which of the fallowing functions has a slope 3/2 and contains the midpoint segment between (6, 3) and (-2, 11)?
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[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 6}}\quad ,&{{ 3}})\quad % (c,d) &({{ -2}}\quad ,&{{ 11}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{-2+6}{2}~~,~~\cfrac{11+3}{2} \right)\implies (2,7)[/tex]
so, what's the equation of a line whose slope is 3/2 and runs through 2,7?
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ 7}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=\cfrac{3}{2}(x-2) \\\\\\ y-7=\cfrac{3}{2}x-3\implies y=\cfrac{3}{2}x+4[/tex]
Related Questions
What is the answer to. Write a polynomial equation with integer coefficients that has the given roots, x=7 and x=-5
Answers
Buford and Bobbie had a combined gross income of $154,900 in 2009. When filing their federal income tax return with the Married Filing Jointly filing status, they took the standard deduction of $11,400, claimed themselves as exemptions for $3650 each, and did not have any other adjustments to income. According to the following table, which income tax bracket did they fall into?
Answers
Answer:25%
Step-by-step explanation:
What is difference between 164 and 220
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The difference between 164 and 220 is 56.
The difference between 164 and 220 is 56. In mathematical terms, you calculate the difference by subtracting the smaller number from the larger one:
220 - 164 = 56.
Suppose that about 58% of the people who are murdered actually knew the person who committed the murder. suppose that a detective file in boston has 60 current unsolved murders. what is the probability that fewer than 32 victims did not know their murderer?
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Final answer:
The probability that fewer than 32 out of 60 victims did not know their murderer can be found using the binomial probability formula, summing the probabilities where x ranges from 0 to 31 with a success rate of 42% for each trial.
Explanation:
To find the probability that fewer than 32 out of 60 murder victims did not know their murderer, given that 58% of victims did know their murderer, we can use the binomial probability formula. Considering that 42% (=100%-58%) of the victims did not know their murderer, we want the cumulative probability of x=0 to x=31 successes (victims not knowing the murderer) out of n=60 trials (total murder cases).
This can be calculated using a statistical program or a binomial probability table, as manually computing this would be time-consuming and complex. However, the specific steps would involve summing up the probabilities of all scenarios where the number of victims not knowing their murderer ranged from 0 to 31, factoring in the binomial coefficient, the probability of a single victim not knowing the murderer (42%), and its complement for each case.
Given rectangular prism ABCD.
Choose all of the terms that best describe each of the sets of lines or points.
Points A, E, and J
collinear
intersecting
coplanar
noncollinear
noncoplanar
Answers
Answer: Fourth and Fifth options are correct.
Step-by-step explanation:
Since we have given two points i.e. A, E, and J
We can see from the graph that
A, E, J are non coplanar and non collinear.
Coplanar means that all the points lie in the same plane.
Collinear means that all the points lie in the same line.
But A, E, and J are neither in the same plane nor in the same line.
Hence, Fourth and Fifth options are correct.
A fisherman caught one fish that was 12 5 feet long and a second fish that was 9 4 feet long. How much longer was the first fish?
Answers
The answer is A) 3 / 20 on USA Test Prep!
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Naomi has 50 red beads and white beads. The number of red beads is 1 more than 6 times the number of white beads. How many red beads does Noami have?
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Let the number of white beads be w.
r + w = 50
r = 6w + 1
Substitute 6w + 1 in for r in the first equation.
6w + 1 + w = 50
7w + 1 = 50
7w = 49
w = 7
She has 7 white beads.
Now we use the first equation to find the number of red beads.
r + w = 50
r + 7 = 50
r = 43
She has 43 red beads.
Taryn grandmother took her family out to dinner if the dinner was 74$ and Taryn dinner was 20% of the bill how much was Taryns dinner
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In a right triangle, one leg measures 4 inches and the other measures 6 inches. What is the length of th hypotenuse in inches
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Write 7.625 as a mixed number in simplest form
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You divide 625 by 1000 (because the last number is in the thousandths place) to get 125/200, which simplified to 5/8.
How can i use decimal models to add decimals?
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What would you do isolate the variable in the equation below,using only one step?
X-3=7
Select the correct answer below.
A.add 7 to both sides
B. Subtract 3 from both sides of the equation
C.add 3 to the left, 7 to the right.
D.add 3 to both sides
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Help me please
which graph shows a triangle and it's reflection image over the x-axis?
Answers
Choose the value of X that makes the open sentence true
30 - x^2 < 3x + 7
A 4
B 3
C 2
D 1
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b 30-9=21 3*3+7=16 21>16 incorrect
c 30-4=26 3*2+7=13 26>13 incorrect
d 30-1=29 3*1+7=10 29>10 incorrect
the answer is a
Answer:
Option A - 4
Step-by-step explanation:
Given : Inequality [tex]30 - x^2 < 3x + 7[/tex]
To find : Choose the value of x that makes the open sentence true ?
Solution :
We substitute the value of x from options to check which is true,
A) x=4
[tex]30 - 4^2 < 3(4) + 7[/tex]
[tex]30-16 < 12+ 7[/tex]
[tex]14< 19[/tex]
It is true.
B) x=3
[tex]30 - 3^2 < 3(3) + 7[/tex]
[tex]30-9< 9+ 7[/tex]
[tex]21< 16[/tex]
It is false.
C) x=2
[tex]30 - 2^2 < 3(2) + 7[/tex]
[tex]30-4<6+ 7[/tex]
[tex]26< 13[/tex]
It is false.
D) x=1
[tex]30 - 1^2 < 3(1) + 7[/tex]
[tex]30-1<3+ 7[/tex]
[tex]29< 10[/tex]
It is false.
Therefore, Option A is correct.
Cookies are sold singly or in packages of 10
or 30
.
With this packaging, how many ways can you buy 60
cookies?
Answers
30+30
10+10+10+10+10+10
The sum of two numbers is equal to 70. Which of the following functions can be use to find the product of the two numbers if one of the numbers is x?
a) p = x^2
b) p = x (x-70)
c) p = x (70 - x)
d) p = (x - 70)^2
Answers
there sum is equal to 70
then
number1+number2=70
substituting
x+y=70
y=70-x
let there product will be p
p=xy
substituting
p=x(70-x)
which is choice c
Consider the graph of the linear function h(x) = –6 + x. Which quadrant will the graph not go through and why? Quadrant I, because the slope is negative and the y-intercept is positive Quadrant II, because the slope is positive and the y-intercept is negative Quadrant III, because the slope is negative and the y-intercept is positive Quadrant IV, because the slope is positive and the y-intercept is negative
Answers
Slope is +1 = 1/1 = rise / run
y-intercept is -6, that is, (0,-6)
To graph this, plot the point (0,-6). Starting at this point, go 1 unit to the right, to (1,-6), and then from (1,-6) go 1 unit up, to (1,-5). Draw a line thru (0,-6) and (1,-5). You will see that this line is BELOW the origin; it never enters Quadrant II.
The line of linear function h(x) = –6 + x is not going to enter in the second quadrant so option second will be correct.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network.
A graph is made up of some points and the distance between two. It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.
Given equation is h(x) = –6 + x
at x = 0 , h(x) = -6 so ( 0 , -6 ) is first point.
at x =1 , h(x) = -5 so ( 1 , -5 ) is second point.
If we draw a line by the two-point which I have attached then you can see it not going to the second quarter.
For more details about the graph
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THIS IS URGENT PLZ HELP ME!!!!!!!
The graph shown is for the inequality y ≥ x. The graph has one thing wrong. What is it?
A)The shading is on the wrong side of the boundary line.
B)The boundary line should be dotted or dashed
C)The boundary line has the wrong y-intercept
D)The boundary line has the wrong slope
Answers
hope this helps!
For the inequality y ≥ x, the boundary line should be solid, the slope should be 1, the y-intercept should be 0, and shading should be above the line. Therefore, the error could be an incorrect slope, an incorrect y-intercept, or shading below the line.
Explanation:Without seeing the graph it is difficult to determine exactly what is wrong, but based on the question and the options given, we can review the conditions of the inequality y ≥ x. For this inequality:
The boundary line should be solid, not dashed or dotted, because the inequality includes values where y is equal to x. So, choice B is incorrect. The slope of the boundary line should be 1, which is derived from the coefficient of x in the inequality (plain 'x' implies '1x'). Therefore, the slope being wrong (choice D) could be a possible error. The y-intercept of the boundary line should be 0. An incorrect y-intercept (choice C) could be another possible error. The shading should be above the line for y ≥ x (the portion where y values are greater than or equal to x values), so if the shading is below the line, choice A would be correct.Learn more about Inequality Graphing here:https://brainly.com/question/33662315
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46x12=46x(10+2), find distributive property
Answers
=46*10+46*2
=460+92
=552
if you are told only that you scored 80th percentile do you know from the description exactly how it wad calculated? Explain
Answers
We know that there is no universal acceptance meaning of a percentile. When someone told you that you are in the 80th percentile, the meaning of that is you have achieved the lowest score that is greater than 80 percent of the score. It is calculated by using the formula R = P/100 x (N + 1)
Final answer:
The 80th percentile represents the score below which 80% of the scores fall.
Explanation:
The 80th percentile represents the score below which 80% of the scores fall. It is calculated by finding the value at which 80% of the data is below and 20% is above. For example, if you scored in the 80th percentile on a 60-point assignment, it means that 80% of students scored equal to or below 49 points and 20% scored above.
In a batch of 960 calculators, 8 were found to be defective. What is the probability that a calculator chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary
Answers
Thus P(defective calculator) = 8/960, or 0.008333 ...
As a percent, this is 0.8%.
Answer: 0.8%
Step-by-step explanation:
Given : In a batch of 960 calculators, 8 were found to be defective.
i.e. Total calculators =960
Number of defective calculator = 8
We know that the probability of any event is given by :-
[tex]\dfrac{\text{No. of favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{8}{960}=0.00833333333333[/tex]
In percent, [tex]0.00833333333333\times100=0.833333333333\%\\\\\approx0.8\%\ \ \ [\text{Rounding to the nearest tenth.}][/tex]
Hence, the probability that a calculator chosen at random will be defective=0.8%
The sum of two numbers is 43 . The smaller number is 19 less than the larger number. What are the numbers?
Answers
We can calculate this by using simultaneous equation, aka listing 2 equations out.
From given,
X + y = 43
Let this be equation no. 1
X + 19 = y
Let this number be equation 2.
We can do simultaneous equations either by substitute method or elimination. In this case I'm using substitute.
We can already obtain the value of y (in terms of x) in euqation no. 2, so all we gonna do is to put y into equation 1.
X + x + 19 = 43
Solve this by algebra.
2x = 43 - 19
X = 12
Now we know the exact value of x
Now substitute x = 12 into equation no. 2
12 + 19 = y
Y = 31
So the answer is 12 and 31
By setting up a system of equations, we find that the larger and smaller numbers in question are 31 and 12, respectively. We solve for the larger number first and then use it to find the smaller number.
Explanation:To solve this problem, we can use variables to represent the two unknown numbers. Let's call the larger number x and the smaller number y. We have two pieces of information that can be turned into mathematical equations:
Now we can substitute the second equation into the first one to solve for x:
x + (x - 19) = 43
Simplifying the equation, we get:
2x - 19 = 43
Adding 19 to both sides gives us:
2x = 62
Dividing both sides by 2 gives us:
x = 31
Now that we have the value of x, we can find y:
y = 31 - 19
This gives us:
y = 12
Therefore, the larger number is 31 and the smaller number is 12.
"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.) f (x) = cos(πx/2)
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now, what is the value of the derivative at any extrema on the original function? well, by definition, if the original function has an extrema anywhere, the derivative will be the derivative of a horizontal tangent line to it, and by definition it'll be 0.
What is the value of 2 in 0.812
Answers
It is equal to two thousandths.
The first number after the decimal point is tenths.
The second number after the decimal point is hundredths
The third number after the decimal point is thousandths.
Hope This Helps You!
Good Luck :)
- Hannah ❤
The place of the digit 2 in the decimal number will be hundredths place.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
The decimal number is given below.
⇒ 0.812
The place after the decimal starts from the tenths, hundredths, thousandths, and so on.
The place of the digit 2 in the decimal number will be hundredths place.
More about the Algebra link is given below.
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We draw a random sample of size 36 from a population with the standard deviation 3.5. if the sample mean is 27, what is a 95% confidence interval for the population mean?
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[tex]SE = \frac{s}{\sqrt{n}} = \frac{3.5}{\sqrt{36}} = \frac{3.5}{6} = 0.583[/tex]
Confidence interval is:
[tex][27 -2(.583), 27+2(.583)][/tex]
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f + g)(x).
A. 3x2 + 8
B. 3x2 – 6
C. x2 – 6
D. x2 + 8
Answers
Therefore:
(f+g)(x) = f(x) + g(x) Substitute the functions for f(x) and g(x)
(f+g)(x) = (2x² + 1 )+ (x² - 7)
Notice that we first want to write the functions in as parenthesis before we add them. This helps us keep from getting confused on what signs to give each term.
(f+ g)(x) = 2x² + x² + 1 - 7 Collect like terms
(f + g) (x) = 3x² - 6
Answer is B
Joe tapped his maple tree to get syrup. The tree filled 3/4 of a cup in 1/2 hour.At what rate does syrup flow from the tree?
Answers
The rate of flow of syrup from the tree will be in mixed fraction form, equal to 1 1/2.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data mentioned in the question,
The amount of syrup obtained from the tree = 3/4 cup
The time is taken to fill 3/4 cup = 1/2 hour
Then, the rate of flow of syrup will be,
(3/4) ÷ (1/2)
3/4 × 2/1
= 6/4 = 3/2
It can also be written in mixed fraction form,
= 1 1/2
To know more about arithmetic operations:
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Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces x^2+y^2=81 and z=5x^4.
Answers
y = 9sin)t)
z =5[9cos(t)]^4
Answer:
[tex]s(t)=(9 cost,9 sint , 32805 cos^4 t) , t\in (0,2\pi)[/tex]
Step-by-step explanation:
We are given that two surfaces
[tex]x^2+y^2=81[/tex]
and [tex]z=5x^4[/tex]
We have to find the parametrize the intersection of the given surfaces using cost and sin t with positive coefficient.
We know that intersection curve S(t) is given by
S(t)=(x(t),y(t),z(t)),[tex]t\in(0,2\pi)[/tex]
[tex]x^2+y^2=(9)^2[/tex]
Compare with the equation of circle [tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is center of circle and r is the radius of the circle.
The center and radius of given circle is (0,0) and 9.
[tex]x=9cost,y=9 sint[/tex]
because cost takes along x - axis and sin t takes along y- axis.
When we substitute these values then we get
[tex]81cos^2t+81sin^2t=81(cos^2t+sin^2t)=81 [/tex] ([tex]sin^2t+cos^2t)=1[/tex])
Hence, [tex]x=9 cost, y= 9sint [/tex]
Substitute the value of x in second equation of surface
[tex]z=5(9cost)^4=32805 cos^4t[/tex]
Hence, the intersection curve s(t) is given by
[tex]s(t)=(9 cost,9 sint , 32805 cos^4 t) , t\in (0,2\pi)[/tex]
How do you multiply -5 that has an exponent of 4 but no parenthesis with 4? Please explain
Answers
[tex]\bf -5^4\implies -1\cdot 5^4\implies -1\cdot 625\implies -625 \\\\\\ \textit{as opposed to }(-5)^4\implies (-1\cdot 5)^4\implies (-1)^4\cdot 5^4 \\\\\\ (-1\cdot -1\cdot -1\cdot -1)(5\cdot 5\cdot 5\cdot 5)\implies 1\cdot 625\implies 625[/tex]
Tom has r quarters. Express the value of the quarters in cents.
Answers
this is becasue quarters have a value of 0.25 and c is the total cents
hope this helps and have a great day! :)