MATHEMATICS COLLEGE

A trapezoid has an area of 60 square inches. The height of the trapezoid is 5 inches. What is the length of the longer base if the longer base is three times the length of the shorter base?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Remark

Let the shorter base = x

Let the longer base = 3x

h = 5

Area = 60

Formula

Area = (b1 + b2)*h /2

Solution

60 = (x + 3x)*5 / 2 Multiply both sides by 2

2*60 = (x + 3x)*5 Combine like terms

120 = 4x *5

120 = 20x Divide by 20

120/20 = x

x = 6

Therefore the two bases are

x = 6

3x = 18

Answer 2

Answer:

Step-by-step explanation:

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A warehouse store sells 6.5 ounce cans of tuna in packages of 5. A package of 5 cans cost $11.05. The store also sells 5.5 ounce cans of the same package of 4. A package of 4 cans cost $6.60.The store sells 3.5 ounce cans in packages of 3 cans for 3.36. Which package is the Best Buy?

Answers

Answer:

6.5-once cans is the best buy

Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)

Answers

You can simply expand each product and see whether it gives you a difference of squares.

•   $\mathsf{(-7x+4)\cdot (-7x+4)}$

That's actually $\mathsf{(-7x+4)^2:}$

$\mathsf{(-7x+4)^2}\n\n \mathsf{=(-7x+4)\cdot (-7x+4)}\n\n \mathsf{=(-7x+4)\cdot (-7x)+(-7x+4)\cdot 4}\n\n \mathsf{=49x^2-28x-28x+16}$

$\mathsf{=49x^2-56x+16}$   ✖

which is not a difference of squares.

—————

•   $\mathsf{(-7x+4)\cdot (4-7x)}$

$\mathsf{=(-7x+4)\cdot 4-(-7x+4)\cdot 7x}\n\n \mathsf{=-28x+16-(-49x^2+28x)}\n\n \mathsf{=-28x+16+49x^2-28x}$

$\mathsf{=49x^2-56x+16}$ ✖

which is not a difference of squares.

—————

•   $\mathsf{(-7x+4)\cdot (-7x-4)}$

$\mathsf{=(-7x+4)\cdot (-7x)-(-7x+4)\cdot 4}\n\n \mathsf{=49x^2-28x-(-28x+16)}\n\n \mathsf{=49x^2-\diagup\!\!\!\!\! 28x+\diagup\!\!\!\!\! 28x-16}\n\n \mathsf{=49x^2-16}$

$\mathsf{=(7x)^2-4^2}$   ✔

That is a difference of two squares.

—————

•   $\mathsf{(-7x+4)\cdot (7x-4)}$

$\mathsf{=(-7x+4)\cdot 7x-(-7x+4)\cdot 4)}\n\n \mathsf{=-49x^2+28x-(-28x+16)}\n\n \mathsf{=-49x^2+28x+28x-16}$

$\mathsf{=-49x^2+56x-16}$   ✖

which is not a difference of squares.

—————

Only the third option will result in a difference of squares.

Answer: (− 7x + 4) · (− 7x − 4).

I hope this helps. =)

Answer:

The expression which will result in difference of two squares is:

(–7x + 4)·(–7x – 4)

Step-by-step explanation:

We know that the formula of the type:

$(a-b).(a+b)=a^2-b^2$

i.e. it is a difference of two square quantities. (a^2 and b^2)

Hence the option which satisfies the following expression is:

(-7x + 4)·(-7x-4)

since,

here $a=-7x$ and $b=4$ and

$(-7x+4).(-7x-4)=(-7x)^2-(4)^2=(7x)^2-4^2$

so the expression is a difference of two square quantities:

$(7x)^2$ and $4^2$

Hence, the correct answer is:

(-7x + 4)·(-7x-4)

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 94%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 22 years.