At the end of the day, Mr. Díaz drains the pool. The equation
y = -50x + 300 can be used to find y, the number of gallons of
water left after draining the pool for x minutes. Graph the
equation. How long does it take to drain the pool? Explain.
Answers
Answer: 6 minutes.
Step-by-step explanation: You can use a graphing calculator to see the exact graph, but you're trying to figure out what value of x gives you a y of 0. -50 times 6 is 300, plus 300 equals 0.
The graph of the equation y = -50x + 300 is a straight line, and plotted below. The time it take the pool to drain, according to this equation, is 6 minutes.
How do we make graph of a function?Suppose the considered function whose graph is to be made is f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
For this case, we're specified that:
y = the number of gallons of water left after draining the pool for x minutes.The relationship between x and y given is: y = -50x + 300Take two different values of x, let it be 0 and 1.
Then, the value of y we get is:
Case 1: x = 0:[tex]y = -50x + 300\\y = -50 \times 0 + 300\\y = 300[/tex]
Thus, one point on the equation y = -50x + 300 is (0,300)
Case 2: x = 1:[tex]y = -50x + 300\\y = -50 \times 1 + 300\\y = 300 - 50 = 250[/tex]
Thus, another point on the equation y = -50x + 300 is (1,250)
Plot these points taking x on horizontal and y on vertical axis. Then join those two points by a straight line. This is the graph of the considered equation as equation of type [tex]y = mx +c[/tex] is a straight line's equation and for straight line, two of its points are sufficient to plot it.
The graph is given below.
Since we know that:
y = number of gallons of water left after draining the pool for x minutes,
so when the pool drains of fully, there will be no water left, or y = 0.
Putting y = 0 in the equation y = -50x + 300, we get:
[tex]y = -50x + 300\\0 = -50x + 300\\\\\text{Adding 50x on both the sides}\\\\50x = 300\\\\\text{Dividing both the sides by 50}\\\\x = \dfrac{300}{50}= 6[/tex]
Thus, when y= 0, we get x = 6, so when the fully filled pool is drained for 6 minutes, the whole pool gets drained (for this case).
Thus, the time it take the pool to drain, according to this equation, is 6 minutes. The graph of the equation y = -50x + 300 is given below.
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Related Questions
Select the equivalent expression.
Answers
Answer:
The Answer is B
Step-by-step explanation:
In [tex](a^{-2} * 8^{7})^{2}[/tex], each inner term has its exponent multiplied by the two on the outside. The answer is thus [tex]a^{-4}*8^{14}[/tex] or [tex]\frac{8^{14}}{a^{4}}[/tex]
The line containing the points (30, 40) and (40, 60) has a y-intercept of?
Help help
Answers
Answer:
-20
Step-by-step explanation:
the slope is 2
2*30 = 60
40 - 60 = -20
Pls helpppppppppppppppppp
Answers
Answer: 75
Step-by-step explanation:
Multiple all those numbers together and then divide by 3
Answer:
75
Step-by-step explanation:
V=lwh/3 which =5·7.5·6/3 and that equals 225/3 which results in 75
How was triangle A translated?
O four units left
O four units right
O six units left
O six units right ark this andTetrn
Answers
Answer:
D
Step-by-step explanation:
i know its six units right but i dont know what the rest of the answer says tho
Answer: D
Six units right
Step-by-step explanation:
I got it right on edg2020
Based on the diagram below, find the value of v, u and w: *(round to one decimal place)
Answers
Answer:
u=27 v=9.5 w=28.5
Step-by-step explanation:
Which expression has the same value as 4÷25?
Answers
Answer:
We need the choices, since there are plenty equations with the same value.
Step-by-step explanation:
4/25=0.16
Whichever equation equals 0.16 is your answer.
What is an equation of the line that passes through the point (5,-5) and is parallel to the line x+5y=20
Answers
Answer:
y = [tex]-\frac{1}{5}[/tex]x - 4
Step-by-step explanation:
Given parameters:
Coordinates = (5, -5)
Equation of the line, x + 5y = 20
Unknown:
Equation of the line parallel to this= ?
Solution:
To find the equation of the line, we must first understand that parallel lines are lines having the same slope. They do not cross each other at any point.
The equation of any straight line is given as;
y = mx + c
y and x are the coordinates
m is the slope
c is the y- intercept
Now,
x + 5y = 20
Let us find the slope of this line;
5y = -x + 20
Divide through by 5;
y = [tex]-\frac{1}{5}[/tex]x + 4
The slope of the new line is the coefficient of x;
Slope = [tex]-\frac{1}{5}[/tex]
So, let us find the y-intercept of the new line;
-5 = [tex]-\frac{1}{5}[/tex] x 5 + c
-5 = -1 + c
c = -5 + 1 = -4
Now,
y = [tex]-\frac{1}{5}[/tex]x - 4
Answer: y = -(1/5)x - 4
Step-by-step explanation:
PLEASE HELP!!
For what value of x does 2x-4/x+7 = 1/3?
A. 33/5
B. 2
C. 19/5
D. -7
Answers
Answer:
A i think
Step-by-step explanation:
1 Multiply both sides by 3x3x.
6{x}^{2}-12+21x=x6x
2
−12+21x=x
2 Move all terms to one side.
6{x}^{2}-12+21x-x=06x
2
−12+21x−x=0
3 Simplify 6{x}^{2}-12+21x-x6x
2
−12+21x−x to 6{x}^{2}-12+20x6x
2
−12+20x.
6{x}^{2}-12+20x=06x
2
−12+20x=0
4 Use the Quadratic Formula.
x=\frac{-20+4\sqrt{43}}{12},\frac{-20-4\sqrt{43}}{12}x=
12
−20+4√
43
,
12
−20−4√
43
5 Simplify solutions.
x=-\frac{5-\sqrt{43}}{3},-\frac{5+\sqrt{43}}{3}x=−
3
5−√
43
,−
3
5+√
43
x = y, If y=9, then x = 9
what property is this?
Answers
Answer:
The Transitive Property for x and y
Step-by-step explanation:
This is confusing I need help .
Answers
Answer:
x = 54angle ACD = 124°Step-by-step explanation:
The rule is that the exterior angle (ACD) is equal to the sum of the remote interior angles (the two marked angles on the right).
You are expected to use this relation to write and solve an equation.
exterior angle = angle D + angle B
(2x +16) = 58 + (x+12)
2x +16 = x +70
x + 16 = 70
x = 54
Then angle ACD is ...
angle ACD = (2x +16)° = (2·54 +16)°
angle ACD = 124°
Carmen creates the ratio table below based on one 8-ounce serving of juice
How many total calories will 4 servings of juice contain?
A) 420
B) 520
C) 650
D) 780
Answers
Answer:
B
Step-by-step explanation:
The pattern is adding 130, or multiply the servings by 130.
so if 3x=390, you would divide both sides by 3 and get 130.
This means that x=130
Now plug in 4x=?
You would get 4*130=?
if you do the math through multiplication you would get 520
Answer:
B
Step-by-step explanation:
I got the unit test right on edg 2020
the sum of two numbers is 10 the difference between the two numbers is 4
Answers
Answer:
7 and 3
Step-by-step explanation:
7+3=10. And 7-3=4
PLEASE ANSWER EASY 5 POINTS
Answers
Answer:
15(B)
Step-by-step explanation:
all of those angles add up to 180 on a line
9 times 15 is 135
3 times 15 is 45
135+45 is 180
HelpppppppPPPPPPPPPPPPPPPP
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
If you solve this inequality you should get...
[tex]4<3+4x\\1<4x\\\frac{1}{4} <x[/tex]
So I don't know if you can but the answer is all three because 9, 7, and 1 are all greater than [tex]\frac{1}{4}[/tex].
The cost of 6 1/2 kg of apples is Rs. 520. What is the rate of one kg of apples
Answers
Step-by-step explanation:
So, cost of 6.5 kg of apples is Rs. 520 and we need to find cost of one kg apples.
It can be done just by applying Unitary Method!So,
6.5 kg -- Rs. 520
1 kg -- Rs.(520/6.5) = Rs.80
So, cost of 1 kg apples is Rs.80.Who c is the value of the expression [(10^4)(5^2)/10^3)(5^3)]^3 1 2 8 10
Answers
Answer:
8
10 divided by 5 is 2, and 2 cubed is 8
The length and width of a rectangle are in a ratio of 7:11. If the perimeter of the
rectangle is 72 cm. Find the
length and
width of the rectangle.
Answers
Answer:
14cm and 22cm
Step-by-step explanation:
Given parameters:
Perimeter of rectangle = 72cm
Ratio of length to width = 7: 11
Unknown:
Length and width of the rectangle = ?
Solution:
Since the ratio of length to width is 7: 11,
if the length is 7x , width = 11x
The perimeter of a rectangle can be obtained using
Perimeter = 2(L + W)
Insert the parameters and solve;
72 = 2(7x + 11x )
72 = 2(18x)
x = [tex]\frac{72}{36}[/tex] = 2
The length = 7x = 7x2 = 14cm
width = 11x = 11 x 2 = 22cm
Solve the system equation for X and using the elimination method .
- 2x + Зу = -1
2х + 5y= 25
Answers
Answer: 2х+5y=25= Slope = -0.800/2.000 = -0.400
x-intercept = 25/2 = 12.50000
y-intercept = 25/5 = 5
so slope form =0,400
x intercept form = 12.50000
y intercept =5
and the answer to 2x+3y=-1= Slope = 1.333/2.000 = 0.667
x-intercept = 1/2 = 0.50000
y-intercept = -1/3 = -0.33333
Step-by-step explanation: an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x+5y-25 = 0 and calculate its properties
Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000
y-intercept = 25/5 = 5
When y = 0 the value of x is 25/2 Our line therefore "cuts" the x axis at x=12.50000
x-intercept = 25/2 = 12.50000
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 5.000 and for x=2.000, the value of y is 4.200. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 4.200 - 5.000 = -0.800 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -0.800/2.000 = -0.400
Geometric figure: Straight Line
Slope = -0.800/2.000 = -0.400
x-intercept = 25/2 = 12.50000
y-intercept = 25/5 = 5
A carpenter can build 8 cabinets in 3 hours. At this rate, how long will it take for the carpenter to build 26 cabinets?
a. 8 hours
c. 21 hours
b. 9 hours 45 minutes
d. 69 hours 20 minutes
Answers
Answer: 21 hours
Step-by-step explanation:
i’m not sure how to solve it i just guessed and got it right
Answer:
21
Step-by-step explanation:
Learning Task 2.
A. Translate the following verbal sentences to mathematical sentence. Then ex-
press into quadratic equations in terms of "x".
Given
Quadratic Equations
1. The length of a wooden frame is 1 foot
longer than its width and its area is equal
to 12 ft2
2. The length of the floor is 8 m longer than
its width and there is 20 square meters.
3. The length of a plywood is 0.9 m more
than its width and its area is 0.36 m2.
4. The area of rectangle whose length is six
less than twice its width is thirty-six,
5. The width of a rectangular plot is 5 m
less than its length and its area is 84 m2.☹️
Answers
Answer:
1)[tex]x^2+x-12=0[/tex]
2)[tex]x^2+8x-20=0[/tex]
3)[tex]x^2+0.9x-0.36=0[/tex]
4)[tex]2x^2-6x-36=0[/tex]
5)[tex]x^2-5x-84=0[/tex]
Step-by-step explanation:
1) The length of a wooden frame is 1 foot longer than its width and its area is equal to 12 sq. ft.
Let the width be x
We are given that length of a wooden frame is 1 foot longer than its width
So, Length = x+1
Area of rectangular frame =[tex]Length \times Breadth = x(x+1)[/tex]
ATQ
x(x+1)=12
[tex]x^2+x-12=0[/tex]
2)The length of the floor is 8 m longer than its width and there is 20 square meters.
Let the width be x
We are given that length of the floor is 8 m longer than its width
So, Length = x+8
Area of floor= [tex]Length \times Breadth = x(x+8)[/tex]
ATQ
x(x+8)=20
[tex]x^2+8x-20=0[/tex]
3)The length of a plywood is 0.9 m more than its width and its area is 0.36 m2.
Let the width be x
We are given that length of a plywood is 0.9 m more than its width
So, Length = x+0.9
Area of plywood=[tex]Length \times Breadth = x(x+0.9)[/tex]
ATQ
x(x+0.9)=0.36
[tex]x^2+0.9x-0.36=0[/tex]
4)The area of rectangle whose length is six less than twice its width is thirty-six
Let the width be x
We are given that length is six less than twice its width
So, Length = 2x-6
Area of rectangle = Length \times Breadth = x(2x-6)
ATQ
x(2x-6)=36
[tex]2x^2-6x-36=0[/tex]
5)The width of a rectangular plot is 5 m less than its length and its area is 84 m2.
Let the length be x
Width = x-5
Area =[tex]Length \times Breadth = x(x-5)[/tex]
ATQ
x(x-5)=84
[tex]x^2-5x-84=0[/tex]
What is the average rate of change of y with respect to x over the interval [-2, 6] for the function y = 5x + 2?
Answers
Answer:
5
Step-by-step explanation:
Average rate of change is slope, which is change in y over change in x:
[tex]\frac{[5(6)+2]-[5(-2)+2]}{6-(-2)} =\frac{32-(-8)}{8} =5[/tex]
The average rate of change of the function is 5.
What is the average rate of change of a function?The sum of the change in the function values (output values) divided by the change in the input values is the average rate of change between two input values.
The given interval is [-2,6] and the given function is f(x) = y = 5x + 2.
The value of the function for x = 6 is:
f(6) = 5(6) + 2
f(6) = 32
The value of f(x) for x = -2 is:
f (-2) = 5(-2) + 2
f(-2) = -10 + 2
f(-2) = -8
The average rate of change of the function is given by:
( f(6) - f(-2) )/ (6 - (-2))
= ( 32 - (-8))/ (6 + 2)
= ( 32 + 8)/8
= 40/8
= 5
Hence, the average rate of change of the function is 5.
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3 708 000 000 in scientific notation
Answers
3,708,000,000 in scientific notation is [tex]3.708[/tex] × [tex]10^9[/tex]
If 132 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $2.25 and total receipts for the concert was $384, how many of each went to the concert?
Answers
Answer
i'm pretty sure 64 people attended the concert.
Step-by-step explanation:
Tell me if this helped or not.
Find x and y. Need answer ASAP!!!
Answers
Answer:
x = 16, y = 23
Step-by-step explanation:
Consider angles related to the parallel lines and the left transversal
4x + 4 and 7x - 44 are alternate exterior angles and congruent , thus
7x - 44 = 4x + 4 ( subtract 4x from both sides )
3x - 44 = 4 ( add 44 to both sides )
3x = 48 ( divide both sides by 3 )
x = 16
----------------------------------------------------------
Consider angles related to the parallel lines and the right transversal
39 and 8y - 43 are same- side exterior angles and supplementary, thus
39 + 8y - 43 = 180 , that is
8y - 4 = 180 ( add 4 to both sides )
8y = 184 ( divide both sides by 8 )
y = 23
Combine the like terms to create an equivalent expression:
\large{-5+(-5r)+10}−5+(−5r)+10
Answers
Answer:
−10r +10
Step-by-step explanation:
Let's simplify step-by-step.
−5−5r+10−5−5r+10
=−5+−5r+10+−5+−5r+10
Combine Like Terms:
=−5+−5r+10+−5+−5r+10
=(−5r+−5r)+(−5+10+−5+10)
=−10r+10
Answer:
−5r+5
Step-by-step explanation:
100 micrograms of a drug are contained in 2 milliliters. How many milliliters are contained in 15 micrograms?
Answers
Answer:
.3
Step-by-step explanation:
multiply .15 by 2
What is the solution to this system of linear equations?
y − x = 6
y + x = −10
a. (−2, −8)
b. (−8, −2)
c. (6, −10)
d. (−10, 6)
Answers
Answer:
B: (-8,-2)
you add the equation to solve the first variable, then plug in the values to the other equation to find the last variable
good Luck!!!
Factor -6m + 9.
-6(m - 3)
-6(m + 9)
-3(2m + 3)
-3(2m - 3)
Answers
Answer:
-3(2m - 3)
Step-by-step explanation:
Find GCF
-3 so -6m/-3 = 2m
9/-3 = -3
-3(2m-3)
Simplify the expression by
distributing, then combining like
terms!
6(2y +5) - 12
Answers
Analyze the number line below and answer the question that follows.
If jpg, where could point I be?
A.
–7
B.
–6
C.
–5
D.
–4
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
c
Step-by-step explanation:
