Find the slope of the line passing through the points (3,3) and (3,-9)

Answer:

[tex]y=x^2+18x+79[/tex]

[tex]y=(x+9)^2-2[/tex]

Step-by-step explanation:

We want to find a function of the form:

[tex]y=ax^2+bx+c[/tex]

We know that it passes through the three points: (-11, 2); (-9, -2); and (-5,14).

In other words, if we substitute -11 for x, we should get 2 for y. So:

[tex](2)=a(-11)^2+b(-11)+c[/tex]

Simplify:

[tex]2=121a-11b+c[/tex]

We will do it to the two other points as well. So, for (-9, -2):

[tex]\begin{aligned}(-2)&=a(-9)^2+b(-9)+c\\\Rightarrow-2&=81a-9b+c\end{aligned}[/tex]

And similarly:

[tex]\begin{aligned}(14)&=a(-5)^2+b(-5)+c\\\Rightarrow 14&=25a-5b+c\end{aligned}[/tex]

So, to find our function, we will need to determine the values of a, b, and c.

We essentially have a triple system of equations:

[tex]\begin{cases}2=121a-11b+c\\-2=81a-9b+c\\14=25a-5b+c\end{cases}[/tex]

To approach this, we can first whittle it down only using two variables.

So, let's use the First and Second Equation. Let's remove the variable b. To do so, we can use elimination. We can multiply the First Equation by 9 and the Second Equation by -11. This will yield:

[tex]\begin{cases}{\begin{aligned}9(2)&=9(121a-11b+c)\\-11(-2)&=-11(81a-9b+c)\end{cases}}[/tex]

Distribute:

[tex]\begin{cases}18=1089a-99b+9c\\22=-891a+99b-11c\end{cases}[/tex]

Now, we can add the two equations together:

[tex](18+22)=(1089a-891a)+(-99b+99b)+(9c-11c)[/tex]

Simplify:

[tex]40=198a-2c[/tex]

Now, let's do the same using the First and Third Equations. We want to cancel the variable b. So, let's multiply the First Equation by 5 and the Third Equation by -11. So:

[tex]\begin{cases}{\begin{aligned}5(2)=5(121a-11b+c)\\-11(14)=-11(25a-5b+c)\end{cases}[/tex]

Simplify:

[tex]\begin{cases}10=605a-55b+5c\\-154=-275a+55b-11c\end{cases}[/tex]

Now, let's add the two equations together:

[tex](10-154)=(605a-275a)+(-55b+55b)+(5c-11c)[/tex]

Simplify:

[tex]-144=330a-6c[/tex]

Therefore, we now have the two equations:

[tex]\begin{cases}40=198a-2c\\-144=330a-6c\end[/tex]

Let's cancel the c. So, multiply the First Equation by -3. We don't have to do anything special to the second. So:

[tex]-3(40)=-3(198a-2c)[/tex]

Multiply:

[tex]-120=-594a+6c[/tex]

Now, add it to the Second Equation:

[tex](-120+-144)=(-594a+330a)+(6c-6c)[/tex]

Add:

[tex]-264=-264a[/tex]

Divide both sides by -264. So, the value of a is:

[tex]a=1[/tex]

Now, we can use either of the two equations above to obtain c. Let's use the first one. So:

[tex]40=198a-2c[/tex]

Substitute 1 for a:

[tex]40=198(1)-2c[/tex]

Solve for c. Subtract 198 from both sides and divide by -2:

[tex]\begin{aligned}40&=198-2c\\ -158&=-2c \\79 &=c \end{aligned}[/tex]

So, the value of c is 79.

Finally, we can find b. We can use any of the three original equations. Let's use the First Equation. So:

[tex]2=121a-11b+c[/tex]

Substitute 1 for a and 79 for c and determine the value of b:

[tex]\begin{aligned}2&=121(1)-11b+(79)\\2&=121+79-11b\\2&=200-11b\\-198&=-11b\\18&=b\end{cases}[/tex]

Therefore, the value of b is 18.

So, our equation is:

[tex]y=ax^2+bx+c[/tex]

Substitute in the values:

[tex]y=(1)x^2+(18)x+(79)[/tex]

Simplify:

[tex]y=x^2+18x+79[/tex]

Now, let's put this into vertex form. To do so, we will need to complete the square. First, let's group the first two terms together:

[tex]y=(x^2+18x)+79[/tex]

To complete the square, we will divide the b term by 2 and then square it.

b is 18. 18/2 is 9 and 9² is 81. Therefore, we will add 81 into our parentheses:

[tex]y=(x^2+18x+81)+79[/tex]

Since we added 81, we must also subtract 81. So:

[tex]y=(x^2+18x+81)+79-81[/tex]

Subtract:

[tex]y=(x^2+18x+81)-2[/tex]

The grouped terms are a perfect square trinomial. Factor:

[tex]y=(x+9)^2-2[/tex]

And this is in vertex form.

And we are done!

Answer:

2=2

Step-by-step

Y=mx+b

2=9(0)+2

9 x 0=0

2=2

I hope I got it correct and helped you.

Answer:

21 degrees

Step-by-step explanation:

Answer:

(x-4) is a factor of 3x^2-13x+4

(3x^2-13x+4)+(x-4)=(3x-1)

The number 4 is a root of F(x)=3x^2-13x+4

Step-by-step explanation:

The statements that are true are: B. The number 4 is a root of F(x) = 3x²-13x+4; D. (3x² - 13x+4) ÷ (x - 4) = (3x - 1) ; F (x-4) is a factor of 3x²-13x+ 4.

B. 4 is a root of F(x) = 3x2-13x+4

Hence:

F(x) = 3x²-13x + 4

F(x)=(x-4) (3x-1)

x=4, 1/3

x=4 is a root of Fx

D. (3x² - 13x+4)÷ (x - 4) = (3x - 1)

F. (x-4) is a factor of 3x²-13x+ 4

Hence:

3x²-13x+ 4=(x-4) (3x-1)

Therefore the statements that are true are: B. The number 4 is a root of F(x) = 3x²-13x+4; D. (3x² - 13x+4) ÷ (x - 4) = (3x - 1) ; F (x-4) is a factor of 3x²-13x+ 4.

Learn more about statement that are true here: https://brainly.com/question/10538276

#SPJ2

Answer:

It's -4 -4i

Step-by-step explanation:

Because it is

A

-4-4i

For the person that commented. the 5 is an exponent.

9514 1404 393

Answer:

  340

Step-by-step explanation:

The ratio of natural to synthetic is give as ...

  5 : 8

Then the ratio of natural to total would be ...

  5 : (5+8) = 5 : 13

The amount of natural oil in 884 total liters of oil will be ...

  (5/13)(884 L) = 340 L

884 liters of Petrolyn oil will contain 340 liters of natural oil.

Answer:

340

Step-by-step explanation:

Hope I helped

Answer:

440

Step-by-step explanation:

70 + 130 + 140 + 100 = 440

Answer:

What do you mean ?? Say it clearly I really want to help you.

Answer:

1 minus 1 is 0

Step-by-step explanation:

1-1 equals 0

Answer:

y  =  -5x -24

Step-by-step explanation:

 Given parameters:

    Coordinates of the line = (5, - 4)

   Linear function ;

                            2x - 10y = 0

Solution:

The equation of the line perpendicular to this line will have a slope that is the a negative inverse of the given line;

                          2x - 10y = 0

Equation of a line is given as;

                          y  = mx + c

y and x are the coordinates

  m is the slope

  c is the y-intercept

We find the slope and y-intercept of the new line;

                      From:  2x - 10y = 0

 Rewrite;

                        -10y = -2x

                              y  = [tex]\frac{-2}{-10}[/tex]x

                              y = [tex]\frac{1}{5}[/tex]x

The slope of this line is  [tex]\frac{1}{5}[/tex] , the line perpendicular will have slope of -5

For the new line;

                   y  = mx + c

 let us find c;

                    -4  = -5( -4)  + c

                   -4  = 20 + c

                    c  = -20 - 4

                     c = -24

The equation of the perpendicular line is;

            y  =  -5x -24

Answer: 0.0238

Step-by-step explanation:

Given : Proportion of politicians are lawyers: p= 0.56

Sample size : n= 787

Let [tex]\hat{p}[/tex] be th sample proportion.

The the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4% will be :-

[tex]P(|\hat{p}-0.56|>0.04)=P(-0.04>\hat{p}-0.56>0.04)=\\\\ P(-0.04+0.56>\hat{p}>0.04+0.56)\\\\=P(0.52>\hat{p}>0.60)\\\\=P(\dfrac{0.52-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{787}}}>\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.60-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{787}}})\\\\=P(-2.26>z>2.26)\ \ \ [Z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=1-P(-2.26<z<2.26)\\\\=1-(2P(Z > 2.26)-1)\ \ \ [P(-z<Z<z)=2P(Z > |z|)-1]\\\ =2-2P(Z > 2.26)\\\\=2-2(0.9881)=0.0238[/tex]

Hence, the required probability = 0.0238

Answer:

it's D

Step-by-step explanation:

i just put it into desmos and looked for points, none of the answers appeared, therefore it's D

Answer:

Step-by-step explanation:

Perimeter of a garden =  2(L+W)

Area of the gerden = LW

L is the length

W is the width

Given

Perimeter = 155ft

Area = 1400ft²

Substitute

1400 = LW

155 = 2L+2W

from 1;

W = 1400/L

Substitute into 2;

155 = 2L + 2(1400/L)

155 = 2L + 2800/L

155L = 2L² + 2800

2L²-155L + 2800 = 0

Factorize

L = 155±√155²-4(2)(2800)/4

L = 155±√24025-22400/4

L = 155±√1625/4

L = L = 155±40.31/4

L = 194.31/4

L = 48.82 feet and;

L = 155-40.31/4

L = 28.67ft

Hence the approximate length of the garden is at least 28.67 feet and at most 48.82 feet.

The possible lengths of the garden are:

The least approximate length  = 29 feet

The most approximate length  = 49 feet

The area of the rectangle is at least 1400 square feet

That is:

Area  ≤  1400

Let the length be represented by L

Let the width be represented by W

Let the area be represented by A

The area of a rectangle is:

Area  =  Length  x  Width

A  =  LW

LW   ≥   1400....................(1)

The perimeter of the rectangle is 155 feet

P  =  2(L  +  W)

2(L  +  W)   =  155............(2)

Make W the subject of the formula

L  +  W   =  155/2

L + W  =  77.5

W   =   77.5 - L.............(3)

Substitute W = 77.5  - L into equation (1)

L(77.5  -  L)   ≥  1400

77.5L  -  L² ≥ 1400

-L²   ≥  1400  -  77.5L

0   ≥  L²  -  77.5L  +  1400

L²  -  77.5L  +  1400 ≤  0

Solving the quadratic inequality above

29  ≤  L ≤ 49

The least approximate length of the garden = 29 feet

The most approximate length of the garden = 49 feet

Learn more here: https://brainly.com/question/19308936

Answer:

D.

Step-by-step explanation:

If you look at the graph, it says (1, 19.3) for one cubic centimeter.

Hope this helped :)

(Sorry if it is wrong)

Answer:

The answer is 109 degrees.

Step-by-step explanation:

Any triangle's angles add up to 180 in total, so we can create the equation 64+45+__=180. Using some simple algebra we can change this equation into the equation 180-109=71. This solves the inner triangle, and the outside angle, x is supplementary (meaning it adds up to 180) to 71. 180-71 = 109.

Glad I could help!

Answer:

65

Step-by-step explanation

47 + 18 = 65

Answer:

a 37

b 90

c 39

d r0

Step-by-step explanation:

Answer:

The answer is 120

Answer:50

Step-by-step explanation:

Answer: 50

Step-by-step explanation: according to pemdas you do exponets first so 5 over 2=5*5=25 then multiply by 2=25*2=50

Answer:

y=1/3 x2

Step-by-step explanation:

Answer:

y=3x

Step-by-step explanation:

Answer:

Step-by-step explanation:

12

Answer:

Step-by-step explanation:

The two numbers are 14 and 16 their product is 224 and their difference is 2

Answer:

105/16

Step-by-step explanation:

12 * 16 = 192

192 + 13 = 205

I hope this helped, please mark Brainliest, thank you!

Answer:

i+42

Step-by-step explanation:

(3+3i) - (3+2i) + (1+41)

= 3+3i-3-2i+1+41

= 3i-2i+1+41

= i+42

Answer:

its 1/3

Step-by-step explanation:

take the fraction divided by 5

Answer:

20%

Step-by-step explanation:

Percentage Calculator: 3000 is what percent of 15000? = 20%