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3 years ago

Given f(x)=2x^2-3 and g(x) = x+4 What is (fg)(x)?

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

4 0

Answer: $f(g(x))=2x^2+16x+29$

Step-by-step explanation:

$f(x)=2x^2-3\\g(x)=x+4$

f of g of x means "function f, replace x by the value of g of x"

$f(g(x))=2x^2-3\\f(g(x))=2(x+4)^2-3\\f(g(x))=2(x^2+8x+16)-3\\f(g(x))=2x^2+16x+32-3\\f(g(x))=2x^2+16x+29$

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My pigg y bank has only pennies and nicklels in it , and 2/7 of the coins are nickel If i remove 84 pennies then 1/3 of the reme

zubka84 [21]

Answer:

There are 105 pennies in the piggy bank.

There are 42 nickels in the piggy bank.

Step-by-step explanation:

there are:

p pennies in the piggy bank

n nickels in the piggy bank

Then we can define T, the total number of coins, as:

T = p + n

We know that 2/7 of the total number of coins are nickels.

This can be written as:

n = (2/7)*T = (2/7)*(n + p)

And if we remove 84 pennies, 1/3 of the remaining coins are pennies.

This can be written as:

p - 84 = (1/3)*(n + p - 84)

Then we have a system of two equations:

n = (2/7)*(n + p)

p - 84 = (1/3)*(n + p - 84)

Let's solve the system, to do it, we first need to isolate one of the variables in one of the equations.

We can isolate n in the first one, to get:

n = (2/7)*(n + p) = (2/7)*n + (2/7)*p

n - (2/7)*n = (2/7)*p

n*(5/7) = (2/7)*p

n = (7/5)*(2/7)*p = (2/5)*p

n = (2/5)*p

Now we can replace this in the other equation:

p - 84 = (1/3)*(n + p - 84)

p - 84 = (1/3)*( (2/5)*p + p - 84)

Let's solve this for p

p - 84 = (1/3)*( (7/5)*p - 84)

3*(p - 84) = (7/5)*p - 84

3p - 252 = (7/5)*p - 84

3*p - (7/5)*p = 252 - 84

(15/5)*p - (7/5)*p = 168

(8/5)*p = 168

p = (5/8)*168 = 105

There are 105 pennies in the piggy bank.

And we know that:

n = (2/5)*p = (2/5)*105 = 42

There are 42 nickels in the piggy bank.

4 0

3 years ago

The function F(x) = 2x/x+3 is an example of a rational function. True False

PSYCHO15rus [73]

It is true because a rational function is defined as those functions where the variable is placed in the denominator, which must be restricted, because all denominators cannot be equal to zero, other wise it would be undetermined

4 0

4 years ago

Given: ABCD trapezoid BC=1.2m, AD=1.8m AB=1.5m, CD=1.2m AB∩CD=K Find: BK and CK

stepladder [879]

Answer:

The value of BK is 3m and the value of CK is 2.4m.

Step-by-step explanation:

Given information: ABCD trapezoid

, BC=1.2m, AD=1.8m

, AB=1.5m, CD=1.2m

, AB∩CD=K.

Using the given information draw a figure.

Two sides of a trapezoid are parallel.

Since AB∩CD=K, therefore AB and CD are not parallel, because parallel line never intersect.

$AD\parallelBC$

$\angle KBC=\angle KAD$ (Corresponding angles)

$\angle KCB=\angle KDA$ (Corresponding angles)

By AA rule of similarity

$\triangle KBC\sim \triangle KAD$

Corresponding sides of similar triangles are proportional.

$\frac{KB}{KA}=\frac{KC}{KD}=\frac{BC}{AD}$

$\frac{x}{x+1.5}=\frac{y}{y+1.2}=\frac{1.2}{1.8}$

$\frac{x}{x+1.5}=\frac{1.2}{1.8}$

$\frac{x}{x+1.5}=\frac{2}{3}$

$3x=2x+3$

$x=3$

The length of BK is 3 m.

$\frac{y}{y+1.2}=\frac{1.2}{1.8}$

$\frac{y}{y+1.2}=\frac{2}{3}$

$3y=2y+2.4$

$y=2.4$

The length of CK is 2.4 m.

5 0

3 years ago

Read 2 more answers

What is the x for x - 8 = -5

nika2105 [10]

Answer:

Step-by-step explanation:

add 8 to both sides then x=3

5 0

3 years ago

the three median of a triangle intersect as a point. which measurements could represent the segments of one of the medians? 2 an

topjm [15]

2 & 3 is your answer

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4 years ago