To write an equation in slope-intercept form, we can use the given points to find the slope and y-intercept of the line. The equation that represents the amount of water in the can after x seconds is y = -2x + 68.
Explanation:To write an equation in slope-intercept form, we need to find the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
Given that the watering can contains 58 ounces of water after 5 seconds and 28 ounces of water after 20 seconds, we can use these two points to find the slope (m).
m = (28 - 58) / (20 - 5) = -30 / 15 = -2
Next, we can substitute one of the points and the slope into the equation and solve for b:
58 = -2(5) + b
b = 68
Therefore, the equation that represents the amount of water in the can after x seconds is
y = -2x + 68
Therefore, the equation in slope-intercept form that represents the amount y (in ounces) of water in the can after x seconds is y = -2x + 68.
To write the equation in slope-intercept form that represents the amount y (in ounces) of water in the can after x seconds, we need to determine the rate at which the water level decreases over time.
Given data:
- After 5 seconds, the can contains 58 ounces of water.
- After 20 seconds (5 seconds + 15 seconds), the can contains 28 ounces of water.
Let's define our points based on this data:
- First point: (5, 58) (5 seconds, 58 ounces)
- Second point: (20, 28) (20 seconds, 28 ounces)
Now, let's find the slope m of the line passing through these two points. The slope m is calculated as:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
[tex]\[ m = \frac{28 - 58}{20 - 5} \][/tex]
[tex]\[ m = \frac{-30}{15} \][/tex]
[tex]\[ m = -2 \][/tex]
Now that we have the slope m, we can use the point-slope form of the equation of a line, [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is one of our points. Let's use the point (5, 58):
[tex]\[ y - 58 = -2(x - 5) \][/tex]
Now, simplify and solve for y to get the equation in slope-intercept form (y-intercept form), y = mx + b:
[tex]\[ y - 58 = -2x + 10 \][/tex]
[tex]\[ y = -2x + 10 + 58 \][/tex]
[tex]\[ y = -2x + 68 \][/tex]
A hurricane has winds that are at least 74 miles per hour. Suppose a tropical storm Hamm has winds that are 42 miles per hour. Write and solve an inequality to find how much the winds must increase before the storm becomes a hurricane.
Final answer:
To find the necessary increase in wind speed for Tropical Storm Hamm to reach hurricane status, set up the inequality 42 + x >= 74, resulting in x >= 32. Hence, the wind speed must increase by at least 32 miles per hour.
Explanation:
To determine how much the wind speed must increase for Tropical Storm Hamm to become a hurricane, we use an inequality. We know that a storm becomes a hurricane when the wind speeds reach at least 74 miles per hour.
Currently, Tropical Storm Hamm has wind speeds of 42 miles per hour. Let's define the variable x as the increase in wind speed needed for the storm to reach hurricane status.
The inequality that represents this situation is:
42 + x ≥ 74
Now, we solve for x:
Subtract 42 from both sides of the inequality: x ≥ 74 - 42
Simplify: x ≥ 32
Therefore, the wind speed must increase by at least 32 miles per hour for Tropical Storm Hamm to become a hurricane.
While walking outside on a field trip 75%,or 15 of the students in the class wore jackets Find the number of students in the entire class.
Mrs. Ulrich has 3 times as manymarkers as colored pencils. The total number of markers and colored pencilsis 84. How many markers foesMrs. Ulrich have?
Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change. The sandwich cost $7.75 and sales tax was $0.47. What was the cost of her drink?
Given
Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change.
The sandwich cost $7.75 and sales tax was $0.47.
Find out the cost of her drink
To proof
Let the cost of her drink be x.
As given in the question
Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change.
Elysse paid for her sandwich and drink = 10 - 0.63
= $ 9.37
sandwich cost $7.75 and sales tax was $0.47
Than the equation becomes
x = 9.37 - (7.75 + 0.47)
x = 9.37 - 8.22
x = $ 1.15
The cost of the drink is $ 1.15.
Hence proved
Simplify each expression Justify each step
(22+19b)+7
18+(5+6m)
11s(4)
10y(7)
(9+31+5)[(7times5)times4]
A rectangular garden sits next to a house. Three sides of the garden are fenced, and the fourth side is the house. The length of the garden is 9 meters. A total of 21.5 meters of fencing is used. If w stands for the width of the garden in meters, which equation can be used to find its width?
To find the width of the rectangular garden, use the equation 2w + 9 = 21.5, which leads to a width of 6.25 meters after solving step by step. The total fencing used is 21.5 meters for the three sides, with the fourth side being the house.
Finding the Width of the Rectangular Garden
Given that three sides of the rectangular garden are fenced and the fourth side is the house, let's break down the problem step by step:
The length of the garden is given as 9 meters.A total of 21.5 meters of fencing is used for the three sides.We need to find the width w of the garden.Since only three sides are fenced, the total length of the fencing is the sum of two widths and one length of the garden. Therefore, we can write this equation:
2w + 9 = 21.5
To find w, we solve the equation as follows:
Subtract the length from the total fencing: 2w = 21.5 - 9Calculate the difference: 2w = 12.5Divide by 2 to isolate w: w = 12.5 / 2Final result: w = 6.25 metersTherefore, the width of the garden is 6.25 meters.
Please help...........
A ceramic tile is in the shape of a triangle. The angle measurements of this triangle are 30 degrees, 60 degrees, and 90 degrees. The leg across from the 30 degree angle is 6.25 cm long. How long is the hypotenuse of this triangle?
A store offers a $900 to buy a computor the terms of the loan are 9% simple interest and equal monthly payments for three years what is the monthly payment
Gina saves quarters. She has $17.75 in quarters. How many quarters does she have? Show your solution in two ways. Use division to show one way. Use words, nnumbers, or models for the second way.
Using division and a visual method, it is calculated that Gina has 71 quarters, given she has a total of $17.75.
Explanation:Gina has $17.75 and since each quarter is worth $0.25, we need to find out how many quarters make up this amount. First, using division we have 17.75 ÷ 0.25 = 71. Therefore, Gina has 71 quarters.
The second method is a more visual and explanatory one. Since each quarter is 25 cents, four quarters make up a dollar. Therefore, if we have $17, that directly translates to 17 x 4 = 68 quarters. We also have 75 cents left which correspond to another 3 quarters (75 ÷ 25 = 3). Adding these together gives us 68 + 3 = 71 quarters. So, either way, Gina has 71 quarters.
Learn more about Counting Quarters here:https://brainly.com/question/12036455
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A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
(6, 0)
(0, 5)
(1, 4)
(1, 5)
Final answer:
The best estimate of the solution to the system of equations is (1, 5).
Explanation:
In order to find the best estimate of the solution to the system of equations graphed on a coordinate plane, we need to look for the point where the two lines intersect. This point represents the solution to the system of equations.
The coordinates (1, 5) are the best estimate of the solution to the system of equations.
Hi
If you had to do an estimate with numbers: 32kg and 7 kg
What would be your total?
Need ASAP now, thanks
How might a pair of snakes be used for driving in the rain
Answer:
Step-by-step explanation:
Help please!!!!!!!!!!
Explain step by step =) Harry rides his bike 25 3/8 miles. Karen rides her bike 25 2/5 miles. Who rides farther?
We can see Karren rode farther
[tex]25[/tex] [tex]\frac{2}{5}[/tex] with a common denominator is:
[tex]5+3=8[/tex] [tex]2+3=5[/tex]
[tex]\frac{2}{5}+\frac{3}{3}=\frac{5}{8}[/tex]
so we know that Karren rode [tex]25\frac{5}{8}[/tex] miles which is more than Harrys [tex]25\frac{3}{8}[/tex]
is 7 x (6 x t) equivalent to (7 x 6) x t
tim knows the volume and base area of a wooden chest that is in the shape of a rectangular prism. If the volume is 524 cubic unit and the base area is 15 square unit, what is the height of the chest?
The height of the rectangular prism chest is approximately 34.93 units, calculated using the volume and base area formulas for rectangular prisms.
To find the height of the rectangular prism chest, we can use the formula for the volume of a rectangular prism, which is given by the product of its length, width, and height. Let's denote the height of the chest as h the length as l , and the width as w.
Given that the volume of the chest is 524 cubic units and the base area (length times width) is 15 square units, we have two equations:
1. [tex]\( l \times w \) (base area) \( = 15 \)[/tex] square units,
2. [tex]\( l \times w \times h \) (volume) \( = 524[/tex]) cubic units.
From the first equation, we can solve for one variable in terms of the other. Let's solve for l in terms of w :
[tex]\[ l = \frac{15}{w} \][/tex]
Now substitute this expression for l into the second equation:
[tex]\[ \frac{15}{w} \times w \times h = 524 \][/tex]
Simplify:
15h = 524
Solve for h:
[tex]\[ h = \frac{524}{15} \][/tex]
h ≈ 34.93
So, the height of the chest is approximately 34.93 units.
Julie has read 27 pages out of an 80 page book. What percent of the pages has she read
a fair 20 sided dice is rolled 1000 times. how many times would you expect to roll a 6?
(Include working out too plz)
thxx
Please help!
5 pts each!
50 pts in all!
Please give the correct answers or i will report that it was wrong!
help me this egg farm produces 2400 eggs on monday. you can pack them in crates of 144 eggs each. how many eggs would be needed to fill that last crate
7x3.8 find the product mentally
What is the Negative Scale Factor?
a rectangle with a length of x+5 has a perimeter of 4x+14. 1. write the expression for the width of yhe rectangle in terms of x. 2. suppose the perimeter of the rectangle is 42 inches. what are the length and width of the rectangle?
Evaluate for x = 2.
(12x + 8)
4
A) 4
B) 5
C) 6
D) 8
To evaluate the expression (12x + 8) / 4 for x = 2, you multiply 12 by 2, add 8, and then divide by 4. The final answer is 8, which corresponds to option D.
Explanation:To evaluate the expression (12x + 8) / 4 for x = 2, you substitute the value of x into the expression and then simplify. First, multiply 12 by 2 to get 24, then add 8 to get 32. After that, divide 32 by 4 to get the final answer.
Here is the step-by-step calculation:
Substitute x with 2: (12*2 + 8) / 4.Multiply 12 by 2: (24 + 8) / 4.Add 24 and 8: 32 / 4.Divide 32 by 4: 8.The correct answer is D) 8.
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What is the area of the green triangle?
A) 23 cm2
B) 30 cm2
C) 46 cm2
D) 65 cm2
what is the estimate of 119÷23.3
Solve.
(2x+24)(4x+36)
Ethan wants to put a fence around his vegetable garden. The garden is 30 feet wide and 15 feet long. If the total cost of the fence is $810, what is the unit price of the fence per foot?
For a STEM competition, Julienne constructed a model rocket. The rocket can reach an average height of 545 feet. Find the differences between the average heigh and the actual heights reached. Then write then as positive and negative rational numbers. Order the differences from least to greatest.
Actual heights
534.2
556.4
554.0
535.3
Answer: -11.4, -9, 9.7, and 10.8
Step by step explanation: You had to subtract the actual height from the average height and then order the sum of each answer from least to greatest. Hope this helped!