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4 years ago

What common base can be used to rewrite each side of the equation 2^(x+3)-3=5

2 answers:

8 0

We are given with the equation <span>2^(x+3)-3=5 and is asked in the prooblem to determine the common base of each side of the equation. we transpose first 3 to the other side making it 8. 8 is equal to 2^3 which makes the common base then equal to 2.</span>

marin [14]4 years ago

6 0

Answer:

Step-by-step explanation:

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The length of a rectangle is 5 times its width. If the length is decreased by 3 meters, and the width is increased by 10 meters,

adelina 88 [10]

Answer:

The original rectangle had a width of 30 m and a length of 150 m.

Step-by-step explanation:

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3 years ago

A large university accepts 50% of the students who apply. Of the students the university accepts, 35% actually enroll. If 10,

lara31 [8.8K]

Answer:

3,500 students

Equation:

0.35 x 10,000 = 3,500

8 0

3 years ago

The equation 9.95 + 0.30s=c gives the cost c in dollars that a website charges for downloading songs. The variable s stands for

IrinaK [193]

Answer:

$20.45

Step-by-step explanation:

First substitute 35 for s

9.95+0.30(35)=c<-----

If you solve this you would get...

$20.45

3 0

3 years ago

Use the graph to find the slope and y-intercept to write the equation in slope-intercept form.

Fiesta28 [93]

Answer:

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

$y\ intercept = -1$

$y = -\frac{1}{2}x -1$

Step-by-step explanation:

Given

$(x_1,y_1) = (-2,0)$

$(x_2,y_2) = (0,-1)$

Required

Determine the slope and y intercept from graph

To calculate the slope, we have:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{-1-0}{0 - (-2)}$

$m = \frac{-1}{0 +2}$

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

The y intercept is when $x = 0$

So,

$y\ intercept = -1$

The equation is then calculated using:

$y = m(x - x_1) + y_1$

This gives

$y = -\frac{1}{2}(x - (-2)) + 0$

$y = -\frac{1}{2}(x - (-2))$

$y = -\frac{1}{2}(x +2)$

$y = -\frac{1}{2}x -\frac{1}{2}*2$

$y = -\frac{1}{2}x -1$

<em>See attachment for graph</em>

4 0

3 years ago

Read 2 more answers

Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the

german

Answer:

Step-by-step explanation:

We will use a system of equations to solve this. We do not know how much of the 25% bleach solution is used; we will use x to represent this. We know that 5 cups of the 10% solution was used. We do not know how much of the resulting solution we have; we will use y to represent this. This gives us the equation

x+5 = y

Using the decimal forms of the percentages for each solution, we have 0.25x (25% solution for x cups), 0.1(5) (10% solution for 5 cups) and 0.2y (20% solution for y cups); this gives us the equation

0.25x+0.1(5) = 0.2y

This gives us the system

$\left \{ {{x+5=y} \atop {0.25x+0.1(5)=0.2y}} \right.$

To use elimination, we will make the coefficients of x the same by multiplying the top equation by 0.25:

$\left \{ {{0.25(x+5=y)} \atop {0.25x+0.5=0.2y}} \right. \\\\\left \{ {{0.25x+1.25=0.25y} \atop {0.25x+0.5=0.2y}} \right.$

We will now subtract the second equation from the first:

$\left \{ {{0.25x+1.25=0.25y} \atop {-(0.25x+0.5=0.2y)}} \right. \\\\0.75 = 0.05y$

Divide both sides by 0.05:

0.75/0.05 = 0.05y/0.05

15 = y

There were 15 cups of the resulting 20% solution. Substituting this into the first equation, we have

x+5=15

Subtract 5 from each side:

x+5-5=15-5

x = 10

7 0

3 years ago

Read 2 more answers