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3 years ago

For f(x)=3x+1 and g(x)=x^2-6, find (f o g)(x)

1 answer:

8 0

The answer is: " 3x² − 17 " .
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f(x) = 3x + 1 ;
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If g(x) = x² − 6 ;

then: (f o g)(x) = f(x² − 6) = 3x + 1 ;

= 3(x² − 6) + 1 = 3x² − 18 + 1 ;

= 3x² − 17 .
_______________________________________________

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7. Which two equations are equivalent?

sineoko [7]

Answer:

C. $y=(x-3)^2$ and $y=x^2-6x+9$

Step-by-step explanation:

before answering the problem let us remind the formula for square of sum and differences

$(a+b)^2=a^2+2 \times a \times b + b^2$

$(a-b)^2=a^2-2 \times a \times b + b^2$

We are going to use the above two formulas to solve each part and come to an answer

A. $y = (x + 3)^2$

$(x + 3)^2=x^2+2 \times x \times 3 + 3^2$

$(x + 3)^2=x^2+6x+9$

Hence this option is not correct pair

B. $y = (x-5)^2$

$(x - 5)^2=x^2-2 \times x \times 5 + 5^2$

$(x -5)^2=x^2-10x+25$

Hence this option is also not correct pair

C. $y = (x -3)^2$

$(x - 3)^2=x^2-2 \times x \times 3 + 3^2$

$(x -3)^2=x^2-6x+9$

Hence this option is correct as it have equivalent pair

D. $y = (x + 5)^2$

$(x + 5)^2=x^2+2 \times x \times 5 + 5^2$

$(x + 5)^2=x^2+10x+25$

Hence this option is also not correct pair

6 0

3 years ago

Find Sn for the arithmetic series 5+7+9 + … and determine the value of n for which the series has sum 165.

SVETLANKA909090 [29]

Answer:

see explanation

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$ [2a + (n - 1)d ]

where d is the common difference and a is the first term

here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence

$S_{n}$ = $\frac{n}{2}$ [(2 × 5) + 2(n - 1) ]

= $\frac{n}{2}$ (10 + 2n - 2)

= $\frac{n}{2}$ (2n + 8)

= n² + 4n

When sum = 165, then

n² + 4n = 165 ← rearrange into standard form

n² + 4n - 165 = 0 ← in standard form

(n + 15)(n - 11) = 0 ← in factored form

equate each factor to zero and solve for n

n + 15 = 0 ⇒ n = - 15

n - 11 = 0 ⇒ n = 11

but n > 0 ⇒ n = 11

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3 years ago

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mariarad [96]

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2 years ago

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Form the intersection for the following sets.

Luden [163]

Answer:

Your required answer is option is {20}.

Step-by-step explanation:

Hey, there!!

The reason for above answer is we generally find intersections among the sets by extracting the common elements of the sets.

Here,

R = {10,15,20}

S = {20,25}.

Now, 20 is common im both so,

R intersection S = {20}.

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