Write the linear equation in slope-intercept form passing through the given points. (-12, 14) and (6, -1) (Hint: Start by finding slope between the two points, then put in point-slope form and then convert to slope-intercept form.) y= type your answer... X+ type your answer...
Answers
The slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.
Given the following data:
Points on x-axis = (-12, 6).
Points on y-axis = (14, -1).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
\(Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)
Substituting the given points into the formula, we have;
Slope = (6 + 12)/-1 - 14)
Slope = -18/15
Slope = -6/5
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (-12, 14), we have:
14 = -6/5(-12) + c
8 = 72/5 + c
40 = 72 + 5c
5c = 72 - 40
c = 32/5
In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.
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Related Questions
Someone help with this if you can
Answers
Answer:
z=74
x=15
Step-by-step explanation:
74+8x-14=180
step 1 combine like terms
60+8x=180
step 2 subtract each side by 60
8x=120
step 3 divide each side by 8
x=15
Answer:
z=74
x=15
Step-by-step explanation:
z=74 because vertical angles are the same
you have to add the z and 8x-14 and set it equal to 180 because the angles at supplementary
3x : 8 = 7 : 2 Calculate the value of x
Answers
Answer: x = 28/3
\(\frac{3x}{8}=\frac{7}2} \\\\=>3x=\frac{7.8}{2}=28 \\\\=>x=\frac{28}{3}\)
Step-by-step explanation:
Find the length of side x in the simplest radical form with a rational denominator.
Answers
Answer:4.243
Step-by-step explanation:https://www.omnicalculator.com/math/right-triangle-side-angle?c=USD&v=given:0,angle_beta1:45!deg,b1:3!inch
The line plot shows the favorite color of the students in the class. How many students liked red or blue? A. 9 B. 20 C. 25 D. 45
Answers
The line plot shows the favorite color of the students in the class. Option A, 9 students liked red or blue.
The line plot presents four columns with red, blue, orange, and yellow colors at the bottom. The number of students liking the color is represented by the x variable. The line plot presents five x in the column of red and four x in the column of blue. Therefore, a total number of students liking the color red and blue are option 9.
A line plot or line chart presents a chart along the number line. Line dots are often used in the line chart but variables can be presented by alphabet as well. It presents the frequency of the number of times the variable is presented in the data. If the data is big in numbers, the legend is used to present the variable. For instance, the legend of the line plot is x. Therefore, x = 5 students.
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Answer:
A
Step-by-step explanation:
If the function is one-to-one, find its inverse. If not, write "not one to one". F[x]=8/x+8
Answers
The function is one-to-one. The inverse of \(f(x)\) is: \(f^-^1 = x-8\)
To determine if the function \(f(x) =8/x+8\) is one-to-one, we need to check if it satisfies the horizontal line test or vertical line test.
Let's assume \(f(x1)=f(x2)\) for some \(x1\) and \(x2\) in the domain of \(f\). We have:
\(8/x1+8=8/x2+8\)
To find the inverse, we can solve this equation for \(x2\);
\(x2 = 8/8/x1+8 - 8\)
\(x2 = x1 - 8\)
Since the equation doesn't contain any restriction or condition on the domain, we can conclude that the function is one-to-one. The inverse of \(f(x)\) is: \(f^-^1 = x-8\)
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Please Help this is really important.
Answers
By using quadrilateral WBNH, the proof should be completed to prove that side WH is congruent to BN as follows;
It is given that WB || HN, so ∠HNW ≅ ∠BWN because if two parallel lines are intersected by a transversal, then alternate interior angles theorem are congruent. WN ≅ WN by reflexive property. Since it is given that ∠WHN ≅ ∠WBN, then ΔNWH ≅ ΔWNB by ASA. Therefore, WB ≅ HN by CPCTC.
What is the Alternate Interior Angles Theorem?In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:
By applying the alternate interior angles theorem to quadrilateral WBNH, we have the following:
∠HNW ≅ ∠BWN.
ΔNWH ≅ ΔWNB (Angles, Side, Angle).
By applying corresponding parts of congruent triangles are congruent (CPCTC) to quadrilateral WBNH, we have the following:
WB ≅ HN
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(07.02)
What is the value of x in the equation 3(2x + 8) = 0? (4 points)
−8
8
4
−4
Answers
Answer:
your answer is D-4
Step-by-step explanation:
3(2x+8)=0
Step 1: Simplify both sides of the equation.
3(2x+8)=0
(3)(2x)+(3)(8)=0(Distribute)
6x+24=0
Step 2: Subtract 24 from both sides.
6x+24−24=0−24
6x=−24
Step 3: Divide both sides by 6.
6x
6
=
−24
6
x=−4
Hope this helped.
Students at a large university have four places to get lunch: the cafeteria, the hut, the taco wagon, or the pizza place. An article in the school newsletter states that 70% of students prefer to get lunch in the cafeteria and the other three options are preferred equally. To investigate this claim, a random sample of 150 students is selected. It is discovered that 118 prefer to eat in the cafeteria, 10 prefer the hut, 12 prefer the taco wagon, and 10 prefer the pizza place. Someone may want to know if these data provide convincing evidence that the distribution of lunch location preference differs from the claim in the article. What is the value of the chi-square test statistic and P-value?
χ2 = 0.74, P-value is between 0.10 and 0.15
χ2 = 0.74, P-value is greater than 0.25
χ2 = 5.54, P-value is between 0.10 and 0.15
χ2 = 5.54, P-value is between 0.20 and 0.25
Answers
The value of the chi-square test statistic and P-value are χ2 = 5.54 and between 0.10 and 0.15 respectively.
To determine the chi-square test statistic and P-value, we need to perform a chi-square test of independence using the observed frequencies and the expected frequencies based on the null hypothesis.
The null hypothesis states that the distribution of lunch location preference is as claimed in the article: 70% prefer the cafeteria, and the remaining options are preferred equally.
To calculate the expected frequencies, we need to assume that the null hypothesis is true. Since there are four lunch options, each option would be expected to have an equal probability of 0.10 (or 10%) if the null hypothesis is true.
Using the observed and expected frequencies, we can calculate the chi-square test statistic using the formula:
χ2 = Σ((O - E)² / E)
Substituting the values:
χ2 = ((118-105)²/105) + ((10-15)²/15) + ((12-15)²/15) + ((10-15)²/15)
= 5.54285714286
≈ 5.54
To determine the degrees of freedom, we subtract 1 from the number of categories (4 - 1 = 3).
Using the chi-square test statistic and degrees of freedom, we can find the P-value from a chi-square distribution table or using statistical software.
Based on the given answer choices, the correct option is:
χ2 = 5.54, P-value is between 0.10 and 0.15
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Solve the following maximisation problem by applying the Kuhn-Tucker theorem: Max xy subject to –4x^2 – 2xy – 4y^2 x + 2y ≤ 2 2x - y ≤ -1
Answers
By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25
The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1
Let us solve this problem by applying the Kuhn-Tucker theorem.
Let us first write down the Lagrangian function:
L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)
Then, we find the first order conditions for a maximum:
Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0
Ly = x - 8λ₁y - 2λ₁x = 0
Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0
Lλ₂ = 2x - y + 1 = 0
The complementary slackness conditions are:
λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0
λ₂(2x - y + 1) = 0
Now, we solve for the above equations one by one:
From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1
Substitute this in equation (1), we get:
8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0
Simplifying, we get:
10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)
From equation (2), we can write x = 8λ₁y + 2λ₁x
Substitute this in equation (1), we get:
8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0
Simplifying, we get:
-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)
Solving equations (4) and (5) for λ₁ and λ₂, we get:
λ₁ = 1/20 and λ₂ = 9/100
Then, substituting these values in the first order conditions, we get:
x = 2/5 and y = 9/5
Therefore, the maximum value of xy is:
2/5 x 9/5 = 18/25
Hence, the required answer is 18/25.
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base = 7m area= 49m2 height= m whats the height
Answers
Answer:
if it is triangle
area=1/2 base×height
49×2=7×height
height=49/7 ×2=14m
The height of the triangle is 14 m whose base measure is 7 m and the area of the triangle is 49 m²
What is the triangle?The triangle can be defined as a three-sided polygon in geometry and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have:
Base length of the triangle = 7 m
Area of the triangle = 49 m²
We know the area of the triangle is given by:
\(\rm A = \frac{1}{2} (b\times h)\)
Here b = 7 m, A = 49 m², and h is the height of the triangle
Put the above values in the formula, we get:
\(\rm 49 = \frac{1}{2} (7\times h)\)
49×2 = 7×h
h = 14 m (divide by 7 on both sides)
Thus, the height of the triangle is 14 m whose base measure is 7 m and the area of the triangle is 49 m²
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Recently many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken. Suppose that at one firm, it is known that over the past few years employees have taken a mean of 5.4 sick days. This year, the firm introduces telecommuting. Management chooses a simple random sample of 80 employees to follow in detail, and, at the end of the year, these employees average 4.4 sick days with a standard deviation of 2.8 days. Let
μ
represent the mean number of sick days for all employees of the firm.
a.Find the P-value for testing
H0
:
μ
≥ 5.4 versus
H1
:
μ
< 5.4. Round the answer to four decimal places.
b.
The P-value calculated for testing H0 : µ ≥ 5.4 versus H1 : µ < 5.4 is a small probability; hence, it is plausible that the mean number of sick days is at least 5.4.
True or false
Answers
The required P-value is 0.0014. The given statement "The P-value calculated for testing H0 : µ ≥ 5.4 versus H1 : µ < 5.4 is a small probability; hence, it is plausible that the mean number of sick days is at least 5.4" is false because a small P-value indicates that the null hypothesis (H0) is less likely to be true.
a. To find the P-value for testing H0: μ ≥ 5.4 versus H1: μ < 5.4, first calculate the test statistic:
Test statistic (z) = (Sample mean - Population mean) / (Standard deviation / √(Sample size))
z = (4.4 - 5.4) / (2.8 / √(80))
z ≈ -3.19
Now, use the z-table or a calculator to find the P-value corresponding to the test statistic:
P-value ≈ 0.0014 (rounded to four decimal places)
b. The statement "The P-value calculated for testing H0 : µ ≥ 5.4 versus H1 : µ < 5.4 is a small probability; hence, it is plausible that the mean number of sick days is at least 5.4" is FALSE.
A small P-value indicates that the null hypothesis (H0) is less likely to be true and we have evidence to support the alternative hypothesis (H1) that the mean number of sick days is less than 5.4.
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The required P-value is 0.0014. The given statement "The P-value calculated for testing H0 : µ ≥ 5.4 versus H1 : µ < 5.4 is a small probability; hence, it is plausible that the mean number of sick days is at least 5.4" is false because a small P-value indicates that the null hypothesis (H0) is less likely to be true.
a. To find the P-value for testing H0: μ ≥ 5.4 versus H1: μ < 5.4, first calculate the test statistic:
Test statistic (z) = (Sample mean - Population mean) / (Standard deviation / √(Sample size))
z = (4.4 - 5.4) / (2.8 / √(80))
z ≈ -3.19
Now, use the z-table or a calculator to find the P-value corresponding to the test statistic:
P-value ≈ 0.0014 (rounded to four decimal places)
b. The statement "The P-value calculated for testing H0 : µ ≥ 5.4 versus H1 : µ < 5.4 is a small probability; hence, it is plausible that the mean number of sick days is at least 5.4" is FALSE.
A small P-value indicates that the null hypothesis (H0) is less likely to be true and we have evidence to support the alternative hypothesis (H1) that the mean number of sick days is less than 5.4.
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What is the rate of change of the function y= -7?
Answers
Answer:
Zero
Step-by-step explanation:
Average rate of change can also be called as gradient or change in the respective variable , in this case we need the average rate of change of y which has the function y = -7
Since this is a linear function and if we draw the graph of y = -7 the graph would be parallel to the x-axis, and any line parallel to the x-axis has slope of zero , hence the average rate of change of the function y = -7 is zero
Factor each expression that can be factored. For an expression that cannot be factored into a product of two binomials, explain why. x²+2 x+1 .
Answers
The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
⇒ x² + 2x + 1
Factorize the expression, then the factor of the expression will be
⇒ x² + x + x + 1
⇒ x(x + 1)x + 1(x + 1)
⇒ (x + 1)(x + 1)
⇒ (x + 1)²
The product of two binomials will be (x + 1) and (x + 1).
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PLEASE HELP WILL MARK BRAINLIEST FOR WHOEVER IS FIRST
Answers
Answer: 3/8 cups
Step-by-step explanation: Did this help?
448 / 28 show your work
Answers
Answer:
16
Step-by-step explanation:
When you just Put 448 divided 28 it 16
PLEASE ANSWER I WILL GIVE BRAINLIEST!!!!! PLEASE ASAP!!
Answers
A circular pizza that is 17 inches in diameter is cut into 6 equal slices. What is the area of one of the slices?
The area of one slice is in?
Answers
Answer:
51
Step-by-step explanation:
17x6=51
Sam bought 95.9 pounds of peanuts and 0.02 pounds of raisins. How many pounds of snacks did he buy in all?
Answers
Answer:
95.92
I think this is right
360 = 37.50x + 60 solve for x
hellppppp
Answers
-60 on both sides
300 = 37.50x
/37.50 on both sides
8 = x
Answer:
x = 8
The probability that a hockey team will win a match is 0.4. The probability that the team will draw is 0.3. Work out the probability that the team will not win. (1 Point)
Answers
Answer:
P(team will win)=0.4
P(team will draw)=0.3
P(t want will not win) = 1 - 0.4+0.3
=1-0.7=0.3
fraction help
im stuck in tis problme kindly help
Answers
Answer:
\(\frac{7}{48} = B\)
Step-by-step explanation:
Convert 3 to fraction 12\4
5\8 - 5\12( 12\4 - 1\4 ) + 2\3
-
Since 12\4 and 1\4 have the same denominator, subtract them by subtracting their numerators.
5\8 - 5\12 ( 12-1\4 ) + 2\3
-
Subtract 1 from 12 to get 11.
5\8 - 5\12 ( 11\4 ) + 2\3
-
multiply 5\12 times 11\4 by multiplying numerator times numerator and denominator times denominator.
5\8 - 5 x 11 \ 12 x 4 + 2\3
Do the multiplications in the fraction
5 x 11 \ 12 x 4
= 5\8 - 55\48 + 2\3
-
Least common multiple of 8 and 48 is 48.Convert 5\8 and 55\48 to fractions with denominator 48.
30\48 - 55\48 + 2\3
-
Since 30\48 and 55\48 have the same denominator, subtract them by subtracting their numerators.
30 - 55 \ 48 + 2\3
-
Subtract 55 from 30 to get −25.
-25\48 + 2\3
Least common multiple of 48 and 3 is 48. Convert -25\48 and 2\3 to fractions with denominator 48.
-25\48 + 32\48
Since -25\48 and 32\48 have the same denominator, add them by adding their numerators.
-
-25 + 32 \ 48
Add −25 and 32 to get 7.
7\48
Can someone help me with these answers please
Answers
Answer:
7. 7x
8. -2v+19
9. 8p-26
10. 14y-5
11. 7m-13
12. -8k+25
13. -3w-13
14. -9c+27
15. m+4n
16.-7s
17. 6x-13y-24
18. 6h-16b
19. -9p+9q+12
20. 2k/5+ 31/4
Step-by-step explanation:
Sophia scored 92% on a math test. If the test had 50 questions, how many did she get correct?
Answers
Answer:46 answers :)
Step-by-step explanation:
explanation:
92% of 50 is 46, therefore she got 46 correct!:)
what are two numbers that have a product of 12 and a sum of 5
Answers
Answer:
there are no two numbers that have a product of 12 and a sum of 5 make sure that the question is correct
yo can find two numbers that have a product of 12 and a sum of 7 the answer is 3 and 4 .
Step-by-step explanation:
1. What is the m2<5? Explain how you know. (2 points)
2.What is the measure of the sum of the angles in a triangle? (2 points)
3. L3 is in a triangle with L4 and L5. Write and solve an equation to find the m L3. (2 points)
4. What is the measure of a straight angle? (2 points)
5. L2 is in a straight line with L1 and L3. Write and solve an equation to find the m L2 (2 points)
Answers
using the rule y=8x + 5 find the value of y when x is 6
Answers
Answer:
y = 8x + 5
y = 8 * 6 + 5
y = 48 + 5
y = 53
please help me I need some help asap
Answers
Answer:
The answer is 4.
Step-by-step explanation:
Subtracy 2 from 4.
Then divide 2 by 8
I am confused how they were able to get the constraints in ch6
problem 10P
Answers
In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.
However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.
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show that v is an eigenvector of A and find the corresponding eigenvalue, λ.A= [\begin{ccc}-1&1\\6&0\end{array}\right], v = [\begin{ccc}1\\3\end{array}\right]λ=_____
Answers
The matrix A does not eigenvector v corresponding to the given eigen value.
λ.A = [ -11 60 ]
v = [ 1 3λ ]
v is an eigenvector of A calculate corresponding eigenvalue,
A × v = λ × v
where A is the given matrix.
v is the given vector.
λ is the corresponding eigenvalue.
× denotes matrix multiplication.
Let's first calculate A × v we have,
A × v
= [-11 60] × [ 1 3λ]
= [-11-33λ 60+ 180λ]
Check A× v is equal to λ × v ,
λ × v =
λ × [ 1 3λ]
= [λ 3λ^2]
Set these two vectors equal to each other and get the following system of equations ,
-11-33λ = λ __(1)
60+ 180λ = 3λ^2 ___(2)
From equation (1) we get,
⇒34λ = -11
⇒ λ = -11/34
Substituting this value of λ into the second equation, we have,
60+ 180λ = 3λ^2
⇒ 60 + 180(-11/34) = 3(-11/34)^2
⇒ (2040 -1980)/ 34 = 3(-11/34)^2
⇒ 60/34 = 3( 11/34)^2
⇒ 60 × 34 = 3 × 11 × 11
⇒20× 34 = 11 × 11
Which is not true.
so the value of λ does not satisfies both equations.
Therefore, v is not an eigenvector of A with corresponding eigenvalue λ.
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The above question is incomplete, the complete question is:
Check whether v is an eigen vector of A if yes find the corresponding eigen value.
λ.A = [ -11 60 ]
v = [ 1 3λ ]
hii can someone please help me on this problem?
Answers
Answer:
Please write the problem
Step-by-step explanation:
So i can help you :)