Find the slope of the line that is parallel and perpendicular to the following equation.
y + 4 = -3(x +1)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

If it passes through x, then let's find x when y = 0

[tex]\qquad \tt \dashrightarrow \:0 = {x}^{2} - x - 6[/tex]

[tex]\qquad \tt \dashrightarrow \: {x}^{2} - 3x + 2x - 6 = 0[/tex]

[tex]\qquad \tt \dashrightarrow \:x(x - 3) + 2(x - 3) = 0[/tex]

[tex]\qquad \tt \dashrightarrow \:(x - 3) (x + 2) = 0[/tex]

So, required values of x are 3 and -2

Now, let's differentiate the equation to get slope slope for tangent ~

[tex]\qquad \tt \dashrightarrow \: m = \dfrac{d}{dx} ( {x}^{2} - x - 6)[/tex]

[tex]\qquad \tt \dashrightarrow \: m = 2 x - 1[/tex]

Now, plug in the values of x to find slopes of tangents

[tex]\qquad \tt \dashrightarrow \: m _1 = (2 \times 3) - 1[/tex]

[tex]\qquad \tt \dashrightarrow \: m_1 = 6 - 1[/tex]

[tex]\qquad \tt \dashrightarrow \: m _1 = 5[/tex]

and

[tex]\qquad \tt \dashrightarrow \:m_2 = (2 \times - 2) - 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m_2 = - 4- 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m_2 = - 5[/tex]

We know, tangent are normal are perpendicular. so let's find out slopes of normals m1' and m2'

[tex]\qquad \tt \dashrightarrow \:m _1\cdot m_1 ' = - 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{m_1}[/tex]

[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{ 5}[/tex]

and

[tex]\qquad \tt \dashrightarrow \:m _2\cdot m_2 ' = - 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{m_2}[/tex]

[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{ -5}[/tex]

[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{1}{ 5}[/tex]

Now, write the equations of normals using point slope form :

Normal 1 : passing through (3 , 0), and slope = -1/5

[tex]\qquad \tt \dashrightarrow \:y - 0 = - \dfrac{1}{5} (x - 3)[/tex]

[tex]\qquad \tt \dashrightarrow \:5y = - (x - 3)[/tex]

[tex]\qquad \tt \dashrightarrow \:5y = - x + 3[/tex]

[tex]\qquad \tt \dashrightarrow \:x + 5y - 3 = 0[/tex]

and

Normal 2 : passing through (-2 , 0), and slope = 1/5

[tex]\qquad \tt \dashrightarrow \:y - 0 = \dfrac{1}{5} (x - ( - 2))[/tex]

[tex]\qquad \tt \dashrightarrow \:5y = x + 2[/tex]

[tex]\qquad \tt \dashrightarrow \ x - 5y + 2 = 0[/tex]

That's all for Aunty ~ hope it helps !

Differentiate

[tex]\\ \rm\rightarrowtail f'(x)=\dfrac{d}{dx}(2x^2+9x)[/tex]

[tex]\\ \rm\rightarrowtail 4x+9[/tex]

f'(5):-

Option C

instantaneous rate can be found by differentiating the function.

Here,

so differentiating:

So when x = 5,

Answer:

k>1 1/3

Step-by-step explanation:

i have rsm too bro

The given equation has no solution when K is any real number  and k>12

We have given that

3x^2−4x+k=0

△=b^2−4ac=k^2−4(3)(12)=k^2−144.

If Δ=0, it has 1 real solution,

Δ<0 it has no real solution,

Δ>0 it has 2 real solutions.

We get,

Δ=k^2−144 here Δ is not zero.

It is either >0 or <0

Δ<0 it has no real solution,

Therefore the given equation has no solution when K is any real number.

To learn more about the solution visit:

https://brainly.com/question/1397278

The correct answer would be:

-10x + y = 4

10x - y = -4

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

[tex]x1 = 2 \: \: y1 = 1 \\ x2 = 8 \: \: \: y = 9 \\ \\ \\ distance \: between \: two \: poit \: \\ = \sqrt{(x2 - x1) {}^{2} + (y2 - y1}) {}^{2} \\ \sqrt{(8 - 2) {}^{2} + (9 - 1) {}^{2} } \\ \sqrt{(6) {}^{2} + (8) {}^{2} } \\ \ = \sqrt{36 + 64} \\ = \sqrt{100 } \\ = 10[/tex]

Answer:

C

Step-by-step explanation:

d / rate = time

d / 90  + d/60  = 6 hours

(2d+ 3d)/180 = 6

5d = 1080

d = 216 miles

The distance from NYC to Boston is 216 miles.

We have a guy named Steve travels from NYC to Boston at 90 mph and returns to NYC at 60 mph taking 6 hours total for the round-trip without stopping.

We have to determine distance between NYC and Boston.

The distance covered by the body will be -

d = v x t

According to question, we have -

Assume that the distance travelled by Steve from NYC to Boston be x.

Then, total distance covered for the round trip = 2x.

From NYC to Boston -

Suppose that in going from NYC to Boston, Steve takes t hours. Then

x =  90 x t            (1)

From Boston to NYC -

Steve will take (6 - t) hours to travel the distance. Then -

x = 60 x (6 - t)         (2)

Now, Equating the equations (1) and (2), we get -

90 x t = 60 x (6 - t)

1.5t = 6 - t

1.5t + t = 6

2.5 t = 6

t = [tex]\frac{12}{5}[/tex] = 2.4 hours

Therefore -

x = 90 x 2.4 = 216 miles

Hence, the distance from NYC to Boston is 216 miles.

To solve more questions on Speed, time and Distance visit the link below -

https://brainly.com/question/24999473

#SPJ2

Answer:

2,250 yd^3

Step-by-step explanation:

formula for pyramid is lwh/3

Answer:

Step-by-step explanation:it is the degree of 4

Answer:

110 cm

Step-by-step explanation:

Hope it will help you.

Answer:

the answer could be 60

Step-by-step explanation:

I could be wrong sorry if I am

Answer:

12.3

Step-by-step explanation:

cause it's to the tenth which is the decimal place right after the decimal which make 12.342 12.3

Answer:

WE CANT ANSWER WITH THAT LITTLE OF INFORMATION

Answer:

x = 2√7

using Pythagoras theorem:

For the bottom part:

Answer:

this is my answer

5.29

Step-by-step explanation:

Hope this helps

Answer:

67.85 kph

Step-by-step explanation:

Formula: Distance / Time = Speed per hour
135.7 / 2 = 67.85

Answer:

76.6%

Step-by-step explanation:

345/450 * 100%

I hope it helps and sorry if I'm wrong

3w(x+y) - 4z(x+y)

Step-by-step explanation:

Hope it helps......

3w(x + y) + 4z(x - y) correctly shows the first step when factoring 3wx + 3wy - 4zx - 4zy by grouping. Option B

To factor by grouping, we first pair up the terms and then check if there is a common factor in each pair.

The given expression is  3wx + 3wy - 4zx - 4zy

First, put the terms into pairs.

The simplified version of the expression (3wx + 3wy) - (4zx + 4zy) is 3wx + 3wy - 4zx - 4zy.

Next, separate and remove the terms that are the same from each group.

The expression 3w(x + y) - 4z(x + y) can be simplified to (3w - 4z)(x + y).

This is a summary:

In option B, we have correctly put the terms together in pairs and found the common factors in each group. In the first group, we take out 3w from 3wx and 3wy, and in the second group, we take out 4z from 4zx and 4zy. This means that the expression is correct when it is written as factors.

Learn more about factoring by grouping from

https://brainly.com/question/11919471

#SPJ2

The height of the shot starts to increase when x is -5 feet, It continues to increase until x = 10 feet and then the height decreases until x = 25 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h(x) represent the height of the shot put, when the horizontal distance is x feet.

h(x)= -0.05x² + x + 6

From the graph of h(x):

The height of the shot starts to increase when x is -5 feet, It continues to increase until x = 10 feet and then the height decreases until x = 25 feet

Find out more on equation at: https://brainly.com/question/2972832

Answer:

its simple just add all of the numbers and then divide it by the total frequency

Step-by-step explanation:

4+5+5+7+8+8+8+10+10

            8

=65

  8

=8.125

Answer:

Step-by-step explanation:

Put the term x on one side of the equation.

Subtract by 2 from both sides.

[tex]\Longrightarrow: \sf{-5x+2-2 < 12-2}[/tex]

Solve.

Subtract the numbers from left to right.

⇒ 12-2=10

⇒ -5x<10

Multiply by -1 from both sides.

⇒ (-5x)(-1)>10(-1)

Solve.

Multiply the numbers from left to right.

-5x*-1=5x

10*-1=-10

→ 5x>-10

Divide by 5 from both sides.

→ 5x/5>-10/5

Solve.

Divide the numbers from left to right.

-10/5=-2

[tex]\Longrightarrow: \boxed{\sf{x > -2}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

[tex]x > -2[/tex]

Step-by-step explanation:

Given the following question:

[tex]-5x+2 < 12[/tex]

To find this answer we subtract two on both sides then isolate the variable by dividing 5 on both sides.

[tex]-5x+2 < 12[/tex]
[tex]2-2=0[/tex]
[tex]12-2=0[/tex]
[tex]-5x < 10[/tex]
[tex]-5x\div-5=x[/tex]
[tex]10\div-5=-2[/tex]
[tex]x > -2[/tex]

Which means your answer is "x > -2."

Hope this helps.

Answer: x is 125

Step-by-step explanation: Angles P and S are also consecutive angles, adding up to 180 degrees. 180-55 = 125, so adding the two angles together is 180 degrees. Thus, x is 125.

Answer:

that would be 1/2 because its the only one that could reduce the numbers.

Step-by-step explanation:

hope this helps,

kleann

The scale factor of the triangle ΔABC to ΔDEF will be 1/2. Then the correct option is A.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The triangle ΔABC is similar to the triangle ΔDEF. Then the ratio of the corresponding sides will be constant. Then the scale factor is calculated as,

SF = 10 / 20

SF = 1 / 2

The scale factor of the triangle ΔABC to ΔDEF will be 1/2. Then the correct option is A.

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ7

mean formula number of values divided by the total of all the values

so

100 divided by 10

ans 10

ANSWER

solution

here,

Correct option is B)

Total age of 40 old students =40×15=600years.

Total age of 40 old and 10 new students =50×15.2=760years

∴ Total age of 10 new students =760−600=160years

∴ Required average age =

10

160

=16years

Answer:

16 years is the answer

Step-by-step explanation:

My account got deactivated I am about to cry

Check the picture below.

now, keeping in mind that ratio of the sides is the same as the ratio of the perimeters.

[tex]\cfrac{\stackrel{small}{trapezoid}}{\stackrel{large}{trapezoid}}\qquad \stackrel{sides}{\cfrac{6}{9}}~~ = ~~\stackrel{perimeters}{\cfrac{20}{p}}\implies \cfrac{2}{3}=\cfrac{20}{p}\implies 2p=60 \\\\\\ p=\cfrac{60}{2}\implies p=30 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{\stackrel{small}{trapezoid}}{\stackrel{large}{trapezoid}}\qquad \stackrel{sides^2}{\cfrac{6^2}{9^2}}~~ = ~~\stackrel{areas}{\cfrac{A}{45}}\implies \cfrac{36}{81}=\cfrac{A}{45}\implies \cfrac{4}{9}=\cfrac{A}{45} \\\\\\ 180=9A\implies \cfrac{180}{9}=A\implies 20=A[/tex]

Step-by-step explanation:

the formula is distance/time

since it is miles per hour and the time is given in minutes. you divide 45minutes by 60(to convert it to hour) and then you divide 27 by the answer

Answer:

obtuse

Step-by-step explanation:

It is obtuse because it is greater than 90 degrees!

Answer:

the answer is B

Step-by-step explanation:

Answer:

inactivity fee

Step-by-step explanation:

Answer:

The answer is 6.

Step-by-step explanation:

The degree is the largest exponent on the variable. And in this case the answer is 6.

Answer:

2x

Step-by-step explanation:

X = chris's money

2 times chris's money = 2x

Answer:

the answer is k= -12

Step-by-step explanation:

use x-5= 0

x=5