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Alisiya [41]
3 years ago
12

Your friend asks you to help him with his snow shoveling business and will pay you 3 pennies for the first job. You agree to hel

p if he triples your payment for each job completed. After 2 shoveling jobs, you will receive 9 pennies, and after 3 shoveling jobs, you will receive 27 pennies.
Complete and solve the equation that finds the number of pennies he will pay you after the seventh shoveling job.


= number of pennies for seventh shoveling job

Payment for the seventh shoveling job =
pennies
Mathematics
2 answers:
ratelena [41]3 years ago
8 0

Total = 3^x, where x is the number of jobs worked.

Let x = 7th job:

Total = 3^7 = 2187 pennies. = $21.87

Whitepunk [10]3 years ago
5 0

Answer: 21.87

Step-by-step explanation:

First job = 3 pennies

Second job = 9 pennies 

Third job = 27 pennies 

Do you see the pattern? The pennies are being multiplied by 3 every job or tripling.

Fourth job = 81 pennies

Fifth job = 243 pennies

Sixth job = 729 pennies

Seventh job = 2,187

So the answer would be that after the seventh shoveling job you'd receive 21.87 pennies.

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Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.
sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =<em>I</em>.

First, we have to identify the matrix <em>I. </em>As it was said, the matrix is the identiy matrix, which means

<em>I</em> = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

So, \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Isolating the X, we have

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right] -  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Resolving:

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]=\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X=\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]⁻¹·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]·\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a=\frac{2}{11}; b=\frac{7}{33}; c=\frac{-1}{11} and d=\frac{-3}{11}. Substituting:

X= \left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11}  \end{array}\right]·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Multiplying the matrices, we have

X=\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11}  \end{array}\right]

6 0
3 years ago
Kathy is fencing in her yard that has an area of 800 square feet. Her yard is in the shape of a rectangle where the length is 60
anygoal [31]

Answer:

The dimensions of the yard are W=20ft and L=40ft.

Step-by-step explanation:

Let be:

W: width of the yard.

L:length.

Now, we can write the equation of that relates length and width:

L=5W-60 (Equation #1)

The area of the yard can be expressed as (using equation #1 into #2):

Area=W*L=W*(5W-60) (Equation #2)

Since the Area of the yard is 800 ft^2, then equation #2 turns into:

800=W*(5W-60)

Now, we rearrange this equation:  

800=W*(5W-60)//800=5W^2-60W//5W^2-60W-800=0

We can divide the equation by 5 :

W^2-12W-160=0

We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since (-20)*8=160 and -20+8=-12. The equation factorised looks like this:

(W-20)(W+8)=0

Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:

5*20-60=40

Therefore, the dimensions of the yard are W=20ft and L=40ft.

7 0
2 years ago
Simplify -2.3f+0.9f-14-4
Setler [38]

Answer:

The Answer would be 1.4f-18

Step-by-step explanation:

-2.3f+0.9f-14-4

then you do

-1.4f-14-4

Then u would get 1.4f-18.

7 0
3 years ago
Read 2 more answers
29. Determine the value of x.<br> abc<br> X + 42°<br> 147°<br> 2x
suter [353]

Answer:

x=35

Step-by-step explanation:

180-147=33 (angles in a straight line)

33+3x+42=180 (angles in a triangle)

3x+42=147

147-42=105

105/3=35

5 0
1 year ago
Which of the following equations is the result of completing the square on x^2 - 6x - 9 = 0?
lina2011 [118]
X² - 6x - 9 = 0
x² - 3x - 3x - 9 = 0
x (x-3) -3(x + 3) = 0
(x - 3)² = 0

In short, Your Answer would be Option A

Hope this helps!
6 0
3 years ago
Read 2 more answers
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