Given A = {18, 6, -3, -12} Determine all elements of set A that are in the solution of the inequality 2/3x + 3 < -2x -7

Answers

Answer 1

Plug in each value in the set into x, and evaluate both sides.
The values of x that make the inequality true are the answer.

Start with 18.
2/3x + 3 < -2x -7
2/3(18) + 3 < -2(18) - 7
12 + 3 < -36 - 7
15 < -43 is false, so 18 does not work.

Now do 6.
2/3x + 3 < -2x -7
2/3(6) + 3 < -2(6) - 7
4 + 3 < -12 - 7
7 < -19 is false, so 6 does not work.

Now do -3.
2/3x + 3 < -2x -7
2/3(-3) + 3 < -2(-3) - 7
-2 + 3 < 6 - 7
1 < -1 is false, so -3 does not work.

Now do -12.
2/3x + 3 < -2x -7
2/3(-12) + 3 < -2(-12) - 7
-8 + 3 < 24 - 7
-5 < 17 is true, so -12 does not work.

Related Questions

Jesse had 3 long jumps during a track meet of 17 feet,18 feet and 15 feet. Andrew had 3 long jumps during a track meet of 17 feet,15 feet and 18 feet. Overall, who had a greater total jump distance?which addition property can you use to find this answer?

Answers

Final answer:

To find out who had a greater total jump distance, we need to add up the distances of each person's jumps. Jesse and Andrew both had the same total jump distance of 50 feet.

Explanation:

To find out who had a greater total jump distance, we need to add up the distances of each person's jumps.

For Jesse, the total distance is 17 feet + 18 feet + 15 feet = 50 feet.

For Andrew, the total distance is 17 feet + 15 feet + 18 feet = 50 feet.

Both Jesse and Andrew had the same total jump distance of 50 feet.

We can use the addition property of equality to find this answer.

True ir false: multiplying 7x43, a reasonable estimate of the product is 280? Why?

Answers

No because 280 is 21 numbers away from 301

Final answer:

Multiplying 7 by 43 gives an exact result of 301. Thus, estimating this product as 280 isn't entirely accurate but might be seen as a reasonable approximation in certain contexts.

Explanation:

The statement 'multiplying 7 by 43, a reasonable estimate of the product is 280' is known as the question. For this multiplication equation, 7 x 43, the accurate result is 301. Therefore, estimating the product as 280 is not fully correct, however it is relatively close and might be considered a reasonable approximation depending on the context. For a stronger approximation, the product could be rounded up to 300.

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What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ? Enter your answer in the box. Do not round any side lengths.

Answers

First, we use the formula for the distance between two points to find the width and the length of the rectangle.

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Using the formula above, we get

Width = distance between (-3,-1) and (1,3) = [tex] \sqrt{(1-(-3))^2 + (3-(-1))^2} = \sqrt{32} = 4 \sqrt{2} [/tex]

Length = distance between (1,3) and (-1,-3) =

16 square units. Using the pythagorean theorem, calculate the length and width of the rectangle. sqrt((-3 - 1)^2 + (-1 - 3)^2) = sqrt(-4^2 + -4^2) = sqrt(16+16) = sqrt(32) = 4sqrt(2) sqrt((1-3)^2 + (3-1)^2) = sqrt(-2^2 + 2^2) = sqrt(4 + 4) = sqrt(8) = 2sqrt(2) You can check using the rest of the points to insure you actually have the length and width of the rectangle, I've done so, but am not going to demonstrate it here. We now have the length and width of the rectangle at 4sqrt(2) and 2sqrt(2). So just multiply them together to get the area, so 4sqrt(2) * 2sqrt(2) = 4 * 2 * sqrt(2) * sqrt(2) = 4 * 2 * 2 = 16 Therefore the area of the rectangle is 16.

while alex was surfing he rose 36 feet above the water as he rode a wave. within seconds he fell 48 feet where he hit the ocean floor. how deep was the ocean where alex was surfing?

Answers

12 ft, I think. Because he rose 36 above the water

and so it's 36 - 48, which equals -12.
And it's absolute value, so the answer is 12.

The ocean where Alex was surfing will be 12 feet deep.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Alex was surfing he rose 36 feet above the water as he rode a wave. within seconds he fell 48 feet where he hit the ocean floor.

The position of Alex will be:-

Deepness = 336 - 48

Deepness = -12 feet

| Deepness | = |-12| feet = 12 feet

Therefore, the ocean, where Alex was surfing, will be 12 feet deep.

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Andy has 310 in his account. Each week w he withdraws 30 for his expences which expression could be used if he wanted to find out how much money he had left after 8 weeks?

Answers

310-30x=y
310-30(8)=y
310-240=y
$60=y

andy is 5 kilogram less than twice his brother's. together they weigh 100 kilograms what are they weights

Answers

Let x be the brother's weight.
Then 2x-5 is Andy's weight.
x+(2x-5)=100
3x-5=100
3x=105

Andy is 45 kilograms and his brother is 55 kilograms. 55+45=100

Find a degree 3 polynomial having zeros -3, 3 and 7 and the coefficient of x^3 equal 1.

Answers

JJJ I’d Neuhaus irk krm jr

Select the next two terms in the pattern. 243, 81, 27, 9, . . .

Answers

3 and 1 because it is dividing by 3 each time

We are dividing the previous term by 3 in this pattern. Thus, the next term would be 3, and the term after that would be 1.

1. 7 2/3 + 2 7/12

2. 3/8 x 5/6

3. 4 1/2 x 1 2/3

4. 20 divided by 3 1/2

5. 13 5/9 - 8 1/6

6. 3/4 divided by 7/10

7. 8 1/3 divided by 3 3/4

8. 1 3/5 x 2 5/16

9. 6 1/2 - 1 9/10

10. 2/5 of 40

11. 2 5/8 x 4/7 x 12

12. 4 2/3 divided by 10

Answers please!

Answers

It's just not realistic to present a list of 12 math questions and ask for the answers to all of them at once. Please post only one question at a time and please share your thoughts about how to solve that question.

I'll focus on one problem: 7 2/3 + 2 7/12

Here the LCD (lowest common denominator) is 12. 7 2/3 becomes 7 8/12.

Add 7 8/12 and 2 7/12:

7 8/12
+2 7/12
-----------
9 15/12 15/12 is not a proper fraction. Write it as 1 3/12, or 1 1/4.

Then your 9 15/12 becomes (9+1) 1/4, or 10 1/4.

The expressions given above are solved.

What is system of equations?

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought

Given are the expressions as given in the question.

{ 1 } -

7 2/3 + 2 7/12

23/3 + 31/12

92/12 + 31/12

123/12

{ 2 } -

3/8 x 5/6

15/48

5/16

{ 3 } -

4 1/2 x 1 2/3

9/2 x 5/3

3/2 x 5

15/2

{ 4 } -

20 ÷ 3 1/2

20 ÷ 7/2

20 × 2/7

40/7

{ 5 } -

13 5/9 - 8 1/6

122/9 - 49/6

244/18 - 147/18

97/18

Similarly the remaining parts can be solved.

Therefore, the expressions given above are solved.

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If (5^4)^m = 5^12, what is the value of m?

Answer Choices:
A:2
B:3
C:5
D:8

Answers

(5^4)^m = 5^12
(5^4)^m = (5^4)^3
m = 3

answer
B:3

The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. Show your work. Convert your answer into scientific notation if necessary.

Answers

42857.1428571/km per hour

It will take [tex]$ 5.299643 \times 10^4 $[/tex] hours for the space shuttle to reach Saturn from Earth.

To calculate the time it takes for the space shuttle to reach Saturn from Earth, we need to use the formula:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \][/tex]

Given:

Distance from Earth to Saturn = 1,483,900,000 km

Speed of the space shuttle = 28,000 km/h

Convert distance to kilometers in scientific notation:

[tex]\[ 1,483,900,000 = 1.4839 \times 10^9 \][/tex]

Plug values into the formula:

[tex]\[ \text{Time} = \frac{1.4839 \times 10^9 \, \text{km}}{28,000 \, \text{km/h}} \][/tex]

Calculate:

[tex]\[ \text{Time} = \frac{1.4839 \times 10^9}{28,000} \][/tex]

[tex]\[ \text{Time} = 52,996.43 \, \text{hours} \][/tex]

Convert to scientific notation:

[tex]\[ 52,996.43 = 5.299643 \times 10^4 \, \text{hours} \][/tex]

So, it will take [tex]$ 5.299643 \times 10^4 $[/tex] hours for the space shuttle to reach Saturn from Earth.

Complete Question:

The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach from Earth. Show your work. Convert your answer into scientific notation if necessary. Earth =15000000 Saturn =1483900000

A radio station had 155 tickets to a concert. They gave away 4 times as many tickets to listeners as to employees. How many tickets did they give away to employees?

Answers

4(employees) = listeners
listeners + employees = 155
plug the first equation into the second, substituting 4(employees) for listeners, so
4(employees) + employees = 155.
5(employees) = 155
employees = 31

500,000,000,000 in scientific notation

Answers

500,000,000,000 in scientific notation:
First you count to 0 zeros behind the 5 which is 11 zeros.
the scientific notation of 500,000,000,000 is:

₁₁
Answer: 5 x 10

I hop this helps :)

5*10^11 is your answer because you have to move the decimal 11 times :)

This one's a doozy and I really need some help!

At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money.
What was the individual cost of each person's items?

(a) Write an expression that shows Tanya's purchased items.

(b) Write an expression that shows Tony's purchased items.

(c) Write an equation. Let x represent the cost of one of Tanya's items.

(d) Solve the equation. Show your work.

I need help ASAP! Pleaseee :D

Answers

a) 3x as they were three items of the same price
b) 4(x-2.25)= 4x-9 as each item cost $2.25 less than tanya's items and there were four of them
c) 3x=4x-9 as all the items bought by tony and tanya cost the same amount
d) 3x=4x-9
-4x on both sides
-x=-9 so x=9
The individual costs of each person's item was $9

Please someone help! Algebra 1

Answers

1.) 2/9 (explanation: the square root squares both the denominator and the numerator if it is a perfect square)

2.) 2 (the fraction 0.8/0.2 simplifies to 4 which is them square rooted)

3.)0.6

4.)-7

5.) 11i (i stands for the square root of -1 since it is imaginary. Squares of numbers are imaginary when the number under the radical is negative since a real number squared can never be negative )

3.5kg:800g in simplest ratio

Answers

3.5 kg: 800g
=3.5*1000 g: 800 g
=35/8

In the eighth grade 322 students voted for the new mascot to be a tiger this was 7/10 of the total number of students in the eighth grade how many students are in the eighth grade

Answers

So first divide by 10 to get 32.2 then multiply by the remaining which is 3/10 so 3. 32.2 times 3 is 96.9 round up 97 add to 322 to get 419.
Your welcome

What is the perpendicular line slope of -2x-9y=4

Answers

The perpendicular slope of the original equation,[tex]-2x-9y=4[/tex], is the negative reciprocal (flip the numerator and denominator).

But first we need to put it in y=mx+b form...

[tex]-2x-9y=4[/tex] Equation

[tex]-9y=2x+4[/tex] Add 2x to both sides

[tex]y= -\frac{2}{9}x- \frac{4}{9} [/tex] Standard format

Since now we know that the slope is [tex]-\frac{2}{9} [/tex], the perpendicular slope is [tex] \frac{9}{2} [/tex]

For the function f(x)=-5x witch ordered park will be a point on the graph

Answers

HI not sure but I think it is the third one

what is -9/10 • -2/3 ?

Answers

Multiplying two fractions together corresponds to multiplying together their components, so multiplying -9/10 · -2/3 looks like:

[tex] \frac{-9}{10} \cdot \frac{-2}{3}= \frac{(-9)(-2)}{(10)(3)} [/tex]

If we rearrange the fractions, we can perform some simplification:

[tex] \frac{(-9)(-2)}{(3)(10)} = \frac{-9}{3} \cdot \frac{-2}{10} =-3\cdot \frac{-1}{5} [/tex]

When gets us:

[tex] \frac{(-3)(-1)}{5}= \frac{3}{5} [/tex]

If i have two similar parallelograms that have areas of 18in squared and 32in squared . how do i find the ratio ?

Answers

by dividing both of them

You will have to divide.

______ numbers can be written as a product of _______ factors.This called the prime factorization of a number.

Answers

The fist blank is Compasit and the 2nd is prime

What is the fifth term of the sequence defined by
f(n)=3(n−3)

Answers

The answer is 6 since to get the fifth term in the sequence, you replace n with 5 and you get 3(5-3). You subtract 5 by 3 and get 2. Then you multiply all of it by 3 and get 6 as the final answer.

Simplify the following expression 12 1/2 + (-25)

Answers

The answer for this question is: -12 1/2

Negative 15 divided by 3/5

Answers

-25 is your answer to the question

Kittens weigh about 100 grams when born and gain 7 to 15 grams per day. If a kitten weighed 100 grams at birth and gained 8 pounds per day, in how many days will the kitten triple it's weight? How do I write this as an equation, and how do I find the answer?

Answers

You can set up an equation such as 300=100+8x where x is equal to the number of days gone by since birth. The answer would be 25 days.

The equation would be 300=100+8d. All you would have to do is solve for d.

How is the underlined pronoun used in the sentence?

This gift with the big red bow is from me.

A.
subject

B.
subject complement

C.
direct object

D.
object of a preposition

Answers

I say its C but I'm not to sure

b is the right answer

13/20 - 2/7 + 11/35 = ?

Please include steps on how to solve!!!!

Answers

13/20 - 2/7 + 11/35

find the least common denominator which is 140.

(13 × 7/20 × 7) - (2 × 20/7 × 20) + (11 × 4/35 × 4)

91/140 - 40/140 + 44/140

91 - 40 + 44/140

95/140

19/28 <<< answer

hope this helped, God bless!

PLEASE HELP GEOMETRY Use the word bank to help you with possible answers (there are extra options that are not to be used)

Word Bank:
ASA
SAS
BC=EF
BC=ED
Given
CPCTC
BC = EF

Answers

Short Answers:

Answer for part A: Given
Answer for part B: Angle A = Angle D (not sure why this isn't in word bank?)
Answer for part C: ASA
Answer for part D: BC = EF
Answer for part E: CPCTC

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

Explanations:

Part A:

AB = DE is given at the very top of the problem. So we simply say "given". We always repeat what we are given at the very start of the proof. You can see this for lines 1 through 3, which are repeating the three givens.

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

Part B:

The three givens are:
AB = DE
angle A = angle D
angle B = angle E
the first and last of this trio is used (for statements 1 and 3 respectively). So the only thing left is "angle A = angle D"

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

Part C:

We're using ASA (angle side angle) because we're given two pairs of congruent angles. The side for each triangle is between the two angles. See the attached diagram for more info.

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

Part D:

For any proof, you will ALWAYS have the last statement be the thing you want to prove. In this case, we want to prove BC = EF.

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

Part E:

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"

If the two whole triangles are congruent, then the smaller corresponding parts that make up the triangles must be congruent as well.

Jenny needs of a stick of butter for a recipe. She cuts the half-stick of butter into four equal pieces. What portion of the whole stick of butter is each of the pieces?

Answers

Final answer:

Each piece represents 1/8 of the whole stick of butter.

Explanation:

Jenny needs of a stick of butter. She cuts the half-stick of butter intoTo find the portion of the whole stick of butter that each piece represents, we need to divide the numerator (1) by the denominator (2 x 4 = 8). So each piece represents of the whole stick of butter.

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