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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

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

$Steps:$

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

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

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

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

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

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

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

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

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Choose the property of addition that justifies the equation.

Studentka2010 [4]

Answer:

Associative

Step-by-step explanation:

Associative property is the one that says that when 3 or more numbers are summed, the grouping of such numbers has no effect on the result of the sum. It is:

(a + b) + c = a + (b + c) for every a, b and c real numbers.

6 0

3 years ago

Maximize the objective function P = 2x + 1.5y for the feasible region shown. State the maximum value for P and the ordered pair

umka2103 [35]

Incomplete question. However, let's assume this are feasible regions to consider:

Points:

- (0, 100)

- (0, 125)

- (0, 325)

- (1, 200)

Answer:

<u>Maximum value occurs at 325 at the point (0, 325)</u>

<u>Step-by-step explanation:</u>

Remember, we substitute the points value for x, y in the objective function P = 2x + 1.5y.

- For point (0, 100): P= 2(0) + 1.5 (100) =150

- For point (0, 125): P= 2(0) + 1.5 (125) =187.5

For point (0, 325): P= 2(0) + 1.5 (325) = 487.5

For point (1, 200): P= 2(1) + 1.5 (200) = 302

Therefore, we could notice from the above solutions that at point (0,325) we attain the maximum value of P.

7 0

3 years ago

Which statement is true about the graph of

Alekssandra [29.7K]

The answer is C it’s vertex is at (2,4) because a quadratic formula is suppose to look like y= a ( x - h )^2 + k and the vertex is (h,k) when you look back at Your question h=-2 and but Bc of the formula then it’ll be h=2 and then k=4 and that’s how you get the vertex from a quadratic formula. Hope this helps :)

6 0

3 years ago

Helps please does that look right to y’all ?

ladessa [460]

<h3>You have the correct answer</h3><h3>Interest rate = 21.5%</h3>

===============================================

Work Shown:

i = P*r*t .... simple interest formula

i = simple interest

i = 2075-1000 = 1075

P = 1000 = amount borrowed (principal)

r = unknown interest rate

t = 5 = time in years

So,

i = P*r*t

1075 = 1000*r*5

1075 = 5000r

5000r = 1075

r = 1075/5000

r = 0.215

r = 21.5%

5 0

3 years ago

Amar keeps picking playing cards out of a standard deck of 52 cards in the hopes that he will

lapo4ka [179]

Answer:

The required probability is, 0.78

Step-by-step explanation:

There are, (52 - 13) = 39 cards which are not spade

5 cards can be chosen from the deck of 52 cards in

$^{52}{C}_{5}$ ways

and out of these 5 choices, none of them will be spade in,

$^{39}{C}_{5}$ ways

So,

P(None of the chosen cards is spade)

= $\frac {^{39}{C}_{5}}{^{52}{C}_{5}}$

$\simeq 0.22$

Hence,

P(out of these 5 choices, at least one card is spade)

$\simeq (1 - 0.22)$

= 0.78

4 0

3 years ago