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2 years ago

Which is the graph of the linear inequality x – 2y > –6?

Mathematics

2 answers:

Zina [86]2 years ago

8 0

Answer:

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Step-by-step explanation:

The first step is writing in the general form of the first order equation

y = f(x) or y > f(x) or y < f(x)

And

f(x) = ax + b

In which a is the slope.

We have that:

x - 2y > -6

-2y > -6 - x

When multiplying by -1, the signal changes, from > to <

2y < x + 6

y < 0.5x + 3

The slope is positive, since 0.5 is positive.

Since it is y lesser than, it is everything below and to the right of f(x) is painted.

The line is dashed because this is just lesser, not lesser or equal.

The correct answer is:

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Marrrta [24]2 years ago

4 0

Answer:

D. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Step-by-step explanation:

Given inequality is x-2y > -6

Now assume that x-2y = -6

The above equation is a line which meets the x-axis at (-6,0) and y-axis at (0,3)

We know that the slope of the line joining the points (a , b) and (c , d) is

$m=\frac{d-b}{c-a}$

now the slope the given line is $m=\frac{3-0}{0-(-6)}$ = $\frac{1}{2}$ .

The given line has a positive slope.

The given two points in all the options is (-4 , 2) and (4 , 4).

For any point above this line say (0 , 4) does not satisfy the given inequality.

So all the points lied below the given line towards the origin satisfy the given inequality.

Now for deciding wether it is a solid or dashed straight line the following is used,

If the inequality is > or < then it is a dashed line otherwise (in the case of ≤ and ≥) it is a solid line.

So from all the above we can conclude that the option is

On a coordinate plane , a dashed straight line which has a positive slope and goes through (-4 , 2) and (4 , 4).Everything below and to the right of the line is shaded.

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What is the radical form of the expression?<br><br> (5x3y4)37<br> ↡

hram777 [196]

Option 4: $\sqrt[7]{125x^9y^{12}}$ is the right answer

Step-by-step explanation:

Given expression is:

$(\sqrt{5x^3y^4})^{\frac{3}{7}$

In order to convert an exponent into radical form, the power should be in the form of 1/x where x is any number

so,

in case of 3/7, it will be broken down

$(\sqrt{5x^3y^4})^{3*\frac{1}{7}}$

The 1/7 will be converted into base of radical while 3 will be he exponent

$\sqrt[7]{(5x^3y^4)^3}$

Multiplying exponents

$=\sqrt[7]{5^3x^{3*3}y^{4*3}}\\=\sqrt[7]{125x^9y^{12}}$

Hence,

Option 4: $\sqrt[7]{125x^9y^{12}}$ is the right answer

Keywords: Radicals, Exponents

Learn more about exponents at:

#LearnwithBrainly

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2 years ago

Jason has 75 feet of wallpaper border. He wants to put up a wallpaper border around his rectangular bed room that measures 12 fe

Rama09 [41]

y don't he just paint it green then he will have a green house and he can let the smoke roll

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2 years ago

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A manager at a local manufacturing company has been monitoring the output of one of the machines used to manufacture chromium sh

denpristay [2]

Answer:

0.682 = 68.2% probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly".

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Normally distributed with a mean of 118 centimeters and a standard deviation of 8 centimeters.

This means that $\mu = 118, \sigma = 8$

Sample of 16 shells

This means that $n = 16, s = \frac{8}{\sqrt{16}} = 2$

What is the probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly?"

This is the pvalue of Z when X = 120 subtracted by the pvalue of Z when X = 116.

X = 120

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{120 - 118}{2}$

$Z = 1$

$Z = 1$ has a pvalue of 0.841

X = 116

$Z = \frac{X - \mu}{s}$

$Z = \frac{116 - 118}{2}$

$Z = -1$

$Z = -1$ has a pvalue of 0.159

0.841 - 0.159 = 0.682

0.682 = 68.2% probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly".

3 0

2 years ago

In a standard game of pool, there are 15 balls labeled 1 through 15. a) In how many ways can the 15 balls be ordered? (5 points)

katovenus [111]

Answer:

Step-by-step explanation:

If there are 15 balls labeled 1 through 15 in a standard football game, the order of arrangement of the 15 balls can be done in 15! ways.

15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2

15! = 1.308*10¹² ways

b) If 3 of the 15 balls are to be chosen if order does not matter, this can be done in 15C3 number of ways. Since we are selecting some balls out of the total number of balls, we will use the concept of combination.

Using the combination formula nCr = n!/(n-r)!r!

15C3 = 15!/(15-3)!3!

15C3 = 15!/12!3!

15C3 = 15*14*13*12!/12!*6

15C3 = 15*14*13/6

15C3 = 455 ways

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2 years ago

here is a list of numbers. 7,12,16,20,27,40,56,64. a work out the difference between the two square numbers in the list. b work

poizon [28]

Answer:

see below

Step-by-step explanation:

7,12,16,20,27,40,56,64

The square numbers are 16 = 4^2 and 64 = 8^2

The difference is 64 - 16 =48

The cube numbers are 27 = 3^3 and 64 = 4^3

64 - 27 =37

4 0

2 years ago

Read 2 more answers