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strojnjashka [21]
3 years ago
11

Which is the longest? A. 2 km B. 25 m C. 2,500 cm D. 3,000 mm

Mathematics
1 answer:
Leona [35]3 years ago
8 0
2km=2000m
25m=25m
2500cm=25m
3000mm=3m

Hence the longest is 2km=2000m
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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 prime factorization of 60
jeka57 [31]

Answer:

2*2*3*5

Step-by-step explanation:

We need to factor 60 until it is prime numbers

60 = 12*5           5 is prime 12 is not

     =3*4   *5       3,5 prime   4 is not

    = 3 *2*2 *5     2,3,5 are prime

Rearranging the order

    =2*2*3*5

                     

5 0
3 years ago
A figure is made up of a triangle and a rectangle. The triangle has a height of 8.5 inches and a base of 10 inches. The rectangl
Brilliant_brown [7]

\sf  are a \  of \   triangle : \frac{1}{2}*base *height

\sf  are a \  of \   rectangle : Length * Width

total area :

\sf  are a \  of \   rectangle  + area \ of \  triangle

\rightarrow  \sf 9 * 10 + \frac{1}{2} *8.5*10

\rightarrow  \sf 132.5 \ in^2

5 0
2 years ago
Which expression is equal to 1/4
grandymaker [24]

Answer: An option is 3/12...

Step-by-step explanation:

You can just multiply the numerator and denominator my the same number to find an equivalent

6 0
3 years ago
List the next three terms in the following sequence:
BlackZzzverrR [31]
1 + 1 = 2
2 + 2 = 4
4 + 3 = 7
7 + 4 = 11
11 + 5 = 16
16 + 6 = 22
22 + 7 = 29
29 + 8 = 37

sorry that I do not know the equation for this problem...but ur next 3 numbers are : 22,29,37.....so ur answer is D
8 0
3 years ago
Read 2 more answers
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