saseflower

I actually found a similar question back in 2020 that Melody answered, so I'm just going to reuse her method (thank you Melody!)

You can use the Tangent-Secant Power Theorem for this problem.

"If a tangent and a secant intersect in the exterior of a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external secant segment."

XY² = XB(AX)

Plug in your numbers

(8)² = XB(16)

Simplify

64 = 16XB

Divide by 16 on both sides

4 = XB

Now, to find AB, you subtract XB from AX

AB = 16 - 4

AB = 12

Hope that helps!

Let x = the number of hours Naomi worked

Let y = the number of hours Hudson worked

Using the numbers they gave us regarding how many shirts each of them can iron per hour, you multiply the number of shirts Naomi can iron per hour by x (the number of hours Naomi worked), and vice versa for Hudson. Combined, they ironed 395 shirts. That is what it will be equal to.

Combined, they worked 13 hours. You dont know how many hours they each worked, so it becomes x + y = 13.

Here is your system of equations:

35x + 20y = 395

x + y = 13

Since the pizza order is larger than $75, it qualifies for the coupon.

In order to find the percent they saved, you take 12 and divide it by 96.

\(\frac{12}{96}\) = 0.125

Convert this to a decimal by multiplying 0.125 by 100.

12.5%

They saved 12.5% by using the coupon.

In order to find k, you need to plug (\(\frac{1}{4}\),-6) into the equation and solve for k.

-\(\frac{1}{2}\) - kx = 6y

Plug in x and y (x,y)

-\(\frac{1}{2}\) - k(\(\frac{1}{4}\)) = 6(-6)

Simplify

-\(\frac{1}{2}\) - \(\frac{1}{4}\)k = -36

Add \(\frac{1}{2}\) to both sides

In order to do this, -36 turns into -\(\frac{72}{2}\) 

-\(\frac{1}{4}\)k = -\(\frac{71}{2}\)

Divide each side by -\(\frac{1}{4}\)

This means it's actually being multiplied by -4: -\(\frac{71}{2}\)(-4)

k = \(\frac{284}{2}\)

Simplify

k = 142

Alternatively:

-\(\frac{1}{4}\)k = -35.5 instead of -\(\frac{71}{2}\)

Multiply by -4 on both sides

k = 142

It saves you the step of simplification, but some prefer to keep the fraction instead of switching to decimals. Figured I would show both!

10 - x = 5

Add x to both sides

10 = 5 + x

Subtract 5 from both sides

5 = x

There you go! :) Hope this helps

Thank you so much! I fixed it

3y - 49 = 0

x^2 + y^2 - 281 = 0

First I would isolate the variable (y) in the first equation

3y - 49 = 0

Add 49 on both sides

3y = 49

Divide by 3 on both sides

y = 49/3

Then take your new equation and plug it into the second equation

x^2 + (49/3)^2 - 281 = 0

Simplify

x^2 + (2401/9) - 281 = 0

Subtract 281 from the fraction

x^2 + (-128/9) = 0

Add (128/9) on both sides

x^2 = (128/9)

Root on both sides

|x| = \(\sqrt{\frac{128}{9}}\)

Simplify (the x is a multiplication)

|x| = \(\frac{\sqrt{64 x 2}}{3}\)

Simplify again

|x| = \(\frac{8\sqrt{2}}{3}\)

Then the absolute value turns the other side into ±

x = ±\(\frac{8\sqrt{2}}{3}\)

And there's your answer! :) Hope this helps

Thank you so much! :)

2009 = 328/(1 - r)

Solve for r, and there you go! :)

This is using the formula:

S = term1/(1 - r)

In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In simple cases the logarithm counts repeated multiplication.

Incase you didn't know the highlighted word:

Exponentiation is an expression that involves exponents. When the base is a positive integer, exponentiation is also a mathematical operation that involves a finite number of multiplication problems involving the same number or variable. For example: 2*2*2*2*2.

This is from Google, since I haven't learned it yet! :)