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Ivanshal [37]
2 years ago
9

Comparing Absolute Values

Mathematics
2 answers:
AURORKA [14]2 years ago
7 0

Answer:

i don not know this. but I think

Step-by-step explanation:

Feliz [49]2 years ago
5 0
No, the student is not correct
Absolute value depends on the distance from zero, -9 is 9 values from zero as 4 is 4 values from zero

9 is greater than 4; the answer is false
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A linear equation in two variables has infinitely many solution the set of all solutions to a linear equation in two variables f
Greeley [361]
<span>1, During a 1-hr television program, there were 22 commercials, Some commercials were 15 sec and some were 30 sec long. Find the number of 15- sec commercials and the number of 30 sec commercial if the total playing time for commercial was 9.5 minutes.

</span>a) <span>show how to formulate your system of equations for your problem,

Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language

b) state the two equations:

- translate the word statement into algebraic equations:

</span><span>* there were 22 commercials => x + y = 22
* the total playing time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>

Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y =  570

c) state which method you will use to solve either addition or substitution

Answer:
adition: multiply the first equation times - 15 and add the two equations.

d) solve your system showing and explaining each step of the process

Answer:
- muliply eq (1) times - 15

-15x - 15y = - 330

- add that to the eq (2):

-15x + 15x - 15y + 30y = -330 + 570

- add like terms: 15y = 240

- divide both members by 15: 15y/15 = 240 / 15 => y = 16

- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6

Solution: x = 6, y = 16

e) Be sure to check your solution!

x + y = 22
6 + 16 = 22
22 = 22 --> check

15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check

f) Once a solution is found explain what this solution means in the context of the problem, write the answer to the word problem in words</span><span>

The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.

2, How many quarts of water should be mixed with a 30% vinegar solution to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>

a) variables:

- state the variables
x: number of quarters of water
y: number of quarters of vinegar

- translate the words into mathematical language

12 qt 25% vinegar solution

=> total number of quarts = 12 = x + y

balance in vinegar:

vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution

0 + 0.3y = 0.25 (x + y)

c) Equations

Eq (1) x + y = 12

Eq (2): 0.3y = 0.25x + 0.25y

=> 0.25x - 0.05y = 0

d) solve

- multiply eq (1) times 0.05 and add to eq (2)

0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6

x = 0.6 / 0.3 = 2

x + y = 12 => y = 12 - y = 12 - 2 = 10

Solution: x = 2, y = 10

e) check:

x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check

vinegar:

10*0.3 = 12*0.25
3 = 3 -> check

f) Explanation of the solution

The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.

5 0
3 years ago
What is the answer to 8x^3+125 by factoring the perfect cube?
expeople1 [14]

Answer:

\large\boxed{8x^3+125=(2x+5)(4x^2-10x+25)}

Step-by-step explanation:

8x^3+125=2^3x^3+5^3=(2x)^3+5^3\\\\\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+5)((2x)^2-(2x)(5)+5^2)\\\\=(2x+5)(4x^2-10x+25)

3 0
3 years ago
In a class of 22 students, 15 play an instrument and 11 play a sport. There are 9
ollegr [7]

Answer:7/22

Sorry I don’t know how to explain.But here the answer.

Hope this helped!

Have a great day!

6 0
2 years ago
What is the range of the values shown on the table? What does the range represent?
hjlf

Answer:

Option D)R: {0 ≤ y ≤ 360}; The range represents the number of miles the car can travel

Step-by-step explanation:

The table in the attached figure

Let

x -----> the amount of gas used in gallons (independent variable)

y ----> the number of miles the car can travel (dependent variable)

In this problem

The domain is the interval -----> [0,12]

0\ gal \leq x \leq 12\ gal

The range is the interval ----> [0,360]

0\ miles \leq y \leq 360\ miles

3 0
3 years ago
On a trip you had to change your money from dollars to British pounds. You got 560 pounds for 800 dollars. How many pounds will
guapka [62]

Answer:

B. 210

Step-by-step explanation:

800/560 = 1.42857142857

300/1.42857142857= 210

7 0
2 years ago
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