the area of a rectangle is 54x^9y^8 square yards if the length of the rectangle is 6x^3y^4 yards what expression represents the width of the rectangle in yards

Answers

Answer 1

Answer: For this case we have:
The area of a rectangle is given by:
A = (w) * (l)
Where,
w: width
l: long
Substituting values we have:
(54x ^ 9y ^ 8) = (w) * (6x ^ 3y ^ 4)
Clearing w we have:
w = (54x ^ 9y ^ 8) / (6x ^ 3y ^ 4)
Rewriting:
w = (9 * x ^ 6y ^ 4)
Answer:
the length of the rectangle is:
w = (9 * x ^ 6y ^ 4)

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sandy has a total of 35 coins in her money jar is sandy's jar contains only nickels and dimes and the value of all the coins is $2.50, how many nickels does sandy have?

Answers

By solving a system of equations we will see that Sandy has 20 nickels and 15 dimes.

How to solve a system of equations?

We need to define the variables:

x = number of dimes
y = number of nickels.

We know that there are 35 coins so:

x + y = 35

And the total values if $2.50, then:

x*$0.10 + y*$0.05 = $2.50

Then our system is:

x + y = 35

x*$0.10 + y*$0.05 = $2.50

To solve this, we need to isolate one of the variables in one of the equations. I will isolate x on the first equation:

x = 35 - y

Now we replace this on the other equation:

(35 - y)*$0.10 + y*$0.05 = $2.50

$3.5 - y*$0.05 = $2.50

$3.50 - $2.50 = y*$0.05

$1.00/$0.05 = y = 20

So there are 20 nickels and the other 15 coins are dimes.

If you want to learn more about systems of equations, you can read:

brainly.com/question/13729904

0.05x + 0.10(35-x) = 2.50 Get rid of decimals by multiplying every term by 100: 5x + 10(35-x) = 250 5x + 350 - 10x = 250 -5x + 350 = 250 -5x = -100 x = 20 = the number of nickels. The number of dimes is 35-x or 35-20 or 15 dimes. Checking: 20 nickels is $1.00 and 15 dimes is $1.50 And indeed $1.00 + $1.50 = $2.50 Edwin

Solve by factoring.. m^2 + 8m + 7 = 0

Answers

In order to solve an equation by factoring, it should be that the equation is equal to zero.
m^2 + 8m + 7 = 0
For this case we have, to do completing the square in order to factor this equation.

m^2 + 8m = -7
m^2 + 8m + 16 = -7 +16
(m+4) (m+4) = 9
(m+4)^2 = 9

Take the square root of both sides,
m+4 = 3
m = -1

Which facts are true for the graph of the function below? Check all that apply.F(x) = 3 * 4^x
A. The range of F(x) is y > 4.
B. It is decreasing.
C. It is increasing.
D. The y-intercept is (0, 4).
E. The y-intercept is (0, 3).
F. The domain of F(x) is all real numbers.

Answers

facts thay are true for the graph of the function f(x) = 3(4)^x are:

It is increasing.
The y-intercept is (0, 3).
The domain of F(x) is all real numbers.

Final answer:

The true statements for the given function F(x) = 3 * 4^x are: it is increasing, the y-intercept is (0, 3), and the domain of F(x) is all real numbers.

Explanation:

The function given is F(x) = 3 * 4^x. Let's check each statement given:

A. The range of F(x) is y > 4. This statement is not true because for all x≥0, y≥3. When x<0, 4^x tends towards 0, thus y tends towards 3.
B. It is decreasing. This is not true because the function F(x) = 3 * 4^x is an exponential function with a base greater than 1 that is 4 in this context which means that the graph of this function is increasing.
C. It is increasing. This statement is true. As explained for option B, F(x) = 3 * 4^x is an exponential function with a base greater than 1 so it will be increasing.
D. The y-intercept is (0, 4). This is not true. The y-intercept is the value of y when x=0. When plugged x=0 into F(x) = 3 * 4^x, we get F(0) = 3 * 1 = 3.
E. The y-intercept is (0, 3). This statement is true since F(0) = 3.
F. The domain of F(x) is all real numbers. This is true because any real number can be used as an input x for the function F(x) = 3 * 4^x.

Learn more about Exponential Function here:

brainly.com/question/37289664

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7) 2.1x + 45.2 = 3.2 -8.4x

Answers

Answer:

x=-4

Step-by-step explanation:

brainliest please

Answer:

x=-4, Give brainliest please

Step-by-step explanation:

Step 1: Add 8.4x to both sides.

2.1x+45.2 = -8.4x +3.2

+8.4x +8.4x

10.5x+45.2=3.2

Step 2: Subtract 45.2 from both sides.

10.5x + 45.2 = 3.2

-45.2 -45.2

10.5x=−42

Step 3: Divide both sides by 10.5.

$(10.5x)/(10\n)$ = $(-42)/(10)$

x=−4

Help answer all questions please and tell me how you got the answers

Answers

8. You start with 240 gallons if in march you use 40% (.4(240)=96) you used 96 gallons in march, leaving you with 144 gallons. If you then used 25% in April (.25(144)=36) you would have used 36 gallons leaving you with 108 gallons at the end of April.

9. If 2277 is 110% the number of 2013 to find what 2013 was you would divide by 110%(1.1)
2277/1,1=2070 at the end of 2013
If 2070 is 90% then we will want to divide by 90% (.9) to get the year before that
2070/.9=2300 so 2300 people were signed up in the year 2012

10. 57.5=p(250)
to solve this divide both sides by 250 to get p=.23
As for the different elements to the equation, there are various answers such as what percentage of people donated $250 if the average amount of money donate from each one is 57.5 although that may no be what you instructor is looking for. pretty much just make up something that sounds okay and you should be fine

Four sisters bought a present for their father. They received a 10% discount on the original price of the gift. After the discount was taken, each sister paid $9.00. What was the original price of the gift?