If a line has a slope of 2 and contains the point (-2, 1), what is its equation in point-slope form?

Answers

Answer 1

Point slope form is y-y1= m(x-x1) where m is slope and y1 and x1 are the x and y of the coordinate given.

y-1= 2(x-(-2))
y-1= 2(x+2)

Final answer: y-1= 2(x+2)

Related Questions

A coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. What statistic should he study?

Answers

The statistic that the coach should study is mean or the average score of the two teams. If the coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. After counting them, add the scores of the group that he divided and then divided it by the number of player in that group to get an average score on teams that warm up or do not warm up before the game.

Which expression represents the area of the shaded triangle?

Answers

Answer:

B. [tex]\frac{1}{2}\times (5.7)\times (1.9)[/tex]

Step-by-step explanation:

We have been given an image of a triangle. We are asked to choose the correct option that represents the area of the shaded region.

We know that the area of a triangle is half the product of its height and base.

Upon looking at our given diagram we can that shaded region is in form of triangle and the height of both triangles is 5.7 meters. We can also see that the base of shaded triangle is 1.9 meters.

[tex]\text{Area of triangle}=\frac{1}{2}\times (\text{Height *Base})[/tex]

[tex]\text{Area of shaded region}=\frac{1}{2}\times (5.7)\times (1.9)[/tex]

Therefore, option B is the correct choice.

Answer:

Step-by-step explanation:

C: -5/2 D: 5/2 help please

Answers

The answer is A. Parallel lines always have the same slope.

(06.02)The graph shows the number of weeks a movie has been in theaters and the number of tickets sold each week
Which statement best describes the relationship between the number of weeks a movie has been in theaters and the number of tickets sold?

As the number of weeks increases, the number of tickets sold decreases.
As the number of weeks increases, the number of tickets sold increases.
As the number of weeks decreases, the number of tickets sold decreases.
No relationship can be determined.

Answers

Looking at the graph, you can see that as more weeks pass, the amount of tickets sold are slowly decreasing.

Therefore, A) As the number of weeks increases, the number of tickets sold decreases would be the correct answer.

As the number of weeks increases, the number of tickets sold decreases so option (A) 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.

In another word, graph is geometrical relation of the analytical variable.

For example to draw the equation y = 6x +8 this will draw a straight line in the coordinate geometry.

In the given question it is clearly visible that as the weeks in theater are increasing the points are going down on the y-axis which is tickets sold.

As the number of weeks increases, the number of tickets sold decreases hence option (A) will be correct.

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Calculate each unit rate
$11.49 for 3 packages

Answers

For the total it would be like $34.47 and so the unit rate might be $3.83

The product of three and a number is thirty-three. What is the number? N = 11 N = 30 N = 36

Answers

Answer:

Step-by-step explanation:

N=11

PLEASEEEEE HELPPPP ASAP NEED TO GET RIGHT!!!! WILL GIVE THANKS

Answers

You are given the function sin θ = 3/√34. You are asked to find the possible coordinates of point Pp on the terminal arm of θ in the first quadrant. The sine function is equal to the opposite side over the hypotenuse side. Let us assign variables as x, y and r where x is the distance of the line to the x - axis, y is the distance of the line to the y - axis and r is the distance of the hypotenuse line. Apply pythagoreas theorem

r² = x² + y²
(√34)² = x² + 3²
34 = x² + 9
x² = 25
x = 5

the coordinates is placed as (x,y) and you already solved these values and so (5, 3)

Merlin industries bought a laptop for $2100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar.

Answers

This is exponential growth/decay function, in this case decay, of the form:

f=ir^t, f=final value, i=initial value, r=common ratio or "rate", and t=times rate is applied or "time".

In this case i=2100 and r=(100-14)/100=0.86 so the equation is:

f=2100(0.86^t) and in five years...

f(5)=2100(0.86^5)

f(5)≈$987.90 (to nearest whole cent)

(15 POINTS) Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0).

Answers

i had this question. the correct answer was B for it.

An equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

The correct answer is option (A)

What is equation of ellipse?

"The standard form of equation of ellipse with center (0, 0) is, [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]

What are vertices of the standard ellipse?

"The vertices of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm a,0)[/tex] "

What is focus of the standard ellipse?

"The foci of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm c,0)[/tex], where [tex]c^{2} =a^{2}- b^{2}[/tex] "

For given question,

The center of the ellipse is at the origin.

Using the standard form of equation of the ellipse,

[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]

A vertex at (13, 0)

⇒ (a, 0) = (13, 0)

⇒ a = 13

And a focus at (12, 0).

⇒ (c, 0) = (12, 0)

⇒ c = 12

We know, [tex]c^{2}= a^{2}- b^{2}[/tex]

Now, we find the value of b i.e., minor axis

[tex]\Rightarrow 12^{2} =13^{2}- b^{2}\\\\\Rightarrow b^2=169-144\\\\ \Rightarrow b^2=25\\\\\Rightarrow b=\pm 5[/tex]

Substituting these values in the standard form of equation of ellipse with center (0, 0),

[tex]\Rightarrow \frac{x^2}{a^2} +\frac{y^2}{b^2} =1\\\\\Rightarrow \bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

Therefore, an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

The correct answer is option (A)

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Is it possible for one point to be in two different planes?

Answers

Yes, it is possible for one point to be in two different planes. Imagine this: take the point in the corner of a room. That point is part of 3 planes (both walls and the floor).

To add, in mathematics, a plane is a flat, two-dimensional surface.

Answer:

Yes, it is possible for one point to be in two different Planes.

This can be explained in following way.

The Intersection of two plane is a line.And on a line infinite number of point lies.

So,"yes" one point or Infinite number of points can be common between two different planes.

If you were to add all odd numbers between 1 and 11 (both inclusive), the result would be

Answers

The sequence of all odd numbers between 1 and 11 (both inclusive) is
1,3,5,7,9,11

This is an arithmetic sequence with common difference of d=2
The first term is a₁=1.

The number of the term 11 (without counting) is found from
1 + (n-1)*2 = 11
1 + 2n - 2 = 11
2n -1 = 11
2n = 12
n = 6

The sum of the first n terms of an arithmetic sequence is
[tex]S_{n} = \frac{n(a_{1}+a_{n})}{2} [/tex]

Therefore, the sum of the sequence is
S₆ = [6*(1 + 11)]/2
= (6*12)/2
= 36

Answer: 36

Final answer:

By adding all the odd numbers from 1 to 11 inclusive (1, 3, 5, 7, 9, 11), the sum is 36.

Explanation:

If you were to add all odd numbers between 1 and 11 (both inclusive), the odd numbers are: 1, 3, 5, 7, 9, and 11. To find the result of adding these numbers together, you simply add each one sequentially:

1 + 3 = 4

4 + 5 = 9

9 + 7 = 16

16 + 9 = 25

25 + 11 = 36

So, the result of adding all the odd numbers from 1 to 11 inclusive is 36.

Which statement is true about the equations –3x + 4y = 12 and x – y = 1? The system of the equations has exactly one solution at (–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.

Answers

Final answer:

The system of equations has exactly one solution, but it is located at (16,15), not (–8, 3), (–4, 3) or any other points. So, none of the provided options are true.

Explanation:

The task is to identify the statement that is correct about the system of equations –3x + 4y = 12 and x – y = 1. To discover this, we must solve the system which consists of these two linear equations. Adjust equation two to be in the same format as equation one by adding y to both sides which gives x = y + 1. Substitute it into the first equation: -3(y + 1) + 4y = 12, which simplifies to -3y - 3 + 4y = 12, giving y = 15. Substitute y = 15 to the second equation, it gives us x = 16. Hence, none of the provided solutions is correct, because the system has exactly one solution at (16,15).

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Simplify 7x + (x – 4)(x + 5) – 5x.

Answers

7x+(x-4)(X+5)-5x
7x+(X*2+ 5x-4x-20)-5x
7x+(X*2+ x-20)-5x
X*2+3x-20

Answer:

x^2 + 3x – 20

Step-by-step explanation:

I just did the assignment

what is the exact solutions of x2=5x+2

Answers

Move all terms to the left of equal with changed sign

x²-5x-2 = 0

Solve with x₁,₂ = (-b±√Δ)/2a

Δ = b²-4ac

call a (1)x², b -5 and c -2

x1,2 = (-(-5)±√(-5)²-4*1*(-2))/2*1

x1,2 = (5±√25+8)/2

x1,2 = (5±√33)/2

x1 = (5+√33)/2

x2 = (5-√33)/2

Answer:

The answer has a positive 5 and 33.

Step-by-step explanation:

I used a calculator.

A company performs linear regressions to compare data sets of two similar products. If the residuals for brand A form an increasing curve, and the residuals for brand B form a U-shaped pattern, what can be concluded?

A. Brand A's data are probably linear, while brand B's data are probably not. B.Neither data is likely to be linear.
C.Both data sets are probably linear.
D.Brand B's data are probably linear, while brand A's data are probably not.

Answers

I think the correct answer would be B. If the residuals for brand A form an increasing curve, and the residuals for brand B form a U-shaped pattern, then neither of the data is likely to be linear. In order to be linear, the residuals of both data set should be, more or less, linear or approaching linearity in nature. Therefore, the linear regression that was done would not give good results since it is only applicable to linear data sets. Also, you can say that the relation of the data sets of the products are not linear. It would be best to do a curve fitting for both sets by using different functions like parabolic functions.

Brand A's data are probably linear, while brand B's data are probably not.

What can be concluded from a graph?

A graph shows how much a set of data fits into a pattern. This data is defined by the regression line.

Now, when we have the graph for brand A as an increasing curve, and the residuals for brand B form a U-shaped pattern, we can conclude that Brand A's data are probably linear, while brand B's data are probably not.

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Choose the point on the terminal side of -45°. (-3, -3) (4, -4) (5, 5) (-2, 2)

Answers

(4, -4) is the answer

-45° is in quadrant IV and the point (4, -4) is the only point out of the points given that is also in quadrant IV

The angle of -45 its terminal side lies in the fourth quadrant, i.e. the x-coordinates is *positive* and y-coordinates is *negative*

The point (4,-4) is the only one that satisfies that condition

hope that helps

Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. (1 point)

Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.

Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.

Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.

Step 4: x equals negative 8 plus or minus six all over two.

Step 1

Step 2

Step 3

Step 4

Answers

To solve for the roots of a quadratic equation, you use the equation

[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]

The parameters a, b and c represent the coefficients of the standard form of the quadratic equation: y = ax^2 + bx + c. Thus, for the equation y = x2 − 8x + 7,

a = 1
b = -8
c = 7

The mistake Joyce made was in Step 1. Because Step 1 is wrong, the rest of the equation is wrong consequently. The mistake was made by Joyce when she assigned b = 8. She forgot to include the negative sign of -8x.

Her mistake is in the first step, she wrote the equation incorrectly.

Solving quadratic equations:

A general quadratic equation:

ax^2 + bx + c = 0

has the solutions:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, the equation is:

y = x^2 - 8x + 7

And what Joyce writes in each step is:

Step 1:

x = (-8 ± √(8^2 - 4*1*7))/(2*1)

Then we can already see the mistake.

Notice that in the given equation, we have:

b = -8

And the general solution has:

x = (-b ± √(b^2 - 4ac))/(2a)

-b would be equal to 8, then what Joyce must have written here is:

x = (8 ± √((-8)^2 - 4*1*7))/(2*1)

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simplify 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³

a) -4m³ + 8p²

b) 8p² - 4

c) 4m³ - 13p³ + 5p

d) -4m³ + 13p³ - 5p

Answers

7p³ + 2m³ - 6m³ + 4p - 9p + 6p³
= 13p³ - 4m³ - 5p
= -4m³ + 13p³ - 5p

answer
d) -4m³ + 13p³ - 5p

Final answer:

The simplified expression of 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³ is -4m³ + 13p³ - 5p, which is option d).

Explanation:

To simplify the expression 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³, we need to combine like terms.

Like terms have the same variable raised to the same power.

In this case, terms with p raised to the third power can be combined, and terms with m raised to the third power can also be combined, as well as the terms with just p.

Combine terms with p³: 7p³ + 6p³ = 13p³.Combine terms with m³: 2m³ - 6m³ = -4m³.Combine terms with p: 4p - 9p = -5p.

Now the expression is simplified to -4m³ + 13p³ - 5p, which corresponds to option d).

Susie and Amelia solved the same equation using two separate methods. Their work is shown in the table below:

Answers

Susie made the error when she subtracted 2

Answer:

(C)

Step-by-step explanation:

Explanation of Susie's method:

The given equation is:

[tex]2x-3=4x-2[/tex]

[tex]2x-2x-3=4x-2x-2[/tex]

[tex]-3=2x-2[/tex]

[tex]-3+2=2x[/tex] ( she made a mistake when she subtracted 2)

[tex]-1=2x[/tex]

[tex]x=-\frac{1}{2}[/tex]

Susie made a mistake in step 4 when she subtracted 2,

Thus, option C is correct.

Bao Yu is completing the square to solve the polynomial equation.

x2 – x – 3 = 0

What should be her first step?

adding –x to both sides of the equation

adding –3 to both sides of the equation

isolating the first term, x2

isolating the constant, –3

Answers

Solution:

The square of the given equation can be completed as below:

Here we will make the terms on left hand side such that it gets the form of [tex]a^2\pm2ab+b^2=(a\pm b)^2[/tex]

[tex]x^2-x-3=0\\\\\text{Isolate the constant}\\\\x^2-x=3\\\\x^2-2\times\frac{1}{2}\times x +\frac{1}{2}^2=3+ \frac{1}{2}^2\\\\(x-\frac{1}{2})^2=\frac{13}{4}\\[/tex]

Hence the correct option is isolating the constant , -3.

The polynomial equation x^2 – x – 3 = 0 is a quadratic equation, and the first step in completing the square is (d) isolating the constant, –3

What are polynomials?

Polynomials are expressions that are represented with variables and coefficients

Below are the steps taken to determine Bao Yu's first step

The equation is given as:

x^2 – x – 3 = 0

Isolate the constant -3 in the equation.

So, we have:

x^2 – x = 3

Hence, the first step in completing the square is (d) isolating the constant, –3

Answers

7h+3s=27.95 subtract 7h from both sides

3s=27.95-7h divide both sides by 3

s=(27.95-7h)/3

Then we are told:

5h+4s=23.4, using s found above makes this equation become:

5h+4(27.95-7h)/3=23.4 multiply both sides by 3

15h+4(27.95-7h=70.2 perform indicated multiplication on left side

15h+111.8-28h=70.2 combine like terms on left side

-13h+111.8=70.2 subtract 111.8 from both sides

-13h=-41.6 divide both sides by -13

h=$3.20

Please help me ASAP.

David had a coupon for the grocery store. He graphed on the x-axis what his total bill would be if he didn’t use the coupon and graphed on the y-axis what his total bill would be if he used the coupon.

Based on the information in the graph, if David’s bill came to $66 after the coupon was applied, how much would his bill have been if he hadn’t used the coupon?

a.$64
b. $65
c. $67
d. $68

Answers

I would say D. $68 since the graph shows each bill with coupon being two dollars less than without.

Answer:

d. $68

Step-by-step explanation:

First, let's find the equation of the line.

The slope is defined by

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Where we are gonna use points (2,0) and (9,7).

[tex]m=\frac{7-0}{9-2}=\frac{7}{7}=1[/tex]

Then, we use the point-slope formula to find the equation.

[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]

So, if David's bill came to $66 after coupon, it means [tex]y=66[/tex].

Replacing this value in the equation, we have

[tex]y=x-2\\66=x-2\\x=66+2\\x=68[/tex]

Therefore, the price without coupon is $68.

Eduardo bought a refrigerator with a sticker price of $2400. If he paid $35 a week for two years, what was the approximate markup rate on the refrigerator?
A. 65.9%
B. 51.7%
C. 34.1%
D. 75.8%

Answers

There are 52 weeks a year
In 2 years there are 104 weeks

Total paid
35×104=3,640

markup rate
((3,640−2,400)÷2,400)×100=51.7%

It's b

Answer:

The correct answer is option B

Step-by-step explanation:

Payment done per week [tex]= 35 dollar\\[/tex]

Total number of weeks in a year [tex]= 52 weeks\\[/tex]

Total number of weeks in two year [tex]= 104 weeks\\[/tex]

Total amount paid in two weeks

[tex]= 35 * 104\\=3,640\\[/tex]

The make up rate is basically the amount paid over and above $2400

[tex]=(\frac{3640 - 2400}{2400} ) * 100\\= 51. 7 perecent[/tex]

15 * 4 2/3 please help

Answers

4 2/3 = 14/3

15 = 15/1

14/3 * 15/1 = 14*15=210, 3*1 = 3

210/3 = 70

answer is 70

[tex]15 \cdot 4\frac{2}{3}=\\\\15 \cdot \frac{4\cdot 3+2}{3}\\\\ = \frac{\not15^5 }{1}\cdot \frac{14}{\not3^1}\\\\= \frac{5\cdot 14}{1}\\\\= 70[/tex]

HELP ME PLEASE !! IM SO CONFUSED

Answers

1. 2.0 x 10^-2
2. 2.2 x10^6
3. 2.0 x 10^4

Just covert each until you reach the end, like you know that there are 356 days in a year and 100 years in a century.

PS They're in scientific notation

Are the two triangles below similar?

Yes, because there are two pairs of congruent corresponding angles
No, because there are not two pairs of congruent corresponding angles
Yes, because the corresponding sides are proportional
No, because the corresponding sides are not proportional

Answers

Answer :- Yes the two triangles are similar because there are two pairs of congruent corresponding angles.

Explanation:-

In Δ ABC

∠A=30° , ∠C=65 °

By angle sum property of triangle

∠A + ∠B + ∠C= 180°

⇒∠B= 180°-∠A-∠C=180°-30°-65°=85°

⇒∠B=85°

Now in ΔABC and ΔDEF

∠A=∠D=30° and ∠B=∠E=85°

⇒ there are two pairs of congruent corresponding angles.

So by AA-similarity criteria

ΔABC ≈ ΔDEF

Answer:

Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

Two triangles ABC and DEF are given .

The measure of angles in triangle ABC are:

m<A=30°,m< C=65°,

m<B= 180-(30+65)=85°(measure of sum of angles in any triangle is 180°)

In triangle DEF the measure of the angles are :

m<D=30°,m<E=85°,m<F=180-(30+85)=65°(sum of angles in a triangle add to 180°)

In triangles ABC and DEF,

< A=<D=30°

<B=<E=85°

<C=<F=65°

The two triangles are similar by AAA property.

anna owes home antiques Whose value is 160000 today assuming normal growth. however anna believes the value will grow at 16% per year for the next three years she wants to take this rapis growth ibto consideration when valuing the buisness for potential sale find the future value of the buisness in three years then use that future value to find the present value at a rate 8% compounded annually

Answers

The formula is
A=p (1+r)^t
A future value?
P present value 160000
R interest rate 0.16
T time 3years
A=160,000×(1+0.16)^(3)
A=249,743.36

Use that future value to find the present value at a rate 8% compounded annually
To find p (present value) solve the formula for p
P=A÷ (1+r)^t
Where r is 0.08
P=249,743.36÷(1+0.08)^(3)
p=198,254.33

What is 320 1/4 rounded to the nearest whole number?

Answers

So 1/4=0.25
320.25=320
I would say the correct answer is 320
hope this helps:)

Hi!

Let's first turn the number into a decimal.

320.25

Now round to the nearest whole number

The answer is 320

Hope this helps! :)

Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the x-coordinates is 2.445, and the standard deviation of the y-coordinates is 9.902, what is the slope of the line to three decimal places?

Answers

We are given a line with the following data:

r-value = 0.657 (r)
standard deviation of x-coordinates = 2.445 (Sx)
standard deviation of y-coordinates = 9.902 (Sy)

We are asked to find the slope of the line up to 3 decimal places.

To find the slope of the line, based on the data that we have, we can use this formula:

slope, b = r * (Sy / Sx)

substitute the values to the formula:

b = 0.657 * ( 9.902 / 2.445 )

Solve for the b.

Therefore, the slope of the line is

b = 2.66078, round off to three decimal places:

b = 2.661 is the slope of the line.

Answer: 2.661

Step-by-step explanation:

A P E X

-10-2v<6 and 6v+12<-6.
need some help with this problem i keep messing a step

Answers

-10 - 2v < 6 6v + 12 < -6
-2v < 6 + 10 6v < -6 - 12
-2v < 16 6v < -18
v > -16/2 v < -18/6
v > -8 v < -3

solution is : -8 < v < -3

Other Questions

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