From the choices below, choose an expression that is equivalent to the expression below

Given a+b=7 and a-b=3, find the following<br><br> 3^a÷3^b

gulaghasi [49]

Answer:

27

Step-by-step explanation:

a + b = 7

a - b = 3

2a = 10

a = 5

b = 7 - 5

b = 2

3⁵ / 3² = 3³ using law of indices

3³ = 27.

3 0

2 years ago

PLEASE HELP!!! <br> show work if possible!:)

satela [25.4K]

Answer:

The answer to your question is y = 2x + 11

Step-by-step explanation:

Data

Original line y = -(1/2)x + 5

Point (-4, 3)

Process

1.- Get the slope of the new line

- Slope of the original line = -1/2

If the lines are perpendicular, the slopes must be reciprocal

-1/2 reciprocal = 2

2.- Get the equation of the new line

y - y1 = m(x - x1)

y - 3 = 2(x + 4)

- Simplification

y - 3 = 2x + 8

- Solve for y

y = 2x + 8 + 3

y = 2x + 11

7 0

3 years ago

Read 2 more answers

2

svet-max [94.6K]

Answer:

B. 4200

Step-by-step explanation:

A suitable calculator can add the terms for you. (See attached)

__

The first term is 69, and the common difference is 75-69 = 6. The general term is ...

an = a1 +d(n -1)

an = 69 +6(n -1)

Then the 28th term is ...

a28 = 69 +6(27) = 231

The average term is (a28 +a1)/2 = (231 +69)/2 = 150.

The sum is the number of terms multiplied by the average term:

sum = 28×150= 4200

5 0

2 years ago

The function y = x * ln(x + e) has two distinct x intercepts. One is at x = a and the other is at x = b. The value of a + b is

Snezhnost [94]

As points, x-intercepts take the form $(x,0)$ , so to find the intercepts we can set $y=0$ and solve for $x$ .

$x\ln(x+e)=0\implies\begin{cases}x=0\\\ln(x+e)=0\end{cases}$

From the first equation alone, we already know that $x=0$ is a solution, which means one intercept is $(0,0)$ .

The second equation gives

$\ln(x+e)=0\implies e^{\ln(x+e)}=e^0\implies x+e=1\implies x=1-e$

so that the second intercept occurs at $(1-e,0)$ .

So if $a=0$ and $b=1-e$ , we have $a+b=1-e$ , giving C as the answer.

3 0

3 years ago

Myra is a scientist and needs 45 gallons of a 16% acid solution. The lab is currently stocked only with a 20% acid solution and

asambeis [7]

Answer:

The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons

Step-by-step explanation:

Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:

x + y = 45

The concentration of acid of the final solution is:

0.2*x + 0.1*y = 45*0.16

0.2*x + 0.1*y = 7.2

Therefore we have a system of equation:

x + y = 45

0.2*x + 0.1*y = 7.2

We need to multiply the first equation by -0.1:

-0.1*x -0.1*y = -4.5

0.2*x + 0.1*y = 7.2

We now sum both equation:

0.1*x = 2.7

x = 2.7/0.1 = 27 gallons

y = 45 - 27 = 18 gallons

6 0

3 years ago