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3 years ago

Given that f(x) = 3x + 1 and g(x) = the quantity of 4x plus 2 divided by 3, solve for g(f(0))

Mathematics

2 answers:

Yuliya22 [10]3 years ago

5 0

F(0)=1

g(1)=(4*1+2)/3 = 6/3=2

hope helped

a_sh-v [17]3 years ago

4 0

$f(x) = 3x + 1$
$g(x) = \frac{4x + 2}{3}$

$g[f(0)] = \frac{4[3(0) + 1] + 2}{3}$
$g[f(0)] = \frac{4[0 + 1] + 2}{3}$
$g[f(0)] = \frac{4(1) + 2}{3}$
$g[f(0)] = \frac{4 + 2}{3}$
$g[f(0)] = \frac{6}{3}$
$g[f(0)] = 2$

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Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!

Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

$\frac{3}{x + 4} - \frac{1}{x + 3} = \frac{x + 9}{(x^2 + 7x + 12)}$

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

$\frac{3*(x + 4)}{x + 4} - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

$3 - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x + 3)

$3*(x + 3) - \frac{(x + 4)*(x+3)}{x + 3} = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$3*(x + 3) - (x + 4) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$(2*x + 5) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x^2 + 7*x + 12)

$(2*x + 5)*(x^2 + 7x + 12) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)$

$(2*x + 5)*(x^2 + 7x + 12) = (x + 9)*(x + 4)*(x+3)$

Now we need to solve this:

we will get

$2*x^3 + 19*x^2 + 59*x + 60 = (x^2 + 13*x + 3)*(x + 3)$

$2*x^3 + 19*x^2 + 59*x + 60 = x^3 + 16*x^2 + 42*x + 9$

Then we get:

$2*x^3 + 19*x^2 + 59*x + 60 - ( x^3 + 16*x^2 + 42*x + 9) = 0$

$x^3 + 3x^2 + 17*x + 51 = 0$

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

$x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0$

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

6 0

2 years ago

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miskamm [114]

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8 0

2 years ago

A x + b y is equal to 12

Nikitich [7]

Answer:

y= -a*x + 12

b b

Step-by-step explanation:

ax+by=12 (subtract "ax" from both sides so that the one on the left will become zero and we will have "by" )

by= -ax+12(divide both side by "by" so that we will have the equation as "y=mx+b")

finally the result will be:

y= -a*x + 12

b b

7 0

2 years ago

Consider the next 1000 90% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on whi

Ivenika [448]

Answer:

90% CI expects to capture u 90% of time

(a) This means 0.9 * 1000 = 900 intervals will capture u

(b) Here we treat CI as binomial random variable, having probability 0.9 for success

n = 1000

p = 0.9

For this case, applying normal approximation to binomial, we get:

mean = n*p= 900

variance = n*p*(1-p) = 90

std dev = 9.4868

We want to Find : P(890 <= X <= 910) = P( 889.5 < X < 910.5) (integer continuity correction)

We convert to standard normal form, Z ~ N(0,1) by z1 = (x1 - u )/s

so z1 = (889.5 - 900 )/9.4868 = -1.11

so z2 = (910.5 - 900 )/9.4868 = 1.11

P( 889.5 < X < 910.5) = P(z1 < Z < z2) = P( Z < 1.11) - P(Z < -1.11)

= 0.8665 - 0.1335

= 0.733

6 0

3 years ago

Felix has $50 in a savings account that earns 5% interest, compounded annually. To the nearest cent, how much interest will he e

qwelly [4]

Answer:

$55.13

Step-by-step explanation:

50 * 1.05 = 52.5

We do this step twice because the interest is for 2 years.

52.5 * 1.05 = 55.125

This rounds up to 55.13, your final answer!

8 0

3 years ago