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lions [1.4K]
2 years ago
5

What is the solution set to the inequality 5(x - 2)(x + 4) > 0?

Mathematics
1 answer:
Butoxors [25]2 years ago
8 0

Answer:

You selected the correct answer: {x | x <<em> </em>-4 or x > 2}

Step-by-step explanation:

5(x - 2)(x + 4) > 0

Use FOIL method to expand (x - 2)(x + 4):

5(x^{2} + 2x - 8) > 0

Distribute 5 into (x^{2} + 2x - 8)

5x^{2} + 10x - 40 > 0

Divide all terms by 5 from both sides of the inequality:

\frac{5x^{2}}{5}  + \frac{10x}{5}  - \frac{40}{5} > \frac{0}{5}

x^{2} + 2x - 8 > 0

Factor the trinomial:

(x + 4) ( x - 2)  > 0

x < -4 or x > -2

Therefore, the solution set to the inequality is {x | x < -4 or x > 2}

<em>Interval notation:  </em>(-∞, -4) ∪ (2, ∞)

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The longer leg of a right triangle is 3 inches more than the length of the shorter leg tripled. the hypotenuse is 3 inches less
lukranit [14]
We have this equation.
A²+B²=C²
We have bits of information that'll help us simplify the equation so there's only one variable.
The longer leg, A, is 3 inches more than the length of the shorter leg, B, tripled.
A=3B+3
Let's plug that in.
(3b+3)²+B²=C²
The hypotenuse, C, is 3 inches less than four times the length of the shorter leg. C=4B-3
Let's plug that in.
(3b+3)²+B²=(4B-3)²
Let's solve.
9B²+18B+9+B²=16B²-24B+9
10B²+18B+9=16b²-24b+9
Let's subtract 9 from both sides.
10b²+18b=16b²-24b
Let's subtract 10b² from both sides.
18b=6b²-24b
Let's add 24b from both sides.
42b=6b²
Let's divide each side by 6.
7b=b²
With this, you can tell that b is 7 since it times 7 equal itself squared.
The shorter leg is 7 inches.
Now, let's look back at the bits of information.
The longer leg of a right triangle is 3 inches more than the length of the shorter side tripled.
3(7)+3=24
So, the longer side is 24. We can either use the other information or plug it into the equation. We can do both. 
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√625=25
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4 0
3 years ago
Find the result when 5 + 2 is subtracted from 9.
Kamila [148]

Answer:

it is 2

Step-by-step explanation:

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2 years ago
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VMariaS [17]

Answer:

a. 1/13

b. 1/52

c. 2/13

d. 1/2

e. 15/26

f. 17/52

g. 1/2

Step-by-step explanation:

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P(7) = 4/52 = 1/13

b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:

P(6 of clubs) = 1/52

c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen​​​​​​​​​​​ is:

P(5 or Q) = P(5) + P(Q)

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d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:

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P(R or J) = P(R) + P(J)

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g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:

P(D or S) = P(D) + P(S)

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P(D or S) = 1/2

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