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Arada [10]
4 years ago
14

a rectangle is 4 times as long as it wide. if the length is increased by 4 inches and the width is decreased by 1 inch, the area

will be 60 square inches. what were the dimensions of the original rectangle. and please help me
Mathematics
1 answer:
Mekhanik [1.2K]4 years ago
6 0
x-\ width\\
y-\ length\\
4x=y\\
(y+4)(x-1)=60\\
(4x+4)(x-1)=60\\
4x^2-4x+4x+4=60\ \  | subtract\ 4\\
4x^2=56\ \ | divide\ by\ 4\\
x^2=14\\
x=\sqrt{14}\\
y=4\sqrt{14}\\\\
Dimensions:\ width=\sqrt{14}in,\ length=4\sqrt{14}in.
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Angles L and M are complementary. If m∠L = (x + 2)° and m∠M = (x – 6)°,<br> what is the value of x?
nevsk [136]

Answer: 47°

Step-by-step explanation:

(x + 2)° + (x - 6)° = 90°

x + 2 + x - 6 = 90

2x - 4 = 90

2x - 4 + 4 = 90 + 4

2x = 94

\frac{2x}{2} = \frac{94}{2}

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6 0
3 years ago
Coach Shaw is buying baseball equipment for his team. He gets a reduced rate if he buys 8 baseballs for every 3 batting helmets.
Natalija [7]

Answer:

Helmets-12

Baseballs-32

Step-by-step explanation:

Given the tax rate as 6% and the reduced prices as $2.25/baseball and $22.50/helmet and that the budget is $400:

The new prices are reduced price plus tax:

Baseball \ Price =2.25\times (1.06\%)=2.39\\\\Helmet \ Price= 22.50\times (1.06\%)=23.85

Let x be the number of groups of 8 baseballs as well as the number of groups of 3 helmets,therefore:

8x(2.39)+3x(23.85)=400\\\\19.12x+71.55x=400\\\\x=4.4116\\\\x\approx 4

Substitute for x=4 to find the highest number of baseballs and helmets:

Helmets=4x3=12

Baseball=4x8=32

#Price cost will be 12x23.85+32x2.39=362.68 (balance=37.32)

Hence, Shaw can buy 12 helmets and 32 baseballs and still remain with $37.32

3 0
3 years ago
Which of the following is another way to express the equation 8 - (-) = 43?
Olin [163]

<em><u>Question:</u></em>

Which of the following is another way to express the equation 8 - (-d) = 43?

A.8-d=43

B.-d+8=43

C.-8+d=43

D.8+d=43

<em><u>Answer:</u></em>

8 + d = 43 is another way to express the given equation

<em><u>Solution:</u></em>

Consider the given equation

8 - (-d) = 43

We have to find the another way to express the above equation

We know that,

We we multiply negative sign number by another negative sign number, then the result is positive sign number

Therefore from given,

-(-d) = -1 \times -d = d

<em><u>Thus the given equation becomes,</u></em>

8 + d = 43

Thus option D is correct

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