You are adding orange juice to a 10-liter capacity jar. The equation 3x – 2y = -5 relates the amount of juice y, in liters, with the number of minutes, x, you add juice. How much juice was in the jar to start?
At what rate is the jar filled?

Answers

Answer 1

Answer: 5/2 liters (or 2.5 liters) of juice were in the jar to start.

The jar was filled at a rate of 5 minutes.

Step-by-step explanation: Firstly, rearrange the equation so that y = mx + b. If you move the x over, you get -2y = -3x -5. To get rid of the -2 in front of the y, divide both sides by -2. Then you get y = 3/2x + 5/2.

The amount of juice in the jar initially is b, also known as the y-intercept.

If you look at the equation, you see that 5/2 is our y-intercept which means the jar initially had 5/2 liters of juice at the start (this is the same as 2.5 liters because 5 divided by 2 is 2.5).

To find the rate at which the jar was filled, you need to solve for x. Plug in the 10 liters for the y and solve.

y = 3/2x + 5/2

10 = 3/2x + 5/2

Now, subtract 5/2 from both sides.

7.5 = 3/2x

Divided both sides by 3/2 to get x alone, which will give you the number of minutes in which the jar was filled.

5 = x

The jar was filled at a rate of 5 minutes.


Related Questions

Jim is 50% as tall as a ladder. The ladder is 12 feet tall. How tall is Jim?

Answers

Answer:

Jim is 6ft tall

Step-by-step explanation:

This ladder is 12 feet tall. And Jim is half of it (Fifty %) So, Therefore Jim is 6ft tall

6 ft tall

50% of (multiplied by) 12 feet equals 6 feet

A robot can complete 8 tasks in ⅚ hour. Each task takes the same amount of time. How long does it take the robot to complete one task? It takes the robot ___1___ hour(s) to complete one task. How many tasks can the robot complete in one hour? The robot can complete ______ task(s) in one hour.

Answers

Answer:

1 task = 6.25 minutes

The robot can complete 9.6 task in 1 hour

Step-by-step explanation:

Number of task = 8

Time taken = 5/6 of 1 hour

5/8 of 1 hour = 5/6 × 60 minutes

= 300/6

= 50 minutes

8 task takes 50 minutes

1 task = 50 minutes / 8 task

= 6.25 minutes

1 task = 6.25 minutes

x task = 60 minutes

1 : 6.25 = x : 60

1/6.25 = x / 60

1*60 = 6.25*x

60 = 6.25x

x = 60/6.25

= 9.6

x= 9.6

The robot can complete 9.6 task in 1 hour

The opposite angles of cyclic quadrilateral are(3X+10) and (2X+20). Find the angles.​

Answers

Answer:

40°

Step-by-step explanation:

Opposite angles in a cyclic quadrilateral are equal

3x + 10 = 2x + 20

Take away 2x from both sides

x + 10 = 20

Take away 10 from both sides

x = 10

Now that we know the value of x, substitute it back into the equations

3x + 10 = 3 x 10 + 10 = 30 + 10 = 40

2x + 20 = 2 x 10 + 20 = 20 + 20 = 40

Both angles are equal to 40°

Step-by-step explanation:

Need to FinD :

We have to find the angles.

[tex] \red{\frak{Given}} \begin{cases} & \sf {We\ are\ given\ a\ cyclic\ quadrilateral.} \\ & \sf {The\ measures\ of\ the\ opposite\ angles\ of\ the\ quadrilateral\ are\ {\pmb{\sf{(3x\ +\ 10)^{\circ}}}}\ and\ {\pmb{\sf{(2x\ +\ 20)^{\circ}}}}.} \end{cases}[/tex]

We know that,

The opposite angles of the cyclic quadrilateral are (3x + 10)° and (2x + 20)°. And we have to find the angles.

In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle. The opposite angles in a cyclic quadrilateral add up to 180°. So simply, we just simplify the measures and find the value of x. And at last, we'll find the angles of the quadrilateral.

[tex]\rule{200}{3}[/tex]

[tex] \sf \dashrightarrow {(3x\ +\ 10)\ +\ (2x\ +\ 20)\ =\ 180} \\ \\ \\ \sf \dashrightarrow {3x\ +\ 10\ +\ 2x\ +\ 20\ =\ 180} \\ \\ \\ \sf \dashrightarrow {5x\ +\ 30\ =\ 180} \\ \\ \\ \sf \dashrightarrow {5x\ =\ 180\ -\ 30} \\ \\ \\ \sf \dashrightarrow {5x\ =\ 150} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{150}}{\cancel{5}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 30.}}}}_{\sf \blue{\tiny{Value\ of\ x}}}} [/tex]

∴ Hence, the required value of x is 30. Now, let us find out the angles.

[tex]\rule{200}{3}[/tex]

First AnglE :

3x + 103(30) + 1090 + 10100

∴ Hence, the measure of the first angle of the quadrilateral is 100°.

[tex]\rule{200}{3}[/tex]

Second AnglE :

2x + 202(30) + 2060 + 2080

∴ Hence, the measure of the second angle of the quadrilateral is 80°.


PLEASE HELP!!! I REALLY NEED THIS

Answers

Answer:

The length of the third side is √73

Step-by-step explanation:

To find the third side, we use the Pythagorean Theorem: a² + b² = c²

a² and b² are the two smaller sides

c² is the longest side

The two shortest sides are 4√2 and ?

The longest side is 9

a² = 4√2²

b² = ?

c² = 9²

Now we put together the equation:

4(√2)² + b² = 9²

The square of √2 is 2

4 × 2 + b² = 9²

Multiply 4 and 2 to get 8

8 + b² = 9²

Calculate 9 to the power of 2 and get 81

8 + b² = 81

Subtract 8 from both sides

8 + b² - 8 = 81 - 8

Subtract 8 from 81 to get 73

b² = 73

Take the square root of both sides of the equation

√b² = √73

Simplify

b = √73

Length of third side: √73

Answer in decimal form: 8.5440037453175311678716483262397

Which statements are true when solving x^2=81

Answers

Answer:

d.) the only solution is 9.

Step-by-step explanation:

The only way to solve this equation is to get the square root:

x^2 = 81

[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{81}[/tex]

x = 9

The square root of 81 is 9 and the square root of x^2 is just x.

Please mark me the brainliest!?!

Answer:nahh , had that question & i picked "D" but it said its E & A.

Step-by-step explanation:

A (x) = x ^ 4-2022x ^ 3-2022x ^ 2-2022x-2022
A (2023)?

Answers

Answer:

1

Step-by-step explanation:

Through simply substituting your value into everywhere there is an 'x', you can get your answer.

[tex]A(2023)=(2023)^4-2022(2023)^3-2022(2023)^2-2022(2023)-2022\\A(2023)=1[/tex]

Can anybody help me with this?

Answers

The answer is 183 and the is 123 and 194 and 823

In a survey of 930 students in a school, 92% reported having pets at home. What is the margin of error?

Answers

Answer:

8% or 74

Step-by-step explanation:

930 x 0.92 = 856

930 - 856 = 74

Have a great day!!

Please rate and mark brainliest!!

In a survey of 930 students in a school, 92% reported having pets at home then margin of error is 3.3%.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

In a survey of 930 students in a school.

92% reported having pets at home.

We need to find the margin of error.

The formula for margin of error=±1/√n

Where n is number of students

margin of error=±1/√930

=±1/√930

=±1/30.45

=±0.033

Now let us multiply with hundred.

=3.3%

Hence, In a survey of 930 students in a school, 92% reported having pets at home then margin of error is 3.3%.

To learn more on Percentage click:

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John and kim shared $2400 dollars in the ratio 2:6.What is kim's share ?

Answers

Answer:

she has $1,800

Step-by-step explanation:

to solve we divide 2,400 by 8, which is the total amount of the 2 together. then we get 300 per share, and so we multiply that by kim's 6. to check, we can do 2(300)+6(200) which gives us our origional value of 2,400.

Hope this helps, please rate 5 stars and give brainlest!

We want to cut an apple pie of 9-inch diameter into equal slices, so that the area of each slice is at
least 10 square inches. What’s the maximum number of slices we can cut? please help

Answers

Answer:

Step-by-step explanation:

A'=25.4469 square inches Explanation:diameter is 18shape is circularArea of full pizza is A= ×1824Number of slices is 10 equalArea of each slice is A'=110AA'=110×π×1824A'=25.4469 square inches

Choose the equation that represents the graph below: (1 point)
-6
O y = x-3
O y = -x +3
Oy=-x-3
O y = x+3

Answers

the answer should be the 4th choice

how do u find the constant RATIO of the exponential curve

Answers

Answer:

We call base 2 the constant ratio. In fact, for any exponential function with the form f(x)=abx f ( x ) = a b x , b is the constant ratio of the function. This means that as the input increases by 1, the output value will be the product of the base and the previous output, regardless of the value of a.

Step-by-step explanation:

Notice from the table that:

the output values are positive for all values of x

as x increases, the output values increase without bound

as x decreases, the output values grow smaller, approaching zero

The graph below shows the exponential growth function

f(x)=2x

Help!! Thank you so much beforehand

Answers

Answer: x=8

Step-by-step explanation: these two polygons are similar. 96 divided by 8 equals 12. So 64 divided by 8 equals 8, which is the answer. I really hope this helps and I hope you have a great day!

Weldon bought a pair of hiking boots that cost $64.00 before tax. If a 7.5% tax is added to Weldon's total, how much did he spend in total on the hiking boots? Round to the nearest cent, if necessary.

Answers

Answer:

68.80

Step-by-step explanation:

64 x (7.5% +1)

64 x 1.075 = 68.80

Tritium is a radioactive isotope of hydrogen that decays by about 5% per year. A large bottle of water that contained 856,000 tritium atoms remained undisturbed for 13 years. How much tritium does the bottle contain now?

Answers

Answer: if you’re rounding to the nearest whole number it’s

439,421

Step-by-step explanation:

The number of tritium atoms that the bottle contains now is; 439,384.8 atoms.

How much tritium does the bottle contain now?

It follows from the task content that;

The large bottle of water that contained 856,000 tritium atoms remained undisturbed for 13 years.

On this note, the number of atoms remaining is;

N = 856,000 × (0.95)¹³

N = 856,000 × 0.5133

N = 439,384.8 atoms

Read more on radioactive decay;

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You can multiply -2.2 by 6.2 to find the total variation in water level. What decimal represents the total variation in water level that Ericka observed?

Answers

Answer:-13.64

Step-by-step explanation:

8w2x + w2x you have to simplify but it polynomial equations

Answers

Answer:

9w2x.

Step-by-step explanation:

8w2x + w2x

= 9w2x.

3(2x + y) + 4(x – 4y) + x2

Answers

X^2+10x-13y
Hope I helped :D

Answer:

12x-13y

Step-by-step explanation:

6x+3y+4x-16y+2x

combine like terms

12x-13y

Steve spent 1/4 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill. If $867 was left, what was his monthly salary?

Answers

Answer:x=(45/31)*1426=$2070. ANSWER

20% of that is $414

1/9 of that is $230

They add to $644

What is left is $1426.

Step-by-step explanation:

Answer:1428

Step-by-step explanation:

x−1128x

=867

(1−1128)x

=867

Factor out x.

1728x

=867

Simplify.

x

=1428

Solve for x.

Byron’s income last year was $61,700. He made $48,000 at his plumbing job and had income from an apartment that he rented out. If Byron earned the same amount of rent each month for the entire year, approximately how much per month did he collect? a. $940 b. $1,140 c. $4,000 d. $5,140 Please select the best answer from the choices provided A B C D.

Answers

Answer:

c

Step-by-step explanation:

i got i wrong with b and d and it showed me the right aswer

Need help with this math problem please

Answers

X is greater than or equal to 20

Haley’s work evaluating (Negative 2) Superscript 8 is shown below.

(Negative 2) Superscript 8 = (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) = negative 256

Which statement best describe Haley’s first error?

Haley’s work evaluating (Negative 2) Superscript 8 is shown below.

(Negative 2) Superscript 8 = (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) = negative 256

Which statement best describe Haley’s first error?

Answers

Answer:

256

Step-by-step explanation:

You multiply -2 an even amount of time which gives you a positive answer, if you were to multiply them an odd amount of times then it would be a negative number.

Answer:

The other guy is correct it is d Haley misinterpreted and got the wrong sign

Step-by-step explanation:

which is the equation of a parabola with vertex (0,0) that opens to the left and has a focal width of 12? please select the best answer from the choices provided

Answers

Answer:

Mention any Two study routes(courses or program) that higher education could offer.

I need help on this problem ASAP !!! :)

Answers

Answer:

[tex]\displaystyle 8,9[/tex]

Step-by-step explanation:

Deduct one from nine to get eight, then use the Pythagorean Theorem:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 8^2 + 4^2 = x^2 \hookrightarrow 64 + 16 = x^2 \hookrightarrow \sqrt{80} = \sqrt{x^2}; 4\sqrt{5}\:[or\:8,94427191...] = x \\ \\ \boxed{8,9 \approx x}[/tex]

I am joyous to assist you at any time.

A rectangle's length, f(x), is 2 more than three times a unit length, x, and its width, g(x), is twice the unit length, x. Combine functions f(x) and g(x) to get h(x). Which is h(x) written in the simplest form? H(x) = 5x + 2 h(x) = 6x + 2 h(x) = 6x2 + 2 h(x) = 6x2 + 4x

Answers

Answer:

[tex]h(x)=6x^2+4x[/tex]

Step-by-step explanation:

As the rectangle's length, f(x), is 2 more than three times a unit length, x, so,

f(x)=3x+2

As the rectangle's width, g(x), is twice the unit length, x, so,

g(x)=2x.

The length and width of the rectangle are related to the area and the perimeter of the rectangle. So, the length, f(x), and the width, g(x), can be combined to give the area or perimeter, h(x).

So, h(x) might be the area or the perimeter of the rectangle.

If h(x) is the area, then

[tex]h(x)=f(x) \times g(x)[/tex] [as area=lenght x width]

[tex]\Rightarrow h(x)=(3x+2)\times 2x[/tex]

[tex]\Rightarrow h(x)=6x^2+4x[/tex] (this is in the given options)

If h(x) is the perimeter, then

[tex]h(x)=2\{f(x) + g(x)\}[/tex] [as perimeter=2(lenght + width)]

[tex]\Rightarrow h(x)=2\{(3x+2)+ 2x\}[/tex]

[tex]\Rightarrow h(x)=2(5x+2)[/tex]

[tex]\Rightarrow h(x)=10x+4[/tex] (not in the given options)

So, from the given options [tex]h(x)=6x^2+4x[/tex] is correct.

Answer:

h(x) = 6x^2 + 4x

Step-by-step explanation:

Got it right on lesson.

In the trapezoid below, DE is parallel to AB. If CE = 6, AC = 6.4, and
DC = 4, find the length of CB. Figures are not necessarily drawn to scale.
E
D
-
А
B

Answers

Answer:

Hi po the answer is ab

Step-by-step explanation:

hope it help

Answer:

hope its help

Step-by-step explanation:

godblesscarry on learning

Find the equation of the hyperbola if y=2x−5 and y=−2x+3 are the asymptotes, and it is known that one of the vertices is on the y-axis.

Answers

Answer:

(x-2)^2/4 - (y+1)^2/16 = 1

Step-by-step explanation:

The first thing you want to do is find the center of the hyperbola. Since you have the two equations of the asymptotes, their intersection must be what you want. setting 2x - 5 equal to -2x + 3, you get that x = 2, meaning that 2 is the x-coord of your center. Plugging this value of x into the equations, you get that y = -1. Now that you have your center, you have the information that one of the vertices is on the y-axis. Since the distance from the center to the vertice must be a straight line, you know for sure that this hyperbola is a horizontal one (a vertical one would not have a vertice on the y-axis given this center). Knowing this, you have the equation form (x-2)^2/a^2 - (y+1)^2/b^2 = 1. I got a little confused here, but remember that you now know the center and the equations of the asymptotes. y = 2x - 5 is equal to 2(x - 2) - 1. The form of the asymptotes of a horizontal hyperbola is b/a(x-h) + k, which means that b/a must be equal to 2. This also means that 2a = b, and 4a^2 = b^2. Now you can substitute b^2 for 4a^2, leaving you with the equation (x-2)^2/a^2 - (y+1)^2/ 4a^2 = 1. Remember that vertice on the y-axis? Since it must be at the same y-coordinate (since you know that it must be a horizontal line from the center to the vertice), you know the vertice has to be (0, -1). You can plug these values into the previous equation, which gives you (0 - 2)^2 / a^2 - 0 = 1. This leaves you with 4/a^2 = 1, which means that a must be 2. Since you already know that b is 2a, b must be equal to 4. Plugging those values into the equation, you get your final answer, (x-2)^2/4 - (y+1)^2/16 = 1.

The equation of a line is y = -3x – 2. What are the slope and the y-intercept of the line? * -3. y-intercept = 2 slope
3. y-intercept = -2 slope
3. y-intercept = 2 slope
-3. y-intercept = -2 slope

Answers

Answers:

Slope = -3

y intercept = -2

Explanation:

Compare the given equation with y = mx+b

We see that m = -3 is the slope and b = -2 is the y intercept.

hello!

[tex]===========================================[/tex]

we're given the line's equation; it's written in slope-intercept form, which looks like so:

[tex]\pmb{y=mx+b}[/tex]

where

[tex]\pmb{m}[/tex] is the line's slope

[tex]\pmb{b}[/tex] is the y-intercept of the line

in this case,

slope: [tex]\pmb{-3}[/tex]

y-intercept: [tex]\pmb{-2}[/tex]

[tex]=====================================[/tex]

note:-

Hope everything is clear; if you need any more explanation, kindly let me know.

We have a circle with origin O, diameter AD and AB||CB. Prove AB=CD. ​

Answers

Answer:

draw a start to D to A and to B

then put some period to O

Step-by-step explanation:

THANKS ME LATER TYYY AND MAKE ME BRAINLESS

I am thinking of a number, I multiply it by 12 and subtract 194, I get the same answer if I multiply by 5 and subtract 12

Answers

The answer is 26
26 x 12 - 194 =118
26 x 5 - 12 = 118
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