The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln (9t + 4), where y is the number of mowers sold. How many mowers will be sold 4.5 years after a model is introduced?

Answer:

Step-by-step explanation:

[tex]\text{The distributive property:}\ a(b+c)=ab+ac\\\\15=3\cdot5\\21=3\cdot7\\\\15+17=3\cdot5+3\cdot7=3\cdot(5+7)[/tex]

Answer:

3x² - 2x + 5 ; will be a polynomial ⇒ answer A

Step-by-step explanation:

* Lets explain what is the polynomial

- A polynomial is an expression containing two or more algebraic terms.

- Polynomial is often the sum of some terms containing different powers

 of variables.  

- If you add or subtract polynomials, you get another polynomial.

- If you multiply polynomials, you get another polynomial.

* Lets solve the problem

∵ 5x² + 3x + 4 is polynomial

∵ 2x² + 5x - 1 is polynomial

- When we subtract them the answer will be polynomial

∵ (5x² + 3x + 4) - (2x² + 5x - 1)

- Open the second bracket by multiplying the negative sign by

  each term in the bracket

∵ -(2x²) = -2x²

∵ -(5x) = -5x

∵ -(-1) = 1

∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 5x² + 3x + 4 - 2x² - 5x + 1

- Add the like terms

∴ (5x² - 2x²) = 3x²

∴ (3x - 5x) = -2x

∵ (4 + 1) = 5

∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 3x² - 2x + 5

∴ 3x² - 2x + 5 is a polynomial

∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 3x² - 2x + 5 ; will be a polynomial

* The answer is A

Answer:

A. 3[tex]x^{2}[/tex] − 2x + 5; will be a polynomial

Step-by-step explanation:

Give The Dood Above Brainliest

[tex]\huge{\boxed{\text{2000 pounds}}}[/tex]

One ton is equal to [tex]\boxed{\text{2000 pounds}}[/tex].

For example, two tons is equal to [tex]4000[/tex] pounds, because [tex]2000*2=4000[/tex].

Answer is provided in the image attached.

Answer: Second Option

[tex]P (-1.17 <z <1.17) = 0.7580[/tex]

Step-by-step explanation:

The shaded area corresponds to the interval

[tex]-1.17 <z <1.17.[/tex]

By definition, for a standard normal distribution the area under the curve in the interval (b <z <h) is equal to:

[tex]P (b <z <h)[/tex]

So in this case we look for:

[tex]P (-1.17 <z <1.17)[/tex]

This is:

[tex]P (-1.17 <z <1.17) = P (z <1.17) - P (z <-1.17)[/tex]

Looking at the standard normal table we have to:

[tex]P (z <1.17) = 0.8790\\P (z <-1.17) = 0.1210[/tex]

So:

[tex]P (-1.17 <z <1.17) = 0.8790- 0.1210\\\\P (-1.17 <z <1.17) = 0.7580[/tex]

Answer:

1.25 mi

Step-by-step explanation:

Think of this in terms of a graph in the x-y axis

Bill starts out at point (0,0)

He walks 1/2 mile south (i.e 0.5 miles in the -y direction) and ends up at (0,-0.5)

Next he walks 3/4 mile (0.75 miles) in the +x direction and ends up at (0.75, -0.5)

Then he continues to walk 1/2 mile (0.5 miles) in south in the -y direction and ends up at (0.75, -1).

His final distance from the starting point (0,0) from his end point (0.75,-1) is simply the distance between the 2 coordinates (see picture for formula).

hence,

D = √ (0.75 -0)² + (-1 - 0)²

D = √ (0.75)² + (-1)²

D = 1.25

Answer:

1.25 M

Step-by-step explanation:

Answer:

(6,6) only goes with Line 2

(3,4) goes with neither

(7,2) goes with both

Step-by-step explanation:

Ok to decide if a point is on a line you plug it in.  If you get the same thing on both sides, then that point is on that line.  If you don't get the same thing on both sides, then that point is not on that line.

Test (6,6) for -5x+6y=-23.

(x,y)=(6,6) gives us

-5x+6y=-23

-5(6)+6(6)=-23

-30+36=-23

6=-23

So (6,6) is not on -5x+6y=-23.

Test (6,6) for y=-4x+30

(x,y)=(6,6) give us

y=-4x+30

6=-4(6)+30

6=-24+30

6=6

So (6,6) is on y=-4x+30.

Test (3,4) for -5x+6y=-23.

(x,y)=(3,4) gives us

-5x+6y=-23

-5(3)+6(4)=-23

-15+24=-23

9=-23

So (3,4) is not on -5x+6y=-23.

Test (3,4) for y=-4x+30.

(x,y)=(3,4) gives us

y=-4x+30

4=-4(3)+30

4=-12+30

4=18

So (3,4) is not on y=-4x+30.

Test (7,2) for -5x+6y=-23.

(x,y)=(7,2) gives us

-5x+6y=-23

-5(7)+6(2)=-23

-35+12=-23

-23=-23

So (7,2) is on -5x+6u=-23.

Test (7,2) for y=-4x+30.

(x,y)=(7,2) gives us

y=-4x+30

2=-4(7)+30

2=-28+30

2=2

So (7,2) is on y=-4x+30

(x,y)  Line 1    Line 2     Both     Neither

(6,6)                  *

(3,4)                                                   *

(7,2)                                  *

(6,6) only goes with Line 2

(3,4) goes with neither

(7,2) goes with both

Answer:

[tex]\large\boxed{V=\pi r^3}[/tex]

Step-by-step explanation:

The formula of a volume of a pyramid:

[tex]V=\dfrac{1}{3}BH[/tex]

B - base area

H - height

Let r - radius of the cone.

We have H = 3r.

The base of the cone: [tex]B=\pi r^2[/tex].

Substitute:

[tex]V=\dfrac{1}{3}\pi(r^2)(3r)[/tex]           cancel 3

[tex]V=\pi r^3[/tex]

Answer:

For plato users is option A

Step-by-step explanation:

A. V =[tex]\pi[/tex]r3

[tex]\huge{\boxed{c+148}}[/tex]

We need to find the number of pies baked in years 1 and 2.

There were 148 pies baked in year 1. [tex]148[/tex]

There were [tex]c[/tex] pies baked in year 2. [tex]148+c[/tex]

Rearrange the terms so the variable is first. [tex]c+148[/tex]

Answer:

since we know that there were 148 pies sold the first year, and c number of pies sold this year. You would add these two to find the total amount of both years.

148+c

Answer:

(D) 6 & 7

Step-by-step explanation:

You are plugging in numbers into the question marks to make the equation true. In this case, plug in the numbers, 6 & 7 or (D)

Plug in 6 in the first ? mark and 7 in the second:

?1 - 2? = 34 = (61) - (27) = 34

61 - 27 = 34

34 = 34 (True) ∴ 6 & 7 is your answer.

~

Answer:

Please read explanation below.

Step-by-step explanation:

Let's go over what some of the symbols of inequalities represent:

[tex]>[/tex]: greater than

[tex]<[/tex]: less than

[tex]\ge[/tex]: greater than or equal to

[tex]\le[/tex]: less than or equal to

The symbol in the equation that is given to you is [tex]\ge[/tex]. It seems as though each of the answer choices have everything written as the same thing except for the description of the inequalities. Check the one that applies.

The radius of the circle is 11, so the area is

[tex]A=\pi r^2 = 121\pi[/tex]

The central angles of the shaded and non-shaded regions sum up to 360 degrees, so the central angle of the shaded region is

[tex]360-217=143[/tex]

The area of the shaded region is in proportion with the area of the whole circle: if the whole area is given by a sector of 360°, the area of a 143° sector will be given by

[tex]A_{360}\div A_{143} = 360\div 143[/tex]

Since we know that the whole area is [tex]121\pi[/tex], we can solve for the area of the 143° sector:

[tex]121\pi\div A_{143} = 360\div 143 \iff A_{143}=\dfrac{121\pi\cdot 143}{360} \approx 151[/tex]

Answer:

121

143

151

Step-by-step explanation:

Answer:

y = - 2

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

The points (2, - 2) and (0, - 2) have the same y- coordinate and therefore lie on a horizontal line with equation

y = - 2

For this case we have a function of the form[tex]y = g (x)[/tex]

Where:

[tex]g (x) = 2 (x-4)[/tex]

We must find the value of "x" when the function has a value of 20, that is, [tex]g (x) = 20[/tex]:

[tex]2 (x-4) = 20[/tex]

We apply distributive property:

[tex]2x-8 = 20[/tex]

We add 8 to both sides of the equation:

[tex]2x = 20 + 8\\2x = 28[/tex]

We divide between 2 on both sides of the equation:

[tex]x = \frac {28} {2}\\x = 14[/tex]

Answer:

Option C

Answer:

option c 14

Step-by-step explanation:

did the test

Answer:

[tex]\large\boxed{x^\frac{4}{5}}[/tex]

Step-by-step explanation:

[tex]\sqrt[n]{a}=a^\frac{1}{n}\Rightarrow\sqrt[5]{x}=x^\frac{1}{5}\\\\\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}=x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}=x^\frac{4}{5}[/tex]

Answer:

[tex]x^{\frac{4}{5}}[/tex]

Step-by-step explanation:

fifth root of x can be written in exponential for as:

[tex]x^\frac{1}{5}[/tex]

[tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex]

WE apply exponential property to multiply it

a^m times a^n= a^{m+n}

[tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex]

[tex]x^{\frac{1}{5} +\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}[/tex]

The denominator of the fractions are same so we add the numerators

[tex]x^{\frac{4}{5}}[/tex]

Answer:

7 friends multiply $2

Its product is: $14

Step-by-step explanation:

Answer:

A 18%

Step-by-step explanation:

I believe it should be A because there is no specific type a marble specified therefore if you do

12/33--> 0.36 times 100= 36 % which isn't an option

15/33->0.45 times 100= 45 % which also isn't an option

6/33= 0.18 times 100= 18% this is the only option given

Answer:

B. 82%

Step-by-step explanation:

From the question; A marble is randomly selected from a bag containing 15 black, 12 white, and 6 clear marbles. Find P(not clear).

To find p(not clear), we use this formula;

P(not clear) = 1 -  p(clear)

To proceed we first have to find p(clear) and the minus it from 1

But,

probability =  Required outcome/ all possible outcome

In the question, since what we are looking for now is probability of clear, so our 'required outcome' is the number of marble which is 6,

all possible outcome is the number of all the marbles; 15 + 12 + 6 = 33

We can now proceed to find the probability of clear marble, hence;

probability =  Required outcome/ all possible outcome

p(clear marble) = 6/33

Now, we go ahead to find the probability of 'not clear marble'

P(not clear) = 1 -  p(clear)

                   =   1 - 6/33

                    = 1 -   0.181818

                     =0.818182

P(not clear) = 0.818182

But the question says we should round our answer to the nearest percent, so we will multiply our answer by 100%

p(not clear)  = 0.818182 ×  100%

p(not clear) = 82% to the  nearest percent

Answer:

The officer saves $91.45 per month

~Step-by-step explanation~

Ok this is how I do fractions and its not very good, but it works.

First I divided 6400 by 5, 6, and 7, (I didn't do 3 because you can just multiply the answer to 6 by 2.) the reason I divided these is to see how much 1 part of their fraction is worth. So in total I got  1066.66 (irrational number) for insurance which means I got 2133.32 for his monthly living ( had to multiply by 2). For his car payment I got 1828.57 (I divided and then multiplied by 2) and for his rent I got 1280. I added these all together to get the total he spends each month which was 6308.55, and I subtracted that from 6400 to figure out that he puts $91.45 in his savings account

Answer:

The answer is R91.43.

Step-by-step explanation:

Monthly salary of the worker = R6400

The monthly expenses are 1/5 for rent that is [tex]\frac{1}{5}\times6400= 1280[/tex]

The car payment is 2/7 that is [tex]\frac{2}{7}\times6400= 1828.57[/tex]

The insurance is 1/6 that is [tex]\frac{1}{6}\times6400= 1066.67[/tex]

Few other monthly living expenses are 1/3 that is [tex]\frac{1}{3}\times6400= 2133.33[/tex]

We will total these values:

[tex]1280+1828.57+1066.67+2133.33=6308.57[/tex]

So, the amount that is saved per month = [tex]6400-6308.57=91.43[/tex]

The answer is R91.43.

Answer:

Step-by-step explanation:

[tex]a_n-\text{geometric sequence}\\\\a_1,\ a_2,\ a_3,\ ...,\ a_n-\text{terms of a geometric sequence}\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\hdots=\dfrac{a_n}{a_{n-1}}-\text{common ratio}\\\\\text{We have:}\ a_1=2,\ a_2=4,\ a_3=8,\ a_4=16,\ ...\\\\\text{The common ratio:}\\\\r=\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=2[/tex]

Answer:

The equation of the line is y = -x + 1

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope-intercept form of the equation is y = mx + c, where m is

 the slope of the line and c is the y-intercept

- To make this equation you need slope (m) and a point on the line to

 find the value of c

- The parallel lines have same slopes

* Lets solve the problem

- The line is parallel to the line y = -x - 5

∵ y = mx + c

∵ The slope of the line y = -x - 5 is the coefficient of x

∴ m = -1

∵ Parallel lines have same slopes

∴ The slope of the line is -1

∴ the equation of the line is y = -x + c

- To find c substitute x and y in the equation by the coordinates of

  any point lies on the line

∵ The line passes through point (3 , -2)

∵ y = -x + c

∴ -2 = -(3) + c

∴ -2 = -3 + c ⇒ add 3 for both sides

∴ c = 1

∴ The equation of the line is y = -x + 1

Answer:

111

Step-by-step explanation:

a1 = -12

a27 = 66

Now using the formula  an = a1+(n-1)d we will find the value of d

here n = 27

a1 = -12

a27 = 66

Now substitute the values in the formula:

a27 = -12+(27-1)d

66= -12+(26)d

66 = -12+26 * d

66+12 = 26d

78 = 26d

now divide both the sides by 26

78/26= 26d/26

3 = d

Now put all the values in the formula to find the 42 term

an = a1+(n-1)d

a42 = -12 +(42-1)*3

a42 = -12+41 *3

a42 = -12+123

a42 = 111

Therefore 42 term is 111....

Answer:

Assuming it is arithmetic, the 42nd term is 111.

Assuming it is geometric, the conclusion says it isn't geometric.

Step-by-step explanation:

Let's assume arithmetic first.

Arithmetic sequences are linear. They go up or down by the same number over and over.  This is called the common difference.

We are giving two points on our line (1,-12) and (27,66).

Let's find the point-slope form of this line.

To do this I will need the slope.  The slope is the change of y over the change of x.

So I'm going to line up the points and subtract vertically, then put 2nd difference over 1st difference.

(1  , -12)

-(27,66)

------------

-26   -78

The slope is -78/-26=78/26=3.  The slope is also the common difference.

I'm going to use point [tex](x_1,y_1)=(1,-12)[/tex] and [tex]m=3[/tex] in the point-slope form of a line:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-12)=3(x-1)[/tex]

Distribute:

[tex]y+12=3x-3[/tex]

Subtract 12 on both sides:

[tex]y=3x-3-12[/tex]

[tex]y=3x-15[/tex]

So we want to know what y is when x=42.

[tex]y=3(42)-15[/tex]

[tex]y=126-15[/tex]

[tex]y=111[/tex]

So [tex]a_{42}=111[/tex] since the explicit form for this arithmetic sequence is

[tex]a_n=3n-15[/tex]

-----------------------------------------------------------------------------------------

Let's assume not the sequence is geometric. That means you can keep multiplying by the same number over and over to generate the terms given a term to start with.  That is called the common ratio.

The explicit form of a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex].

We are given [tex]a_1=-12[/tex]

so this means we have

[tex]a_n=-12 \cdot r^{n-1}[/tex].

We just need to find r, the common ratio.

If we divide 27th term by 1st term we get:

[tex]\frac{a_{27}}{a_1}=\frac{-12r^{27-1}}{-12r^{1-1}}=\frac{-12r^{26}}{-12}=r^{26}[/tex]

We are also given this ration should be equal to 66/-12.

So we have

[tex]r^{26}=\frac{66}{-12}[/tex].

[tex]r^{26}=-5.5[/tex]

So the given sequence is not geometric because we have an even powered r equaling a negative number.

Answer:

No

Step-by-step explanation:

Given a function f(x)

For the function to be odd then f(- x) = - f(x)

f(- x) = 3(- x)² + (- x) = 3x² - x

- f(x) = - (3x² + x) = - 3x² - x

Since f(- x) ≠ - f(x) then f(x) is not an odd function

Answer:
it’s a circle graph

Answer:

B.

Step-by-step explanation:

So [tex]2x^2+5x+3[/tex] will have two factors if one factor in the form [tex](ax+b)[/tex] is given.

The other factor will also be in the form of [tex](cx+d)[/tex].

So we have

[tex](x+1)(cx+d)[/tex]:

Let's use foil.

First:  x(cx)=cx^2

Outer: x(d)=dx

Inner: 1(cx)=cx

Last: 1(d)=d

---------------------Adding like terms:

cx^2+(d+c)x+d

We are comparing this to:

2x^2+     5x+3

So we see that c=2 and d=3 where the other factor is cx+d=2x+3.

Also this works since c+d=5 (we know this because 2+3=5).

Answer:

B

Step-by-step explanation:

Answer:

x= 3

y= 2

Step-by-step explanation:

The given equations are :

2x-5y = -4    equation 1

x +6y = 15    equation 2

We will multiply the equation:2 by 2

2(x+6y=15)

2x+12y=30   equation 3

Lets call this equation:3

Now we will use the elimination method:

Subtract equation 3 from equation 1:

2x-5y = -4

2x+12y=30

_________

   -17y = -34

y= -34/-17

y = 2

Now put the value of y in any equation:

We will use equation 1

2x-5y = -4

2x-5(2)= -4

2x-10= -4

Move the constant to the R.H.S

2x= -4+10

2x=6

Divide both the terms by 2

x= 3

Therefore the solution set is (x,y){(3,2)}....

Answer:

A

Step-by-step explanation:

Given :

2x + 4y = 14  ---------- eq 1

4x + y = 20 ---------- eq 2

if you multiply eq 2 by -4 on both sides, you get

-4 (4x + y = 20) = -4 (20)

-16x -4y = -80 --------- eq3

we can see that eq. 1 and eq 2 together forms the system of equations presented in option A, Hence A is equvalent to the orginal system of equations given in the question.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&(2)\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{multiply both sides by (-4)}\end{array}\right\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-16x-4y=-80&(2)\end{array}\right\to \boxed{A.}[/tex]

B.

[tex]\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{change the signs}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-4x-y=-20&\text{it's different to (2)}\end{array}\right[/tex]

C.

[tex]\left\{\begin{array}{ccc}2x+4y=14&\text{multiply both sides by 2}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}4x+8y=28&\text{different to (1)}\\4x+y=20&(2)\end{array}\right[/tex]

D.

[tex]\left\{\begin{array}{ccc}2x+4y=14&\text{change the signs}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}-2x-4y=-14&\text{different to (1)}\\4x+y=20&(2)\end{array}\right\\\\A.[/tex]

Answer:

The points C(1,2) and E(2,2) make both inequalities true

Step-by-step explanation:

we have

[tex]y < 5x+2[/tex] -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

[tex]y\geq \frac{1}{2}x+1[/tex] ------> inequality B

The solution of the inequality B is the shaded area above the solid line

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities and the point lie on the shaded area of the solution

Plot the points and verify if lie on the shaded area

Let

[tex]A(-1,3),B(0,2),C(1,2),D(2,-1),E(2,2)[/tex]

see the attached figure

The points C(1,2) and E(2,2) lie on the shaded area

Note

The points A(-1,3) and B(0,2) satisfy inequality B but don't satisfy inequality A

The point D(2,-1) satisfy inequality A but don't satisfy inequality B

therefore

The points C(1,2) and E(2,2) make both inequalities true

Answer:

c and e

Step-by-step explanation:

Answer:

x = 8/9

Step-by-step explanation:

5x + 2(x - 3) = -2(x - 1)

Distribute on both sides.

5x + 2x - 6 = -2x + 2

Combine like terms on the left side.

7x - 6 = -2x + 2

Add 2x to both sides.

9x - 6 = 2

Add 6 to both sides.

9x = 8

Divide both sides by 9.

x = 8/9

The equation that represents the line passing through the points (-1, 2) and (3, 1) is  [tex]\[ x + 4y = 7 \][/tex]

The correct option is (B).

To find the equation of the line that passes through the points (-1, 2) and (3, 1), we need to determine the slope of the line and use the point-slope form of the equation of a line, which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.

First, let's calculate the slope [tex]\( m \)[/tex] using the two given points [tex]\( (x_1, y_1)[/tex]= [tex](-1, 2) \) and \( (x_2, y_2) = (3, 1) \)[/tex]:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Let's compute the slope.

The slope \( m \) of the line that passes through the points (-1, 2) and (3, 1) is [tex]\( -0.25 \)[/tex].

Next, we'll use one of the points and the slope to write the equation of the line in point-slope form and then convert it to slope-intercept form[tex]\( y = mx + b \)[/tex]. Let's use the point (-1, 2) to find the equation of the line.

The equation of the line in slope-intercept form is [tex]\( y = -0.25x + 1.75 \)[/tex].

Now let's convert this to the standard form of the line equation, [tex]\( Ax + By = C \),[/tex] and compare it with the given options.

To get the standard form, we will multiply through by 4 to eliminate the decimals and then rearrange the terms:

[tex]\[ y = -0.25x + 1.75 \][/tex]

[tex]\[ 4y = -x + 7 \][/tex]

[tex]\[ x - 4y = -7 \][/tex]

This standard form equation needs to be matched with one of the given options by comparing coefficients. Let's do this by checking which of the given options has the same ratio of coefficients for[tex]\( x \) and \( y \)[/tex] as the equation we found.

The equation that represents the line passing through the points (-1, 2) and (3, 1) is given by option B, which is:

[tex]\[ x + 4y = 7 \][/tex]

Choose the equation that represents a line that passes through points (-1,2) and (3,1)

A. 4x-y=6

B.x+4y=7

C. x-4y =-9

D.4x+y=2​

Answer:

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (2, - 4), thus

y = a(x - 2)² - 4

To find a substitute (- 3, - 3) into the equation

- 3 = a(- 3 - 2)² - 4

- 3 = 25a - 4 ( add 4 to both sides )

1 = 25a ( divide both sides by 25 ), hence

a = [tex]\frac{1}{25}[/tex]

y = [tex]\frac{1}{25}[/tex] (x - 2)² - 4 ← in vertex form

  = [tex]\frac{1}{25}[/tex] (x² - 4x + 4) - 4 ← in expanded form

Hence the coefficient of the x² term is [tex]\frac{1}{25}[/tex]

Answer:-5

Step-by-step explanation:

Answer:

Area =  16 units²

Step-by-step explanation:

Points to remember

Distance formula

The distance between two points (x1, y1) and (x2, y2) is given by

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the length and breadth of rectangle

Let the points be  (1, 7) , (5, 3)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(5 - 1)² + (3 - 7)²]

 =  √[(4)² + (-4)²]

 = √32 = 4√2

If the points be  (5, 3) , (3, 1)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(3 - 5)² + (1 - 3)²]

 =  √[(-2)² + (-2)²]

 = √8 = 2√2

Length = 4√2 and breadth = 2√2

To find the area of rectangle

Area = Length * Breadth

 = 4√2 * 2√2

 = 16 units²

Answer:

16 units

Step-by-step explanation:

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