sin {}^{ - 1} ( \frac{y - 3}{4} ) = \sin {}^{ - 1} ( \sin(x) )$

Remeber that sin^-1x and sin x are inverse functions so they will cancel out to x. So we get

$\sin {}^{ - 1} ( \frac{y - 3}{4} ) = x$

Swap x and y. So our inverse function is

$\sin {}^{ - 1} ( \frac{x - 3}{4} ) = y$

If you want another proof: Here's one,

Let plug an a x value for the orginal equation,

4 sin x+3. Let say that

$x = \frac{\pi}{2}$

We then would get

$4 \sin( \frac{\pi}{2 } ) + 3 = 4 \times (1) + 3 = 4 + 3 = 7$

So when x=pi/2, y=7.

By definition of a inverse function, if we let 7 be our input, we should get pi/2. as a output.

So let see.

$\sin {}^{ - 1} ( \frac{7 - 3}{4} ) = \sin {}^{ - 1} ( \frac{4}{4} ) = \sin {}^{ - 1} (1) = \frac{\pi}{2}$

So this is the inverse function of 4 sin x+3.

1b. The range of f(x) is [-1,7).

We can use transformations to describe range.

We have

$f(x) = 4 \sin(x) + 3$

Parent function is

$\sin(x)$

with a range of [-1,1].

We then vertical stretch by 4 so we get

$4 \sin(x)$

and our range will be

[-4,4].

Then we add a vertical shift of 3.

$4 \sin(x) + 3$

So our range of 4 sin x+3.

[-1,7].

1c. Domain of a inverse function is the range of the orginal function.

The range of f(x) is [-1,7) so the domain of f^-1(x) is [-1,7].

f(x) domain was restricted to -pi/2 to pi/2 so the range of f^-1(x) is [-pi/2, pi/2]

6 0

3 years ago

8 Stephanie was doing a science

True [87]

Answer:

counted 27 raisins. If

there were 12

7 0

3 years ago