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3 years ago

Find the Least Common Multiple of 9 and 20.

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

8 0

180, because 9 and 20 don’t have any common multiple (both numbers couldn’t be simplified)

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What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

kramer

Option C: $a=3, b=4$ is the value of a and b

Explanation:

Given that the expression $\sqrt{648}=\sqrt{2^a\times3^b}$

We need to determine the value of a and b

Let us consider the term $\sqrt{648}$ and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

$648=2 \cdot 324$

324 divides by 2,

$648=2 \cdot 2 \cdot 162$

162 divides by 2,

$648=2 \cdot 2 \cdot 2 \cdot 81$

81 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27$

27 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9$

9 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

Thus, we have,

$\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}$

Therefore, equating the powers of 2 and 3, we get,

$a=3, b=4$

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

4 0

3 years ago

Read 2 more answers

Martin runs a 5 kilometer race in 25 minutes. What is his unit rate?

SOVA2 [1]

Answer:

[ 60/25 ] x 5 km/h = 12 km/h

Step-by-step explanation:

4 0

3 years ago

Use the functions to find x

suter [353]

Answer:

x = 14

Step-by-step explanation:

$f(x) = 10 - \frac{9}{2} x \\ \\ plug \: f(x) = - 53 \\ \\ - 53 = 10 - \frac{9}{2} x \\ \\ \frac{9}{2} x = 10 + 53 \\ \\ \frac{9}{2} x = 63 \\ \\ x = 63 \times \frac{2}{9} \\ \\ x = 7 \times 2 \\ \\ x = 14$

5 0

3 years ago

On average, water flows over a particular water fall at a rate of 2.08 x 105 cubic feet per second. One cubic foot of water weig

34kurt

Answer:

5.61×10^8 ton/day

Step-by-step explanation:

(2.08×10^5 ft³/s)·(8.64×10^4 s/day)·(6.24×10^1 lb/ft³)/(2×10^3 lb/ton)

= (2.08·8.64·6.24/2)×10^(5+4+1-3) ton/day

≈ 56.07×10^7 ton/day

≈ 5.61×10^8 ton/day

_____

We have expressed the answer using 3 significant digits, to match the precision of the rate and weight.

4 0

3 years ago

If a printer prints 28 copies in 1 minute how many would it print in 3 minutes and 45 seconds?

Wittaler [7]

3minutes 45 seconds = 3 45/60 = 3.75 minutes

28 copies/ 1 minute = x copies/3.75 minutes

using cross products

28 * 3.75 = 1 * x

105 = x

We can print 105 copies in 3 3/4 minutes

3 0

3 years ago