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mihalych1998 [28]
3 years ago
14

The length of a rectangle is 6 in. more than the width. The perimeter of the rectangle is 24 in. Find the dimensions of the rect

angle.
Mathematics
1 answer:
klasskru [66]3 years ago
8 0

1. First, let us define the width of the rectangle as w and the length as l.

2. Now, given that the length of the rectangle is 6 in. more than the width, we can write this out as:

l = w + 6

3. The formula for the perimeter of a rectangle is P = 2w + 2l. We know that the perimeter of the rectangle in the problem is 24 in. so we can rewrite this as:

24 = 2w + 2l

4. Given that we know that l = w + 6, we can substitute this into the formula for the perimeter above so that we will have only one variable to solve for. Thus:

24 = 2w + 2l

if l = w + 6, then: 24 = 2w + 2(w + 6)

24 = 2w + 2w + 12 (Expand 2(w + 6) )

24 = 4w + 12

12 = 4w (Subtract 12 from each side)

w = 12/4 (Divide each side by 4)

w = 3 in.

5. Now that we know that the width is 3 in., we can substitute this into our formula for length that we found in 2. :

l = w + 6

l = 3 + 6

l = 9 in.

6. Therefor the rectangle has a width of 3 in. and a length of 9 in.

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Aliun [14]

Answer:  The guage block height is 4.98 m

The base of the right triangle that is formed is 7.3784 m

The last angle in the triangle is 56 degrees

Step-by-step explanation:

Redraw the triangle formed in the picture and use H for the hypotenuse, O for the block height, and A for the base.  Now we can use trig (SOHCAHTOA) to find the answaers.

Using sine, we can first find the gauge block height, O (Opposite).  Given the Hypotenuse (H) is 8.9 m, we can use the definition of the sine of an angle to find the height, O.

Sine(34) = Opposite/Hypotenuse (O/H), or O = H*Sine(34)

O = (8.9)*(0.5592)

O = 4.98 m, the height of the gauge block,

The base of the triangle, A, can be determined with cosine.

Cosine(34) = A/O, or A = Cosine(34)*O

A = (0.82904)*(8.9)

A = 7.3784 m

The sum of all angles in a triangle is 180 degrees.  

180 = X + 34 + 90

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3 years ago
in a hostel of 50 girls food provision is 40 days. if 30 girls are added how long will the provision last
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if 30 girls are added then for 25 days the food will last.

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3 years ago
According to the Census Bureau, 3.36 people reside in the typical American household. A sample of 25 households in Arizona retir
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Answer:

We conclude that  the mean number of residents in the retirement community household is less than 3.36 persons.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 3.36

Sample mean, \bar{x} = 2.71

Sample size, n =  25

Alpha, α = 0.10

Sample standard deviation, s = 1.10

First, we design the null and the alternate hypothesis

H_{0}: \mu = 3.36\text{ residents per household}\\H_A: \mu < 3.36\text{ residents per household}

We use One-tailed(left) t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} } Putting all the values, we have

t_{stat} = \displaystyle\frac{2.71 - 3.36}{\frac{1.10}{\sqrt{25}} } = -2.95

Now, t_{critical} \text{ at 0.10 level of significance, 24 degree of freedom } =-1.31

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t_{stat} < t_{critical}

We reject the null hypothesis and fail to accept it.

Thus, we conclude that  the mean number of residents in the retirement community household is less than 3.36 persons.

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3 years ago
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Zinaya Equation: 1,500 x .08 = 120
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Hope this helps!!
5 0
3 years ago
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