6. What is the solution set of the inequality below? *-x + 2>-72O x5-82O x2-8O x2-9/2O X28

Mathematics High School

6. What is the solution set of the inequality below? *х-x + 2>-72O x5-82O x2-8O x2-9/2O X28

6. What Is The Solution Set Of The Inequality Below? *-x + 2>-72O X5-82O X2-8O X2-9/2O X28

Answers

Answer 1

[tex]\frac{x+2}{2}\ge-7-\frac{x}{2}[/tex]

Multiply both sides by 2:

[tex]x+2\ge-14-x[/tex]

Add x to both sides:

[tex]2x+2\ge-14[/tex]

Subtract 2 from both sides:

[tex]2x\ge-16[/tex]

Divide both sides by 2:

[tex]\begin{gathered} x\ge-\frac{16}{2} \\ x\ge-8 \\ \end{gathered}[/tex]

Answer:

[tex]x\ge-8[/tex]

Related Questions

4(-8x + 5) - (-33x - 26)

Answers

Answer:

x+46

Step-by-step explanation:

Distribute

Combine like terms

6b³ +16b² -15b-40
Factor

Answers

Answer:

(2[tex]b^{2}[/tex] - 5) (3b + 8)

Step-by-step explanation:

First factor out 2[tex]b^{2}[/tex] from the first set of parentheses and -5 from the second

2[tex]b^{2}[/tex] ( 3b + 8) - 5 (3b + 8)

Next factor out (3b + 8)

(2[tex]b^{2}[/tex] - 5) (3b + 8)

Mia is factoring the polynomial
x^2+4x−12. She uses the steps shown.

x^2+4x−12
Step 1
x^2+6x−2x−12
Step 2
(x^2+6x)−(2x+12)
Step 3
x(x+6)−2(x+6)
Step 4
(x+6)(x+2)
In which step did Mia make an error?

Answers

Answer:

Step 4

Step-by-step explanation:

Mia made a mistake in step 4.

Step3: x(x + 6) -2(x + 6)

In both terms, (x + 6) is common.

Step 4: When we take (x + 6) out, it will be (x + 6 ) (x - 2)

Find the absolute value of x
4-|x|=1

Answers

Answer:

Step-by-step explanation:

Absolute value is how far away the value is from 0. The only value of x that would make this equation true is 3.

On a plane, 2 men had 135 kilograms of luggage added together. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage. The charge was at a flat rate. If all of the luggage belonged to one person, the ecess luggage charge would have been $8.10. At most, how many kilograms of luggag is each person permitted to bring onto the plane free of an additional charge?A. 55 kilogramsB. 50 kilogramsC. 45 kilogramsD. 40 kilograms

Answers

Let's call the amount of lugagge the first men had as x, and the amount of lugagge the second men had as y.

Since both had to pay for excess of luggage, both had the permitted amount of luggage plus an extra amount. Let's call the permitted amount as a, the extra the first men had as z, and the extra the second man had as w. Then, our total amounts of luggage can be rewritten as

[tex]\begin{gathered} x=a+z \\ y=a+w \end{gathered}[/tex]

Since their total amount of luggage added together was 135 kg, this gives to us the following equation

[tex]x+y=135[/tex]

The charge for the extra luggage is a flat rate, let's call it r, then, the price you pay for the extra luggage is given by the product between this rate and the amount of extar luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage, therefore

[tex]\begin{gathered} zr=1.35 \\ wr=2.70 \end{gathered}[/tex]

If we divide one equation by the other, we can write the excess of luggage of one as a function of the other.

[tex]\begin{gathered} \frac{zr}{wr}=\frac{1.35}{2.70} \\ \frac{z}{w}=\frac{1}{2} \\ w=2z \end{gathered}[/tex]

If all of the luggage belonged to one person, this person would have to pay $8.10 for the excess. If we call the excess of this person as p, the amount of luggage this person had would be

[tex]a+p=135[/tex]

Using the "rate formula" we created before, we can also write p as a function of z.

[tex]pr=8.10\Rightarrow\frac{pr}{zr}=\frac{8.10}{1.35}\Rightarrow p=6z[/tex]

Rewritting all the total amounts, we have

[tex]\begin{gathered} a+6z=135 \\ a+2z=y \\ a+z=x \end{gathered}[/tex]

If we add the equations for x and y together, we have

[tex]\begin{gathered} (a+z)+(a+2z)=(x)+(y) \\ a+z+a+2z=x+y \\ 2a+3z=x+y \end{gathered}[/tex]

From the first equation, we know that the sum between both total amounts of luggage is equal to 135.

[tex]\begin{cases}x+y=135 \\ 2a+3z=x+y\end{cases}\Rightarrow2a+3z=135[/tex]

Now, we have two equations for our two variables.

[tex]\begin{cases}2a+3z=135 \\ a+6z=135\end{cases}[/tex]

If we multiply the first equation by 2, and subtract the second equation, we're going to get a new equation only for a(the amount in kilograms of permitted luggage).

[tex]\begin{gathered} 2\cdot(2a+3z)-(a+6z)=2\cdot(135)-135 \\ 4a+6z-a-6z=270-135 \\ 3a=135 \\ a=45 \end{gathered}[/tex]

The amount of luggage permitted to bring onto the plane for free is 45 kilograms.

Sum of 8 consecutive numbers is 124. Find the numbers

i will mark you as brainliest for giving breif explanation step by step

Answers

Answer:

x = 12

Step-by-step explanation:

Be the 8 consecutive numbers like this:

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) = 124

8x + 28 = 124

8x = 124 - 28

8x = 96

x = 12

Find the area of square plot of land whose each side measures 17/2

Answers

The area of the land is 289/4 square units

What are areas?

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

How to determine the area of the shape?

The given parameters are

Shape = Square

Side length = 17/2

The area of a square shape is

Area = Side length^2

So, we have

Area = (17/2)^2

Evaluate the exponent

Area = 289/4

Hence, the area of square plot of land whose each side measures 17/2 is 289/4 square units

Answers

Answer:

$3,690

Explanation:

The shipping charge for all 3 TVs =$90

Cost of a TV = $1200

Therefore, the cost of 3 TVs = 3 x $1200 =$3,600

The total amount paid by Gordon will be:

=$3600+90

=$3,690

(9) 0.5= A. 3 B. 4.5 C. 1/81

Answers

The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]. The evaluated expression is 3a+4.5b+c=40.5

Given that,

The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]

We have to evaluate the expression

Evaluating an algebraic expression involves determining its value when a particular integer is substituted for a variable. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

Take,

0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]

0.5×81=a×3+b×4.5+c

40.5=3a+4.5b+c

The expression can be written in 4 ways

1st- 3a+4.5b+c=40.5

2nd- a=[tex]\frac{40.4-4.5b-c}{3}[/tex]=13.4-1.5b-c (this is the expression with subject a)

3rd- b= [tex]\frac{40.5-3a-c}{4.5}[/tex]=9-1.6a-c (this is the expression with subject b)

4th- c= 40.5-3a-4.5b (this is the expression with subject c)

Therefore, The evaluated expression is 3a+4.5b+c=40.5

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What is the percentage of 150 out of 329.5 million?

Answers

The number 150 is 0.0000455 % out of 329.5 million

How to determine the percentage?

The statement is given as

the percentage of 150 out of 329.5 million

The percentage can be calculated as

Percentage = 150 out of 329.5 million *100%

Express as fraction

So, we have

Percentage = 150/329.5 million *100%

Rewrite as

Percentage = 150 *100/329.5 million %

Evaluate the product

Percentage = 15000/329.5 million %

Evaluate the quotient

Percentage = 0.0000455 %

Hence, the percentage of 150 out of 329.5 million is 0.0000455 %

Answers

Answer:8.7:1.2

Step-by-step explanation: divide both by 3

Solve the following equation: 2=|3x-3|

Answers

Answer:

x = 5/3, 1/3

x=1.6 repeating ,0.3 repeating

A line has a slope of 1/4 and includes the points (-6, -7) and (z, -5) what is the value of z

Answers

2

Slope is rise divided by run, which is (change in y) divided by (change in x).

See details:

the value of z is 2

The table shows information about the
masses of some dogs.
a) Work out the minimum number of
dogs that could have a mass of more than 27 kg.
b) Work out the maximum number of
dogs that could have a mass of more than 27 kg.

Answers

a) The minimum number of dogs that could have a mass of more than 27 kg is 4.

b) The maximum number of dogs that could have a mass of more than 27 kg is 17.

The given table shows information about the masses of some dogs.

a) Because we need the minimum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the minimum value out of 13 and 4 is 4.

b) Because we need the maximum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17

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Answer:

Step3

-by-step explanation:

Find the sum of (2.8 × 10−9) and (9.1 × 10−10). Write the final answer in scientific notation.

11.9 × 10−19
1.19 × 10−18
3.71 × 10−10
3.71 × 10−9

Answers

Answer: [tex]3.71 \times 10^{-9}[/tex]

Step-by-step explanation:

[tex](2.8 \times 10^{-9})+(9.1 \times 10^{-10})\\\\=10^{-10}(28+9.1)\\\\=10^{-10}(37.1)\\\\=3.71 \times 10^{-9}[/tex]

Answer:

The answer is C: 3.71 × 10−9.

Step-by-step explanation:

Question 1 (10 points)

Answers

[tex] = 2^{3} \\ = 2 \times 2 \times 2 \\ = (2 \times 2) \times 2 \\ = 4 \times 2 \\ = 8[/tex]

ATTACHED IS THE SOLUTION

LAST OPTION IS THE ANSWER.

-(8-²)=

Evaluate the expressions

Answers

After evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which means 2 times x plus 3.

So, -(8⁻²):

Now, evaluate -(8⁻²) as follows:

-(8⁻²)-(1/64)- 1/64

Therefore, after evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

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Hello, please I need the right answer for this:

Answers

Answer: (4) [tex]y=2x[/tex]

When you look at the table, you can see that the y values are double the x values they are associated with. Therefore, to get to the y value, the x values must be multiplied by 2, which would be the equation [tex]y=2x[/tex]

Michelle has an average score of 70 for three tests.
What must she score on the next test to increase her average to 74?

Answers

Answer:

Step-by-step explanation:

average is calculated as

average = [tex]\frac{sum}{count}[/tex]

given her average was 70 in 3 tests , then

[tex]\frac{sum}{3}[/tex] = 70 ( multiply both sides by 3 )

sum = 210

let the score she must get in test 4 be x for an average of 74 , then

[tex]\frac{210+x}{4}[/tex] = 74 ( multiply both sides by 4 )

210 + x = 296 ( subtract 210 from both sides )

x = 86

she must score 86 in her next test

Answer:

[tex]\frac{x}{3}[/tex]= 70

x=210

[tex]\frac{210+x}{4}[/tex] = 74

210+x=74x4

210+x=296

x=296-210

x=86

Plss mark as brainliest

What is the slope of the ramp from the ground to the landing? Write your answer as a fraction with a whole-number numerator and denominator.

Answers

The slope of the ramp is m = h/√(r² - h²).

What is mean by square root of a number?

A square root of a number is a value that multiplied by itself gives the same number.

Let h = height of the landing.

And, r = the length of the ramp.

Then, the length from the ground where the ramp touches it, to the ground directly below the landing is

⇒ √(r² - h²)

And, The slope of the ramp is m = h/√(r² - h²)

For example, if the ramp is 5 meters long and the landing height is 3 meters high, the slope of the ramp is 3/4.

As, Slope of the ramp (m) = 3/√(25-9) = 3/√16 = 3/4

Thus, The slope of the ramp is m = h/√(r² - h²).

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help me i need help.

Answers

Answer:108 inches

Step-by-step explanation:

to find the area of one of the right triangles you do.

base = 6/2 =3

3x6=18

18/2=9

there are 8 right triangles so you would do

9x8 = 72.

then you would add 72 and the area of the square in the middle

6x6=36

36+72= 108

so Area of SA = 108 inches ^2

twice the diffrence of a number and 2 equals 8

Answers

Answer:

2(x - 2) = 8

x = 6

Step-by-step explanation:

2(x - 2) = 8

2x - 4 = 8

+4 +4

-----------------

2x = 12

÷2 ÷2

----------

x = 6

I hope this helps!

The vertex form of the equation of a parabola is y = (x- 5)2 + 16.
What is the standard form of the equation?

Answers

Answer: [tex]y=x^2 -10x+41[/tex]

Step-by-step explanation:

[tex]y=(x-5)^2 +16\\\\y=x^2 -10x+25+16\\\\y=x^2 -10x+41[/tex]

Please help!!!
Have school tomorrow
This is due tomorrow!
I have no clue how to do this

Answers

Yes , ∠WGR is congruent ∠GHR because both angles are on one line.

What does the word "congruent" mean in math?

If it is possible to impose one geometric figure on the other such that their surface area coincides, that geometric figure is seen to be congruent, or to be in the connection of congruence.Congruent Figures Examples Two butterflies that are the same size and form. Two candy ice creams of equal size and shape. Two equal Lego bricks in respect of size and shape.

a) No, ∠PHG is not congruent ∠MGH because both angles are not equal.

b) No, ∠RHG and ∠MGH are not supplementary angle because in supplementary angle is equal to 180° .

c) No, ∠SGW is not congruent ∠PHV.

d) Yes , ∠WGR is congruent ∠GHR because both angles are on one line.

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Julie is flying to New York. She has budgeted $200 to
rent a car for 3 days while she is there. If the car rental
is $44 per day plus $0.25 per mile, what is the
maximum number of miles Julie can drive the car?

Answers

The maximum number of miles Julie can drive the car is 272 miles.

Let's check how:

Julie's budget for renting a car is $200.

number of days she'll rent a car is 3.

car rental per day is $44 + $0.25 per mile.

so to know maximum no. of miles she can drive

we'll first subtract the 3 days rent from Julie's budget = $200 - ( 3 x $44 )

= $200 - $132

= $132

Now, the left money is $68.

so, we will divide $68 by $0.25 to know how much miles she can drive.

= $68 ÷ $0.25

= 272 miles

Hence, the maximum number of miles Julie can drive the car for 3 days is 272 miles.

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Answer:

Step-by-step explanation:

Which of the contexts below represents exponential growth?
The amount of a certain medication in a person's bloodstream decreases by
every hour.
Snow was falling at a rate of 1.75 inches per hour.
A population of 200 bacteria quintuples every week.
A car depreciates at a rate of 5.3% per year.

Answers

Answer:

I believe it would be "A population of 200 bacteria quintuples every week"

Step-by-step explanation:

If it is quintupling each week then the number is getting larger and larger exponentially.

he function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval −1≤x≤0?

Answers

The estimate of the average rate of change f is -2

How to estimate the average rate of change f?

The possible graph that completes the question is added as an attachment

The interval is given as

-1 ≤ x ≤ 0

This can be rewritten as

x = -1 to x = 0

This can also be represented as

(a, b) = (-1, 0)

From the attached graph, we have

f(-1) = 7

f(0) = 5

The estimate (to one decimal place) of the average rate of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(-1) - f(0)]/[-1 - 0]

So, we have

Rate = [7 - 5]/[-1 - 0]

Evaluate

Rate = -2

Hence, the average rate of change f is -22

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The height of square room is Sm and volume is 180m³. Find the length.

Answers

Answer:

length = 6m

Step-by-step explanation:

H=5m

V=180m^3

Here

V=l^2 ×H ( being a square)

180=a^2×5

a^2=36

a=6m

By what number should you multiply $3\frac{1}{3}$ to get a product of $4$? Express your answer as a mixed number.

Answers

The number you should multiply 3 1/3 to get a product of 4 is 1 1/5

How to determine the number?

From the question, the statement is given as

What number should you multiply 3 1/3 to get a product of 4

Let the number be x

So, we have the following representation

3 1/3 * x = 4

Express 3 1/3 as an improper fraction

So, we have the following representation

10/3 * x = 4

Multply both sides by 3

So, we have

10 * x = 12

Divide both sides by 10

This gives

x = 12/10

Express as mixed numbers

x = 1 1/5

Hence, the number is 1 1/5

Answers

The value obtained for z-score for the given sample mean is 0.5.

What is described as the z-score?A Z-score is a numerical quantification that describes the relationship of a value to the mean of a set of values. The Z-score is expressed in standard deviations of the mean. A Z-score of 0 signifies that the data point's points tally is the same as the mean score.

For the given question;

The formula for finding the z-score is;

z = (x - μ)/σ

x = sample size

μ = population mean

σ = standard deviation population.

The given values are-

μ = 25σ = 20x = 35

Put the value in the z-score.

z = (35 - 25)/20

z = 10/20

z = 0.5

Therefore, the value obtained for z-score for the given sample mean is 0.5.

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The correct question is-

Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.

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