The equation of a line is given as y = -2/3x + 7/3
Equation of a lineThe formula for calculating the equation of a line is expressed as;
y = mx + b
where;
m is the slope
b is the y-intercept
Given the coordinate points (2, 1) and (-1, 3)
m = 3-1/-1-2
m = 2/-3
m = -2/3
Determine the y-intercept
1 = -2/3(2) + b
1= -4/3 +b
b = 1 + 4/3
b = 7/3
Hence the equation of a line is given as y = -2/3x + 7/3
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(04.01 MC) A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 10 inches. Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 10) would represent a height of 10 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points) Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points) Part C: If the rate at which the candle burned was 0.75 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
The ordered pairs, justification of the function with different order pairs is required.
The ordered pairs are [tex](0,10),(1,9.5),(2,9),(3,8.5),(4,8),(5,7.5)[/tex]
All values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.
y = Height of candle
x = Number of hours
m = Rate = 0.5 inches per hour
c = y intercept = Initial height = 10 inches
The required function is
[tex]y=-0.5x+10[/tex]
Six ordered pairs would be
[tex]x=0,1,2,3,4,5[/tex]
[tex]y=-0.5\times 0+10=10[/tex]
[tex]y=-0.5\times 1+10=9.5[/tex]
[tex]y=-0.5\times 2+10=9[/tex]
[tex]y=-0.5\times 3+10=8.5[/tex]
[tex]y=-0.5\times 4+10=8[/tex]
[tex]y=-0.5\times 5+10=7.5[/tex]
The ordered pairs are
[tex](0,10),(1,9.5),(2,9),(3,8.5),(4,8),(5,7.5)[/tex]
It can be seen that all values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.
If m = 0.75 inches per hour
The function would change to
[tex]y=-0.75x+10[/tex]
Some ordered pairs would be
[tex]y=-0.75\times 0+10[/tex]
[tex]y=-0.75\times 1+10[/tex]
[tex](0,10),(1,9.25)[/tex]
The same is seen in this function, all values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.
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It cost $36.75 for three tickets to visit the science center. It cost $51 for 4 tickets to visit the zoo. Which attraction will cost more money for a group of 12 students to visit? How much more?
Use the number line to identify the least value, first quartile, median, third quartile, and greatest value of the data.
Ages of teachers (in years): 30, 62, 26, 35, 45, 22, 49, 32, 28, 50, 42, 35
Answer: least value - 22
first quartile - 29
median - 35
third quartile - 47
greatest value - 62
Step-by-step explanation:
The table represents the function f.
What is f3)?
X
f(x)
0
As per the given data the required answer is 9............
Angles that form a linear pair
add up to [?]°
Answer:
180°
Step-by-step explanation:
Two adjacent angles whose sum add up to 180°are called Linear pair. The uncommon arms of two adjacent angles form a straight line.
David wants to start a lawn care business. He offers his clients two different service options: Plan A charges $20 per month plus $5 an hour. Plan B charges $30 per month plus $3 an hour. He used the system of equations below to determine how much money he can make on both plans. y = 5x + 20 y = 3x + 30 If x represents the number of hours he works, and y represents the total money he makes, how many hours would he have to work to make the same amount of money with both plans?
Answer:
1440 hrs
Step-by-step explanation:
5 is the number of hours he works, and 45 is the total money David makes.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that David offers his clients two different service options.
Plan A charges $20 per month plus $5 an hour.
Plan B charges $30 per month plus $3 an hour.
y = 5x + 20 and y = 3x + 30 are the system of equations to determine how much money he can make on both plans.
y = 5x + 20..(1)
y = 3x + 30..(2)
Substitute equation 2 from equation 1.
y-y=5x+20-3x-30
0=2x-10
2x=10
Divide both sides by 2
x=5.
Now substitute x in equation 1.
y=25+20
y=45
Hence, 5 is the number of hours he works, and 45 is the total money David makes.
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help me lol
50 points for whoever answers correctly
Answer:
C
Step-by-step explanation:
You want to choose the number line graph that appropriately represents the inequality 0 < x ≤ 26.
Graphing inequalitiesThe given compound inequality is conveniently written with the "arrows" pointing to the left. This means the lower limit of the variable is on the left side of the inequality, just as it is on the left end of the number line graph.
The inequality symbols used are "less than" (<) and "less than or equal to" (≤). The "less than" symbol is represented on a number line graph by an open circle. The "less than or equal to" symbol is represented by a filled dot on the number line.
This means you are looking for a graph that has an open circle on the left end of a solid line, and a filled dot on the right end. Only graphs B and C have finite-length lines, and only graph C has a filled dot at the right end.
Car seatsIn English, the word "between" often implies "and including" when it is describing an interval between two limits. Here, you are given 3 car seat specifications:
A: 0 < x ≤ 26 . . . . . up to 26 lbsB: 18 ≤ x ≤ 35 . . . . . between 18 and 35 poundsC: 26 ≤ x ≤ 75 . . . . . between 26 and 76 poundsThe seats appropriate for a 33-lb child would be seats B and C, because 33 is included in each of those intervals.
WILL GIVE BRAINLIEST!!
Ignore the $
Meyer rolls two fair, ordinary dice with the numbers $1,2,3,4,5,6$ on their sides. What is the probability that at least one of the dice shows a square number?
Two numbers on each die are squares: 1 and 4. 4 numbers on each die are not squares: 2 , 3, 5, and 6. there are 16 ways for him to roll a non-square die, out of 36 outcomes for the pair of dice. The other 20 options each have a square number showing on one or both dice. So, the probability is 5/9. hope this helps please pick my answer as brainliest, have a good day!
help was 2+2??
this is the before
Answer:
169
Step-by-step explanation:
I will give brainliest i will also give a lot of points
Answer:
-12y^10
Step-by-step explanation:
First let's rewrite the equation using the commutative property of multiplication
3 x (-4)y^8y^2
Multiply y^8 by y^2 by adding the exponents
y^8+y^2= y^10
3 x (-4)y^10
Now multiply 3 by -4
3 x -4= -12
Finally put them together
-12 + y^10= -12y^10
Answer:
[tex] - 12 {y}^{10} [/tex]
Step-by-step explanation:
We are to simplify:
[tex](3 {y}^{8} )( - 4 {y}^{2} )[/tex]
3 multiplies -4 to get -12, as shown below
[tex]3 \times - 4 = - 12[/tex]
Now, to multiply the exponents which are 8 and 2, we have to use the exponential rule of multiplication: [tex] {a}^{b} \times {a}^{c} = {a}^{b + c} [/tex]
Therefore:
[tex] {y}^{8} \times {y}^{2} = = > {y}^{8 + 2} = {y}^{10} [/tex]
Now, combine -12 and [tex] {y}^{10} [/tex] to get your final answer.
Final answer [tex] = - 12 {y}^{10} [/tex]
I hope this helpsthe larger of 2 consecutive integers is 10 more than twice the smaller. Find the integers
Solve for x for the triangle
Answer:
(appx) 4.3
Step-by-step explanation:
[tex] \sin(64) = \frac{x}{10} [/tex]
[tex] = > 0.43 = \frac{x}{10} [/tex]
[tex] = > x = 4.3[/tex]
if the measure of the angle WXZ is equal to the measure of XYZ, which statement si true
Answer:
ray XZ is the angle bisector of angle WXY.
please answer correctly!!
Answer:
Undefined
Step-by-step explanation:
Subtract the following polynomials, then place the answer in the proper location on the grid.
2x^2+5x-10
3x2 - x + 9
Answer:
[tex]-x^2+6x-19[/tex]
Step-by-step explanation:
Step one:
given
[tex]2x^2+5x-10\\\\3x^2 - x + 9[/tex]
we want to perform a subtraction operation
[tex]2x^2+5x-10-(3x^2 - x + 9)\\\\ 2x^2+5x-10-3x^2 + x - 9 \\\\[/tex]
collect like terms
[tex]2x^2-3x^2+5x+x-10-9\\\\-x^2+6x-19[/tex]
Find the scale factor of trapezoid QRST if it’s dilated to Q’R’S’T’. Type your result in the empty box provided below. HELPP PLEASE!!!!!!
Answer:
5 units
Step-by-step explanation:
its hard to tell but i think it dilated 5 units
We want to find the scale factor at which QRST is dilated to form Q'R'S'T'
We will find that the scale factor is 2.
In a general dilation, we will see that all the measures change in the same way, by the scale factor.
This means that:
QR*k = Q'R'
RS*k = R'S'
And so on, where k is the scale factor.
Then we can just find one of the equivalent measures in both trapezoids and find the value of k.
For example, we have:
Q'R' = 8
QR = 4
Replacing these on the above equation we get:
4*k = 8
k = 8/4 = 2
k = 2
The scale factor of dilation is 2.
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A store pays by the ounce to have different types of bracelets made and wants categorize them by price drag each purchase to the category that shows the ratio of dollars
Answer:
include a picture
Answer:
THIS IS THE CORRECT ANSWER FOR IMAGINE MATH BRAINLIEST PLZ
Step-by-step explanation:
yw!
What linear function models the table of values?
a boat travelled 36 miles in 2 hours. At this rate how many miles will the boat travel in 1/3 hour
Answer:
6 miles
Step-by-step explanation:
36/2=18 mph
18/3=6 per 1/3 hour
The National Science Institute was conducting research on the speed of Cheetahs. After
concluding their research, they were able to predict the cheetahs speed or distance when given
certain times or miles that the cheetah traveled. Complete the table of values and graph the
data on the coordinate plane.
Time(min) |. Distance(mi)
0. 0
1/2. 2/3
1. ?
? 3
8. ?
Answer the following questions using the information above.
1.) Is the relationship proportional? Why or why not?
2.) What is the unit rate?
The table of values is:
Time(min) | Distance(mi)
0 0
1/2 2/3
1 4/3
9/4 3
8 32/3
1) The relationship between Distance and Time is proportional.
2) The unit rate is 4/3 miles
To complete the table, we need to find the missing values of time and distance.
We use the relation between Distance, speed and time ,to find the missing values, which is given by,
Distance = Speed x Time
Given when time = 1/2 minute, the distance = 2/3 miles
Speed = Distance/Time
= 2/3 x 2/1
= 4/3 mile per minute.
This is the constant speed of the cheetah. We use this constant speed to find the other values to complete the table.
So If we take 'y' as the distance and 'x' as the time, then the relationship between time and distance can be expressed as
y = (4/3)x [since Distance = Speed x Time ].
So this relationship is proportional because there is a constant of proportionality 4/3 in the linear equation above and hence can be graphed as well.
The graph will contain the time values on the x-axis and distance values on the y-axis.
So now we need to find the missing values on the table using the above linear equation.
When time, x = 1 minute, distance, y = (4/3) x 1 = 4/3 miles.
When distance, y = 3 miles, 3 = (4/3)x
⇒ time, x = 3 x (3/4) = 9/4 minutes.
When time, x = 8 minutes, distance, y = (4/3) x 8 = 32/3 miles.
So the table is:
Time(min) | Distance(mi)
0 0
1/2 2/3
1 4/3
9/4 3
8 32/3
The unit rate refers to the y-value when the x-value is unity(1). So the unit rate here is found when time = 1 minute.
From the table, distance when time = 1 minute is 4/3 miles.
Hence, unit rate = 4/3 miles.
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galaxy a has 8x10 stars. galaxy b has 6x10 stars. choose which galaxy has more stars. then fill in the blank with a number written in standard notation
Answer: 750 times more stars.
Step-by-step explanation:
You already know the answer (Galaxy B is quite obviously larger) but the amount of times larger is dependent on the value you get when you divide;
6 billion by 8 million (6,000,000,000/8,000,000)
...which is 750.
Burj Khalifa in Dubai is the tallest building in the world, standing at 828 meters. An adjacent
building, 100 meters away, stands at 550 meters tall. What is the angle of depression from Burj
Khalifa to the adjacent building?
Answer:
Approximately 70 degrees
Step-by-step explanation:
If we make a right triangle connecting the two buildings, we get a triangle with height 278m and length 100m
We can connect these two values to the theta by using the inverse tan formula
arctan(278/100) = 70.21572110836 degrees.
The angle of depression is approximately 70 degrees
what is 7 7/8 dvided by 3 1/8 mixed numbers
Answer:
2.52
Step-by-step explanation:
Answer:
2.52
Step-by-step explanation:
Max purchased a solar pool cover for his swimming pool. What is the area of the
solar cover for the swimming pool?
10ft
32 ft
Square Feet
Answer:
320 ft^2
Step-by-step explanation:
(Lots of points)PLEASE HELP ME Due today at 8:59 in Texas
Answer:
6.) So 8 of 24 hours is 1/3. So the percent of his time used was 33.33333 . . % (etc)
7.) The easiest way to figure out a percentage is dividing it. So if it was 30 hit out of 75 people, then divide 30 by 75. So 40% of them got hit.
Hope that helps
A hula hoop has a diameter of 44 inches. What is the circumference of the hula hoop? Use 3.14 for tt
Answer:
i think 126 sorry if im wrong
Step-by-step explanation:
(7-6)•w
simplify the variable expression
Answer:
7w-6w
Step-by-step explanation:
I think this is what your asking for. If it is, you distribute the w
Answer:
w
Step-by-step explanation:
You complete the subtraction in the parentheses first, then multiple that by w. So:
(7-6) x w
(7-6) = 1
1 x w = w
Juanita makes $26 an hour at work. She has to take time off work to purchase her skirt, so each hour away from work costs her $26 in lost income. Assume that returning to work takes Juanita the same amount of time as getting to a store and that it takes her 30 minutes to shop. As you answer
the following questions, ignore the cost of gasoline and depreciation of her car when traveling.
Answer: Local Department Store: $6.5, $118.5
Across Town: $13, $102
Neighboring City: $26, $96
Step-by-step explanation:
Local Department Store: 1 hr=60 min.
60/15=4
26/4=$6.5
112+6.5=$118.5
Across Town: 60/30=2
26/2=$13
89+13=$102
Neighboring City: 60/60=1
26/1=$26
70+26=$96
If a student is taking classes, math, English, P.E., history, biology and Spanish, then what is the chance that the student will take math period? Assume that there are six periods in one day.
10%
17%
25%
60%
Answer:
60%
Step-by-step explanation: i hope this heple
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The mean of four number is 30. if three of the numbers are 12, 50, and 48 what's the fourth number?
Answer:
if the mean of 4 numbers is 30 then that means that the total of all the numbers added together must add up to 120 (30 x 4)
then you subtract the three numbers that you have from the total
120-12-50-48 = 10
so the last number is 10
Step-by-step explanation: