1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LuckyWell [14K]
3 years ago
11

Problem PageQuestion The Russell family and the Gonzalez family each used their sprinklers last summer. The water output rate fo

r the Russell family's sprinkler was 35L per hour. The water output rate for the Gonzalez family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total water output of 2200L. How long was each sprinkler used?
Mathematics
1 answer:
Agata [3.3K]3 years ago
5 0

Answer: the Russell family used their sprinkler for 40 hours.

the Gonzalez family used their sprinkler for 20 hours.

Step-by-step explanation:

Let x represent the number of hours for which the Russell family used their sprinkler.

Let y represent the number of hours for which the Gonzalez family used their sprinkler.

The families used their sprinklers for a combined total of 60 hours. It means that

x + y = 60

The water output rate for the Russell family's sprinkler was 35L per hour. The water output rate for the Gonzalez family's sprinkler was 40L per hour. The total water output of both families was 2200L. It means that

35x + 40y = 2200- - - - - - - - - - --1

Substituting x = 60 - y into equation 1, it becomes.

35(60 - y) + 40y = 2200

2100 - 35y + 40y = 2200

- 35y + 40y = 2200 - 2100

5y = 100

y = 100/5

y = 20

x = 60 - y = 60 - 20

x = 40

You might be interested in
(a) Let R = {(a,b): a² + 3b <= 12, a, b € z+} be a relation defined on z+)
grin007 [14]

Answer:

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Step-by-step explanation:

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

((a, b), (a, b)) ∈ R since a·b = b·a

Therefore, R is reflexive

If ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ R

Therefore, R is symmetric

If ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·c

Multiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈R

Therefore R is transitive

From the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

The relation, R, is reflexive.

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Therefore, the relation, R, is symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

brainly.com/question/1503196

4 0
2 years ago
How do you round money to the nearest cent?Like for ex.:$2.15 to the nearest cent
Digiron [165]


To round money to the nearest cent you would see in the ones place what that number is and if it is at or higher than 5 it would round up to 2.20               

Did that help any I hope so:) if not tell me I will have another strategy

7 0
2 years ago
Write 13/40 as a decimal?
borishaifa [10]
0.325 is the answer. :)

6 0
3 years ago
Read 2 more answers
Identify the distance between points (−1,7,10) and (6,−3,2), and identify the midpoint of the segment for which these are the en
svetlana [45]

Answer:

d ≈ 14.6 units; M (2.5, 2, 6)

Step-by-step explanation:

Using the distance formula for 3-D dimensions, you get the √(213) which equals 14.6

Then, using the midpoint formula for 3-D dimensions, you find the coordinates 2.5 for x, 2 for y, and 6 for z.

3 0
2 years ago
The graphs below have the same shape. What is the equation of the red
anyanavicka [17]

Answer:

Option B is correct .

Step-by-step explanation:

According to Question , both the graph have same shape . If we look at the the first graph it cuts x - axis at (0 , 2) and ( 0 , -2) . Hence x = 2 and -2 are the zeroes of the equation .

And ,the given function is ,

\implies f(x) = 4 - x^2 \\\\\implies f(x) = 4-x^2=0 \\\\\implies 2^2-x^2=0\\\\\implies (2-x)(2+x) = 0 \\\\\boxed{\red{\bf \implies x = 2 , (-2) }}

<u>Hence ,we can can see that x = </u><u> </u><u>2</u><u> </u><u>and</u><u> </u><u>(</u><u>-</u><u>2</u><u>)</u><u> </u><u>are</u><u> </u><u>the</u><u> </u><u>zeroes </u><u>of </u><u>graph</u><u>. </u><u> </u>

This implies that if we know the zeroes , we can frame the Equation.

On looking at second parabola , it's clear that cuts x - axis at ( 1, 0 ) and (-1,0). So , 1 and -1 are the zeroes of the quadratic equation . Let the function be g(x) . Here , a and ß are the zeroes.

\implies g(x) = (x-\alpha)(x-\beta) \\\\\implies g(x) = (1+x)(1-x) \\\\\boxed{\pink{\bf \implies g(x) = 1 - x^2}}

<u>Hence </u><u>option </u><u>B</u><u> </u><u>is</u><u> </u><u>corre</u><u>ct</u><u> </u><u>.</u>

8 0
2 years ago
Read 2 more answers
Other questions:
  • What is the solution for the equation sinx=cosx?
    11·1 answer
  • Solve 2/3-4x+7/2=-9x+5/6<br><br> A.x=-3/2<br><br> B.x=-2/3<br><br> C.x=2/3<br><br> D.x=3/2
    9·1 answer
  • Find x if y=-3<br> 2x/y+6=-4
    11·1 answer
  • I NEED HELP PLEASE, THANKS! :) Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.
    5·1 answer
  • What is the scientific notation 523,120,000
    5·2 answers
  • What's the answer plz help?
    6·1 answer
  • The first five terms of an arithmetic sequence are 4, 10, 16, 22, and 28. Which function f(x) could be used to describe the xth
    8·1 answer
  • Hep with this please
    12·1 answer
  • PLEASE HELP ME ASAP I NEED TO DO THIS
    8·1 answer
  • Use technology, what is the solution to this system? 4x+8y=30
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!