The graph of a linear equation contains the points (4,1) and (-2,-11). Which point also lies on the graph?
A. (1,1)
B.(1,-5)
C.(1,-2)
D.(1,-7)
Answers
Answer:
Option B is correct.
(1 , -5) lies on the graph.
Step-by-step explanation:
Given the points (4,1) and (-2 , -11)
First find the linear equation for the given points.
Equation of line for two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
is given by: [tex]y-y_1 = (\frac{y_2-y_1}{x_2 - x_1}) (x-x_1)[/tex]
Substitute the given points (4,1) and (-2 , -11) in above equation to find the equation of line:
[tex]y-1=(\frac{-11-1}{-2-4})(x-4)[/tex]
or
[tex]y-1=(\frac{-12}{-6})(x-4)[/tex]
or
[tex]y-1=2(x-4)[/tex]
Using distributive property on RHS ( i.e, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex] )
we have;
y -1 = 2x-8
Add 1 to both sides of an equation;
y-1+1 = 2x-8+1
Simplify:
y = 2x -7
Therefore, the equation of line for the given point is: y =2x - 7 ....[1]
To find which points lies on the graph ( i.e, Line)
Substituting the given options in equation [1] we have;
A . (1,1)
Put x =1 and y =1
[tex]1 = 2\cdot 1 -7 = 2-7[/tex]
1 = -5 which is not true.
Similarly
B. for (1, -5)
[tex]-5= 2\cdot 1 -7 = 2-7[/tex]
-5 = -5 which is true.
C. for (1, 2)
[tex]2= 2\cdot 1 -7 = 2-7[/tex]
2 = -5 which is not true.
And
D. For (1 , -7)
[tex]-7= 2\cdot 1 -7 = 2-7[/tex]
-7 = -5 which is also not true.
Therefore, the only point which lies on the line graph [1] is; (1 ,-5)
Related Questions
Each marble bag sold by leila's marble company contains 5 yellow marbles for every 8 green marbles. if a bag has 35 yellow marbles, how many green marbles does it contain?
Answers
5 : 8
35:x
To get from 5 to 35 for the yellow's, you multiply the ratio by 7.
Multiply the 8 for greens by 7 = 56
There are 56 green marbles.
Solve for x: 8x + 10 - 5x = 15.
Answers
3x + 10 = 15
3x = 5
x = 5/3
hope it helps
8x+10-5x = 15
3x+10 = 15
3x = 5
x = 5/3
Geometry please help !!
Answers
If any internal angle is greater than 180° then the polygon is concave
Given the points A (3,2) and B (-21,0) determine:
a. the slope of line AB
b. the length of AB
c. the midpoint of AB
d. an equation of AB
Answers
(0-2)/(-21-3)=-2/-24=1/12
B)sqaureroot((-2)^2+(-24)^2)=squareroot(580)=2squareroot(145)
C)((x1+x2)/2,(y1+y2)/2)=(-9,1)
D)y=1/12(x+21)
The slope of the line passing through the points (6, -1) and (7, -2) is
Answers
Change in y: -1
Change in x: +1
-1/1 = -1
Slope: -1
Hope it helped :)
Please give brainliest
m=(y2-y1)/(x2-x1) where m represent slope, (x1,y1) represent point (6,-1) and (x2,y2) represent point (7,-2) in this case, so we need to solve it
m=(y2-y1)/(x2-x1)
m=(-2-(-1))/(7-6)
m=(-2+1)/1
m=-1. As a result, the slope of the line passing through the points (6, -1) and (7, -2) is -1. Hope it help!
After John worked at a job for 10 years, his salary doubled. If he started at $ x , his salary after 10 years is _____.
$ x
$ x + 2
$ x - 2
$2 x
Answers
Since it doubled it's twice(2) the amount he started with. $2x
Your class has 30 students. if 1313 of them walk to school, how many students in your class walk to school?
Answers
Answer:10
Step-by-step explanation:
A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. If b = the rate of the boat in still water and c = the rate of the current, which of the following equations represents the trip downstream?
3(b - c) = 120
3(b + c) = 120
4(b + c) = 120
Answers
also time downstream = 3 hours
time * rate = distance
3 * (b + c) = 120
so its the second choice.
What are the difference between polynomial long division and arithmetic long division?
Answers
Answer:
The purpose of long division with polynomials is similar to long division with integers; to find whether the divisor is a factor of the dividend and, if not, the remainder after the divisor is factored into the dividend. The primary difference here is that you are now dividing with variables.
Which of the following shows the graph of a line through (-2,2) and (2,4)
Answers
You can find the equation of the line that passes through two known points in this way:
[Y -Y1] / [X -X1] = [Y2 - Y1] / [X2 -X1]
in this case (X1,Y1) = (-2,2) and (X2,Y2) = (2,4)
=> [Y - (2) ] / [X - (-2) ] = [4 - 2] / [2 - (-2) ]
=> [Y -2] / [X + 2] = 2/4 = 1/2
=> 2 * (Y - 2) = X + 2
=> 2Y - 4 = X + 2
=> 2Y = X + 2 + 4
=> 2y = x + 6
=> y = x/2 + 3
So you must look the graph of that equation.
Some of the points of that graph are:
x y
-6 -6/2 + 3 = 0
-4 -4/2 + 3 = 1
-2 -2/2 + 3 = 2
0 0 + 3 = 3
2 2/2 + 3 = 4
4 4/2 + 3 = 5
So, you should find the correspondant graph easily.
Answer:
Attachment for graph.
Step-by-step explanation:
Given: (-2,2) and (2,4)
Two points are given and to find the equation of line passing through the points.
First we find the slope of the line.
[tex]\text{Slope }=\dfrac{4-2}{2+2}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Point: (2,4)
using point slope form:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-4=\dfrac{1}{2}(x-2)[/tex]
[tex]y=\dfrac{1}{2}x+3[/tex]
Now, we draw the graph using two given points. Plot the points on graph and join them.
Please find the attachment for graph.
There is a traffic light at the intersection of Walnut Street and Lawrence Avenue. The traffic light on Walnut Street follows a cycle. It is green for 50 seconds, yellow for 10 seconds, and red for 30 seconds. As you travel along Walnut and approach the intersection, what is the probability that the first color you see is red?
1/5
1/3
3/5
1/2
Answers
total time = 30 s + 10 s + 50 s = 90s
Hence, the total time is equal to 90 s. From this, we calculate for the probability that the first light that will be seen is a red light by dividing the duration of the red light in the cycle by the total time.
Probability = (30 seconds) / (90 seconds)
= 1/3
Therefore, the probability that the red light will be seen first is equal to 1/3. The answer is second choice.
You cut a 90 cm long rope into two pieces. the longer piece is 2 times as long as the shorter piece. what is length of the longer piece and the shorter piece respectively?
Answers
Let the shorter piece be x.
Thus, the length of the longer piece = 2x.
2x + x = 90
3x = 90
x = 30.
Therefore, the shorter piece is 30 cm and the longer piece is 60 cm.
The sum of the first three terms of a convergent geometric series is 19. the sum of the series is 27. find the first term and the common ratio.
Answers
2nd, sum of a GP = a₁(1-rⁿ)/(1-r), where a₁ = 1st term and n=number of terms
3rd, for any convergent GP, r<1 and the sum of all terms =a₁/(1-r): Why?
[since r<1 → lim rⁿ when n→∞, =0 in the formula of the 2nd)]
Now let's solve :
a) Sum = a₁(1-r³)/(1-r) = 19 (sum of the first 3 terms)
b) Σ(Sum) = a₁/(1-r) = 27 (sum of all terms of this CONVERGENT GP)
Divide a) by b):
[a₁(1-r³)/(1-r)] / [a₁/(1-r)] = 19 /27 ↔ [a₁(1-r³)/(1-r)] x [(1-r)/a₁]=19/27.
Simplify:
(1-r³) = 19/27
-r³ = 19/27 - 1
r³ = 8/27
r = ∛(8/27)
r = 2/3 and a₁ = 9 (Plug r in the Σ sum)
Hence first term a₁ = 9
and common ration r =2/3
Solve the system of equations by substitution. x + y = x + 7y = 8
Answers
Answer:
1 and 1
Step-by-step explanation:
The height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).the height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).
Answers
The probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.
Here's how we can calculate this:
Standardize the values: Convert the heights of 67 inches and 69 inches to z-scores using the formula:
z = (x - mean) / standard deviation.
In this case, z for 67 inches is -0.33 and z for 69 inches is 0.33.
Calculate the area between the z-scores: Using a standard normal distribution table or calculator, find the area between -0.33 and 0.33. This represents the probability of an 18-year-old man having a height within that range.
Round the answer: The calculated area is approximately 0.261, which is the probability of a randomly selected man being between 67 and 69 inches tall.
Therefore, the probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.
The probability that an 18-year-old man selected at random is between 67 and 69 inches tall is approximately 0.259.
To find the probability that an 18-year-old man selected at random is between 67 and 69 inches tall, we first need to standardize the values using the z-score formula:
[tex]\( z = \frac{x - \mu}{\sigma} \)[/tex]
where x is the value
[tex]\( \mu \)[/tex] is the mean, and
[tex]\( \sigma \)[/tex] is the standard deviation.
For x = 67 inches: [tex]\( z = \frac{67 - 68}{3} = -0.333 \)[/tex]
For x = 69 inches: [tex]\( z = \frac{69 - 68}{3} = 0.333 \)[/tex]
Using the standard normal distribution table or calculator, we find the corresponding probabilities:
P(z < -0.333) and P(z < 0.333)
P(z < -0.333) = 0.3707 and P(z < 0.333) = 0.6293
To find the probability between 67 and 69 inches, we subtract the smaller probability from the larger:
0.6293 - 0.3707 = 0.2586
Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month? (2 points)
Answers
19779 - 57(11) = 19779 - 627 = 19152
m = 19152*2/(56*57)
m = 12
she saved $12 more every month
Find an equation of the vertical line that passes through (x, y) = (5, 11).
Answers
A reflecting telescope is purchased by a library for a new astronomy program. The telescope has a horizontal parabolic frame and contains two mirrors, 3 inches apart from each other- the first in the base and the second at the focal point. The astronomy teacher would like to attach a digital monitoring system on the edge of the telescope, creating a straight line distance above the focal point. Assuming that the telescope is placed on the edge of the roof in such a way that it is parallel to the ground, the position of the monitoring system, in relationship to the distance between the base and the focal point is modeled by the equation, x = 1/12y2 (x = the distance between the base and the focal point; y= the height of the monitoring system).
Rewrite the model so that the height of the digital monitoring system is a function of the distance between the base and the focal point of the telescope. How high above the focal point is the digital monitoring system attached to the telescope? Include your function and the height, rounded to the nearest tenth of an inch, in your final answer.
Answers
[tex]\bf x=\cfrac{1}{12}y^2\implies 12x=y^2\implies \sqrt{12x}=y \\\\\\ \textit{now, what's \underline{y} when x = 3?}\qquad \sqrt{12(3)}=y[/tex]
The digital monitoring system attached at 6 inch from telescope.
What is Parabola?A curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a stationary point is equal to its distance from a fixed line.
Here, we have a parabolic frame with the focus point and on the tip from the stem coming from its center, the digital monitoring system.
So, the equation that in this situation is
x = y² / 12
12x = y²
y= √12x
So, at x= 3 the y will be
y = √12(3)
y = √36
y = 6
Thus, the digital monitoring system attached at 6 inch from telescope.
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A bacteria culture starts with 120 and after 3 hours the population consists of 200 bacteria. What is the rate of the increase to the nearest percent?
Answers
The rate of the increase would be 18.56% to the nearest percent.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Seema obtained a score of 57% on her exam, that corresponds to 67 out of 100.
We have been given 120 bacteria to start, which increases to 200 bacteria in 3 hours.
The population-increasing formula is given by
⇒ P(n) = P₀(1+ r)ⁿ
Here P(n) = 200, P₀ = 120, and n = 3
Substitute the values in the above equation,
⇒ 200 = 120(1+ r)³
⇒ 200 / 120 = (1+ r)³
⇒ 5/3 = (1+ r)³
⇒ ∛5/3 = 1+ r
⇒ ∛5/3 - 1 = r
⇒ r = 0.18563
⇒ % r = 18.56%
Therefore, the rate of the increase would be 18.56% to the nearest percent.
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The rate of increase for a bacteria culture that starts with 120 bacteria and grows to 200 after 3 hours is calculated by dividing the increase in population (80) by the initial population (120) and then multiplying by 100 to get the percentage. The rate of increase is 66.67%, which rounds to 67% to the nearest percent.
To find the rate of increase to the nearest percent for a bacteria culture that starts with 120 bacteria and grows to 200 bacteria after 3 hours, we must calculate the percentage growth over the time period given.
First, we need to find the absolute increase in the number of bacteria:
Final population - Initial population = Increase in population
200 - 120 = 80
Next, we calculate the rate of increase based on the initial population:
(Increase in population / Initial population)
(80 / 120)
Multiplying by 100 to get the percentage: (80 / 120) ×100
Rate of increase = 66.67%
Rounded to the nearest percent, the rate of increase is 67%
In circle Y, what is m?
59°
67°
71°
118°
Answers
[tex] \frac{arc \ SR+arc \ TU}{2}=63 \\ \\ 55+arc \ TU=63*2 \\ \\55+arc \ TU=126\\\\ \ arc \ TU = 126-55=71^o[/tex]
Answer:
[tex]arc\ TU=71\°[/tex]
Step-by-step explanation:
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite
In this problem we have that
[tex]63\° =\frac{1}{2}(arc\ SR+arc\ TU)[/tex]
we have
[tex]arc\ SR=55\°[/tex]
substitute and solve for arc TU
[tex]63\° =\frac{1}{2}(55\°+arc\ TU)[/tex]
[tex]126\° =(55\°+arc\ TU)[/tex]
[tex]arc\ TU=126\°-55\°=71\°[/tex]
Is 70 thousand written in standard form or word form explain.
Answers
70,000 is standard form
seventy-thousand is word form
Julio is playing a trivia game .on his first turn ,he lost 100 points on his second turn ,he lost 75 points . On his third, he lost 85 points. Write a sum of three nagative integer that models the change to julio score after his first three turns
Answers
True or false the opposite angles of a quadrilateral in a circumscribed circle are always complementary
Answers
Answer: This statement is false.
Step-by-step explanation:
False, the opposite angles of a quadrilateral in a circumscribed circle is not complementary.
As we know that the sum of opposite angles of a cyclic quadrilateral ( quadrilateral circumscribed circle ) is always supplementary.
So, Sum of opposite angles is 180° .
Hence, this statement is false.
Answer:
False
Step-by-step explanation:
We are given that
Opposite angles of a quadrilateral in a circumscribed circle are always complementary.
We have to find that this statement is true or not.
We know that
When a quadrilateral in a circumscribed circle is called cyclic quadrilateral.
We know that
Sum of opposite angles of cyclic quadrilateral is always 180 degrees.
When sum of two angle is equal to 180 degrees then , the angles are called supplementary.
Hence, the sum of opposite angles of cyclic quadrilateral is always supplementary.
Therefore, the given statement is false.
The sum of the page numbers on the facing pages of a book is 81. what are the page? numbers?
Answers
Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches. use 3.14 for pi. (1 point) 3 inches 4 inches 8 inches 16 inches
Answers
83.74 = 1/3 x 3.14 x r^2 x 5 = 5.233r^2
r^2 = 83.74/5.233 = 16
r = sqrt(16) = 4
Answer: d = 2(4) = 8 inches.
Answer: 8 inches
Step-by-step explanation:
The volume of a cone is given by :-
[tex]\text{Volume}=\dfrac{1}{3}\pi r^2 h[/tex], where r is radius and h is height of the cone.
Given : The volume of cone = 83.74 cubic inches
The height of cone = 5 inches
Then by using the above formula , we have
[tex]83.74=\dfrac{1}{3}(3.14) r^2 5\\\\\Rightarrow\ r^2=\dfrac{3\times83.74}{3.14\times5}\\\\\Rightarrow\ r^2=16.0012738854\approx16\\\\\Righatrrow\ r=\sqrt{16}=4\text{ inches}[/tex]
Diameter of cone = [tex]2r=2(4)=8\text{ inches}[/tex]
Hence, the diameter of cone = 8 inches
The dot plot shows the number of words students spelled correctly on a pre-test. Which statement best describes the shape of the graph?
A.) The graph is skewed right.
B.) The graph is nearly symmetrical.
C.) The graph is skewed left.
D.) The graph is perfectly symmetrical.
Answers
Let's think of this problem easily by looking at it instead of going through rigorous mathematics.
When a graph is skewed right, most of the values are to the left side.
When a graph is skewed left, most of the values are to the right side.
Perfectly symmetrical is that both sides, with respect to the median, are same. Here mean and median is equal.
Nearly symmetrical would really close to perfect symmetry, only varying a bit on both sides. Mean would be approximately equal to median.
Now counting the dots as well as looking closely, we can rule out skewed right and skewed left. Now, is the graph perfectly symmetrical? No! So the correct answer is "nearly symmetrical". Correct choice is B.
ANSWER: B
Answer:
The answer is neary symmetrical or answer B
Step-by-step explanation:
If you cut the graph in half exactly, both side would almost line up perfectly.
a rectangle has a perimeter of 182 in and length of 52 in. What is the width?
Answers
If you apply the changes below to the absolute value parent function, F(x)=|x|, what is the equation of the new function? Shift 8 units left, shift 3 units down.
A. G(x)=|x-3|-8
B. G(x)=|x-3|+8
C. G(x)=|x-8|-3
G(x)=|x+8|-3
Answers
The transformation that shifts a function along the [tex]y-axis[/tex] is [tex]f(x)+a[/tex], which shifts the function up, and [tex]f(x)-a[/tex], which shifts the function down
Hence, the correct answer is D: [tex]g(x)=f(x+8)-3[/tex]
write a function g whose graph represents a translation 2 units to the right followed by a horizontal stretch by a factor or 2 on the graph of f(x)=|x|
Answers
The graph of the function g(x) = 2(|x - 2|) represents a translation 2 units to the right followed by a horizontal stretch by a factor of 2 on the graph of f(x) = |x|.
Explanation:To represent a translation 2 units to the right followed by a horizontal stretch by a factor of 2 on the graph of f(x) = |x|, we can define the function g(x) as g(x) = 2(|x - 2|).
The function |x - 2| represents the translation 2 units to the right, while the factor of 2 in front of the absolute value represents the horizontal stretch by a factor of 2.
For example, when x = 1, g(x) = 2(|1 - 2|) = 2(|-1|) = 2.
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A quadratic equation is shown below: 4x2 − 12x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 9x2 − 30x + 25 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
The discriminant (radicand) is √(b^2-4ac), let us call this "d" for the discriminant.
If:
d<0, there are no real solutions (though there are two imaginary ones)
d=0, there is one real solution
d>0, there are two real solutions.
In this case, d=12^2-4(4)9
d=144-144
d=0
So there is one real solution.
B)
9x^2-30x+25=0
9x^2-15x-15x+25=0
3x(3x-5)-5(3x-5)=0
(3x-5)(3x-5)=0
(3x-5)^2=0
x=5/3
x=1 2/3