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2 years ago

A number n is multiplied with —9 to give 63. Find the value of n.

Mathematics

2 answers:

FrozenT [24]2 years ago

5 0

Answer:

n = -7

Step-by-step explanation:

63÷-9

a_sh-v [17]2 years ago

3 0

N= -7. -9*-7=63 n is equal to -7

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Translate to an algebraic statement.<br> "The quotient of twice a number and 7 is 20."

Genrish500 [490]

<u>Answer:</u>

Translation: 2x/7 = 20

<u>Step-by-step explanation:</u>

<em>When we listen to the word "quotient", it means the solution to a division problem. </em>
<em>An unknown number that has been multiplied by 2 is in the numerator because it came before the 7 in the statement. </em>
<em>The number "7" is in the denominator because it came after the 2x in the statement. </em>
<em>The word "is" represents an equal sign.</em>
<em>The solution to the division problem (quotient) is 20. </em>

<u><em>If we put these clues together, we get 2x/7 = 20 as our translated equation.</em></u>

<u>Hence, our algebraic statement is 2x/7 = 20. The key is to listen to the statement. </u>

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2 years ago

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3 years ago

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nadezda [96]

<h2> $\large\mathfrak{{\pmb{\underline{\red{Given}}{\red{:}}}}}$ </h2>

∠RSU and ∠USV are complementary angles
∠RSU = (4x – 15)°
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The value of x

<h2> $\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}$ </h2>

∠RSU and ∠USV are complementary angles

$\sf\implies{ \angle RSU + \angle USV = 90 \degree }$

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2 years ago

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. The ball c

juin [17]

1 st hit=12 ft
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2 years ago

Read 2 more answers

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)

vichka [17]

Answers:

a = -6/37

b = -1/37

============================================================

Explanation:

Let's start things off by computing the derivatives we'll need

$y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\$

Apply substitution to get

$y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right) + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x) + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x) + \left(a - 6b\right)\cos(x) = \sin(x)\\\\$

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0

2 years ago