Write a quadratic equation in vertex form (use y = a(x

Adam is 9 years older than and 13 years ago he was twice as old as she was then.How oldare adam and Brianna now /10196172/aa3db3

vekshin1

Who is Adam 9 years older than?

6 0

4 years ago

Determine a series of transformation that would map figure h onto Figure I

Novosadov [1.4K]

Answer:

isnt it figure h???

Step-by-step explanation:

7 0

3 years ago

What is the extraneous solution found in solving the equation log2 4x + log₂ (x + 1) = 3

yan [13]

Answer:

x = -2

Step-by-step explanation:

We are given the logarithmic base 2 equation of:

$\displaystyle{\log_2 (4x) + \log_2 (x+1) = 3}$

Apply logarithm property of addition where:

$\displaystyle{\log_a M + \log_a N = \log_a MN}$

Therefore, we will write new equation as:

$\displaystyle{\log_2 [4x(x+1)] = 3}$

Apply logarithm to exponential form using:

$\displaystyle{\log_a M = N \to a^N = M}$

Thus, another new rewritten equation is:

$\displaystyle{2^3 = 4x(x+1)}\\\\\displaystyle{8 = 4x(x+1)}\\\\\displaystyle{2=x(x+1)}$

Expand the expression in and arrange the terms in quadratic expression:

$\displaystyle{2=x^2+x}\\\\\displaystyle{0=x^2+x-2}\\\\\displaystyle{x^2+x-2=0}$

Solve for x:

$\displaystyle{(x+2)(x-1)=0}\\\\\displaystyle{x=-2,1}$

These are potential solutions to the equation. To find extraneous solution, you’ll have to know the domain of logarithm function. We know that logarithm’s domain is defined to be greater than 0. Henceforth, anti-logarithm must be greater than 0.

( 1 ) 4x > 0, x > 0

( 2 ) x + 1 > 0, x > -1

Therefore, our anti-log must be greater than 0, so any solutions that are equal or less than 0 will be considered as extraneous solution.

Hence, x = -2 is the extraneous solution.

7 0

2 years ago

After 2 years, a certain car is worth $16600. When it is 9 years old, the same car is then worth

Lubov Fominskaja [6]

The linear function that describes the situation is:

y = -950x + 18500.

The slope of -950 means that the price of the car decays $950 per year.

The y-intercept of 18500 means that the initial value of the car is of $18,500.

The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.

<h3>What is a linear function?</h3>

A linear function is modeled by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

In this problem, in 7 years, the price of the car decays by $6,650, hence the slope is given by:

m = -6650/7 = -950.

The slope of -950 means that the price of the car decays $950 per year.

Then, the equation is:

y = -950x + b.

After 2 years, a certain car is worth $16600, hence when x = 2, y = 16600, and:

16600 = -950(2) + b

b = 18500.

The equation is:

y = -950x + 18500.

The y-intercept of 18500 means that the initial value of the car is of $18,500.

The x-intercept is found when y = 0, hence:

-950x + 18500 = 0.

x = 18500/950

x = 19.47.

The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.

More can be learned about linear functions at brainly.com/question/24808124

8 0

2 years ago

Evaluate using the finite geometric sum formula

Sever21 [200]

Answer:

$S_9=-18.703$ .

Step-by-step explanation:

The given series is,

$\sum_{i=1}^9(-\frac{1}{2})^{i-1}$

When we substitute $i=1$ , we get the first term, which is $a_1=-28(-\frac{1}{2})^{1-1}$

This implies that,

$a_1=-28(-\frac{1}{2})^{0}$

$a_1=-28(1)=-28$ .

The common ratio is

$r=-\frac{1}{2}$

The finite geometric sum is given by the formula,

$S_n=\frac{a_1(r^n-1)}{r-1} , -1\:$ .

Since there are 9 terms, we find the sum of the first nine terms by putting $n=9$ in to the formula to get,

$S_9=\frac{-28((-\frac{1}{2})^9-1)}{-\frac{1}{2}-1}$ .

$S_9=\frac{-28((-\frac{1}{512})-1)}{-\frac{3}{2}}$ .

$S_9=\frac{-28(-\frac{513}{512})}{-\frac{3}{2}}$ .

$S_9=-28(\frac{171}{256})$ .

$S_9=-\frac{1197}{64}$ .

$S_9=-18.703$ .

The correct answer is B

4 0

3 years ago

Read 2 more answers

Write a quadratic equation in vertex form (use y = a(x - h)^2 +