Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.

Which points did the manager label?

(0, 6) and (2, 0)

(0, 12) and (36, 0)
(6, 0) and (0, 2)
(0, 36) and (12, 0)

Answers

Answer 1

Given that the x-axis represented the number of small tanks and the y-axis represented the number of large tanks.

Given that his small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner and there are a total of 72 oz of water conditioners available.

The line representing the various combinations of tanks he could put the water conditioner into is given by 2x + 6y = 72.

Since, the manager labeled only the intercepts.

The x-intercept is the value of x when y = 0 and is given by

2x + 6(0) = 72

x = 72 / 2 = 36

Thus, the x-intercept is (36, 0)

The y-intercept is the value of y when x = 0 and is given by

2(0) + 6y = 72

y = 72 / 6 = 12

Thus, the x-intercept is (0, 12)

Therefore, the points labeled by the manager are: (0, 12) and (36, 0)

Related Questions

There is 1/4 ounce of yeast in every 2 1/4 teaspoons of yeast. A recipe for bread calls for 2 teaspoons of yeast. How many ounces of yeast are needed for this ecipe

Answers

Here is the set up:

(1/4)/2 = (9/4)/y

Solve for y.

Y=(3/5)x -3 and 5y =3x-10 these lines are and the second question?

Answers

Look at the first line: y = (3/5)x - 3. What happens if you multiply each term by 5, to eliminate the fraction?

5y = 3x - 3

Compare this to the second equation,

5y - 3x = -10, or 5y = 3x - 10.

The coefficients of x and y (as 3 and 5 here) determine the slope of a straight line. Since 5y = 3x is present in both equations, the two lines MUST be parallel.

y = 4
4y = 6 => y = 6/4

y+4 and y =3/2 are both horizontal lines. Since they are horiz., they are parallel.

Final answer:

The given lines Y=(3/5)x -3 and 5y =3x-10 are examples of linear equations which, when solved, are found to be parallel due to their identical slope.

Explanation:

The lines given in the question are in the format y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The equations are Y=(3/5)x -3 and 5y =3x-10. By comparing the coefficients, the slope of the first line is 3/5 and the y-intercept is -3. For the second equation, we first need to convert it into the 'y = mx + b' form. Dividing every term by 5 gives us y = (3/5)x - 2. Therefore, the slope of the second line is also 3/5 and the y-intercept is -2. Since both lines have the same slope, they are parallel lines.

Learn more about Parallel Lines here:

https://brainly.com/question/29762825

#SPJ3

When Milo got promoted at work he received a 20% pay raise. He now earns $72,000 a year. What was his annual salary before the raise?

Answers

$57600 is the answer. 72,000 times 0.8=57600

choose the ratio that you would use to convert 5.5 pounds to ounces

Answers

We want "pounds" to disappear, in favor of "ounces."

Thus, multiply 5.5 pounds by (16 oz / 1 pound). "pounds" cancels, leaving you with "88 oz."

Answer:

A. 16 ounces/1 pound

Step-by-step explanation:

Remember that: 1 pound (lb) is equal to 16 Ounces (oz).

Then you have to find a ratio to convert 5.5 pounds to ounces.

If you write: 5.5 pounds, you have to find a ratio that eliminates pounds in order to get ounces:

5.5 pounds*16 ounces/1 pound

In this way pounds in the numerator is eliminated with pounds from the denominator and the result you get is in units of ounces.

5.5 pounds*16 ounces/1 pound=88 ounces

point slope for (3,21) and (6,12)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 3}}\quad ,&{{ 21}})\quad % (c,d) &({{ 6}}\quad ,&{{ 12}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{12-21}{6-3}\implies \cfrac{9}{3}\implies 3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-21=3(x-3)[/tex]

can 0.91919191 be written as a fraction?

Answers

Final answer:

Yes, 0.91919191 can be written as a fraction. The fraction form is 91919191/9999999.

Explanation:

Yes, 0.91919191 can be written as a fraction. To convert a repeating decimal to a fraction, we can use the following steps:

Let x be the repeating decimal.Multiply both sides of the equation x = 0.91919191... by a power of 10 that moves the decimal point to the right of the repeating part (8 digits in this case): 10000000x = 91919191.91919191...Subtract the original equation (x) from the new equation (10000000x) to eliminate the repeating part: 10000000x - x = 91919191.91919191... - 0.91919191...Simplify the equation: 9999999x = 91919191Divide both sides of the equation by 9999999 to solve for x: x = 91919191/9999999

Therefore, 0.91919191 can be written as the fraction 91919191/9999999.

Sarah bought a shirt on sale for $35 the original price of the shirt was 3 times that amount sarah also bought a pair of shoes on sale for $28 the original price of the shoes was 5 times that amount together how much money did the shirt and shoes cost before they went on sale

Answers

To find the original price of the shirt:
35*3=105

To find the original price of the shoes:
28*5=140

To find the total amount of money the shirt and shoes cost before they went on sale:
105+140=145

There's your answer.

Remember: realistically, there would be sales tax, so this wouldn't be the exact amount of money they would be paying.

Ratio equivalents to 1:2

Answers

2:4 3:6 4:8

Any ratio equals 1:2 as long as you can divide the first number by itself to get 1 and the second number with the 1st number.
Example
2:4
Divide the first number by 2 and you get 1
Divide the second number by 2 and you get 2
So the ratio equals 1:2

Please make me brainliest

Some ratios that are equivalent to 1:2 include

2:4
3:6
4:8
5:10

and so on and so forth
hope this helps

write the numerical expression in words then solve (98-78)×11

Answers

Find the difference between ninety-eight and seventy-eight, then multiply by eleven. Ninety-eight minus seventy-eight is twenty, take this and multiply if by eleven to arrive at an answer of eleven. Following the order of operations the math within the parentheses must be done first, then the multiplication. The answer is two-hundred and twenty.

soymeal is 14 percent protein cornmeal is 7 percent protein how many pounds of each should be mixed together in order to get 280-lb mixture that is 9 percent protein

Answers

Let the weight of soymeal be s, and let the weight of cornmeal be c.
You need a total of 280 lb, so that gives us one equation.

s + c = 280

Now we use the protein to write another equation.
The protein in s lb of soymeal is 0.14s.
The protein in c lb of cornmeal is 0.07c.
The protein in 280 lb of 0.09% protein mix is 0.09(280).
This gives us a second equation.

0.14s + 0.07c = 0.09(280)

Now we solve the two equations as a system of equations.

s + c = 280
0.14s + 0.07c = 0.09(280)

Solve the first equation for s and plug in tot eh second equation.

s = 280 - c

0.14(280 - c) + 0.07c = 25.2

39.2 - 0.14c + 0.07c = 25.2

-0.07c = -14

c = 200

Now we substitute c = 200 in the first equation to find s.

s + 200 = 280

s = 80

Answer: 200 lb of soymeal and 80 lb of cornmeal

What is -3 -4 in integers

Answers

They are intergers hoped this help

it is -7 b/c you owe even more if you think about in with debts

Abby did 121 sit ups in 8 minutes .estimate the number of sit-ups she did in 1 minute.

Answers

Isnt the answer 15? I think so

I thank the the answer is 15r1. That's what is got

Which ordered pair comes from the table?

X Y
2 1
3 4
4 4
5 2

A. (1,2)
B. (4,3)
C. (2,1)
D. (2,5)

Answers

The only (x, y) ordered pair in the table is ...
C. (2, 1)

Answer:

Option C is correct

(2, 1) ordered pair comes from the table

Step-by-step explanation:

Ordered pair states that an ordered pair contains the coordinate of points in the coordinate plane in the form of (x, y)

Given the table:

X Y

2 1

3 4

4 4

5 2

Ordered pairs for this table are:

From the definition, we have;

(2, 1), (3, 4), (4, 4) and (5, 2)

Therefore, the only ordered pairs comes from the table is, (2, 1)

On a survey mission,a pilot flew out to a parcel of land and back in 7h. The rate flying out was 120mph. The rate flying back was 90mph.how far away was the parcel of

Answers

The answer is 750 mph

Final answer:

To find the distance, multiply the speed by the time for each leg of the trip and add them together to get the total distance of 735 miles.

Explanation:

To find the distance to the parcel of land, we can use the formula Distance = Speed x Time. Since the pilot flew out and back, we can calculate the distance for each leg of the trip and then add them together.

Distance going out = Speed x Time = 120 mph x (7/2) hours = 420 miles

Distance coming back = Speed x Time = 90 mph x (7/2) hours = 315 miles

Total distance = Distance going out + Distance coming back = 420 miles + 315 miles = 735 miles

Give one example of when would use the friendly numbers strategy to substract. Explain why

Answers

Here is one example of when you would use the friendly number strategy to subtract.
42 - 18

We will turn the 18 into a friendly number, which is going to be 20.

(42 + 2) - (18 + 3)
44 - 20
Now it is easier to subtract 44 - 20 than it is 42 -18. With 42 - 18 we would have to barrow whereas with 44 -20 we do not have to barrow and we can do it in our head easier and makes it faster.

Can you help me please.........................

Answers

area of shaded figure = l x w = 24 *18 = 432

area of white square = 12*12 = 144

area of shaded part = 432-144 = 288 m^2

Answer is A

What function is represented below? graph begins in the first quadrant and decreases quickly while crossing the ordered pair 2, 1. Then the graph begins to decrease slowly as it approaches the x axis. f(x) = one fourth to the power of x plus 2 f(x) = one fourth to the power of x + 2 f(x) = one fourth to the power of x minus 2 f(x) = one fourth to the power of x − 2

Answers

f(x) = one fourth to the power of x-2 f(x) = (1/4)^(x-2)
It is a decreasing function that when x= 2, (1/4) is raised to the zero power which is 1, which is what the point (2,1) asks for.

Answer:

The represented function is :

[tex]f(x)=(\frac{1}{4})^{x-2}[/tex]

Step-by-step explanation:

[tex]1.\thinspace f(x)=(\frac{1}{4})^x +2[/tex]

And the equation must pass through (2,1) as given,

But, f(2) = 2.0625 ≠ 1 so this is not the required function.

[tex]2.\thinspace f(x)=(\frac{1}{4})^{x+2}[/tex]

And the equation must pass through (2,1) as given,

But, f(2) = 0.0039 ≠ 1 so this is not the required function.

[tex]3.\thinspace f(x)=(\frac{1}{4})^x -2[/tex]

And the equation must pass through (2,1) as given,

But, f(2) = -1.94 ≠ 1 so this is not the required function.

[tex]4.\thinspace f(x)=(\frac{1}{4})^{x-2}[/tex]

And the equation must pass through (2,1) as given,

We see, f(2) = 1 so this is the required function and the corresponding graph of the function is attached below :

Hence, The correct option is (4)

factor a number, variable, or expression out of the trinomal shown below

Answers

Ok, to start, let's look at the terms given in this trinomial: 6x^2, -12x, and 9.
Now, let's try to find the greatest common factor of the three terms, which would be 3. One way to do this would be to take each term and break it down using prime factorization, which would look like this:
6x^2= 2*3*x*x
-12x= -1*3*2*2*x
9= 3*3

When you look at the numbers when they are broken down, they all seem to share one factor, which is 3. This would be the greatest common factor you would factor out of the trinomial, and when you do so it should look like this

3(2x^2-4x+3) which would be your answer

Which choice shows the numbers correctly ordered?
A) 2 < 1.1 < 1.5 < π
B) 1.1 < 2 < 1.5 < π
C) 1.1 < 1.5 < 2 < π
D) 2 < π < 1.1 < 1.5

Answers

The answer is C, It shows it from least to greatist since pie is 3.14, it makes seance

Chen is checking a division problem by doing the following:

152
× 4
______

+ 2
______

What problem is Chen checking?

Answers

That "+2" is the remainder of a division. Note that 152 times 4 is 608.
Dividing 608 by 4 results in 152 with no remainder.
Dividing 610 by 4 results in 152 with the remainder 2.
____
Chen is checking the division problem 4 / 610 .

the sum of 5 consecutive integers is 110. what is the fourth number in the sequence

Answers

Thanks for the question!

The equation is:

(Note that the last term is x+4, not x+5)
x + (x+1) +(x+2) + (x+3) + (x+4) = 110
5x + 10 = 110

Solving:

5x = 100
x = 20

So the fourth term is:

20 + 3
23

Hope this helps!

Answer:

Step-by-step explanation:

Solve for w . =−40−w6 Simplify your answer as much as possible.

Answers

Assuming that the left side of the equation is equal to zero, w=6.667

This is a square pyramid. What is the length of the base? h=3 v=36

Answers

volume of square pyramid = S^2*h/3

volume = 36

h = 3

36 = S^2 *3/3

36 = S^2

S = sqrt(36)

S = 6

length of base = 6

The perimeter of a triangle is 26 centimeters. Side *a* of the triangle is 3 centimeters longer than side *b.* Side *c* is 1 centimeter shorter than twice side *b.* find the length of each side. (Show work)

Answers

a+b+c=26
a=b+3
c=2b-1

b+3+b+2b-1=26
4b=24
b=6 cm
a=6+3=9cm
c=2*6-1=11 cm

side *a* is 9 cm
side *b* is 6 cm
side *c* is 11 cm

Derrick’s parents are finalizing a budget for his college expenses. His first year of college will cost $8,000, and his expenses will increase by 12% each year. What is the amount they should budget for Derrick’s four-year college education, to the nearest dollar?
$38,235 is needed.
$42,823 is needed.
$32,072 is needed.
$39,200 is needed.

Answers

1st year = 8000

2nd year = 8000 * 1.12 = 8960

3rd year = 8960*1.12 = 10035.20

4th year = 10035.20 * 1.12 = 11239.42

8000 + 8960 + 10035.20 + 11239.42 = 38234.62 round to $38,235

Answer:

$38,235 is needed.

Step-by-step explanation:

Given,

The cost of first year of college is $ 8000 and it is increasing by 12 % each year,

So, His first year's cost = $ 8000,

Second year's cost = 12 % more than the first year's cost = 112 % of first year's cost = 112 % of 8000 = 1.12 × 8000 = $ 8960,

Third year's cost = 112 % of second year's cost = 112 % of 8960 = 1.12 × 8960 = $ 10035.2

Fourth year's cost = 112% of third year's cost = 1.12 × 10035.2 = $ 11239.424

Hence, Total cost for four-year college education = 8000 + 8960 + 10035.2 + 11239.424 = $ 38234.624 ≈ $ 38235

⇒ $38,235 is needed.

The least squares method is a mathematical procedure used to identify the linear equation that best fits a set of ordered pairs.
a. True
b. False

Answers

This is true, answer a.

Enter the values to complete the statement. To determine whether (−1,4) (−1,4) is a solution to the equation 3x+8y=29 3x+8y=29 , substitute for x and and for y

Answers

To determine whether (−1,4) is a solution to the equation 3x+8y=29, substitute ...-1... for x and ...4... and for y.

In a pair of values like (-1, 4), the first coordinate, or entry, occupied by -1 always represents x.

Similarly, the second coordinate occupied by 4 represents y.

Answer: substitute ...-1... for x and ...4... and for y.

What's the answer to find y when x=9 if y varies directly as the square of x ,and y =100 when x= 5

Answers

"y varies directly with square of x"
y = kx²
where "k" is the constant of variation you need to solve for first.

when y = 100 ; x = 5
100 = k(5)²
100 = 25k
100/25 = k
4 = k

Now you can solve for y when x = 9
y = 4(9)²
y = 4(81)
y = 324

Round each number to the nearest tenth.

What is the best estimate for the difference of 376.64 – 109.38?

A.
267.2

B.

267.3

C.

268

D.

270

Answers

Hello!

To find this, we need to solve the solution.

376.64 - 109.38 = 267.

267.26 rounded to the nearest tenth is 267.3

Let x be the number of successes throughout n independent repetitions of a random experiment having probability of success p=1/4. determine the smallest value of n so that p(1<=x)>=0.7

Answers

To answer problems like this you have to use binomial:

P (x > 1) = 1 – p (0 < x < 1) > .7

So:

1 – p (0) – p (1) > .7

1 – (3/ 4) ^n – (3/ 4) ^n (n – 1 ) (1/ 4) > .7

Therefore n > 5.185, and the smallest value of n so that we can satisfy the given condition is 6 (rounded up)

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