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2 years ago

the value of n is both 5times as much as the value of m and 36more than the value of m. What are the values of n and m?

Mathematics

2 answers:

LuckyWell [14K]2 years ago

8 0

Answer:

m = 9, n = 36

Step-by-step explanation:

Here, according to the question:

(a) value of n is 5 times as much as the value of m

⇒ n = 5 x ( value of m) = 5 m

or, n = 5 m

(b) value of n is 36 more than the value of m

⇒ n = 36 + ( value of m) = 36 + m

or, n = 36 + m

Now, compering both equations, we get

5 m = 36 + m

or, 5 m - m = 36

⇒ 4 m = 36, or m = 36 / 4 = 9

or,m = 9

Now, for m = 9, n = 5 x m = 5 x ( 9) = 45

Hence, m = 9, n = 36

Mnenie [13.5K]2 years ago

8 0

Answer: m = 9, n = 45

Step-by-step explanation:

For us to solve the question, we have to find the numbers that represent m and n.

From the question, we were told that the value of n is both 5times as much as the value of m. This means that:

n = 5 × m

n = 5m ............ equation i

We were also informed that n is 36 more than the value of m. This means that:

n = m + 36 ......... equation ii

We can write out both equations

n = 5m ............ equation i

n = m + 36....... equation ii

We substitute n= 5m into equation ii

n = m + 36

5m = m + 36

Collect like terms

5m - m = 36

4m = 36

Divide both side by 4

4m/4 = 36/4

m = 9

Since we know the value of m,we substitute it into any of the equations

n = m + 36

n = 9 + 36

n = 45

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Note: Since you missed to mention the the expression of the function $p(x)$ . After a little research, I was able to find the complete question. So, I am assuming the expression as $p(x)=x^4-9x^2-4x+12$ and will solve the question based on this assumption expression of $p(x)$ , which anyways would solve your query.

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$p\left(-2\right)=0$

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Step-by-step explanation:

As we know that for any polynomial let say $p(x)$ , $c$ is the root of the polynomial if $p(c)=0$ .

In order to find which of the given values will be a root of the polynomial, $p(x)=x^4-9x^2-4x+12$ , we must have to evaluate $p(x)$ for each of these values to determine if the output of the function gets zero.

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Solving for $p\left(-2\right)$

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$p\left(-2\right)=\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Simplify\:}\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12:\quad 0$

$\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Apply\:rule}\:-\left(-a\right)=a$

$=\left(-2\right)^4-9\left(-2\right)^2+4\cdot \:2+12$

$\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}$

$=2^4-2^2\cdot \:9+8+12$

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Therefore, $x=-2$ is a root of the polynomial $p(x)=x^4-9x^2-4x+12$ .

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$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$p\left(2\right)=2^4-9\cdot \:2^2-4\cdot \:2+12$

$p\left(2\right)=2^4-2^2\cdot \:9-8+12$

$p\left(2\right)=2^4+4-2^2\cdot \:9$

$p\left(2\right)=16+4-36$

$p\left(2\right)=-16$

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$p\left(2\right)=-16$

Therefore, $x=2$ is not a root of the polynomial $p(x)=x^4-9x^2-4x+12$ .

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the value of n is both 5times as much as the value of m and 36more than the value of m. What are the values of n and m?​

the value of n is both 5times as much as the value of m and 36more than the value of m. What are the values of n and m?