The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is y = -2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is given as,
y = mx + c
The line passes through the points (0, -2) and (4, -2).
Now,
Slope = m
m = (-2 + 2) / (4 - 0)
m = 0 / 4
m = 0
Now,
(x, y) = (0, -2)
y = mx + c
-2 = 0 x 0 + c
c = -2
Now,
m = 0 and c = -2
y = 0x -2
y = -2
Thus,
The equation of the line is y = -2.
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(*6./Sean drives from Manchester to Gretna Green.
He drives at an average speed of 50 mph for the first 3 hours of his journey.
He then has 150 miles to drive to get to Gretna Green.
Sean drives these 150 miles at an average speed of 30 mph.
Sean says,
"My average speed from Manchester to Gretna Green was 40 mph."
Is Sean right?
You must show how you get your answer.
Sean's real average speed was less than his predicted 40 mph.
What is average speed?Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time.
Student must calculate average speed, compare it to Sean's response, and determine total distance traveled and time expended. First, the formula must be stated: Average speed = Total distance traveled / Time required.We can rearrange this to determine the distance traveled.Total mileage equals time divided by average speed.We only need to compute the first leg of his travel as we already know the total distance was 150 miles. As a result, we can calculate 150 miles at 50 mph for 3 hours.We now know that the overall distance from Manchester to Greta Green was 300 miles after including the second half of the voyage.Now we have to think about how long it took overall. Rearranging the equation yields the necessary result: Time taken=distance/speed. This brings us back to the comparatively easy formula of 150 miles at 30 miles per hour equals 5 hours. This indicates that the total travel time from Manchester to Gretna Green was 8 hours, not including the initial 3 hours. We now possess all the knowledge required to calculate his average speed over the entire journey. The original equation is still used: Average speed = Total distance traveled / Time taken. After entering all the data, we get the result 300 miles in 8 hours = 37.5 miles per hour.Hence, Sean's real average speed was less than his predicted 40 mph.
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you spin two wheels with equal size wedges labeled with numbers 1 through 6. what is the probability that either wheel lands on an odd value ?
The probability that either of spin two wheel lands on an odd value is 1.
Define the term probability?Probability is a way to gauge how likely something is to happen. Even though no event can be predicted with absolute certainty, probability can be used to express how likely it is that it will happen.For the stated question-
Total number marked on the wheel (1 to 6) = 6 numbers.
Total odd number (1, 3, 5) = 3 numbers
Probability of of getting odd number on one wheel = 3/6 = 1/2.
Let the probability of of getting odd number on one wheel P(A).
Then, Probability of of getting odd number on second wheel P(B).
Then,
Only only wheel have the odd number,
P(A∩B) = 0.
Thus,
Probability that either wheel lands on an odd value;
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 1/2 + 1/2 - 0
P(A∪B) = 1
Thus, probability that either wheel lands on an odd value is 1.
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You are standing on a ledge and throw a ball from 10 feet above the ground. The speed the ball leaves your hand is 16 feet per second and the acceleration of gravity is -16 feet per second squared.
1. How many seconds does it take to reach the highest point (vertex)?
The ball reached its maximum height at a time of 1 second.
How many time is needed for the ball to reach its maximum height?
In this problem we have the case of a ball that experiments a free fall, that is, a case of an uniform accelerated motion due to gravity. The position of the ball as a function of time is represented by a quadratic equation:
y' = y + v · t + 0.5 · g · t²
Where:
y - Initial position, in feet.v - Initial velocity, in feet per second.t - Time, in seconds.g - Gravitational acceleration, in feet per square second.And to determine the time related to the highest point, we need to rearrange the expression into its standard form:
y' - k = C · (t - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantFirst, write the quadratic equation:
y' = y + v · t + 0.5 · g · t²
y' = 10 + 16 · t - 8 · t²
Second, complete the square until the standard form is found:
y' - 10 = 16 · t - 8 · t²
y' - 10 = - 8 · (t² - 2 · t)
y' - 18 = - 8 · (t² - 2 · t + 1)
y' - 18 = - 8 · (t - 1)²
The ball takes a time of 1 second to reach its maximum height.
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If f(x) = 3x² - x, find f{-3, 0, 3}
Step-by-step explanation:
so pretty much replace -3, 0 and 3 into the equation
-3 to the power of 2 is 9 and 9(3) is 27. 27-(-3) is 27+3, 30
0 squared is 0 so the 2nd one would be 0
3 squared times 3 is 27 and subtracted by 3 is 24.
Chad is decorating a rectangular ballroom ceiling with decorative lights. Beginning in a corner, Chad strings the lights along the length of the ceiling, a distance of 55 feet. Next, Chad strings the lights along the width of the ceiling, a distance of 48 feet. Then Chad strings the lights straight back to the original corner. At this point, how many feet of lights has Chad used? If necessary, round your answer to the nearest tenth. feet
The number of feet of light used by Chad is 176 feet
How to determine the number of feet of light?From the question, we have the following parameters that can be used in our computation:
Length = 55 feet
Width = 48 feet
We start by calculating the distance from the end of the width till the beginning of the length
This is represented by the following Pythagoras theorem
Distance = √(Length² + Width²)
So, we have
Distance = √(55² + 48²)
Evaluate
Distance = 73
The number of feet is then calculated as
Feet = Length + width + distance
So, we have
Feet = 55 + 48 + 73
Evaluate
Feet = 176
Hence, the total distance is 176 feet
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HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: It's in the picture.
Step-by-step explanation:
For males in a certain town, the systolic blood pressure is normally distributed with a
mean of 110 and a standard deviation of 5. Using the empirical rule, determine the
interval of systolic blood pressures that represent the middle 99.7% of males.
There are 300 teenagers in a park. 32% of them are boys, how
many more girls than boys are there in the park?
Answer: 108
Step-by-step explanation:
We find the number of boys by taking 300 timed 0.32 = 96 boys
Then we subtract 300 from 96 = 204 girls
Then we removed 204 by 96 = 108
So there are 106 girls more than boys
If you can, please give me a Brainliest, I only need 1 more to become an Ace, thank you!
Answer: 108
Step-by-step explanation: There are 300 teenagers in all. To find how many boys they are, multiply 32/100 times 300/1. You get 96, so there are 96 boys. This means that there are 204 girls. There are 108 more girls than boys. Hope this helps!
Solve for X, the figure is a trapezoid. I will give brainiest!!
Answer:
6
Step-by-step explanation:
RS and QT are parallel because it is a trapezoid. This means that the transversal applies. Look at the picture attached to understand what I mean.
So, we know that 18x - 13 = 180(degree of a line)-85. Then, solve the equation.
18x-13=95
18x=108
x=6
Work out the area of this semicircle. Take pi to be 3.142 and give your answer to 2 decimal places.
The area of the semicircle is 39.275 square cm
How to determine the area of the semicircle?From the question, we have the following parameters that can be used in our computation:
Diameter = 10 cm
Start by calculating the radius of the semicircle
So, we have the following representation
radius = Diameter/2
This gives
radius = 10/2
Evaluate
radius = 5
The area of the semicircle is then calculated as
Area = πr²/2
So, we have
Area = 3.142 * 5²/2
Evaluate
Area = 39.275
Hence, the area is 39.275 square cm
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Boy : girl
11 : 9
there are 124 more boy than girl
how many pupil are in the chool?
There are 1240 students in the school.
What is Proportionalities (Ratios)?
It is possible to represent absolute connections using ratios or proportions, independent of the variables' actual raw values. For instance, if your business always produces widgets packaged in bundles of 20 widgets each, you will always have a 20 widgets to 1 bundle ratio regardless of how many bundles you produce. Accordingly, if you produce 100 bundles per day, you will have produced 2000 widgets in a single day. The proportion of widgets to bundles is constant and does not change. As long as the other ratio factor quantity is known or can be known, the ratio or proportion can then be used as a conversion factor to calculate the number of an unknown quantity of one ratio factor.
In our problem, we know that there are 11 boys : 9 girls in the school. We also know that there are 124 more boys than girls.
If we let x equal the number of girls in the school, the number of boys will then be x+124. We know the ratio of boys to girls and produce a conversion factor to determine the number of girls present in the school:
( number of boys)[tex]$\left(\frac{\text { girls }}{\text { boys }}\right)=$[/tex] number of girls
[tex](x+124)\left(\frac{9}{11}\right)=x[/tex]
Note that since we are looking to find the number of girls, it appears in the numerator of the conversion factor and boys in the denominator. If we were looking for the number of boys, we would flip the conversion factor to have the number of boys in the numerator and girls in the denominator.
Now let's simplify the equation and solve for x :
[tex]\begin{aligned}(x+124)\left(\frac{9}{11}\right) & =x \\\frac{9 x+1116}{11} & =x \\9 x+1116 & =11 x \\1116 & =11 x-9 x \\1116 & =2 x \\\frac{1116}{2} & =x=558\end{aligned}[/tex]
If we have 558 girls, the number of boys is then:
x+124=558+124=682boys
Adding the number of boys and girls together, we will have the total number of students in the school: 558+682=1240 students
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The price of a video game console was
marked down $25, but then marked up by
12. If the original price was $225, what
is the new price?
Answer:
$227
Step-by-step explanation: if the console gets marked downed $25 it will be $200 then the 12% increase which it $27 so that will be $227
a square has two diagonals, and a convex pentagon has five diagonals. how many diagonals does a convex decagon have?
35 is diagonals does a convex decagon have .
What does a pentagon basic definition entail?
A geometric figure with five sides and five angles is called a pentagon. Here, "Penta" stands for five, while "gon" is an angle.
One of the different kinds of polygons is the pentagon. For a standard pentagon, the total internal angles come to 540 degrees.
There are a total of ¹⁰C₂ ways to connect two different vertices. But connecting neighbouring vertices doesn't count, so we have to exclude the sides from our consideration. There are 10 sides, so we need to take away 10 ways from the 45 ways possible to get the number of diagonals.
Number of diagonals in a decagon = 35
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The coordinates of the vertices of a polygon are (-2, -1), (-2, 3), (2, 3), (2, 0), and (1,-4).
What is the perimeter of the polygon to the nearest tenth of a unit?
Check the picture below.
so hmmm let's only find the lines in red and add them up all
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-4}) ~\hfill d1=\sqrt{(~~ 1- (-2)~~)^2 + (~~ -4- (-1)~~)^2} \\\\\\ ~\hfill d1=\sqrt{( 3)^2 + ( -3)^2} \implies d1=\sqrt{ 18 }[/tex]
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill d2=\sqrt{(~~ 2- 1~~)^2 + (~~ 0- (-4)~~)^2} \\\\\\ ~\hfill d2=\sqrt{( 1)^2 + ( 4)^2} \implies d2=\sqrt{ 17 } \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{4~~ + ~~4~~ + ~~3~~ + ~~\sqrt{18}~~ + ~~\sqrt{17}} ~~ \approx ~~ \text{\LARGE 19.4}[/tex]
waiting times to receive food after placing an order at the local subway sandwich shop follow an exponential distribution with a mean of 60 seconds. calculate the probability a customer waits: a. less than 30 seconds. (round your answer to 4 decimal places.) b. more than 120 seconds. (round your answer to 4 decimal places.) c. between 45 and 75 seconds. (round your answer to 4 decimal places.)
Waiting time follows an exponential distribution with mean
μ=60
μ=60 seconds. This implies λ=1μ=160λ= μ1= 601
Let X be the waiting time. for first we have to calculate the probability of customers who wait less than 30 secs.
a. X is less than 30 seconds, then we have to find ,
P(X<X1)=1−e−λX1⇒P(X<30)=1−e−λ×0
=1−e−160×30 =1−e−12=1−0.6065
=0.3935P(X<X 1)⇒
P(X<30)
=1−e −λX 1=
1−e −λ×30 1−e − 601×30 =
1−e − 21
=1−0.6065
=0.3935
b. X is more than 120 seconds, then we have to find less than 120 sec
b. X is more than 120 seconds
P(X>X1)=1−P(X<X1)=1−(1−e−λX1)⇒P(X>120)=1−(1−e−λ×120=e−60×120=e−2=0.135
P(X>X 1)⇒P(X>120)=1−P(X<X 1)=1−(1−e −λX 1)=1−(1−e −λ×120= − 601×120 =e −2=0.135
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Let f(x) be a continuous function such that f(1) = 3 and f '(x) = [tex]\sqrt{x^3+4}[/tex]. What is the value of f(5)?
how do i solve (4x-5)/(3x+5)>=3?
Answer:
x = -4
Step-by-step explanation:
(4x-5)/(3x+5) = 3
1. Multiply both sides by 3x+5
4x-5 = 3(3x+5)
2. Expand
4x-5 = 9x+15
3. -4x from both sides
-5 = 5x+15
4. -15 from both sides
-20 = 5x
x = -4
It is greater than 3
x = 4
We can solve the equation as
(4x-5) = (3x+5)*3
4x-5=9x+15
x = 4
i need assistance with this
Answer:
Step-by-step explanation:
Oh I don't really know but I will find it out for you right now
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Just solve it? (Doing the same thing you did on my question.)
Rose, bill, jean, and candice each received different seat numbers to watch the performance. The seat numbers were either 53, 64, 108, or 216. Candice received the only seat number with a factor of 16. Bill received the seat number that is the greatest multiple of 8 from the group of seats. Rose received the only seat number that is a prime number. Which seat number did jean receive?.
It should be noticed that the seat assigned to Jean as per the given data is 108 .
Jean seat = 108.
The seat numbers were either 53, 64, 108, or 216 based on the information.
The single seat with a factor of 16 went to Candice. The seat is 64 .
In the group of seats, Bill was given the seat with the highest multiple of 8. It's number 216.
Rose was given the sole prime number-containing seat number. It is 53.
Therefore, 108 is the sum that is left.
A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.
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(2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)
Hello,
I hope you and your family are doing well!
To simplify the expression, you can combine like terms and simplify:
[tex](2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)[/tex]
[tex]= 2x^2+x+1 - x^2+x-7 - 4x^2-2x-8[/tex]
[tex]= (2x^2 - x^2 - 4x^2) + (x - x - 2x) + (1 - 7 - 8)[/tex]
[tex]= -3x^2 - 3x - 14[/tex]
Therefore, the simplified expression is [tex]-3x^2 - 3x - 14[/tex]
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Happy Holidays!
You plant a small tree that begins growing at a constant rate. You measure the tree after 3 weeks and find its height is 33 cm. After 7 weeks, you measure the height of the tree again and it’s height is 38.2cm
a) the constant of variation for this situation
b) how tall is the tree when you planted it (“initial value”)?
c) an equation showing the relationship
d) after how many weeks will the plant be 45 cm tall?
and last question
e) how much time has gone by when the plant is 51.3 cm tall?
Please someone help me with this!!
a. The constant of variation is 1.3.
b. Initially the tree is 29.1 cm.
c. The equation showing this relationship is y = 1.3x + 29.1.
d. After 12.2 weeks many weeks will the plant be 45 cm tall.
e. 16.85 weeks of time has gone by when the plant is 51.3 cm tall.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
a. The constant of variation is (y₂ - y₁)/(x₂ - x₁) = (38.2 - 33)/(7 - 3).
= 1.3.
∴ 38.2 = (1.3)7 + b.
38.2 = 9.1 + b.
b = 29.1.
y = mx + 29.1.
b. Now initial constant of variation m = 0.
So, y = 29.1 (cm).
c. The equation showing this relationship is y = 1.3x + 29.1.
d. 45 = 1.3x + 29.1.
1.3x = 15.9.
x = 15.9/1.3.
x = 12.2 weeks.
e. 51 = 1.3x + 29.1.
1.3x = 21.9
x = 16.85 weeks of time have gone.
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The original scale factor for a scale drawing of a house plan is 180, and the length of the original scale drawing is 12 inches. What is the length of a new scale drawing if the scale factor of the new scale drawing to actual length of the house is 1180?.
Answer:mutplion
Step-by-step explanation:
What is the axis symmetry
The axis of symmetry of equation y = 3x² - 18x + 5 is x = 3.
What is axis symmetry?The object's shape becomes symmetrical when a straight line acts as the axis of symmetry. Each side of the axis of symmetry produces a perfect reflection of the other. It can be lateral, vertical, or any combination of the three.
Given equation:
y = 3x² - 18x + 5
The line symmetry of y = [tex]ax^2+bx+c = 0[/tex] is x = -b / 2a,
Hence, x = -(-18) / 2 × 3
Therefore, x = 3 is the axis of symmetry of equation y = 3x² - 18x + 5.
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Select the correct answer from each drop-down menu.
Julia and Kellen are participating in a read-a-thon to raise money for charity. The money each of them raises will be a mix of fixed and per-page
donations.
Function / models the total amount, in dollars, that Julia will raise if she reads x pages:
j(x) = 1.65x + 17.31.
Function k models the total amount, in dollars, that Kellen will raise if he reads x pages:
k(x) = 0.90x + 9.28.
The function
If they both read 500 pages, the difference will be $
entum. All rights reserved.
represents the difference between the amounts Julia and Kellen will raise when they both read x pages.
Reset
1
Next
The difference between the amounts Julia and Kellen will raise when they both read x pages is represented by the function j(x) - k(x) = 0.75x + 8.03. And if they both read 500 pages, the difference will be 383.03.
What is subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.
Given, Julia and Kellen are participating in a read-a-thon to raise money for charity.
The money each of them raises will be a mix of fixed and per-page donations.
Function / models the total amount, in dollars, that Julia will raise if she reads x pages:
j(x) = 1.65x + 17.31.
Function k models the total amount,
in dollars, that Kellen will raise if he reads x pages:
k(x) = 0.90x + 9.28.
To find the difference between the amounts Julia and Kellen will raise when they both read x pages:
j(x) - k(x) = 1.65x + 17.31 - (0.90x + 9.28).
j(x) - k(x) = 1.65x + 17.31 - 0.90x - 9.28.
j(x) - k(x) = 0.75x + 8.03.
If they both read 500 pages, the difference will be;
j(500) - k(500) = 0.75(500) + 8.03 = 375 + 8.03 = 383.03
Therefore, if they both read 500 pages, the difference will be 383.03.
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The complete question is:
Select the correct answer from each drop-down menu.
Julia and Kellen are participating in a read-a-thon to raise money for charity. The money each of them raises will be a mix of fixed and per-page
donations.
Function / models the total amount, in dollars, that Julia will raise if she reads x pages:
j(x) = 1.65x + 17.31.
Function k models the total amount, in dollars, that Kellen will raise if he reads x pages:
k(x) = 0.90x+9.28.
The function
If they both re
h(x)=0.75x+26.59
h(x) = 0.75x+8.03
h(x) = 2.55x+8.03
h(x) = 2.55x+26.59
represents the difference between the amounts Julia and Kellen will raise when they both read x pages.
ence will be $
Reset
Next
please anyone help I need help right or wrong I need to pass my classes
Answer:
B second one
Step-by-step explanation:
2000-750/5=250
Write the equation of the line that is perpendicular to the line (y= 2/3x + 4) in the graph and gird through the point (-1,5)
Answer:y= -2/3+3 is the answer since you are just flipping the same line and move down by 1
Step-by-step explanation:
Fatima wants to fill a circular wading pool.she does not have a hose, so she uses a rectangular pail that she fills from a tap. The inside diameter of the pool is 120 cm and it is 25 cm deep. The inside dimension of the pail are 30 cm x 22 cm x 24 cm deep. How many pails of does fatima have to carry to fill the pool to depth of 18 cm?
Fatima needs to carry 13 pails to fill the pool to a depth of 18 cm.
What is are cube and cuboid?Cube and cuboid are three-dimensional shapes that consist of six faces, eight vertices and twelve edges. The primary difference between them is a cube has all its sides equal whereas the length, width and height of a cuboid are different. Both shapes look almost the same but have different properties. The area and volume of cube, cuboid and also cylinder differ from each other.
Volume of a circular pool to a depth of 18cm = Area of circular pool x depth
π[tex]r^{2}[/tex]h
where r = radius of circular pool which is 120/2 = 60cm
h = depth which is 18cm, [tex]\pi[/tex]( constant) = 3.14
Volume (V) = 3.14 x 60^2 x 18 which is 203472 cubic centimeters
volume of each rectangular pail = 30 x 22 x 24 which is 15840 cubic centimeters
If the volume of 1 rectangular pail is 15840 cubic centimeters then the number of pails to fill 203472 cubic centimeters will be
203472/15840 = 12.84 approximately 13 pails
In conclusion 13 pails is needed to fill the pool to the depth of 18cm
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Jadas sister earns 15 dollars per hour. The store offers her a raise a 9% increase per hour. After the raise , how much will Jadas sister make per hour?
Answer:
$16.35 is jadas sister new hourly pay
Step-by-step explanation:
hope this helps
question 3 in the analyze stage of the data life cycle, what might a data analyst do? select all that apply.
In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle
The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems
The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system
Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
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