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Keith_Richards [23]
2 years ago
10

79 x 31 rounding or compatible numbers . show how you estimate

Mathematics
1 answer:
Lubov Fominskaja [6]2 years ago
8 0

Answer:

80 × 30 = 2,400

Step-by-step explanation:

We can easily round 79 up to 80 and round 31 down to 30. This would make our expression 80 × 30, which is much easier to compute. We just take 8 × 3 (which is 24) and add two zeros onto the end of the number. This yields us an answer of 2,400 which is very close to the actual multiplication of 79 × 31 which is 2,449 (only 49 more than our estimation).

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):
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<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)

First pair of opposite sides:

<u>Slope:</u>

\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}

Second pair of opposite sides:

<u>Slope:</u>

\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\

So the diagonals measure the same, therefore this is a rectangle.

5 0
3 years ago
y varies directly as x, y=14 when x=18. Determine x when y=31. Estimate your answer to two places after the decimal, if necessar
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Y : x
14 : 18
31 : x
18*31/14=x
39.85714286

ANSWER
x=39.86
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Seven less than one half of x
damaskus [11]

Answer:

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Step-by-step explanation:

any number which is said to be less than another number let's say b should be subtracted from b.

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B. No, because it fails the vertical line test.
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inna [77]

Answer:

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Step-by-step explanation:

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