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PolarNik [594]
3 years ago
9

What is the solution to the compound inequality in interval notation?

Mathematics
2 answers:
mars1129 [50]3 years ago
6 0

Answer:  The correct option is

(D) (−∞, −5] or (0, ∞).

Step-by-step explanation:  We are given to select the solution to the following inequality in interval notation :

2(x+3)>6~~\textup{or}~~2x+3\leq-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

To find the correct solution, we need to solve both the inequalities in (i) separately.

The solution of (i) is as follows :

2(x+3)>6\\\\\Rightarrow x+3>\dfrac{6}{2}\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0

and

2x+3\leq -7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq-10\\\\\Rightarrow x\leq-\dfrac{10}{2}\\\\\Rightarrow x\leq -5.

That is, the solution is given by

x\epsilon (-\infty,-5]~or~(0,\infty).

Thus, (D) is the correct option.

Eduardwww [97]3 years ago
5 0
First solve the 2 inequalities for x:-

x > 0  or x <= -5


The last choice is the correct one.
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(y^2+6)^2

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AB is included between<br><br> A. BC and AC<br> B. C. &lt; A and D. AB and BC
Novay_Z [31]

Answer:

Option C.

Step-by-step explanation:

By the property of unique triangles (ASA), one side is included between the two angles.

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2 years ago
The ratio of the price of a tv to the price of a computer is 13:15 if the tv 400 dollars cheaper than the computer, how much doe
Basile [38]

The computer cost is $3000

Step-by-step explanation:

The given is:

  • The ratio of the price of a tv to the price of a computer is 13 : 15
  • The tv 400 dollars cheaper than the computer

We need to find the cost of the computer

Assume that the price of the computer is $x

∵ The ratio between the prices of the tv and the computer is 13 : 15

∵ The price of the computer is $x

∵ The price of the tv 400 dollars cheaper than the computer

- That means the price of the tv is less than the price of the

  computer by $400

∴ The price of the tv is $(x - 400)

By using the ratio method

→  tv              :    computer

→  13              :    15

→  (x - 400)   :    x

By using the cross multiplication

∴ 15(x - 400) = 13(x)

- Simplify the left hand side

∴ 15x - 6000 = 13x

- Add 6000 to both sides

∴ 15x = 13x + 6000

- Subtract 13x from both sides

∴ 2x = 6000

- Divide both sides by 2

∴ x = 3000

The computer cost is $3000

Learn more:

You can learn more about the ratio in brainly.com/question/4847829

#LearnwithBrainly

5 0
2 years ago
Helpie plz my teacher wont answer me
GaryK [48]

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Step-by-step explanation:

-7(-7d - 6) - 4d

49d + 42 - 4d

49d - 4d + 42

45d + 42

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3 years ago
When looking at attendance data for 2014-2015 school year, a principal graphed number of tardies, x, a student had compared to t
svetlana [45]

Answer:

a. Linear relationship.

Step-by-step explanation:

Negative correlation describes a relationship of two variables in which one variable increases while the other decreases. It shows the the level at which the variables moves in opposite directions to each other.

In the given example, the two variables are inversely proportional. On plotting the variables against each other, it would have a downward slope. The correlation coefficient, r = -0.94, shows that the number of tardies of a student, x, and grade point average (GPA), y, have a linear relationship. As correlation coefficient is a measure of linear relationship, which could be negative, zero, or positive.

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