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svetlana [45]
3 years ago
6

If f(x) = x^2 - 4(x) + 6, find x if f(x) = 27

Mathematics
1 answer:
Elena L [17]3 years ago
4 0

Answer:

x = - 3 or x = 7

Step-by-step explanation:

Given

f(x) = x² - 4x + 6

If f(x) = 27, then equating gives

x² - 4x + 6 = 27 ( subtract 27 from both sides )

x² - 4x - 21 = 0 ← in standard form

Consider the factors of the constant term ( - 21) which sum to give the coefficient of the x- term ( - 4)

The factors are - 7 and + 3, since

- 7 × 3 = - 21 and - 7 + 3 = - 4, hence

(x - 7)(x + 3) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 7 = 0 ⇒ x = 7

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Answer:

C

Step-by-step explanation:

x - 7 > -6

x > -6 + 7

x > 1

• We change the inequality sign if we multiply or divide a negative number from both sides. But since it’s positive and we added it we won’t change the inequality sign.

7 0
2 years ago
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Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not corre
Lady bird [3.3K]

Answer:

Solution : Third Option

Step-by-step explanation:

The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.

\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}

Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.

Therefore, the third option is a solution to the system.

6 0
3 years ago
Whats this answer i need it fast uwu
IrinaVladis [17]
Find slope (y2-y1)/(x2-x1)
Pick points: (1,10) , (2,8)
(8-10)/(2-1) = -2/1 = -2
Y = -2x + b
10 = -2 + b, b = 12
It would be the first response
12 = initial while -2 is rate of change
3 0
2 years ago
Identify the diameter of the circular base created by folding the figure into a right cone. HELP ASAP PLEASE!!
Akimi4 [234]

let's notice something, we have a circle with a radius of 12 and one 90° sector is cut off, so only three 90° sectors of the circle are left shaded, so namely the cone will be using 3/4 of that circle.

think of it as, this shaded area is some piece of paper, and you need to pull it upwards and have the cutoff edges meet, and when that happens, you'll end up with a cone-shaped paper cup, and pour in some punch.

now, once we have pulled up the center of the circle to make our paper cup, there will be a circular base, its diameter not going to be 24, it'll be less, but whatever that base is, we know that is going to have the same circumference as those in the shaded area.  Well, what is the circumference of that shaded area?

\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies C=2\pi 12\implies C=24\pi \implies \stackrel{\textit{three quarters of it}}{24\pi \cdot \cfrac{3}{4}} \\\\\\ 6\pi \cdot 3\implies 18\pi

well then, the circumference of that circle at the bottom will be 18π, so, what is the diameter of a circle with a circumferenc of 18π?

\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=18\pi \end{cases}\implies 18\pi =2\pi r\implies \cfrac{18\pi }{2\pi }=r\implies 9=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{diameter is twice the radius}}{d=18}~\hfill

3 0
3 years ago
A square classroom has a wall that is 21 feet long. What is the area of the classroom?
Rasek [7]

<u>Answer and Step-by-Step explaination:</u>

Area =Length time Width

Area= 21*21

Area=441

6 0
3 years ago
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