Marc is looking at the plans for his new garage. the length of the garage is 8 metres. the scale on the drawing is 1:50. what will the length of the garage be on the drawing?
Answers
The scale is the ratio of the model to the real thing.
So, in the scale 1:50, the model is 1, while the real thing is 50.
Now, just make a proportion:
the model : the real thing = the model dimension : the real thing dimension
1 : 50 = x : 8m
From here:
x = 8m * 1 / 50 = 0.16 m = 0.16 * 100 cm = 16 cm.
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What are the exact solutions of x2 − 3x − 5 = 0?
Henry wants to avoid interest capitalization on his $7,800 unsubsidized Stafford loan. Henry will graduate in four years, and the loan has a duration of ten years. The loan has an interest rate of 5.6%, compounded monthly. How much must Henry pay every month to avoid interest capitalization?
b. {2,2,4}
c. (1,2, sqrt of 3 wouldn't it be B because it has all even numbers?
Answers
The only set of numbers that could be the sides of a right triangle is **(b) {2, 2, 4}**.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Therefore, in order for a set of numbers to be the sides of a right triangle, the following equation must hold:
hypotenuse^2 = leg1^2 + leg2^2
Let's check each of the given sets:
(a) {2, 3, √13}
hypotenuse^2 = √13^2 = 13
leg1^2 = 2^2 = 4
leg2^2 = 3^2 = 9
13 ≠ 4 + 9
Therefore, {2, 3, √13} cannot be the sides of a right triangle.
(b) {2, 2, 4}
hypotenuse^2 = 4^2 = 16
leg1^2 = 2^2 = 4
leg2^2 = 2^2 = 4
16 = 4 + 4
Therefore, {2, 2, 4} can be the sides of a right triangle.
(c) {1, 2, √3}
hypotenuse^2 = √3^2 = 3
leg1^2 = 1^2 = 1
leg2^2 = 2^2 = 4
3 ≠ 1 + 4
Therefore, {1, 2, √3} cannot be the sides of a right triangle.
Therefore, the only set of numbers that could be the sides of a right triangle is **(b) {2, 2, 4}**.
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Final answer:
The set of numbers that could be the sides of a right triangle is {2,3, sqrt of 13}.
Explanation:
To determine whether a set of numbers could be the sides of a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's check each set of numbers:
a. {2,3,√13}
b. {2,2,4}
c. (1,2,√3)
For set a, the sum of the squares of 2 and 3 is 13, which is equal to the square of √13. Therefore, set a could be the sides of a right triangle.
For set b, the sum of the squares of 2 and 2 is 8, which is not equal to the square of 4. Therefore, set b could not be the sides of a right triangle.
For set c, the sum of the squares of 1 and 2 is 5, which is not equal to the square of √3. Therefore, set c could not be the sides of a right triangle.
Therefore, the set of numbers that could be the sides of a right triangle is a. {2,3,√13}.
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Answers
32 - 8x = 7x + 2
-7x -7x
--------------------------
32 - 15x = 2
-32 -32
----------------------------
-15x = -30
/-15 /-15
x = 2.
4a+4b+4c
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The formula is as follows:
P: Principal Amount : $273
r: Rate of interest: 5%
n: number of times the interest is compounded: 4 (Since Quarterly)
t: number of years : 5
Answers
multiply out
[8a+24+26]/5=18
add
(8a+50)/5=18
bultiply both sides by 5
8a+50=90
subtract 50 from both sides
8a=40
divide both sides by 8
a=5