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pashok25 [27]
3 years ago
13

What is an equivalent expression to a^3b^2x^4a

Mathematics
1 answer:
lara31 [8.8K]3 years ago
6 0

Answer: a^4 b^2 x^4

Step-by-step explanation:

The exponent "product rule" tells us you, when multiplying two powers that have the same base, you can add the exponents.

so

a^3 b^2 x^4 a^1  

a^3  and a^1 have the same base of a.  So, add 3 + 1 for 4

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To fit between two windows, the width of a bookshelf must be no greater than feet. Mrs. Aguilar purchases a bookshelf that is 77
EastWind [94]

The distance between the windows is not given. I have searched for this question in other sources and came up with 6.5 ft.

6.5 ft = 78 inches

The width of the bookshelf  = 77 inches

Hence the book shelf with fit between the windows and still there will be 78-77  = 1 inch of space remaining

Hence the right option is option C


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Katie cut out a piece of wrapping paper that was 2 times as long and 3times as wide as the box that she was wrapping.The box was
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Answer:

287.1 inches of the canvas.

Step-by-step explanation:

To solve this, we need to first figure out the total area of the canvas. To do that, multiply width by height.

29*33=957

Now set up your equation for solving for the area of the canvas that the rose covers.

x/957=30/100

We did it where: x is the area of the rose covers, 957 is the amount of inches that the canvas takes up, and the right side of the equation is the percent.

Now cross multiply.

100x=28,710

Now divide both sides by 100.

x=287.1

The red rose covers 287.1 inches of the canvas.

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Erica makes a banner using 4 sheets of paper. Each paper measues 9 inches by 10 incjes. What is the total area of ericas banner?
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A bus company took a tour bus on a ferry when there were 30 people aboard. The ferry charged the bus company $180. The following
OLEGan [10]
Problem: A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? How much does each person cost? Show this using y = mx + b form.

Solution:
Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.

Then, when there are 30 people on the bus (x = 30), the cost was $180 (y = 180). This means the point (x, y) = (30, 180).
Also, when there were 50 people on the bus, the cost was $220. So that is the point (50, 220).

You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.

The slope of the line joining two points is the rise divided by the run. That means

m = (y2 - y1) / (x2 - x1)

So we put in the values of (30, 180) and (50, 220):

m = (220 - 180) / (50 - 30)
m = 40 / 20
m = 2.

The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:

y = 2x + b.

This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:

220 = 2(50) + b
220 = 100 + b
b + 100 = 220
b = 120.

Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:

y = 2x + 120.

For the other questions, I can look at the equation I got. The y-intercept (b value) is $120. That means that we are adding $120 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.

Here's an example: if you had just 10 people on the bus, you'd pay $120 for the empty bus and $2 for each person. That's $20 for the people and $120 for the bus. That total is $140. Let's see if (10, 140) works in the equation we got:

y = 2x + 120
140 ?=? 2(10) + 120
140 ?=? 20 + 120
yes. 140 = 140. It does work.

Now you try it with your question.
5 0
2 years ago
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