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3 years ago

Find the value of the variable and MN if N is between M and Q. Round to the nearest hundredth if necessary.

1 answer:

Rudiy273 years ago

3 0

Answer:
MN = 4 units

Explanation:
1- getting the value of m:
We are given that:
NQ = 4m and NQ = 12
This means that:
12 = 4m
$\frac{4m}{4} = \frac{12}{4}$
m = 3

2- getting MQ:
We are given that:
MQ = 5m + 1
We have calculated that:
m = 3
Therefore:
MQ = 5(3) + 1 = 15 + 1 = 16 units

3- getting MN:
We are given that point N is located somewhere between points M and Q.
This means that:
line MQ can be divided into two portions: MN and NQ
This also means that:
length of MQ = length of MN + length of NQ

We have calculated that:
MQ = 16 units
We are given that:
NQ = 12 units
Therefore:
16 = length of MN + 12
length of MN = 16 - 12
length of MN = 4 units

Hope this helps :)

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3 years ago

Factor f(x) = 4x2 + 11x? - 104x + 105 into linear factors given that – 7 is a zero of f(x).

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Answer:

f(x) = 4x + 11x2 - 104x + 105 = (x - 3)(x + 7)(4x - 5)

Step-by-step explanation:

f(x) = 4x^3 + 11x2 - 104x + 105

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-----------------------------------

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Since the remainder is zero (0), we have shown that -7 is a zero of f(x). The coefficients of the quotient (above) are {4, -17, 15}. Let's try factoring the corresponding polynomial again using synthetic division. Start out by using 5 as divisor and determining whether or not the remaindeer is zero:

5 / 4 -17 15

20 15

-------------------------

4 3 30 No, the remainder is 30 and so 5 is not a

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3 / 4 -17 15

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4 -5 0 Yes, the remainder is 0 and so 3 is a root.

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