Answers
Given
Two points (-2, 1 ) and ( 2, 3 )
Find
Equation of a line in slope intercept form
Explanation
as, slope of a line passing two points is
\(m=\frac{y_2-y_1}{x_2-x_1}\)Now, we find slope of a line
\(m=\frac{3-1}{2-(-2)}=\frac{2}{4}=\frac{1}{2}\)Slope intercept form is
\(y=mx+b\)so,
\(\begin{gathered} y=\frac{1}{2}x+b \\ 1=\frac{1}{2}\times(-2)+b \\ 1=-1+b \\ 2=b \end{gathered}\)so, slope intercept form is
\(\begin{gathered} y=\frac{1}{2}x+2 \\ 2y=x+2 \end{gathered}\)Final Answer
Slope intercept form is
\(2y-x=2\)Related Questions
F(x)=1/x g (x)=x-4 can you evaluate (golf)(0)? Explain why or why not.
Answers
If f(x) = 1/x and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .
In the question
it is given that the functions
f(x) = 1/x
and g(x) = x-4
to find g=(gof)(x) ,
(gof)(x) = g(f(x))
= g(1/x) ... because f(x) = 1/x
= 1/x - 4 ....because g(x) = x-4
On simplifying further , we get
= (1-4x)/4x
On substituting x=0 , we get
gof(0) = (1-0)/4(0)
= 1/0
which is not defined , hence cannot be evaluated.
Therefore , if f(x) = 1/x and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .
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Three partners A, B, C start a business. B's Capital is four times C's capital
and twice A's capital is equal to thrice B's capital. If the total profit is Tk. 16500
at the end of a year, Find out B's share in it.
Answers
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A : B : C =6x : 4x : x
= 6 : 4 : 1
B's share = 16500×411
= 1500 × 4 = 6000.
What is meant by Capital?
A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the wide definition of capital.
While money in and of itself might be considered capital, the term is most frequently used to refer to money that is being used for investments or productive purposes. In general, capital is an essential part of managing firm day-to-day and funding its expansion in the future.
Business capital may be generated via activities or obtained through debt or equity finance. Typical sources of funding are as follows:
individual savings
relatives and friends
Angel backers
financiers for startups (VC)
Corporations
State, municipal, or federal governments
Personal loans
Working or conducting business
getting an IPO to go public
Working capital, equity capital, and debt capital are the three types of capital that firms of all sizes commonly concentrate on when creating budgets. A company in the financial sector names trading capital as the fourth element.
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Some values of functions f, g, h, and k are provided in the table on the right.
Find a possible equation of each function Verify your results with a graphing
calculator table. (HINT Use linear or exponential equations]
The equation of function f is f(x) =?
Answers
Without any values of the functions f, g, h, and k, it is not possible to find the equation of each function. The equation of a function can be determined by analyzing the values of the function. Based on the given values, a possible equation can be found and then verified by plotting the points on a graph and seeing if they align with the equation.
It's important to note that the equation can be a linear or exponential equation but it's impossible to determine it without any values.
Perform the operation.
(6x2 – 5x) – (10x² + 8x – 8)
HELP ASAP PLS
Answers
Find the area of the triangle.
3 9
A
5
B
?] units²
![Find the area of the triangle.3 9A5B?] units](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/aWZMIZBnhz8tUKqZNrW2mkI5u8UBMICx.png)
Answers
The area of the triangle is 47.91 units²
How to find the area of the triangle?When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.
Heron’s formula is:
Area =√s(s−a)(s−b)(s−c)
where,
a, b, c are the side length of the triangle
s is the semi-perimeter. s = (a+b+c)/2
In this case:
Using the knowledge of the radius of a circle. We can say:
a = BC = 3 + 9 = 12 units
b = AC = 5 + 3 = 8 units
c = AB = 5 + 9 = 14 units
s = (a+b+c)/2
s = (12+8+14)/2
s = 34/2
s = 17 units
Area = √s(s−a)(s−b)(s−c)
Area = √17(17−12)(17−8)(17−14)
Area = √17(5)(9)(3)
Area = √2295
Area = 47.91 units²
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1. Find the equation of the image of the circle x² + y2 + 16x-24y + 183 = 0 by rotated the line mirror 4x + 7y + 13 = 0. 2. The image of the circle (x - 3)² + (y-2)² = 1 in the line mirror ax + by = 19 is (x-1)³ + (y-16)2 = 1 then, find the values of (a, b). 3. Find the equation of a line passing through the origin and making an angle with the 4 line y-3x-5. 4. A parabola is drawn with its focus at (3,4) and vertex at the focus of the parabola y²-12x - 4y + 4 = 0. The n find equation of the parabola. 5. If the line ax + by + c = 0 touches the circle x² + y² - 2x = and is normal to the circle x² + y² + 2x - 4y + 1 = 0, then find the value of (a, b). 6. If the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. -3 7.1² 14 231= [] then find the matrix A 8. Find the equation of the ellipse having its center at the point (2,-3), one and one vertex at (4, -3). 3 9. Find the value of x if-1 0 10. Solve the linear system using Cramer's rule a) 2 1 2 4 (6x - 4y = -12 8x - 3y = -2 X = 16 -21 3x + 2y = z = 5 b) x-y+3z = -15 (2x + y +7z = -28 one focus at (3,-3) 11. Find the value of k for which the following system of linear equations has infinite solutions: x + (k+1)y = 5 ((k+1)x + 9y = 8k - 1
Answers
Answer:
-72x - 53y + 287 = 0.
Step-by-step explanation:
To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.
The line mirror equation is given as 4x + 7y + 13 = 0.
The reflection of a point (x, y) in the line mirror can be found using the formula:
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
where A, B, and C are the coefficients of the line mirror equation.
For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.
Now, let's find the equations of the image of the circle.
The original circle equation is x² + y² + 16x - 24y + 183 = 0.
Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)
= (x - 8y - 8(4x + 7y + 13)) / 65
= (x - 8y - 32x - 56y - 104) / 65
= (-31x - 64y - 104) / 65
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)
= (y - 14x + 8(Ax + By + C)) / 65
= (y - 14x + 8(4x + 7y + 13)) / 65
= (57x + 35y + 104) / 65
Therefore, the equation of the image of the circle is:
(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0
Simplifying the equation, we get:
-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0
-72x - 53y + 287 = 0
So, the equation of the image of the circle is -72x - 53y + 287 = 0.
A market researcher, having collected data on breakfast cereal expenditures by families with one, two, three, four, or five children living at home, plans to use an ordinary regression model to estimate the mean expenditures at each of these five family size levels. However, the researcher is undecided between fitting a linear or a quadratic regression model, and the data do not give clear evidence in favor of one model or the other. A colleague suggests: "For your purposes, you might simply use an ANOVA model." Is this a useful suggestion? Explain.
Answers
Answer:
Yes it is a useful suggestion
Step-by-step explanation:
Using the ANOVA model is a good idea because using it would give allowance For us to compare the five means of the five different family sizes. By this, during investigation there would be no confusion as to if a quadratic or linear relationship exists between the variables family size and breakfast cereal expenditure.
We would be comparing the mean expenditure of food of these 5 different family size levels so anova is useful.
Answer and Step-by-step explanation:
ANOVA model is mathematical model describe relationship between response and treatment.
One way ANOVA is given by:
YIJ = µ + Ti +Єij
Where, yij represent jth observation on ith treatment.
In this question, researcher collected data on the breakfast expenditure of a family whose size is five.
Yes, we can use ANOVA model. ANOVA can be used even if there is quadratic nonlinear relationship between expenditure and family size.
Since, the family size is five; we have to compare their mean expenditure on food.
The ANOVA one way model is:
YIJ = µ + Ti +Єij
For i=1, 2,3,4,5 and j= 1, 2,3,4,5
With hypothesis,
H01 : µ1 are equal.
H11 : at least two i not equal to j.
Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.
Answers
Answer:
y=0.3x
Step-by-step explanation:
Formula = \(K=\frac{y}{x}\)
y α x
y = kx
Where k is the constant of proportionality.
When y = 1.5; x = 5;
We substitute these known values in the equation,
y = kx
1.5 = k5
Dividing both sides of the equation by 5 to find the value for k, we have
1.5/5= k0.3/5
Therefore,
K = 0.3
Having found the value of k,
We substitute this value into the relationship
y = kx
Therefore we have,
y = 0.3x.
The direct variation function is therefore,
y = 0.3x.
[RevyBreeze]
Answer:
y= 0.3x
Step-by-step explanation:
Since y varies directly as x, use the direct variation equation, y = kx.
1.5 = k(5) Substitute 1.5 for y and 5 for x.
k = 0.3 Solve for k.
Write the direct variation function by using the value for k.
y = 0.3x Substitute 0.3 for k in y = kx.
*WILL GIVE POINTS*
Which factors compose the least common denominator for this difference?
11x/x²+4x-12 - 7/2x²-4x
•(x+6)
•(x+2)
•(x-4)
•(x-6)
•(x-2)
•2x
Answers
Answer:
2x, (x-2), (x+6)
Step-by-step explanation:
I just took the quiz on plato and I got it correct
P.S Can you guys give me the brainliest please
The least common denominator for the function \(\frac{11x}{x^{2} +4x-12} -\frac{7}{2x^{2} -4x}\) is (x -2).
What is least common denominator?The least common multiple of a group of fractions' denominators is known as the lowest common denominator, or Least Common Denominator.
Calculation for the least common denominator:
Consider the given expression,
\(\frac{11x}{x^{2} +4x-12} -\frac{7}{2x^{2} -4x}\)
Further simplifying the equation by factorisation of the denominator part
= \(\frac{11x}{x^{2} +6x-2x-12} -\frac{7}{2x(x -2)}\)
= \(\frac{11x}{(x+6)(x-2)} -\frac{7}{2x(x -2)}\)
= \(\frac{1}{x-2}\)×\([\frac{11x}{(x+6)} -\frac{7}{2x}]\)
Therefore, from the above result, it is found that (x-2) is the least common denominator that can be taken.
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1. A right triangle LMN is given where: side MN = 8 side NL (the hypotenuse) =
10 What is the length of side LM?*
Answers
Step-by-step explanation:
\( \underline{ \underline{ \text{Given}}} : \)
Length of MN ( Base ) = 8 Length of NL ( Hypotenuse ) = 10\( \underline{ \underline{ \text{To \: find}}} : \)
Length of LM ( Perpendicular )\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)
\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)
⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)
⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)
⤑ \( \sf{ \sqrt{100 - 64}} \)
⤑ \( \sf{ \sqrt{36}} \)
⤑ \( \boxed{ \sf{6\: units}}\)
\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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help please!!!!!!!!!
Answers
Answer:
Alright, so, the ratio is 2:5
In total, there are 7
So, 56/7=8
8x2=16
8x5=40
So after moving 2 students,
14 on the van, 42 on the bus
(you can use the true/false now)
Answer:
1. False
2. True
3. True
4. False
Step-by-step explanation:
Going to the museum:
Total: 56 students
van:bus = 2:5
2x + 5x = 56
7x = 56
x = 8
2x = 16
5x = 40
16 students go by van
40 students go by bus
40 - 16 = 24
Going back to school:
14 students go by van
42 students go by bus
van:bus = 14/42 = 1:3
42 - 14 = 28
Questions:
1. False
2. True
3. True
4. False
Please help and explain
True or False: The magnitude of a resultant vector will always be larger than individual vectors that are both in the first quadrant
Answers
Answer:true
Step-by-step explanation:
An author writes 9 pages of her book each week. How many pages does she write in 7 weeks? Use a five fact to solve.
Answers
Answer: she writes 63 pages in 7 weeks.
Step-by-step explanation: simple answer you just multiply 9x7=63!
hope this helped.
The number of pages she write in 7 weeks is 63 pages
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Number of pages she write in a week = 9 pages
Number of weeks she writes = 7 weeks
So , to calculate the number of pages she write in 7 weeks =
Number of pages she write in a week × Number of weeks she writes
Number of pages she write in 7 weeks = 9 × 7
= 63 pages
Hence , the number of pages she write in 7 weeks is 63 pages
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what is volume of sphere if it is 1ft?
Answers
Need help answering question 1what would be the volume of the cylinder?
Answers
Given:
Height of cylinder = 12 inches
Diameter = 4 inches
Let's draw a two dimensional shape that would need to be revolved around the x-axis to create a cylinder.
A cylinder can be created by rotating a rectangle about one of its edges.
Since it is rotated around the x-axis, radius of the cylinder will be the width of the rectangle.
Hence, we have:
radius = diameter /2 = 4/2 = 2 inches
To create the cylinder let's draw a rectangle with the dimensions:
Length = 12 inches
Width = 2 inches.
We have the figure below:
To find the volume of the cylinder, apply the formula:
\(V=\pi r^2h\)Where:
r is the radius = 2 inches
h is the height = 12 inches
We have:
\(\begin{gathered} V=\pi *2^2*12 \\ \\ V=150.8\text{ in}^3 \end{gathered}\)Therefore, the volume of the cylinder is 150.8 in³
ANSWER:
Volume of cylinder = 150.8 in³
Which of the following z-scores is NOT outside the middle 68% of the data for a normal distribution?
a.) -0.8
b.) -2.8
c.) 1.8
d.) 3.8
Answers
Answer:
Step-by-step explanation:
A, use three_digite rounding arithmetic to compute 13- 6 and determine the absolute,relative ,and percentage errors.
tepeat part (b) using three – digit chopping arithmetic.
7.
Kermit solved the equation below and got x = 5, but he isn't sure he solved correctly.
Show Kermit how he can check his equation using his solution. Let him know if he
solved the equation correctly or not, explaining how you know.
5(x - 4) + 20 = 14
Answers
The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To check if Kermit's solution is correct, we can substitute x = 5 back into the original equation and see if it makes a true statement:
5(x - 4) + 20 = 14
5(5 - 4) + 20 = 14
5(1) + 20 = 14
25 ≠ 14
Hence, The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.
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Could someone help me out? I don't get it
Answers
(x-2)(x+1)(x+5)
(x^2-x-2)(x+5)
x^3-x^2-2x+5x^2+5x-10
So after simplifying this, you are left with
A.) x^3+4x^2-7x-10
Hope this helps!
thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. each student was given a choice between the macaroni and cheese and the cajun potato barrels. from the sample, 20 students selected macaroni and cheese and 16 students chose the cajun potato barrels. each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). which of the following prevents this study from being a well-designed experiment?
Answers
The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
Given that,
36 local middle school kids were chosen at random to take part in a taste test to choose a new menu item for a cafeteria. The Cajun potato barrels or the macaroni and cheese were the options offered to each pupil. 20 pupils chose the macaroni and cheese from the sampling, while 16 selected the Cajun potato barrels. On a scale from 1 (very dislike) to 9 (very much like), each student was asked to rank the object they selected (extremely like).
We have to find which of the following keeps this study from being an experiment with a sound design.
Each student was given the option of choosing either the macaroni and cheese or the Cajun potato barrels. Because the students' treatments were not distributed at random, those who preferred their cuisine chose it and gave it high marks. As a result, the study has selection bias.
Therefore, The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
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HELP ASSAP I NEED TO FINISH THIS TEST AND TIS THE LAST ONE
Answers
Answer:
a=4
b=5
Step-by-step explanation:
x + 9y = 8 x − 4y = –18
Answers
Step-by-step explanation:
\(x + 9y = - 18 \\ 8x - 4y = - 18 \\ x = - 18 - 9y \\ 8( - 18 - 9y) - 4y = - 18 \\ - 144 - 72y - 4y = - 18 \\ - 76y = 126 \\ y = - 1.66 \\\)
\(x = - 18 - 9y \\ x = - 18 - 9( - 1.66) \\ x = - 18 + 14.94 \\ x = - 3.06\)
Can someone please help
Answers
If 5 hamburgers cost $10, what is the cost for 3 hamburgers?
Answers
Answer: 6$
Step-by-step explanation: 5 divided by 10 = 2$ so 3 x 2 = 6
I do not hold responsibility if you get it wrong :(
You've received a job offer. The offer states that you will receive $560 per week. If the work is 40hours long, then write an equation that represents your pay with the pay rate(in dollars per hour) represent by x
Answers
Answer:
x = 14
Step-by-step explanation:
You get $560 per week divided by 40 hours, that equals $x per hour
Answer:
560 x 40=22400
Step-by-step explanation:
i say that because i think that you need to use multiplication
Please answer this correctly
Answers
Answer:
66.7%
Step-by-step explanation:
The factors of 18 are as listed: 1, 2, 3, 6, 9, 18
Since 1, 2, 3, and 6 are in the die, that makes 4 out of the 6 numbers.
4/6 can be simplified to .667 or 66.7%
Answer:
66.7%
Step-by-step explanation:
Factors of 18: 1, 2, 3, 6, 9, 18
There are 4 factors of 18 on the die so there is a 4/6 chance or 2/3 chance rolling a factor of 18. As a percent, 66.7%
12+5(4x-6) in distributive property
Answers
answer
20x-18
The test scores for a group of students are shown.
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Calculate the five number summary of the data set? Minimum = First Quartile (Q1) = Median = Third Quartile (Q3) = Maximum = What is the interquartile range (IQR) Which test score is an outlier?
60
69
90
100
Answers
Answer:
Minimum=60
First Quartile(Q1)=79
Median=86
Third Quartile (Q3)=89
Interquartile range (IQR)=10
suface area of cuboid 9 5 4
Answers
The cuboid in question has a surface area of 202 square units.
We must sum together the areas of all six faces to determine a cuboid's surface area.
The dimensions of the given cuboid are:
length (l) = 9 units
width (w) = 5 units
height (h) = 4 units
The area of each face is given by:
Top and bottom faces:\(lw = 9 * 5 = 45\) square units each
Front and back faces: \(lh = 9 *4 = 36\) square units each
Left and right faces: \(wh = 5 * 4 = 20\) square units each
Therefore, the total surface area of the cuboid is:
\(2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units\)
Hence, the surface area of the given cuboid is 202 square units.
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2.704 times 1000=???
Answers
Answer:
2.704 times 1000
2.704*1000
(in multiplication the decimal place goes right side to the digit)
So in =2.704,*1000
=2704
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The price of regular rice is $1 per pound; that of premium rice is $2. Mix 300 pounds
of regular rice with 400 pounds of premium rice. What is the price of the mixture?
Answers
Answer:
1200 dollars
Step-by-step explanation:
2x400 is 800 + 1x400 =1200