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REY [17]
3 years ago
15

Use rounding or compatible numbers to estimate each product or quotient.

Mathematics
1 answer:
zmey [24]3 years ago
3 0
Part 1

<span>Using rounding or compatible numbers, we estimate the product

5\times2 \frac{3}{5}
to
5\times3

Therefore, the estimate of the product </span><span>5\times2 \frac{3}{5}, using rounding and compatible numbers is about 15.</span>



Part 2

<span>Using rounding or compatible numbers, we estimate the quotient

25\frac{7}{8}\div2 \frac{8}{9}
to
27\div3

Therefore, the estimate of the quotient </span><span>25\frac{7}{8}\div2 \frac{8}{9}, using rounding and compatible numbers is about 9.</span>



Part 3

Given that Mr. Garcia's class ate 3\frac{2}{3} pizzas, Mrs Rizzoli's class ate <span>4\frac{1}{8} pizzas, and Mrs. Tindal's class ate </span><span>3\frac{1}{4} pizzas.

Using benchmarks, we estimate the total number of pizzas eaten by all three classes as follows: </span>3\frac{3}{4}, 4 and <span>3\frac{1}{4}

Thus, the </span><span>total number of pizzas eaten by all three classes is given by

3\frac{3}{4}+4+3\frac{1}{4}=11

Therefore, </span>the <span>total number of pizzas eaten by all three classes is about 11.</span>

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Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that  coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}

EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}

FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}

DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}

Slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Slope of DE,

m_1=\frac{4-5}{2+2}= \frac{-1}{4}

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m_2=\frac{0-4}{0-2}= 2

Slope of FG,

m_3=\frac{1-0}{-4-0}= \frac{-1}{4}

Slope of DG,

m_4=\frac{1-5}{-4+2}= 2

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

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