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Komok [63]
3 years ago
10

Logan is flying a kite that is made yo if three similar rectangles. The sides of the three rectangles are in the ratio 1:2:3. If

the area of the smallest rectangle is 72 square inches, what are the areas of the other two rectangles?
Mathematics
1 answer:
Ad libitum [116K]3 years ago
4 0
To solve the question we need to note that:
area scale factor=(linear scale factor)^2
linear scale factor=1:2:3
Area scale factor=1^2:2^2:3^2=1:4:9

Hence, given that the area of the smallest triangle is 72 sq. inches, the area of:
medium triangle will be:
4/1*72=288 sq. inches

largest triangle will be:
9/1*72=649 sq. inches

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Write an equation in slope-intercept form for the line with slope -2/5 and y-intercept 6 .
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y=(-2/5)x + 6

Step-by-step explanation:

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If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ First, find
Evgesh-ka [11]

Answer:

The equation of the circle is (x+3)^2+(y-5)^2 = 17

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ First, find the midpoint of the​ diameter, which is the center of the circle. Then find the​ radius, which is the distance from the center to either endpoint of the diameter. Finally use the​ center-radius form to find the equation.

Find the center-radius  form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

(\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5).

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by \sqrt[]{(a-c)^2+(b-d)^2}. So, let us use (1,4) to calculate the radius.

r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}.

REcall that given a point (x_0,y_0). The equation of a circle centered at the point (x_0,y_0) is

(x-x_0)^2+(y-y_0)^2 = r^2

In our case, (x_0,y_0)=(-3,5) and r=\sqrt[]{17}. Then, the equation is

(x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17

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3 years ago
John goes out to eat at a local restaurant. The bill comes to $47.83. John want to leave a 20% tip. How much of a tip should he
valentina_108 [34]

$10.17 is the 20% tip amount

7 0
2 years ago
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