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Ainat [17]
3 years ago
7

The number of buckets of paint n needed to paint a fence varies directly with the total area of the fence and inversely with the

amount of paint p in a bucket. It takes three 1-gallon buckets of paint to paint 72 square feet of fence. How many 1-gallon buckets will be needed to paint 90 square feet of fence?
(Please show your work so I know how you got your answer and thanks in advance!)
Mathematics
1 answer:
Vesna [10]3 years ago
6 0
It takes three 1-gallon buckets to paint 72sqft, if you simplify or find the unit rate, you can know that you can paint 24sqft with one 1-gallon bucket of paint. Since you need to paint 90 sqft, you can’t use three buckets because it only covers 72sqft, but if you use 4 buckets, it will cover 96sqft.

THE ANSWER IS 4 1-GALLON BUCKETS OF PAINT
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A painter leans a 15 ft ladder against a building. The base of the ladder is 6 ft from the building. To the nearest foot, how hi
stiv31 [10]
Using the Pythagoras theorem 

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3 years ago
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За – 6а + 2 = 8а + 20 – 5а
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Answer:

a = -3

Step-by-step explanation:

3a - 6a + 2 = 8a + 20 - 5a

Combine Like Terms

-3a + 2 = 3a + 20

       -2            -2

-------------------------------------

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-3a  -3a

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a  =  -3

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3 years ago
Classifying quadrilaterals
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7 0
3 years ago
The line y = hx - 2 where h > 0 meets the curve 3y² = 9x² - 6x + 1.
I am Lyosha [343]

Answer:

h=6

Step-by-step explanation:

since y =hx -2 is an equation for a line which intersects with the curve 3y^2 = 9x^2 - 6x +1. The point of intersection, let's say (x_1,y_1), should satisfy the two equations. As a result, the value of y in the second equation can be replaced with the value of y in the first equation as the following,

3y^2 = 3(hx-2)^2 = 9x^2 - 6x +1\\3(h^2x^2 -4hx + 4) = 9x^2 - 6x + 1\\3h^2 x^2 -12hx +12 = 9x^2 - 6x +1

therefore, the latter equation can be rewritten in a quadratic equation form as the following,

(9 - 3h^2) x^2 + (12h-6)x + (1-12) = (9 - 3h^2) x^2 + (12h-6)x -11 = 0

if the line is tangent to the curve, it means that the line touches the curve at one point, therefore the discernment of the second order equation will be equal to zero for the famous quadratic equation solution.

b^2 -4ac =0

where a=9-3h^2, b=12h-6 and c=-11, as a result, the following equations can be deduced,

(12h-6)^2 - 4*(9-3h^2)*(-11) = (144h^2 -144h +36) - (36 -12h^2)*(-11)=\\(144-(-12)*(-11)h^2 )  -144h +36 -(36*(-11)) =\\12 h^2 -144h +432 =0

therefore, dividing both sides by 12

h^2 -12 +36 =0\\(h-6)^2 =0\\h=6

8 0
2 years ago
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hope this helps :)
7 0
3 years ago
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