ΔABC is similar to ΔDEF. The ratio of the perimeter of ΔABC to the perimeter of ΔDEF is 2 : 11. If the longest side of ΔABC measures 15 units, what is the length of the longest side of ΔDEF?
Answers
Answer:
82.5 cm
Step-by-step explanation:
For similar triangles, ratio of perimeter will equal to ratio of sides.
Here we are given that triangles ABC and DEF are similar.
This implies the corresponding sides are proportional.
By corresponding we mean that the longest sides of ABC with the longest side of DEF.
Hence Longest side of ABC/Longest side of DEF = Ratio of sides
= Ratio of perimeter.
Let the longest side of DEF be x.
i.e. 15/x = 2/11
Cross multiply to get
2x = 165
Divide by 2
x = 82.5 cm.
Hence the longest side of Triangle DEF = 82.5 cm.
Verify: Check proportions of longest sides
= which equals ratio of perimeters.
Thus verified.
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Which answer describes the simpler problems that could be used to solve this story problem? Emily paid a total of $109.95 for 4 pairs of sandals and a pair of boots. Each pair of sandals cost the same amount. The pair of boots cost $29.99. How much did 1 pair of sandals cost? A. Subtract the cost of the boots from the total cost. Divide that answer by 4. B. Add the cost of the sandals and the cost of the boots. Divide the sum by 4. C. Multiply the total cost by 4. Subtract the cost of the boots. D. Divide the total cost by 4. Add the cost of the boots.
Estimate. then find the product 1374 x 6
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8g^2 + 3g − 4, the rate that the pool is filled, and 9g^2 − 2g − 5, the rate that water leaves the pool, where g represents the number of gallons entering
or leaving the pool per minute.
a. Write an expression that determines the height of the water in the pool.
b. What will be the height of the water if g = 1, 2, 3, and 4?
c. To the nearest tenth, at which value for g will the water reach its
greatest height? Explain.
Answers
b) g = 1
H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5
g=2
H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7
g=3
H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5
c) Greatest height
Find the vertex of the parabole
The vertex is at the mid point between the two roots.
To find the roots you can use the quadratic equation
The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2
The middle poin is 5/2 = 2.5
Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3
Answers
= 28 cm/ 10
= 2.8 cm
Thus, on average, each book has 2.8 cm thickness.
28cm divided by 10 is 2.8cm.
So the average thickness is 2.8cm!
Answers
(You can check the answer by saying, if each of them get 3/4 of an orange, then multiplying that by the 4 friends should give me the 3 oranges. 3/4 x 4 = 3, so it's correct).
1, -3, 9, -27.....
Answers
multilply by negative three to find the next term. 1, -3, 9, -27, 81, -243, 729, which is the seventh term.
Answers
Answer:
x=11.5
Step-by-step explanation:
18+6x=41+4x
Subtract 4x from each side
18+6x-4x=41+4x-4x
18+2x = 41
Subtract 18 from each side
18-18 +2x = 41-18
2x =23
2x/2 = 23/2
x =11.5
Answers
3/4 can be written as 6/8
5/8 is between 4/8 and 6/8
the equivalent decimal of 5/8 is .625
3/4 = 6/8 = 0.75
therefore, a fraction between 1/2 and 3/4 is 5/8