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stiv31 [10]
4 years ago
8

A square and rectangle have the same perimeters.The lengtj of a side of the square is 4x-1.The length of the rectangle is 2x+1 a

nd the width is x+2 write and solve an equation to find x
Mathematics
1 answer:
Ivanshal [37]4 years ago
7 0

Well, the perimeter of a square is 4 times the side.  The side of THIS square is (4x - 1), so the perimeter is 4 x (4x-1) = 16x - 4 .  Hold that thought while we go over there and work on the rectangle.

The perimeter of a rectangle is (2 lengths) plus (2 widths).  The length of THIS rectangle is (2x + 1), and 2 lengths = 2 x (2x+1) = 4x + 2.  The rectangle's width is (x+2).  Two widths add up to 2 x (x+2) = 2x + 4.

The total perimeter of the rectangle is (4x+2) + (2x+4) = 6x + 6 .

Now we have the expressions for the perimeters of both figures.  

AND we know that their perimeters are EQUAL ... THAT's the very powerful piece of information that's going to bust this whole problem wide open.

(perimeter of the square) = (perimeter of the rectangle)

The equation that the question asked for: 16x - 4  =  6x + 6

That's the answer to the question that was posted.  But we can't just leave it there.  We've got to find out what 'x' actually is, and then find the perimeters of the square and the rectangle.

Add  4  to each side:   16x = 6x + 10

Subtract  6x  from each side:  10x = 10

Divide each side by  10 :     x = 1

Side of the square:  (4x-1) = 3

Perimeter of the square:  4 x 3 = 12

Length of the rectangle:  (2x+1) = 3

Width of the rectangle:  (x+2) = 3

Perimeter of the rectangle = (2 lengths) + (2 widths) = 12

Do you notice anything strange and exciting ?  The "rectangle" is actually another square, exactly the same shape and size as the "square" !

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How to do proportions?
finlep [7]
Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying, and solving the resulting equation. You'll probably start out by just solving proportions, like this: Find the unknown value in the proportion: 2 : x = 3 : 9.
6 0
4 years ago
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Which is an equation of the line through the origin and (3,4)? Please help
kondor19780726 [428]
B is the answers………..
8 0
3 years ago
Suppose that P (A)=0.4 AND P (B)=0.2, If events A & B ARE Mutually EXCLUSIVE :
baherus [9]

Part (a) Finding the probability of either A or B

We are told that events A and B are mutually exclusive. This means they cannot happen at the same time. We can say P(A and B) = 0

Furthermore,

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.4 + 0.2 - 0

P(A or B) = 0.6

<h3>Answer:  0.6</h3>

=======================================================

Part (b) Finding the probability of neither A nor B

P(A or B) + P(neither A nor B) = 1

P(neither A nor B) = 1 - P(A or B)

P(neither A nor B) = 1 - 0.6

P(neither A nor B) = 0.4

The reason why this works is to imagine throwing a dart at the Venn diagram. You'll either...

  • you land in A or B (pick one but not both), OR,
  • you'll land outside both regions A and B.

One or the other must happen. Both events cannot happen simultaneously.

<h3>Answer: 0.4</h3>
7 0
3 years ago
17+p=7p-13 Plz help me asap
Hunter-Best [27]

First you had to subtract by seventeen from both sides of equation form.

17+p-17=7p-13-17

Then simplify.

p=7p-30

Next, subtract by seven-p from both sides of equation form.

p-7p=7p-30-7p

Simplify.

-6p=-30

Then you divide by negative six from both sides of equation form.

\frac{-6p}{-6}= \frac{-30}{-6}

And finally, simplify by equation.

-30/-6=5

Final answer: \boxed{p=5}

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie


4 0
3 years ago
Joint-Serve Prosthetics spends 43% of its total expenses for payroll. It increased its total expenses when it spent $250,000 for
Leni [432]
Answer: $2,150,000

Explanation: Let

T = Total expenses of Joint-Serve

Then, before the company acquired robotic assemblers, the expenses allocated for payroll is given by

Expenses for Payroll = 43% of Total Expenses
Expenses for Payroll = 0.43T     (1)
(Because 43% = 0.43)

Because the total expenses increased by $250,000 after spending for robotic assemblers, the total expenses = T + 250,000

So, the payroll expense is now calculated as

Expenses for Payroll = 38% of Total Expenses
Expenses for Payroll = 0.38(T + 250,000)     (2)
(Because 38% = 0.38 and total expenses = T + 250,000)

By comparing equations (1) and (2),

0.43T = 0.38(T + 250,000)&#10;\\ 0.43T = 0.38T + 0.38(250,000)&#10;\\ 0.43T = 0.38T + 95,000&#10;\\ 0.43T - 0.38T = 95,000&#10;\\  \frac{0.05T}{0.05}  =  \frac{95,000}{0.05} &#10;\\ \boxed{T = \$ 1,900,000}

Thus, the total expense before the purchase of robotic assemblers is T = $ 1,900,000. Therefore, the total expense after purchasing the robotic assemblers is T + 250,000 = 1,900,000 + 250,000 = $2,150,000  
6 0
3 years ago
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