Did I do this right?

Liev is assembling a coffee table. The diagram below is from the instruction manual and shows the table after the first two legs

elixir [45]

Answer:

The support is 41 inches long.

Step-by-step explanation:

There's two ways we can do this: one with the diagonal formula and one without.

Since we know that Point C is halfway down leg A and that the table legs are 18 inches tall, Point C is 9 inches down leg A. The support, from Point C to Point D, will form a diagonal, the length of which we need to find. We know from the diagram that the width of the table is 24 inches and that its length is 32 inches. We have a height, length, and width for this problem, so let's imagine a rectangular prism, which has all three of those things, instead of a table. The formula for finding a rectangular prism's diagonal is $d = \sqrt{l^{2} + w^{2} + h^{2} }$ . Let's put in those numbers:

$d = \sqrt{32^{2} + 24^{2} + 9^{2} } = 41$

Therefore, the support is 41 inches long.

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Another way you can do this is to use the Pythagorean Theorem twice: once to find the diagonal of the tabletop and another time for the support.

$24^{2} + 32^{2} = c^{2} \\576 + 1024 = c^2\\1600 = c^2\\\sqrt{1600} = \sqrt{c^2}\\ 40 = c$

Now that we know the corner-to-corner distance for the tabletop, we'll use that and the 9 inch distance for Point C to find the distance between C and D:

$9^{2} + 40^{2} = c^{2}\\ 81 + 1600 = c^2\\1681 = c^2\\\\sqrt{1681} = \sqrt{c^2} \\41 = c$

Again, the support is 41 inches long.

4 0

3 years ago

Kayla needs $14,000 worth of new equipment for his shop. He can borrow this money at a discount rate of 10% for a year.

arlik [135]

Answer:

$15400

Step-by-step explanation:

Principle amount, P = $14000

Time, T = 1 year

Rate of interest, R = 10%

We know that maturity amount,

$A = P\left (1+\frac{R}{100} \right )^{n}$

where n is number of years

$A = P\left (1+\frac{R}{100} \right )^{n}$

$A = 14000\left (1+\frac{10}{100}\right )^{1}$

$A = 14000\left (1+\frac{1}{10}\right )$

$A = 14000\left (\frac{11}{10}\right )$

$A = 15400$

The maturity amount is $15400

6 0

2 years ago

What is the area of triangle HGF? Round your answer to the nearest tenth of a square centimeter. Recall that you need to round u

denpristay [2]

Answer:

9.8

Step-by-step explanation:

The formula for the area of a triangle is a=bh/2, where a is area, b, is the base, and h is the height. If we substitute the values in the question in the equation, we get:

a=(6.5*3)/2

a=19.5/2

a=9.75

a≈9.8

7 0

2 years ago

Is 85/95 greater than 64/76

madam [21]

85/95 is equal to 0.8947
64/76 is equal to 0.842
Therefore, 85/95 is greater

5 0

3 years ago

(-----×1/4)÷6×3/9 I need the step to this problem so that I explain to my grandson how he he gets the answer

lesya692 [45]

Answer:

-----×1/72

Step-by-step explanation:

The order of operations says do these operations in order left to right. Please note that ÷ means the same as / unless you define it otherwise in your problem statement.

If you intend the ÷ symbol to be used to indicate everything to its left is divided by everything to its right, it is appropriate to use parentheses for that grouping, as in ...

(-----×1/4)÷(6×3/9) = (-----×1/4)÷2 = -----×1/8

_____

Here, we're going to evaluate what you have written according to the usual rules as described above.

(-----×1/4)÷6×3/9 = -----×1/24×3/9 = -----×(3/24)/9

= -----×1/8/9

= -----×1/72

_____

Comment on the arithmetic

Fractions are multiplied and divided in the usual way:

a/b×c = (a×c)/b

a/b/c = (a/b) × (1/c) = a/(b×c)

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Comment on fractions and parentheses

Please note that parentheses are required on any numerator or denominator that consists of anything other than a single number or variable. (The exception is the case where the numerator is a product, because a·b/c = (a·b)/c with or without the parentheses.)

6 0

3 years ago