All categories

3 years ago

What are the solutions of the inequality? -2(3x + 2) ≥ -6x - 4 Question 2 options: all real numbers x ≤ 6 no solution x ≥ 0

1 answer:

8 0

$Solution, -2\left(3x+2\right)\ge \:-6x-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:True\quad \forall \:x\in \mathbb{R}\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$Steps:$

$-2\left(3x+2\right)\ge \:-6x-4$

$\mathrm{Expand\:}-2\left(3x+2\right),\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac,\\a=-2,\:b=3x,\:c=2,\\-2\cdot \:3x+\left(-2\right)\cdot \:2,\\\mathrm{Apply\:minus-plus\:rules},\\+\left(-a\right)=-a,\\-2\cdot \:3x-2\cdot \:2,\\\mathrm{Simplify}\:-2\cdot \:3x-2\cdot \:2,\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6,\\-6x-2\cdot \:2,\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4,\\-6x-4,\\-6x-4\ge \:-6x-4$

$\mathrm{Add\:}4\mathrm{\:to\:both\:sides},\\-6x-4+4\ge \:-6x-4+4$

$\mathrm{Simplify},\\-6x\ge \:-6x$

$\mathrm{Add\:}6x\mathrm{\:to\:both\:sides},\\-6x+6x\ge \:-6x+6x$

$\mathrm{Simplify},\\0\ge \:0$

$\mathrm{Therefore,\:the\:final\:solution\:is},\\True\quad \forall \:x\in \mathbb{R}$

$Or\:No\:Solution\:x\geq 0$

You might be interested in

Scientists believe there is a link between ambient temperature and damage to a head gasket on a car. Using the provided informat

Alex

Is there picture cause I cant draw it but ik how to do scattered plots

4 0

3 years ago

Read 2 more answers

Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that

AfilCa [17]

Answer:

They should put $6750 in the bank account and $20,250 in the stock fund.

Step-by-step explanation:

Consider the provided information that Avery and Caden have saved $27000.

Let x is the money deposit in the bank and y is the money deposit in stock fund.

Therefore,

x + y = 27000

x = 27000 - y

The bank account will pay 2.4% annual interest.

$\frac{2.4}{100}x+x=1.024x$

Stock fund pays 7.2% annual interest.

$\frac{7.2}{100}y+y=1.072y$

Therefore,

1.024 x + 1.072 y = 1.06 × 27000

Substitute the x = 27000 - y in above equation.

1.024 (27000 − y) + 1.072 y = 1.06 × 27000

27648 − 1.024 y + 1.072 y = 28620

0.048 y = 28620-27648

0.048 y = 972

y = 20250

Now, substitute the y = 20250 in x = 27000 - y.

x = 27000 − 20250

x = 6750

Hence, they should put $6750 in the bank account and $20,250 in the stock fund.

7 0

3 years ago

1 p

dlinn [17]

Answer:

V = pi * R^2 * h

R = (V / (pi * h))^1/2 = (141.3 / (3.14 * 5))^1/2 = 3 cm

8 0

3 years ago

Determine the next step for solving the quadratic equation by completing the square.

Studentka2010 [4]

Answer:

The solutions are $x=\frac{1+\sqrt{7}}{2}$ and $x=\frac{1-\sqrt{7}}{2}$

Step-by-step explanation:

we have

$0=-2x^{2}+2x+3$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$-3=-2x^{2}+2x$

Factor the leading coefficient

$-3=-2(x^{2}-x)$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$-3-0.5=-2(x^{2}-x+0.5^{2})$

$-3.5=-2(x^{2}-x+0.5^{2})$

Rewrite as perfect squares

$-3.5=-2(x-0.5)^{2}$

$7/4=(x-0.5)^{2}$

square root both sides

$x-0.5=(+/-)\sqrt{\frac{7}{4}}$

$x-\frac{1}{2}=(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1}{2}(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1+\sqrt{7}}{2}$

$x=\frac{1-\sqrt{7}}{2}$

4 0

3 years ago

Which statement about the following equation is true?

spayn [35]

The given expression is

$3x^2 -8x +5 = 5x^2$

We have to find the discriminant first . And for that, first we need to move whole terms of the left side to right side, that is

$5x^2 -3x^2 +8x -5=0$

$2x^2+ 8x -5 =0$

The formula of discriminant is

$D =b^2 -4ac$

Substituting the values of a,b and c, we will get

$D = 8^2 -4(2)(-5)=64+40 = 104$

And since the discriminant is greater than 0, or it is positive so we have two real roots.

Therefore the correct option is B .

7 0

3 years ago

Read 2 more answers