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xz_007 [3.2K]
3 years ago
9

A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 55 ​seconds, th

e gauge on the bottle indicates that it contains 1919 ounces of water. After it has been filling for 1111 ​seconds, the gauge indicates the bottle contains 3737 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that relates the amount of water in the​ bottle, y, to the time x.
Mathematics
1 answer:
True [87]3 years ago
8 0

Answer:

y=3x+4

Step-by-step explanation:

Let y be the amount of water in the bottle x seconds after the faucet was turned on.

We have been given that the gauge on the bottle indicates that it contains 19 ounces of water after it has been filling for 5 seconds. After it has been filling for 11 ​seconds, the gauge indicates the bottle contains 37 ounces of water.

We have two points on the line (5,19) and (11,37).

Let us find slope of the line passing through these points.

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{37-19}{11-5}

m=\frac{18}{6}

m=3

We will write our required equation in slope-intercept form y=mx+b, where, m represents slope and b represents the y-intercept.

Let us find y-intercept by substituting m=3 and coordinates of point (5,19) in slope intercept form.

19=3\cdot 5+b

19=15+b

19-15=15-15+b

4=b

Therefore, our required equation would be y=3x+4.

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How do I figure this problem 1/5 > d + 4/5
marissa [1.9K]
\frac{1}{5}>d+\frac{4}{5}\ \ \ \ \ \ \ \ |subtract\ \frac{4}{5}\\\\\frac{1}{5}-\frac{4}{5}>d\\\\d
7 0
3 years ago
What is sin -1 (1/2) if the terminal side of 0 is located in quadrant 1
Lady_Fox [76]

Answer:

sin^-1 (1/2) = 30°

Step-by-step explanation:

* Lets explain how to find the trigonometry functions from the unit circle

- The unit circle is the circle whose radius is 1 unit

- It intersects the four axes at:

# Positive part of x-axis at (1 , 0) and negative part at (-1 , 0)

# Positive part of y-axis at (0 , 1) and negative part at (0 , -1)

- The terminal of any angle intersect it at point (x , y) where x² + y² = 1

- If The angle between the terminal side and the x-axis is Ф , then

# The adjacent side of Ф = x

# The opposite side of the angle Ф = y

- In the problem the terminal side lies in the first quadrant

∴ all the trigonometry functions are positive

∵ sin Ф = opposite/hypotenuse

∵ The opposite = 1/2 and the hypotenuse is the terminal side = 1

∴ sin Ф = 1/2 ÷ 1 = 1/2

- To find Ф use the inverse function sin^-1 Ф

∵ sin Ф = 1/2

∴ Ф = sin^-1 (1/2)

∴ Ф = 30°

* sin^-1 (1/2) = 30°

6 0
3 years ago
joes family has compleated 60% of a road trip. if they have traveld 30 miles, how far is the full road trip?
Tems11 [23]

The full road trip is 50 miles.

Step-by-step explanation:

Given,

Distance traveled by Joe's family = 30 miles

This represents 60% of the total distance to be traveled.

Let,

x be the total distance.

60% of x = 30

\frac{60}{100}*x=30\\0.6x=30

Dividing both sides by 0.6

\frac{0.6x}{0.6}=\frac{30}{0.6}\\x=50\ miles

The full road trip is 50 miles.

Keywords: percentage, division

Learn more about percentages at:

  • brainly.com/question/3375830
  • brainly.com/question/3398261

#LearnwithBrainly

4 0
3 years ago
#4 is tough for me can you help me and explain how you got the answers.
Gnoma [55]
You put the scores in order from least to greatest, then you have to find the middle number. Now you will end up with two middle numbers you add them and divide by 2 then u have it answer.
4 0
3 years ago
Will someone please help me with this because I don't understand and I don't want to fail my class.
Marrrta [24]

Answer:

4y + 1 = 4 - 5y

First option

Step-by-step explanation:

x - 4y - 1 =0; add both sides by + 4y + 1

x - 4y - 1 + 4y + 1 = 0 +  4y + 1

Simplifying

x = 4y + 1

x + 5y - 4 = 0; Add (-5y + 4) to both sides

x + 5y - 4 -5y + 4 = 0 -5y + 4

Simplying

x = -5y +4

x = 4 - 5y

Now you have both equations

x = 4y + 1

x= 4 - 5y

Now you can use the comparison method

4y + 1 = 4 - 5y

3 0
3 years ago
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