Answer: PART A : 
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PART B : 5.9 FEET
Step-by-step explanation:
Length of the first sign = 4.4 feet
height of the first sign = 3 feet
Length of the second sign = x feet
height of the second sign = 4 feet
If two shapes are similar , then the ratio of their sides are equal,
That is ;
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PART A
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PART B
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cross multiplying , we have
3x = 4.4 x 4
3x = 17.6
Divide through by 3
x = 17.6/3
x = 5.86666666666667
x≈ 5.9 feet
Therefore , the length of the new sign is 5.9 feet
Let us say that:
o = cost of oranges per pound
p = cost of pears per pound
so that:
o = p – 2
Therefore:
10o + 8p = 61
10 (p – 2) + 8p = 61
10p – 20 + 8p = 61
18p = 81
p = 4.5
p = $4.5 per pound
So 3 pounds of pears would cost:
total cost = 3 * 4.5
total cost = $13.5
<span>Logarithm form is another way to express a number in exponential (exp.) form. log 8 (2) is the same as 8 (x) = 2 or in words, eight with exp. x equals two. If we take that equation and cube both sides, or raise each side to the power of 3, [8 (x)] with exp. 3 = 2 with exp. 3. This simplifies to 8 (3x) = 8. By definition, 8 is the same as 8 with exp. 1. So the equation is now 8 (3x) = 8 (1). This means 3x = 1. We can simplify to x = 1/3.</span>
Answer: The coordinates of point C after the dilation are (-2, 5)
Step-by-step explanation:
I guess that you want to find where the point C ends after the dilation.
Ok, if we have a point (x, y) and we do a dilation with a scale A around the point (a,b), then the dilated point will be:
(a + A*(x - a), b + A*(y - b))
In this case we have:
(a,b) = (2,1) and A = 3.
And the coordinates of point C, before being dilated, are: (1, 2)
Then the new location of the point C will be:
C' = (1 + 3*(1 - 2), 2 + 3*(2 - 1)) = (1 -3, 2 + 3) = (-2, 5)
Frankie's yard is a rectangle with the longer side = 32ft and the shorter side = 20ft. You want to find the length of the diagonal going through the rectangle. In essence, you basically have a triangle with two sides, one 32ft, the other 20ft, and you're looking for the hypotenuse.
Let's call a=32, b=20, and you're looking for the hypotenuse c. Use the Pythagorean theorem:
Plug the numbers in to find c, the length of your path! So
