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3 years ago

Evaluate function expression 5xf(1) + 5xg(9)

Mathematics

1 answer:

muminat3 years ago

3 0

Answer:

5x(f+9g)

Step-by-step explanation:

5xf(1)+5xg(9)

Factor out 5.

5(xf+9xg)

Consider xf+9xg. Factor out x.

x(f+9g)

Rewrite the complete factored expression.

5x(f+9g)

Graph if needed:

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A roof on a castle tower is shaped like a cone with a diameter of 12 feet and has a slant height of 13 feet one bundle of Shingl

marissa [1.9K]

Answer:

Step-by-step explanation:

The lateral area of a cone is ...

LA = (π/2)ds

where d is the diameter, and s is the slant height.

The area of this tower roof is about ...

LA = (π/2)(12 ft)(13 ft) = 78π ft² ≈ 245 ft²

About 245/32 = 7.7 bundles of shingles will be required for coverage.

You should buy 8 bundles of shingles to cover the roof.

8 0

3 years ago

Find the indicated quantities for y equals f (x )equals 3 x squared. (A) Simplify StartFraction f (3 plus Upper Delta x )minus

torisob [31]

Answer:

Step-by-step explanation:

Given that a function f(x) is given as

$y=f(x) = 3x^2$

A) $f(x+ \Delta x) = 3((x+ \Delta x)^2=3(x^2+2x \Delta x+\Delta x^2)\\f(x) = 3x^2\\f(x+ \Delta x) -f(x) = 6x \Delta x +\Delta x^2$

Now divide by delta x

$\frac{f(x+ \Delta x) -f(x)}{\Delta x}\\=6x+\Delta x$

B) When delta x tends to 0, this becomes

$6x$

(NOte: This is the derivative of f(x))

5 0

4 years ago

Please help. Not sure how to do this one

Sladkaya [172]

The correct answer is: Option 3: $(hofog)(x)=\frac{x-14}{x+4}$

Step-by-step explanation:

Given

$f(x)=\frac{x-6}{x}\\g(x)=x+4\\h(x)=3x-2$

We have to find

$(hofog)(x)$

This will be equal to:

$h(f(g(x)))$

So we have to find the composition of (fog)(x) first

$(fog)(x) = f(g(x))\\=\frac{x+4-6}{x+4}\\=\frac{x-2}{x+4}$

Now,

$(hofog)(x)=h(f(g(x)))\\=3(\frac{x-2}{x+4})-2\\=\frac{3x-6}{x+4}-2\\=\frac{3x-6-2(x+4)}{x+4}\\=\frac{3x-6-2x-8}{x+4}\\=\frac{x-14}{x+4}$

The correct answer is: Option 3: $(hofog)(x)=\frac{x-14}{x+4}$

Keywords: Composition, Functions

Learn more about function composition at:

#LearnwithBrainly

8 0

4 years ago

PLEASE HELP ASAP!!!!!

erastova [34]

Answer:

B = (3, 3)

Step-by-step explanation:

Since the line segment is fifteen units long, from the looks of it, chopping ⅓ of A's side, led to the ordered pair of (3, 3).

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

7 0

3 years ago

What is the binomial expansion of (x 2y)7? 2x7 14x6y 42x5y2 70x4y3 70x3y4 42x2y5 14xy6 2y7 x7 14x6y 42x5y2 70x4y3 70x3y4 42x2y5

AysviL [449]

You can take x = a, 2y = b and then can apply the binomial theorem.

The expansion of given expression is given by:

Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is

<h3>What is binomial theorem?</h3>

It provides algebraic expansion of exponentiated(integer) binomial.

According to binomial theorem,

$(a+b)^n = \sum_{i=0}^n ^nC_i a^ib^{n-i}$

<h3>How to use binomial theorem for given expression?</h3>

Taking a = x, and b =2y, we have n = 7, thus:

$(x+2y)^7 = \: ^7C_0x^0(2y)^7 + \: ^7C_1x^1(2y)^6 + \: ^7C_2x^2(2y)^5 + \: ^7C_3x^3(2y)^4 + \:^7C_4x^4(2y)^3 + \:^7C_5x^5(2y)^2 + \:^7C_6x^6y^1 + \: ^7C_0x^7y^0\\\\
(x+2y)^7 = 128y^7 + 448xy^6 + 672x^2y^5 + 560x^3y^4 + 280x^4y^3 + 84x^5y^2 + 14x^6y + x^7\\\\
(x+2y)^7 = x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$

Thus, Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is correct.

Learn more about binomial theorem here:

brainly.com/question/86555

6 0

3 years ago