MATHEMATICS HIGH SCHOOL

Complete the equation to show two equivalent expressions.

g2 – 4g – 21 = (g – )(g + )

Answers

Answer 1

Answer:

Answer:

$g^2-4g-21=(g-7)(g+3)$

Step-by-step explanation:

To complete the left side of the equation, we need to bring it to the form

$(g-a)(g+b)$

expanding this expression we get:

$g^2+bg-ag-ab$

$g^2+(b-a)g-ab$

Thus we have

$g^2-4g-21=g^2+(b-a)g-ab$

from here we see that for both sides of the equation to be equal, it must be that

$b-a=-4$

$-ab=-21$ .

Getting rid of the negative signs we get:

$a-b=4$

$ab=21$

At this point we can either guess the solution to this system (that's how you usually solve these types of problems) or solve for $a$ and $b$ systematically.

The solutions to this set are $a=7$ and $b=3$ . (you have to guess on this—it's easier)

Therefore, we have

$(g-a)(g+b)=(g-7)(g+3)$

which completes our equation

$\boxed{ g^2-4g-21=(g-7)(g+3)}$

Answer 2

Answer:

Answer: -7 and +3

did the assignment

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√110 to the nearest hundredth
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Please help! Correct answer only!For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?$ ___
⅘(10x - 15)+7x >15x-9x

How do I solve n+6 for n=9

Answers

Answer:

Step-by-step explanation:

n + 6

for

n = 9

then:

9 + 6 = 15

Step-by-step explanation:

n=9

n+6=9+6=15

mark as brainlist answer

According to the EPA, about 40 million U.S. tons of hazardous waste is produced each year. If individual household waste makes up 1.6 million tons of this waste, what percent of the total hazardous amount produced is household waste? A. 0.04% B. 0.03% C. 0.25% D. 2.5% E. 4%

Answers

Answer:

C.0.25%

Step-by-step explanation:

40/1.6=25

Then convert to percentage value by moving the decimal 2 places to the left.

25 turns into 0.25.

0.05 is ten times as much as

Answers

0.5
you just need to move the dot to the right

.05 is ten times more than a number so if x is the number, 10x=.05
x=.005

An investor predicts that next month, 1 ton of coal will cost $53.00, with a 3% margin of error. Based on the prediction, what is the range of possible costs, in dollars per ton, for the coal?

Answers

Answer:

"Cost would be between $51.41 and $54.59"

Step-by-step explanation:

3% margin of error means that the cost can be

3% lower, or
3% higher

First we need to find 3% of $53 and then we will "add" and "subtract" from $53 to get the range of values of cost.

To get 3% of $53, we need to convert the percentage to decimal and multiply with $53. To get percentage to decimal, we divide by 100, so we have:

3/100 = 0.03

Now,

0.03 * 53 = $1.59

The range would be:

$53 + $1.59 = $54.59

and

$53 - $1.59 = $51.41

Cost would be between $51.41 and $54.59

John and Julie are planning to have a new house built the architect designs a house instant them the blueprints skilled at the art architect used on the blueprints is 2 1/2 inches equals 10 feet the living room what are the actual dimensions of 12‘ x 16‘ what are the dimensions on the blueprints

Answers

Answer:

3"x4

Step-by-step explanation:

The symbol for a foot is "ft", sometimes denoted by a prime(') , also, the inch is denoted by a double prime(").

Given

2 1/2inces (2.5") blue print represents 10ft living room

We are told that the dimension of the room on the blueprint is

12'x16'

Let us convert 12' to inches

2.5" represents 10'

X ' will be 12'

Cross multiplying

X=(2.5*12)/10

X=3"

Let us convert 16' to inches

2.5" represents 10'

Y ' will be 16'

Cross multiplying

Y=(2.5*16)/10

Y=4"

the dimension of the blue print is

3"x4"

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

Answers

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