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zlopas [31]
3 years ago
6

A rectangular rug has a perimeter of 220 feet. The width of the rug is two feet less than the length. Find the length and the wi

dth.
Mathematics
1 answer:
Gekata [30.6K]3 years ago
7 0

Answer:

The length is 56 and the width is 54.

Step-by-step explanation:

The perimeter of a rectangle is 2x+2y (width and length on both sides). so 2x+2y=220. Also x=y-2, because the width is 2 feet less than the length. Fill x=y-2 in 2x+2y=220 and we get 2(y-2)+2y=220. 2y-4+2y=220. 4y=216. y=54. Fill in y=54 in 2x+2y=220 and we get 2x+2(54)=220. 2x=220-2(54)=112. x=56.

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A square matrix A is said to be idempotent iff A2 = A. (i) Show that if A is idempotent, then so is I − A. (ii) Show that if A i
muminat

Answer:

Step-by-step explanation:

Given that A is a square matrix and A is idempotent

A^2 = A

Consider I-A

i) (I-A)^2 = (I-A).(I-A)\\= I^2 -2A.I+A^2\\= I-2A+A\\=I-A

It follows that I-A is also idempotent

ii) Consider the matrix 2A-I

(2A-I).(2A-I)=\\4A^2-4AI+I^2\\= 4A-4A+I\\=I

So it follows that 2A-I matrix is its own inverse.

7 0
3 years ago
For a party Gary buys cheese pizzas for $5 and pepperoni pizzas for $8 each. His bill comes to $75. Let x represent the number o
Aloiza [94]

Answer:

The answer is the second answer from the image. Which is 5x-8y=$75

Step-by-step explanation:

It is that answer because it costs $5 for one cheese pizza and $8 for a pepperoni pizza, so the answer is 5x-8y=75

still confused?

Its that answer because the first one and the third one are the same, just both equations like in different ways like example 10+2 is 12 right? And 2 + 10 is still 12 so that means the second answer from the image is the answer.

Hope that helps.

3 0
3 years ago
Read 2 more answers
What is the slope of the line 4x – 2y = 5?<br><br> –4<br> –2<br> 2<br> 4
Grace [21]

Answer:

It is 2.

Step-by-step explanation:

The equation becomes -2y=-4x=5

But you divide by -2 to get y solo. So -4/-2=2.

7 0
3 years ago
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Calculate Medicare tax (1.45% of gross pay <br><br> Gross Pay: $576.00
Mkey [24]

Answer: $8.35

Step-by-step explanation:

Given: The amount as gross pay= $576.00

The rate of Medicare tax =1.45%  = 0.0145

Now, to calculate the medicare tax we need to multiply the rate of Medicare tax with the gross pay , we get

\text{Medicare tax=0.0145*Gross Pay}\\\\\Rightarrow\ \text{Medicare tax}=0.0145\times576.00\\\\\Rightarrow\ \text{Medicare tax}=\$8.352\approx\$8.35

5 0
2 years ago
Given that f(x) = 6x +1, find (f of)(-2).<br> (f of)(-2)<br> | (Simplify your answer.)
irakobra [83]

Answer:

(f of)(-2) = -65

Step-by-step explanation:

<u>Set up (f of)(-2)</u>

(f o f)(-2) = f(f(-2))

<u>Once you get (fof)(-2) you then have f(#)</u>

f(6(-2) + 1) = f(-11)

6(-11) + 1 = -66 + 1 = -65

8 0
3 years ago
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