The equation of line can be written as, y = 2/3x + 2
Given,
The points, (x, y) = (-3, 0)
Slope = 2/3
Equation of a line, y = mx + c
Where, m is the slope and c is the y-intercept.
Here, m is 2/3.
The point at the x-intercept has co-ordinates : (-3, 0)
Where, x is -3 and y is 0.
So, substitute the values in equation:
y = mx + c
0 = 2/3 × (-3) + c
0 = -2 + c
c = 2
Therefore, the equation of line will be:
y = 2/3x + 2.
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100POINTS100POINTS100POINTS100POINTS
The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
27 30 41 27 20 22 36 37 44 45 29 29
(a) What is the five-number summary of the data set? Show your work.
(b) What is the range of the data set? Show your work.
(c) What is the interquartile range (IQR) of the data set? Show your work
The five number summary are as follows:
minimum = 20maximum = 45Q₂(median) = 29.5Q₁(first quartile) = 27Q₃(third quartile) = 39The range of the data sets is 25.
The interquartile range of the sets is 12.
How to find five number summary?The five number summary describes where data values occur, their central tendency, variability, and the general shape of their distribution.
The five number summary includes minimum number, maximum number, median(Q₂), first quartile(Q₁) and third quartile(Q₃).
Therefore, the five number summary are as follows:
27, 30, 41, 27, 20, 22, 36, 37, 44, 45, 29, 29
Arrange the data in ascending order.
20, 22, 27, 27, 29, 29, 30, 36, 37, 41, 44, 45
There are as follows;
minimum = 20maximum = 45Q₂(median) = 29 + 30 / 2 = 29.5Q₁(first quartile) = 27 + 27 / 2 = 27Q₃(third quartile) = 37 + 41 / 2 = 39Therefore,
Range of the data sets = 45 - 20 = 25
Interquartile range (IQR) = Q₃ - Q₁ = 39 - 27 = 12
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Gasoline costs $3.79 per gallon.
Write an inequality that can be used to determine how many gallons of fuel can be
purchased for under $20. Clearly indicate what the variable represents.
Solve the inequality in part a, and write your answer in a complete sentence
solve for c enter thr number
Answer: c=√29
Step-by-step explanation:
We use Pythagoras' theorem:
[tex]c^2=5^2+2^2\\c^2=5*5+2*2\\c^2=25+4\\c^2=29\\[/tex]
Extract the square root of both parts of the equation:
[tex]\sqrt{c^2}=\sqrt{29} \\ c=\sqrt{29}[/tex]
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 89 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 571 mg of cholesterol. How much cholesterol is in each item?
If by eating 2 eggs and 1 cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each item are; 19 mg, 276mg, 8 mg.
Amount of cholesterolE + C + P = 303
Where:
Egg=E
Cupcake=C
Pizza=P
Hence,
3C + 4P =89
4P = 89-3C
P = (89-3C)/4
2E + C = 571
2E = 571-C
E = (571-C)/2
(571-C)/2 + C + (89-3C)/4 = 303
(571-C)2 + 4C + 89-3C = 303×4
(571-C)2 + 4C + 89-3C = 1212
1142 -2C + 4C + 89-3C = 1212
-C = 1212-89-1142
C =19mg (1 cupcake)
E = (571-C)/2
E= (571-19)/2
E=552/2
E= 276mg (1 egg)
P = (89-3C)/4
P = (89-3(19))/4
P = (89-57)/4
P=32/4
P=8 mg (1 pizza)
So,
Egg=E=19 mg
Cupcake=C=276 mg
Pizza=P=8 mg
Check:
19+276 + 8 = 303 mg
Therefore If by eating 2 eggs and 1 cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each item are; 19 mg, 276mg, 8 mg.
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Find the center of dilation.
• Triangle B is a dilation of A with approximately what scale factor?
• Triangle A is a dilation of B with approximately what scale factor?
• Triangle B is a dilation of C with approximately what scale factor?
Answer:
Triangle B is a dilation of A with approximately what scale factor
Triangle B is a dilation of A with approximately a scale factor of 8.
Triangle A is a dilation of B with approximately a scale factor of 1/8.
Triangle B is a dilation of C with approximately a scale factor of 3/4.
We have,
In mathematics, dilation refers to the transformation of a shape, object, or figure by uniformly scaling it up or down.
When the constant factor is greater than 1, the dilation results in an enlargement of the shape, making it larger.
Conversely, when the constant factor is between 0 and 1, the dilation leads to a reduction of the shape, making it smaller.
Now,
Triangle B is a dilation of A with approximately by a scale factor of:
Since triangle B is greater than A.
The scale factor is greater than 1.
Triangle B looks 8 times of triangle A.
So,
The scale factor is 8.
And,
Triangle A is a dilation of B with approximately by a scale factor of:
Since triangle B is smaller than A.
The scale factor is less than 1.
Triangle A looks like 12.5 % of triangle C.
12.5% = 1/8
So,
The scale factor is 1/8.
Triangle B is a dilation of C with approximately by a scale factor of:
Since triangle B is smaller than A.
The scale factor is less than 1.
Let's say,
Triangle B looks 75% of triangle C.
So,
The scale factor is 3/4.
Thus,
Triangle B is a dilation of A with approximately a scale factor of 8.
Triangle A is a dilation of B with approximately a scale factor of 1/8.
Triangle B is a dilation of C with approximately a scale factor of 3/4.
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Tell whether each equation is true, false, or open. Explain.
2.) 5x+7 = 17
1.) 85+ (-10) = 95
3.) -8(-2) - 7 = 14 – 5
Answer:
1.) 85+ (-10) = 95 is false.
2.) 5x+7 = 17 is false.
3.) -8(-2) - 7 = 14 – 5 is false.
Step-by-step explanation:
1. is false because since 85 ≠ 95, then 85 + ( - 10) = 95 is false.
2. is false because since 12 ≠ 17, then 5x + 7 = 17 is false.
3. is false because since -15 ≠ 14, then -8( - 2) - 7 = 14–5 is false.
Suppose you go shopping for a new futon bed for your room. The model you really like happens to be on sale for $525. It's original price is $700. What percent of the original price will you save if you purchase it?
Round your percentage to one decimal place.
Do not include
%
sign with your answer.
25 percent of the original price was saved during the purchase of the futon bed
The percent of the original price that is saved can be calculated as follows
The original price is $700
The new price is $525
The first step is to calculate the percentage change
= 700-525
= 175
Therefore the percent saved can be calculated as follows
= 175/700 × 100
= 0.25 × 100
= 25
Hence 25 percent of the original price was saved
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i think i have question b figured out (please correct me if im wrong) but question a is really confusing and i need some help
Find the altitude of the top of the hill by adding the difference to the altitude of the check point 3:
151 + (- 173) = 151 - 173 = - 21 ftQuestion b)Find the difference between the two altitudes:
2237 - (- 69) = 2237 + 69 = 2306 ftYou got it correct.
The table shows the linear relationship between the playing time in minutes of high-definition videos and the file size of these videos in megabytes (MB) What is the rate of change of this function?
180
60
120
30
The rate of change of the linear function for the given table is determined as: C. 120.
What is a Linear Relationship Function?A linear relationship function is represented as a straight line graph which can be expressed as a linear equation in slope-intercept form as, y = mx + b.
The rate of change of the function is represented as m, which is also the slope of the graph, and the y-intercept is b.
How to Find the Rate of Change of a Function?A linear function has a rate of change/slope which can be found using the formula:
m = y2 - y1/x2 - x1.
Given the set of table values that represents a linear function below, we can use two pairs of values to find the rate of change as follows:
(0.5, 60) = (x1, y1)
(1.5, 180) = (x2, y2)
Plug in the values
Rate of change (m) = (180 - 60)/(1.5 - 0.5)
Rate of change (m) = (120)/(1)
Rate of change (m) = 120
Therefore, the rate of change of the linear function for the given table is determined as: C. 120.
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What is the product of −17 • −5 • −12?
Answer:
-1020
Step-by-step explanation:
-17 x - 5 x - 12 =
- 17 x 60 =
- 1020
What are the solutions to the system of equations?
{y=2x2−5x−7y=2x+2
The solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).
How to resolve a system of equation by algebra methods
Herein we find a system formed by one linear equation and one nonlinear equation (quadratic equation). First, we equalize the two equations to eliminate the variable y:
2 · x² - 5 · x - 7 = 2 · x + 2
2 · x² - 7 · x - 9 = 0
2 · [x² - (7 / 2) · x - 9 / 2] = 0
2 · (x - 9 / 2) · (x + 1)
There are two solutions to x: x₁ = 9 / 2, x₂ = - 1. And the solutions for y are:
x₁ = 9 / 2y₁ = 2 · (9 / 2) + 2
y₁ = 11
x₂ = - 1y₂ = 2 · (- 1) + 2
y₂ = 0
Then, the solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).
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explain how you would round 25.691 to the greatest place
Answer:
In order to round 25.691 to the greatest place or the nearest whole number, first start at the last digit behind the decimal, in the case, being the 1. When it comes to things like this, if the digit is 4&under meaning its the number 4,3,2,1 or 0. If it is 5&up, that means it could be 5-9, making the digit go up (but if its 2, then the digit just goes away, you wont have to worry about that one specific number).
Next step is to round the 9 which makes the 6 go up one digit (meaning it turns into a 7). Now, when you round the seven, it will make the whole number go up one digit, but if you want to round that as well, to start, it's first rounding equaled up to 26. If you're rounding it to a whole tens number, it would be 30. I hope that this helps you understand this subject or topic much better! :3
Step-by-step explanation:
What value represents the vertical translation from the graph of the parent function f(x)=x2 to the graph of the function g(x)=(x+5)2+3?
Answer:
3
Step-by-step explanation:
See the attached image.
Two numbers have a sum of 195 and a difference of 45. What are the two numbers
An elevator in a tall building goes up 7 floors then down 9 floors down 4 floors up 8 floors and down 2 floors now it it in floor 14 on what floor did the elevator start
Answer: I'm pretty sure its 14.
Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14
10.The table below shows the recorded temperature on a certain day starting at 6:00 a.m. time 6:00 6:45 7:30 8:30 9:00 9:45 10:30 11:00 temp 65° 67° 68° 72° 74° 75° 77° 80°
a) Find the regression equation.
b) Predict the temperature at 2:00 p.m.
From the temperatures given, we have that:
a) The regression equation is: y = 2.91x + 64.61.
b) The predicted temperature at 2 pm is of 88 ºF.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
In the context of this problem, the input and the output are given as follows:
Input x: number of hours after 6 A.M.Output y: temperature.We have that an hour is 60 minutes, hence:
45 minutes = 0.75 hours.30 minutes = 0.5 hours.Thus the points are given as follows:
(0, 65), (0.75, 67), (1.5, 68), (2.5, 72), (3, 74), (3.75, 75), (4.5, 77), (5,80).
Inserting these points into the calculator, the equation is:
y = 2.91x + 64.61.
2 pm is 8 hours after 6 am, hence x = 8 and the predicted temperature, in ºF, is given by:
y = 2.91(8) + 64.61 = 88 ºF.
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if a polynomial is prime, then it cannot be factored. 5x + 13y is prime.
5x + 13y is prime , it cannot be factored.
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial .
Some trinomials cannot be factored. If none of the pairs total b, then the trinomial cannot be factored.
Given equation is 5x + 13y
If a polynomial is prime, then it cannot be factored. 5x + 13y is prime.
In this regard,
The law of detachment states that
1) If p happens, then q happens;
2) p is true;
Then, a there is a third statement that is
3) q is also true.
In this question,
If a polynomial is prime, then it cannot be factored.
The statements in the question can be represented as:
(1) If 5x + 3y is a polynomial and is prime then it cannot be factored
(2) It cannot be factored
Using the above representations of p and q, as an illustration; the third statement would be:
(3) 5x + 3y is a polynomial and is prime then we can conclude that
5x + 13y cannot be factored.
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Write the expanded form of the expression.
y(0.5 + 5)
Answer:5.05y
Step-by-step explanation:
Therefore, the expanded form of the expression y (0.5 + 8) is 0.5y + 8y
Using this example we can find out that 0.5y+5 y=5.05 y thats the answer
please kindly give me brainiest thank you
Lisa works as a tutor at Springfield high school. She can work up to 20 hours a week and gets paid $15 dollars an hour. Find a reasonable domain and range for Lisa’s possible weekly earnings.
PLS HELP ASAP
(50 POINTS)
Using the image, how will oxygen complete its valence shell?
Answer:b B
Step-by-step explanation:or a
Which is greater 8.391 or 8.371
Answer:
8.391
STEPS:1. Compare the first digit. If they are the same, move on to the next digit. In this case, we have to look at the hundredths place.
2. Check to see which number is bigger. We are looking at 9 and 7. 9 is the bigger number. this means that 8.391 is bigger.
What is the number in scientific notation? 0.000000000093
Check the picture below.
A woman traveled 2437.2 miles in 18 hours 20 minutes. Find the average speed of her flight in miles per hour. (Change
18 hours 20 minutes into hours and use the formula d=rt.)
Answer:Average Speed = 126.6 mph
Step-by-step explanation:
Solve for the value of r.
(9r+2)°
70°
90°
Answer:
If they all had to equal 360 when put together then the answer would be 22. If they All had to equal 180 when put together, then the answer would be 2.
Step-by-step explanation:
The directions are not quite clear but I have two answers just in case.
fraction numerator 6 y plus 2 x over denominator 5 end fraction equals 18
The given statement fraction numerator 6 y plus 2 x over denominator 5 end fraction in numerical form 18 is 6y + 2x = 90.
What is a linear equation in two variable?A linear equation in two variables has the highest degree of 1 and contains two variables generally in x and y.
Given in numerator we have 6y + 2 and in the denominator, we have 5 and this fraction equals to 18, This can be numerically represented as
(6y + 2x)/5 = 18.
6y + 2x = 90.
This is a linear equation in two variables x and y and for every value of x we get a corresponding value of y or vice-versa and all (x,y) ∈ R.
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A sample of 156 runners is taken from a population of 5300 runners who complete a major marathon.
8. How many runners' times are used to calculate u for the finishing times for this event? Answer choice
5300
34
156
26
Answer:
4736 because count add them together or do it your way
2x−3y=−5 4x−4y=−4 Is (2,3)(2,3)left parenthesis, 2, comma, 3, right parenthesis a solution of the system?
(2,3) is a solution to the system of equations.
A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).
Consider the system of equations,
2x - 3y = - 5 --------(1)
4x - 4y = - 4 --------(2)
Multiplying equation (1) with 2.
4x - 6y = - 10
4x - 4y = - 4
Now, subtracting the above equations:
4x - 6y - ( 4x - 4y) = - 10 + 4
4x - 6y - 4x + 4y = - 6
- 2y = - 6
2y = 6
y = 3
Then,
4x - 4y = - 4
4x - 4 × 3 = - 4
4x - 12 = - 4
Adding 12 on both sides of the equation,
4x - 12 + 12 = - 4 + 12
4x = 8
x = ( 8/4 )
x = 2
Therefore, (x, y) = ( 2, 3) is a solution to the system of equations.
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Answer:
Yes
Step-by-step explanation:
I really need help I need to turn this in tmr can someone pls help I beg y a lot pósese
8. A baseball is thrown from a height of 40 feet and goes up at a rate of 2.5 feet per second. A football is
thrown from a height of 25 feet and goes up at a rate of 3 feet per second. After how many seconds
would the two reach the same height?
The time taken depends upon velocity and distance so the time taken by both balls to reach the same height will be 30 seconds.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Units of velocity are given by ⇒ meter/second
For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.
Difference between their initial height = 40 - 25 = 15 feet
It means if baseball cover x feet distance then football will cover x + 15 feet.
Now,
Time = distance covered / velocity
Since the time will be the same for both balls to meet them.
So,
Distance covered by baseball/velocity of baseball = Distance covered by football/ velocity of football
x/2.5 = (x + 15)/3
3x = 2.5x + 37.5
0.5x = 37.5
x = 75
So,
Time taken = 75/2.5 = 30 seconds.
Hence "After 30 seconds both balls will go to reach the same height".
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i need help pleaseeeeee
A coefficient in the algebraic expression is: 5
The constant is: 12
A variable is: x
A term in the algebraic expression can be: 5x or 12.
What are the Parts of an Algebraic Expression?An algebraic expression consist of terms, which can be:
A variable in form of alphabetsA variable multiplied by a coefficientA constant, which is just a number.Thus, given the algebraic expression, 5x + 12, the following parts of the algebraic expression can be identified as shown below:
A coefficient in the algebraic expression is: 5 (tis is the number multiplied by the variable x)
The constant is: 12 (this is the number standing alone)
A variable is: x (this is the alphabet in the algebraic expression)
A term in the algebraic expression can be: 5x or 12.
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