the line with a slope of 9/7 & containing a midpoint of the segment whose end points are (2, -3) & (-6, 5)
Answers
1. Find the midpoint of the segment using the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
2. Use the midpoint and the slope to find the equation of the line in point-slope form. The point-slope form is given by:
y - y1 = m(x - x1), where (x1, y1) is the midpoint and m is the slope.
Substituting the values:
y - 1 = (9/7)(x - (-2))
y - 1 = (9/7)(x + 2)
y - 1 = (9/7)x + (18/7)
3. Simplify the equation to obtain the slope-intercept form:
y = (9/7)x + (18/7) + 1
y = (9/7)x + (18/7) + (7/7)
y = (9/7)x + (25/7)
So, the equation of the line with a slope of 9/7 and containing the midpoint of the segment with endpoints (2, -3) and (-6, 5) is y = (9/7)x + (25/7).
Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:
y = (9/7)x + 25/7.
Step-by-step explanation:Step 1: Find the midpoint of the line segment.
The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
So, the midpoint of the line segment is (-2, 1).
Step 2: Write the equation of the line using the slope-intercept form.
The slope-intercept form of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given the slope as 9/7, we have:
y = (9/7)x + b
Step 3: Substitute the coordinates of the midpoint to find the value of b.
Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:
1 = (9/7)(-2) + b
1 = -18/7 + b
To find the value of b, we can solve this equation:
1 + 18/7 = b
25/7 = b
Step 4: Write the final equation of the line.
Using the value of b, the equation becomes:
y = (9/7)x + 25/7
Related Questions
A coral reef grows 0.14 m every week. How much does it grow in 13 weeks?
Answers
Answer: 1.82 m
Step-by-step explanation:
Ratios
0.14 n 0.14 x 13 = 1.82
1. 13 1.82/1 = 1.82
Describe in words the transformations of the graph of the parent function f(x) = x2 that
would result in the graph of
g(x) = 3(x - 5)^2 + 2.
Describe in words the transformations of the graph of the parent function f(x) = x2 that
would result in the graph of
g(x) = 1/3(x + 6)^2- 4.
Answers
2. The transformations are given as follows:
Vertical stretch by a factor of 3.Translation right 5 units.Translation up 2 units.3. The transformations are given as follows:
Vertical compression by a factor of 3.Translation left 6 units.Translation down 4 units.How to define the transformations?For item 2, the transformations in this problem are given as follows:
Vertical stretch by a factor of 3, due to the multiplication by 3.Translation right 5 units, as x -> x - 5.Translation up 2 units, as y -> y + 2.For item 3, the transformations are given as follows:
Vertical compression by a factor of 3, due to the multiplication by 1/3.Translation left 6 units, as x -> x + 6.Translation down 4 units, as y -> y - 4.More can be learned about translations at brainly.com/question/28174785
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Enter the correct 4 digit code ( no spaces)
Answers
Answer: 5934
Step-by-step explanation:
To find A, add 3+2=5
To find B use the calculated 5 to get 5+4 =9
To find C do the reverse of adding: Subtract 4-1=3 Rewrite as 1+3=4
To find D do the reverse of adding: Subtract 9-5=4 Rewrite as 4+5=9
Lesson 4 Extra Practice Mean Absolute Deviation Determine the mean absolute deviation for e the nearest hundredth if necessary. Then des absolute deviation represents. 1. Number of Sibmas 2 5 8 9 7 6 3 5 1 &
Answers
Data set: 2 5 8 9 7 6 3 5 1
Number of data values: 9
Average: (2 + 5 + 8 + 9 + 7 + 6 + 3 + 5 + 1)/9 = 5.11
|2 - 5.11| = 3.11
|5 - 5.11| = 0.11
|8 - 5.11| = 2.89
|9 - 5.11| = 3.89
|7 - 5.11| = 1.89
|6 - 5.11| = 0.89
|3 - 5.11| = 2.11
|5 - 5.11| = 0.11
|1 - 5.11| = 4.11
Mean Absolute Deviation =
(3.11 + 0.11 + 2.89 + 3.89 + 1.89 + 0.89 + 2.11 + 0.11 + 4.11)/9 = 2.12
Solve for x: -3x-3=-3(x+1)
Answers
Has infinite many solutions. X=1
Step by step:
-3x-3=-3(x+1)
-3x-3=-3x-3
-3x-3+3=-3x-3+3
-3x=-3x
Answer:
x= -6 broo
Step-by-step explanation:
can someone help me please
Answers
Answer:
y = (-1/80)x^2 +2x
Step-by-step explanation:
The graph of the equation for the arch will go through the points ...
(0, 0), (160, 0), (80, 80)
We can start by making use of the zeros to write the function ...
y = a(x -0)(x -160)
To make the graph go through the point (80, 80), we must have ...
80 = a(80 -0)(80 -160) = (-80^2)a
-1/80 = a . . . . . . divide by the coefficient of "a"
So, our equation is ...
y = (-1/80)x(x -160)
y = (-1/80)x^2 +2x
At Davis's Hat Store around the block, they have a total of 300 hats in the store. 14% of the hats are white.
How many of the hats in the store are white?
Answers
Answer:
42.
Step-by-step explanation:
14% of 300 is 42.
hope this helped
Find the value of x that will make l || m
Answers
The numerical value of x that make line l parallel to line m is 7.
What is the numerical value of x that make l parallel to m?When two parallel lines are intersected by any other line, the angles which are formed in corresponding corners with the transversal are called corresponding angles.
Corresponding angles are equal.
From the diagram
The two corresponding angles are 148° and ( 10x + 78 )°.
Since corresponding angles are equal.
( 10x + 78 ) = 148
Solve for x
10x + 78 = 148
10x = 148 - 78
10x = 70
x = 70/10
x = 7
Therefore, the value of x is 7.
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Explain with steps please and thank you! :)
Answers
Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°
How to find the missing angle?The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.
Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.
Now, for the transverse line theorem we can say that:
Angle 1 will be composed of two angles namely:
48 degrees and (180 - 153) degrees.
Thus:
m∠1 = 48° + 27°
m∠1 = 75°
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Charls invested $140. She earned a simple interest of 3% pee year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charls received at the ned of two years?
Answers
Answer:
$148.4
Step-by-step explanation:
140 times 0.03=4.2
4.2=8.4
140+8.4=148.4
Six ice cream bars and four bags of chips cost $13.50. Ten ice cream bars and five bags of chips cost
$20.00. What is the cost for each item sold separately?
Answers
Answer:
For the 6 ice cream bar: $2.25
For the 10 ice cream bar: $4
Step-by-step explanation:
Kindly help me with my statistics problem please. Due today at 4pm >_< Thanks in advance!
One of the 200 business majors at a college is to be chosen for the student senate. If 77 of these students are enrolled in a course in accounting, 64 are enrolled in business law, and 92 are enrolled in either courses, how many of the outcomes corresponds to the choice of a business major who is enrolled in both courses. Use a venn diagram.
Answers
If One of the 200 business majors at a college is to be chosen for the student senate. The outcomes that correspond to a business major who is enrolled in both accounting and business law is: x = 33 - y.
How many of the outcomes corresponds to the choice of a business major who is enrolled in both courses?Since we know that 92 students are enrolled in either course, we can write this number in the intersection of the two circles, which represents the number of students enrolled in both courses. Let x be the number of students enrolled only in accounting, and y be the number of students enrolled only in business law.
Our Venn diagram now looks like this:
Accounting
(77-x) (x)
___________
| |
Total | (92) | y
Business|___________|
Law | |
| x |
|___________|
(64-y) |
Total
Business
Majors
We know that there are 200 business majors in total, so the sum of the four regions in the diagram must add up to 200. Therefore:
x + y + (77-x) + (64-y) + 92 = 200
Simplifying this equation, we get:
x + y = 33
We want to find the number of outcomes that correspond to a business major who is enrolled in both accounting and business law. From the Venn diagram, we can see that this is represented by the intersection of the two circles, which has a value of x.
Therefore, there are x = 33 - y outcomes that correspond to a business major who is enrolled in both accounting and business law. The value of y can range from 0 (if all 33 students enrolled only in accounting) to 33 (if all 33 students enrolled only in business law).
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z varies directly as x2. If z = 16 when x = 2, find z when x = 5.
...
Z=
Answers
Answer:
100
Step-by-step explanation:
it is a bit unclear to me, what that problem description means.
if I understand it correctly, than z is directly depending on x².
so, z = 16 for x = 2. x² = 4
I pondered a little bit, as there are several possibilities to connect 16 with 4 as a driving factor (e.g. 2⁴ = 16, 4×4 = 16, 12 + 4 = 16).
I decided to go with the simplest interpretation with the usual meaning of "varies" (multiplication) : 4×x²
that would mean
z = 4×x² = 4×5² = 4×25 = 100
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 9 of them are worn out. With this data, we test the following hypotheses at the 5% significance level. The P-value is 0.15
H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.
Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
Which of the following conclusions is correct?
A. Accept H0.
B. Fail to reject H0.
C. Reject H0.
Answers
Answer:
Fail to reject H₀
Step-by-step explanation:
To reject the null hypothesis, the P-value must be less than 0.05.
Since the P-value is 0.15 which is greater than 0.05, we would fail to reject the null hypothesis as there is no sufficient evidence against the null hypothesis.
Thus, the conclusion would be to fail to reject H₀.
Set the mean and standard deviation to 0 and 5 , respectively. Approximately 5% of the area under the normal curve lies to the right of 8.2 . Consider what would happen if you were to change the mean to 50 and keep the standard deviation at 5 . Can you predict the new value for which approximately 5% of the area under the normal curve lies to the right of this value? Enter your answer accurate to one decimal place.
Answers
Using z-scores and the normal distribution, it is found that the new value would be of 58.2.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X, which is the area to the left of Z under the normal curve.The area to the right of Z is 1 subtracted by the p-value of Z.In this problem:
Mean of 50 and standard deviation of 5, thus \(\mu = 50, \sigma = 5\).Area to the right of 0.05, thus Z with a p-value of 1 - 0.05 = 0.95, thus \(Z = 1.645\).We have to find the value of X, then:
\(Z = \frac{X - \mu}{\sigma}\)
\(1.645 = \frac{X - 50}{5}\)
\(X - 50 = 1.645(5)\)
\(X = 58.2\)
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Determine which regions contain cube roots of −1. Check all that apply.
Answers
Answer:
its A, C, and F
Step-by-step explanation:
Answer:
A, C, F
Step-by-step explanation:
What is the slope of the line? Please help (50 points) I really need to turn in this assignment.
Answers
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box. radians
Answers
Answer:
The measure of the central angle in radians is 5.6/8 = 0.7 radians.
A coordinate map of the local grocery store is shown below. Ice cream is located at the point (-8,0)(−8,0)left parenthesis, minus, 8, comma, 0, right parenthesis. Sprinkles are located at the point (-8,6)(−8,6)left parenthesis, minus, 8, comma, 6, right parenthesis. Plot the ice cream and sprinkles on the map.
Answers
Answer:
6 units
Step-by-step explanation:
Thank u to everyone who helped me!
I hope this photo helps ;)
1.You are working with Lara and Javier to solve this equation:Lara says that the solution is X =-1. Javier says that the solution is x=-8.5x- (x+3) = 2x - 5a.WHO is correct?(if you have a different solution than Lara and Javier,write YOUR name)b. How do you know who is correct? Show your work and explain your answer.5x- (x+3) = 2x - 5
Answers
You have the following equation:
5x - (x + 3) = 2x - 5
In order to determine who is correct, solve the previous equation as follow:
cancel out parentheses left side by using multiplcation sig rule:
5x - x - 3 = 2x - 5
simplify like terms left side
4x - 3 = 2x - 5
subtract 2x both sides and add 3 both sides and simplify
4x - 2x = -5 + 3
2x = -2
divide by 2 both sides
x = -2/2
x = -1
The solution for x is x = -1
a. LARA is correct
b. The equation was solved and the procedure above prove that Lara was correct.
Which dimensions can create more than one triangle?
three angles measuring 259, 65°, and 90°
three angles measuring 509, 50°, and 50°
three sides measuring 5 in., 12 in., and 13 in.
three sides measuring 4 ft, 8 ft, and 10 ft
Answers
Answer:
three sides measuring 4 ft, 8 ft, and 10 ft
Step-by-step explanation:
To choose which dimensions that can create more than one triangle, we consider the given values carefully and how possible it will be to construct.
The only dimensions given in the option that will be possible to create more than one triangle from it, is three sides measuring 4 ft, 8 ft, and 10 ft.
4 ft, 8 ft, and 10 ft are in simple multiple of 2
4 ft, 8 ft, and 10 ft = 2 (2 ft, 4 ft, and 5 ft ), with this we can construct two triangles with three sides measuring 2 ft, 4 ft, and 5 ft.
Answer:
d
Step-by-step explanation:
The two shapes below are scaled copies
of one another. The base lengths are
shown. What is the scale factor going
from the first figure to the second?
15
6
Answers
Answer:
2/5 or 0.4.
Step-by-step explanation:
6/15 = 2/5
The points (-1, 4) and (2, 9) lie on a line.
What is the slope of the line?
Answers
Answer:
\(\displaystyle m = \frac{5}{3}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Slope Formula: \(\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}\)Step-by-step explanation:
Step 1: Define
Identify
Point (-1, 4)
Point (2, 9)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute in points [Slope Formula]: \(\displaystyle m = \frac{9 - 4}{2 + 1}\)[Order of Operations] Simplify: \(\displaystyle m = \frac{5}{3}\)The average person blink 15 to 20 times per minute how many times does the average person blink in an hour
Answers
Answer:
900-1200
Step-by-step explanation:
mutpliy by 60
Find the volume of a box that has a length of 7 cm, a width of 9 cm, and a height of
11.2 cm.
Answers
Remember that volume of a box, rectangular prism, is: V = LWH.
So, V = 7(9)(11.2) = 705.6 cm^3
Which linear function has the same y-intercept as the one that is represented by the graph?
On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.
Answers
The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).
First, let's find the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - 4) / (5 - 3)
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (3, 4) as our reference point, we have:
y - 4 = -2(x - 3)
Expanding the equation:
y - 4 = -2x + 6
Simplifying:
y = -2x + 10
Now, let's check the given options to find the linear function with the same y-intercept:
Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)
The y-intercept is the same as the given line (10). So, this option is correct.
Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)
The y-intercept is not the same as the given line. So, this option is not correct.
Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
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The ratio of the exterior and interior angle of a regular polygon is 2:3. Find the number of sides in the polygon.
Answers
Answer:
5 sides
Step-by-step explanation:
the sum of the interior angle and exterior angle = 180°
sum the parts of the ratio, 2 + 3 = 5 parts , then
180° ÷ 5 = 36° ← value of 1 part of the ratio
exterior angle = 2 × 36° = 72°
the sum of the exterior angles of a polygon = 360°
since the polygon is regular then the exterior angles are congruent , so
number of sides = 360° ÷ 72° = 5
What is the surface area of the prism below
Answers
The surface area is the total area of the surface of a 3-dimensional object. The surface area of the triangular prism is 63 m².
What is surface area of an object?The surface area is the total area of the surface of a 3-dimensional object. To find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.
The surface area of the prism is,
Surface area of the prism = 2(0.5×1.5×2) + (2.5×10) + (1.5×10) + (2×10)
= 3m² + 25m² + 15m² + 20m²
= 63 m²
Hence, the surface area of the triangular prism is 63 m².
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7⁶ pieces of leaves on a tree and there are 7⁴ trees in a forest how many leaves are there in the forest
answer form a^b
Answers
Answer:
7^10
Step-by-step explanation:
7^6 * 7^4 = 7^10
Six students write an exam. The average score obtained on the exam by the group of students is 71%. If the first two students each obtained a mark of 73%, while the next three students each obtained a mark of 68%, what was the mark obtained by the sixth student?
Answers
The first two students obtained a mark of 73%, which gives us a total of 73 + 73 = 146 marks.
The next three students obtained a mark of 68% each, which gives us a total of 68 + 68 + 68 = 204 marks.
The average score obtained by the group is 71%. Since there are six students, the total marks obtained by all six students would be 6 * 71 = 426 marks.
To find the mark obtained by the sixth student, we can subtract the total marks obtained by the first five students from the total marks obtained by all six students: 426 - (146 + 204) = 76 marks.
Therefore, the mark obtained by the sixth student is 76%.