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dybincka [34]
3 years ago
14

What is the length of the diagonal, d, of the rectangular prism shown below?

Mathematics
1 answer:
vodomira [7]3 years ago
8 0

Answer:

<h2>The diagonal of the volumetric figure is 7 units long.</h2>

Step-by-step explanation:

The figure is attached.

Notice that the dimensions of the prism are

w=2\\l=3\\h=6

First, we need to find the diagonal of the rectangular face on the base, this diagonal of the base is part of the right triangle formed by the diagonal of the volume, that's why we need it.

Let's use the Pythagorean's Theorem

d_{base}=\sqrt{2^{2} +3^{2} }=\sqrt{4+9}=\sqrt{13}

This diagonal of the base is a leg in the right triangle formed by the diagonal of the volume.

Let's use again Pythagorean's Theorem

d_{volume}=\sqrt{(\sqrt{13} )^{2}  +(6)^{2} }  =\sqrt{13+36}=\sqrt{49}\\ d_{volume}=7 \ units

Therefore, the diagonal of the volumetric figure is 7 units long.

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It takes Mia 1/4 hour to pick out all beads and 1/10 hour to string them. If she only has 5 and 1/4 to make bracelets how many w
JulsSmile [24]

Answer:

15

Step-by-step explanation:

Mia take 1/4 and 1/10 hours to create a bracelet. This is 1/4 + 1/10 = 10/40 + 4/40 = 14/40 = 7/20.

It takes her a total of 7/20 hours to make the bracelet. She has 5 1/4 hours to work. To find the number of bracelets she can make divide 5 1/4 by 7/20.

Write first 5 1/4 as a mixed number. 21/4. Then rewrite it as multiplication with the reciprocal of 7/20 to divide fractions.

21/4 * 20/7 = 420/28 = 15

She will make 15 bracelets.

4 0
3 years ago
The value of a car is $30,000 and depreciates at a rate of 6.5% each year.
navik [9.2K]

Answer:$20250

Step-by-step explanation:

6.5% of 30000

6.5/100 x 30000

(6.5 x 30000)/100

195000/100=1950

First year depreciation 30000-1950=28050

Second year=28050-1950=26100

Third year=26100-1950=24150

Fourth year=24150-1950=22200

Fifth year=22200-1950=20250

7 0
2 years ago
PLS SOMEON EHELP PLS IM BEGGING FOR HELP IM SCRAEIMG FOR HELP
ohaa [14]
None of your answers are correct

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for example, find value of 5 in 517,849

the 5 is in the 100 thousands place this means that the value is 500,000
3 0
2 years ago
The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b.
denis-greek [22]
\mathrm{gcd}(a,b)=9\implies9\mid a\text{ and }9\mid b\implies9\mid a+b

which means there is some integer k for which a+b=9k.


Because 9\mid a and 9\mid b, there are integers n_1,n_2 such that a=9n_1 and b=9n_2, and


\mathrm{lcm}(a,b)=\mathrm{lcm}(9n_1,9n_2)=9\mathrm{lcm}(n_1,n_2)=378\implies\mathrm{lcm}(n_1,n_2)=42

We have 42=2\cdot3\cdot7, which means there are four possible choices of n_1,n_2:

1, 42
2, 21
3, 14
6, 7

which is to say there are also four corresponding choices for a,b:

9, 378
18, 189
27, 126
54, 63

whose sums are:

387
207
153
117

So the least possible value of a+b is 117.
6 0
3 years ago
What number is missing in this sequence? 1, 2, 4, 7, 11, ___, 22
Zina [86]

Answer:

16

Step-by-step explanation:

4 0
3 years ago
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