Number 21 please help me !!?!! ONLY THE QUESTION PLEASE
2 answers:
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Answer:
The area of the second enlargement is 1,944 square inches
The area of the second enlargement is (3 squared) squared times the original area.
The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor
Step-by-step explanation:
<u><em>Verify each statement</em></u>
1) The area of the first enlargement is 72 square inches.
The statement is false
Because
we know that
The original dimensions of the rectangle are
length 6 inches and width 4 inches
so
First enlargement
Multiply the original dimensions by a scale factor of 3
The area of the first enlargement is
2) The area of the second enlargement is 1,944 square inches
The statement is true
Multiply the dimensions of the first enlargement by a scale factor of 3
The area of the second enlargement is
3) The area of the second enlargement is (3 squared) squared times the original area.
The statement is true
Because
The original area is 24 square inches
4) The area of the second enlargement is 3 times the area of the first enlargement
The statement is false
Because
so
5) The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor
The statement is true
Because
The square of the scale factor is 3^2=9
and the ratio is equal to
Answer:
(0.5,3.5)
Step-by-step explanation:
First, we can draw the image, as shown. The diagonals in the rectangle are the following lines:
from (-2,9) to (3,-2)
from (-5, 6) to (6,1)
To find where they intersect, we can start by making an equation for the lines. For an equation y=mx+b, m represents the slope and b represents the y intercept, or when x=0
For the first line, from (-2,9) to (3,-2), we can calculate the slope by calculating the change in y/change in x = (y₂-y₁)/(x₂-x₁). If (3,-2) is (x₂,y₂) and (-2,9) is (x₁,y₁), our slope is
(-2-9)/(3-(-2)) = -11/5
Therefore, our equation is
y= (-11/5)x + b
To solve for b, we can plug a point in, like (3,-2). Therefore,
-2=(-11/5)*3+b
-2=-33/5+b
-10/5=-33/5+b
add 33/5 to both sides to isolate b
23/5=b
Our equation for one diagonal is therefore y=(-11/5)x+23/5
For the second line, from (-5, 6) to (6,1), if (6,1) is (x₁,y₁) and (-5,6) is (x₂,y₂), the slope is (1-6)/(6-(-5)) = -5/11 . Plugging (6,1) into the equation y=(-5/11)x+b, we have
1=(-5/11)*6+b
11/11 = -30/11 + b
add 30/11 to both sides to isolate b
41/11 = b
our equation is
y = (-5/11) x + 41/11
Our two equations are thus
y = (-5/11) x + 41/11
y=(-11/5)x+23/5
To find where they intersect, we can set them equal to each other
(-11/5)x+23/5 = y = (-5/11) x + 41/11
(-11/5)x + 23/5 = (-5/11)x + 41/11
subtract 23/5 from both sides as well as add 5/11 to both sides to make one side have only x values and their coefficients
(-11/5)x + (5/11)x = 41/11-23/5
11*5 = 55, so 55 is one value we can use to make the denominators equal.
(-11*11/5*11)x+(5*5/11*5)x=(41*5/11*5)-(23*11/5*11)
(-121/55)x+(25/55)x = (205/55) - (253/55)
(-96/55)x = (-48/55)
multiply both sides by 55 to remove the denominators
-96x=-48
divide both sides by -96 to isolate x
x=-48/-96=0.5
plug x=0.5 into a diagonal to see the y value of the intersection
(-11/5)x + 23/5 = y = (-11/5)* 0.5 + 23/5 = 3.5
