If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)

Answers

Answer 1

Answer: For this case we have the following functions:
$f (x) = 4 - x ^ 2 g (x) = 6x$
The first thing we must do is subtract both functions.
We have then:
$(g - f) (x) = g (x) - f (x)$
Substituting values we have:
$(g - f) (x) = (6x) - (4 - x ^ 2)$
Rewriting we have:
$(g - f) (x) = x ^ 2 + 6x - 4$
Then, we evaluate the function for x = 3.
We have then:
$(g - f) (3) = 3 ^ 2 + 6 (3) - 4$
Rewriting:
$(g - f) (3) = 9 + 18 - 4 (g - f) (3) = 23$
Answer:
An expression that is equivalent to (g - f) (3) is:
$(g - f) (3) = 23$

Answer 2

Answer:

Answer:

$(g-f)(3)=23$

Step-by-step explanation:

Given : $f(x) = 4 -x^2$ and $g(x) = 6x$

To find : The value of $(g -f)(3)$

Solution :

First we find the value of (g-f)

$(g-f)(x)= g(x)-f(x)$

$(g-f)(x)=6x-(4-x^2)$

$(g-f)(x)=6x-4+x^2$

Now, put the value of x=3

$(g-f)(3)=6(3)-4+(3)^2$

$(g-f)(3)=18-4+9$

$(g-f)(3)=23$

Therefore, $(g-f)(3)=23$

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The wingspan of one butterfly is 1 9/16. The wingspan of another butterfly is 1 5/8 inches. write an inequality comparing the two wingspan

Answers

1 9/16 < 1 5/8 one nine sixteenths is larger than one five eighths

19/16< 15/8 one nine sixteenth is larger than one five eighths

100 students take a course pass/fail. If they pass they get 4 points towards their GPA, if they fail they get 0. If 90 students pass, what is the mean and standard deviation (to 1 decimal) of the points earned?Mean: _______a0

Standard Deviation: _________a1

Answers

Given:
100 students:
pass = + 4
fail =+ 0

90 students passed: 90 * 4 = 360
10 students failed: 10 * 0 = 0

mean: 360 / 100 = 36

standard deviation:
36 - 4 = 32 ⇒ 32² = 1,024 * 90 = 92,160
36 - 0 = 36 ⇒ 36² = 1,296 * 10 = 12,960

92,160 + 12,960 = 105,120
105,120 / 100 = 1,051.20 ⇒ variance

Standard deviation = √1,051.20 = 32.42

Factor the polynomial t2+8t

Answers

Answer: The required factored form of the given polynomial is $t(t+8).$

Step-by-step explanation: We are given to factorize the following quadratic polynomial :

$P=t^2+8t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following property :

$ab+ac=a(b+c).$

From expression (i), we get

$P\n\n=t^2+8t\n\n=t(t+8).$

Thus, the required factored form of the given polynomial is $t(t+8).$

Two solutions were found : t = 8 t = 0

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "t2" was replaced by "t^2".

Step by step solution :Skip Ad
Step 1 :Step 2 :Pulling out like terms :

2.1 Pull out like factors :

t2 - 8t = t • (t - 8)

Equation at the end of step 2 : t • (t - 8) = 0Step 3 :Theory - Roots of a product :

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.2 Solve : t = 0

Solution is t = 0

Solving a Single Variable Equation :

3.3      Solve  :    t-8 = 0

Add  8 to both sides of the equation :
                      t = 8

Two solutions were found : t = 8 t = 0

The US exports 200 billion pounds of coal. How many tons does the US export?

Answers

200 billion is 200,000,000,000 lbs
1 ton is 2,000 lbs.
So 200,000,000,000/2,000 = 100,000,000 tons or 100 million tons.

2,000 = 1 ton . 2,000,000,000/2,000 = 1,000,000,000 or 100 million tons

2y = x + 3 5y = x - 7 What is the solution set of the given system?

Answers

2y = x + 3 then x = 2y - 3
5y = x - 7 then x = 5y + 7

so
2y - 3 = 5y + 7
2y - 5y = 7 + 3
-3y = 10
y = -10/3
y = -3 1/3

2y = x + 3
2 (-10/3) = x + 3
-20/3 - 3 =x
-29/3 = x
-9 2/3 =x
or
x = -9 2/3

solutions: x = -9 2/3 and y = -3 1/3

Answer: the solution set would be {(-29/3, -10/3)}

Step-by-step explanation:

jared bought a package of pens containing 20 pens. If 3/4 of the pens had black ink, how do you determine the number of pens with black ink?

Answers

well 1/4 of the pens would be 5 (20/4=5)
so 3/4 would be 5x3= 15
15 of the pens have black ink

wouldn't you take .75 multiplied by 20? .75 is 3/4 obviously.

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