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3 years ago

Tyler used 1 1/2 gallons of paint to paint 5/7 of a fence. How many gallons will it take to paint the whole fence?

Mathematics

1 answer:

Mademuasel [1]3 years ago

3 0

9514 1404 393

Answer:

1) (1 1/2)(7/5) = g

2) (1 1/2)/(5/7) = g

Step-by-step explanation:

1) Tyler has painted 5/7 of the 7/7 of the fence. So the total amount of the fence is (7/7)/(5/7) = 7/5 as much as what was already painted.

The total amount of paint needed is then 7/5 the amount already used:

g = (7/5)(1 1/2) . . . . . gallons of paint needed for the whole fence

2) If g gallons are required for the whole fence, the amount used so far for 5/7 of the fence is 5/7 of the quantity required:

(5/7)g = 1 1/2

g = (1 1/2)/(5/7) . . . . division expression for the paint needed

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Find the length of the segment that joins the points (-5, 4) and (6,-3).

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Answer:

$\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}$

Step-by-step explanation:

We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

x₁= -5
y₁= 4
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y₂ = -3

Substitute the values into the formula.

$d= \sqrt{(6--5)^2+(-3-4)^2$

Solve inside the parentheses.

6--5 (Back to back negative signs become a positive)= 6+5 =11
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$d= \sqrt{(11)^2+(-7)^2$

Solve the exponents.

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$d= \sqrt {(121)+(49)$

Add.

$d= \sqrt {170}$

$d=13.0384048104$

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

13.0384048104

$d\approx 13.04$

The length of the segment is √170 or approximately 13.04.

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