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3 years ago

Given the functions f(x) = 10x + 25 and g(x) = x+8, which of the following functions represents f(g(x)] correctly?

Mathematics

1 answer:

victus00 [196]3 years ago

3 0

Answer:

g(x + 8) = 10x + 105 wherever you see it among your answers.

Step-by-step explanation:

I think I have enough here that I can answer the question, but you should always put in your givens.

f(x) = 10x + 25 Put g(x) where you see x in f(x)

f(g(x)) = 10(g(x) + 25 Put the value for g(x) where you see g(x)

f(x+8) = 10(x + 8) + 25 This might be the answer

From here it is a guess.

f(x+8) = 10x + 80 + 25 Combine the like terms

f(x+8) = 10x + 105

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3 years ago

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Given that P = (-7, 16) and Q = (-8, 7), find the component form and magnitude of vector QP .

Katyanochek1 [597]

Answer:

a)The component form is

$\vec {QP}=\binom{ - 1}{ - 8}$

b)The magnitude is √65

c) <2,14>

Step-by-step explanation:

Recall that:

$\vec {QP}=\vec {OP}-\vec{OQ}$

We substitute the position vectors to get:

$\vec {QP}=\binom{ - 8}{7} - \binom { - 7}{15}$

We subtract the corresponding components to obtain:

$\vec {QP}=\binom{ - 8 - - 7}{7 - 15}$

This gives:

$\vec {QP}=\binom{ - 8 + 7}{7 - 15}$

This simplifies to:

$\vec {QP}=\binom{ - 1}{ - 8}$

The magnitude of a vector in the component form:

$\binom{x}{y}$

$\sqrt{ {x}^{2} + {y}^{2} }$

This means:

$|\vec {QP}|= \sqrt{ {( - 1)}^{2} + {( - 8)}^{2} }$

This simplifies to:

$|\vec {QP}| = \sqrt{ 1 + 64 }$

$|\vec {QP}| = \sqrt{ 65 }$

c) We have the vectors u = <4, 8>, v = <-2, 6>.

We want to find:

u+v

This implies that:

u+v=<4,8>+<-2,6>

We add the corresponding components to get;

u+v=<4+-2,8+6>

This simplifies to:

u+v=<2,14>

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3 years ago