Given side AB in ΔABC has length x, what is the length of side AC?

If the solution to y=4x+3 is (4,16) what would the steps needed to get (4,16) be?

Ainat [17]

<span>Simplifying x4 = 16
Solving x4 = 16
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Simplifying x4 = 16
Reorder the terms: -16 + x4 = 16 + -16
Combine like terms: 16 + -16 = 0 -16 + x4 = 0
Factor a difference between two squares. (4 + x2)(-4 + x2) = 0
Factor a difference between two squares. (4 + x2)((2 + x)(-2 + x)) = 0
Subproblem 1

Set the factor '(4 + x2)' equal to zero and attempt to solve:
Simplifying 4 + x2 = 0 Solving 4 + x2 = 0
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation. 4 + -4 + x2 = 0 + -4
Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4
Combine like terms: 0 + -4 = -4 x2 = -4
Simplifying x2 = -4
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve:
Simplifying 2 + x = 0 Solving 2 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2
Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Sub-problem 3

Set the factor '(-2 + x)' equal to zero and attempt to solve:
Simplifying -2 + x = 0 Solving -2 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '2' to each side of the equation. -2 + 2 + x = 0 + 2
Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2
Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solutionx = {-2, 2}</span>

8 0

2 years ago

A new car is purchased for $17,000 and over time its value depreciates by one half every 3 years. What is the value of the car 1

Jet001 [13]

Answer:

The answer is "$238".

Step-by-step explanation:

Current worth $= \$ 17,000$

depreciates by $\frac{1}{2}$ in 3 years.

time= 19 years

depreciates rate=?

Using formula:

$\to \text{Worth= Current worth}(1- \frac{\text{depreciates rate}}{100})^{time}$

$\to A_t=A_0(1-\frac{r}{100})^t$

calculates depreciate value in 3 year $= \frac{1}{2} \times 17,000$

$= 8,500$

so,

$A_t=8,500\\\\A_0=17,000\\\\t=3\ years$

$\to A_t=A_0(1-\frac{r}{100})^t\\\\\to 8,500= 17,000(1-\frac{r}{100})^3\\\\\to \frac{8,500}{17,000}= (1-\frac{r}{100})^3\\\\\to \frac{1}{2}= (1-\frac{r}{100})^3\\\\\to (\frac{1}{2})^{\frac{1}{3}}= (1-\frac{r}{100})\\\\\to 0.793700526 = (1-\frac{r}{100})\\\\\to \frac{r}{100} = (1-0.793700526)\\\\\to \frac{r}{100} = (1-0.8)\\\\\to r= 0.2 \times 100 \\\\\to r= 20 \%$