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2 years ago

Write the quadratic equation whose roots are -2 and 1, and whose leading coefficient is 4 .

Mathematics

1 answer:

Kaylis [27]2 years ago

7 0

Answer: the equation is

4x^2 + 4x - 12

Step-by-step explanation:

A quadratic equation is an equation in which the highest power of the unknown is 2.

The general form of a quadratic equation is expressed as

ax^2 + bx + c

Where

a is the leading coefficient

c is a constant

Assuming we want to write the quadratic equation in x, from the information given, the roots which are given are -2 and 1 and the leading coefficient is 4.

Therefore, the linear factors of the quadratic equation will be (x+2) and (x-1)

the equation becomes

(x+2)(x-1)

= x^2 - x +2x - 3

= x^2 + x - 3

Given a leading coefficient of 4, we will multiply the quadratic expression by 4. It becomes

4(x^2 + x - 3)

= 4x^2 + 4x - 12

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Find the distance between (2, 2) and (-4, 4). Round answer to the nearest tenth.

Naya [18.7K]

Answer:

6.3

Step-by-step explanation:

First off, we need the distance formula, which is:

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

If we plug in the points, we get:

$\sqrt{(-4 - 2)^2 + (4 - 2)^2}$

If we simplify everything under the square root, we get:

$\sqrt{(-6)^2 + (2)^2}$

$\sqrt{36 + 4}$

$\sqrt{40}$

In decimal, the answer is 6.3

6 0

2 years ago

Hey, Its the same person. This is Algebra 2. Please Help!

suter [353]

Answer:

first option

Step-by-step explanation:

Given

f(x) = $\frac{2x^2+5x-12}{x+4}$ ← factorise the numerator

= $\frac{(x + 4)(2x-3)}{x+4}$ ← cancel (x + 4) on numerator/ denominator

= 2x - 3

Cancelling (x + 4) creates a discontinuity ( a hole ) at x + 4 = 0, that is

x = - 4

Substitute x = - 4 into the simplified f(x) for y- coordinate

f(- 4) = 2(- 4) - 3 = - 8 - 3 = - 11

The discontinuity occurs at (- 4, - 11 )

To obtain the zero let f(x) = 0, that is

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = $\frac{3}{2}$

There is a zero at ( $\frac{3}{2}$ , 0 )

Thus

discontinuity at (- 4, - 11 ), zero at ( $\frac{3}{2}$ , 0 )

7 0

2 years ago

HELP NEED ASAP FOR TOMORROW ITS FOR MY HOMEWORK!! ILL MARK BRAINLIEST IF RIGHT!!

Slav-nsk [51]

Answer:

y ≥ -x +2

Step-by-step explanation:

The solid line has a slope of -1 and a y-intercept of 2, so its equation in slope-intercept form is ...

y = -x +2

The shaded area is above this line, and the line is part of the solution set, so we want an inequality that has "y" and the comparison symbol in this order: "y ≥" or "≤ y".

We already have an equation with "y" on the left, above, so we just need to introduce the comparison symbol:

y ≥ -x +2

Another way to write this is ...

x + y ≥ 2

4 0

2 years ago

The sum of two numbers is at most 12, and the sum of 3 times the first number and 8 times the second number is at least 48 selec

Sever21 [200]

Answer:

(4,8)

Step-by-step explanation:

4 + 8 = 12

3(4) + 8(8)

= 12 + 64

= 76

6 0

2 years ago

Nine times a number decreased by 16

Setler79 [48]

Answer:

9 · x - 16

Explanation:

Nine times a number: 9 · x

Decreased by 16: - 16

Put them together: 9 · x - 16

7 0

2 years ago