What is the slope of the line that passes through the points A (–4, 3) and B (–2, –5)?

Answer:

[tex]\boxed{x = 2+2\sqrt{6} ~~or~~x = 2 - 2 \sqrt{6} }[/tex]

.

Step-by-step explanation:

To find x, use pythagoras form

[tex]c^2 = a^2 + b^2[/tex]

[tex](x + 4)^2 = x^2 + (x + 1)^2[/tex]

[tex]x^2 + 8x + 16 = x^2 + x^2 + 2x + 1[/tex]

[tex]2x^2 + 2x + 1 - x^2 - 8x - 16 = 0[/tex]

[tex]x^2 - 6x - 15 = 0[/tex]

[tex]x^2 - 6x = 15[/tex]

[tex](x - 3)^2 - 9 = 15[/tex]

[tex](x - 3)^2 = 15 + 9[/tex]

[tex](x - 3)^2 = 24[/tex]

[tex]x - 2 = \pm \sqrt{24}[/tex]

[tex]x = 2 \pm 2\sqrt{6}[/tex]

.

[tex]x_1 = 2 + 2\sqrt{6}[/tex]

[tex]x_2 = 2 - 2\sqrt{6}[/tex]

.

Happy to help :)

Answer:

3 dollars and 60 cents

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

Answer:

2*9=18 14*13=182 18+182=200

Step-by-step explanation:

well you multiply 2 times 9 and you get 18 and then you multiply 14 times 13 and you get 182 and then you 18+182 and that will give you 382.

Answer:

A. 19

Step-by-step explanation:

edge 2020

The dot product of the vector u and v is 19 if option (A) is correct.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

We have:

On a coordinate plane, vector u has an origin (0, 0) and terminal point (7, 8). Vector v has origin (0, 0) and terminal point (negative 3, 5).

Vector u = <(7-0, (8-0)> = <7, 8>

Siimilarly, v = <-3, 5>

u · v = (7×(-3)) + (8×5) = -21 + 40 = 19

Thus, the dot product of the vector u and v is 19 if option (A) is correct.

Learn more about the vector here:

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Answer:

Carle is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that has 100 feet? 1 foot= 12 inches. A) 49 pieces.Oct 14, 2016

Step-by-step explanation:

Answer:

1. 6 cookies  2. 5/12 of the pan is left

Step-by-step explanation:

42/2=21

21(2/3)= 14

14-8=6

6 cookies were left

1/4+1/3= 3/12+4/12=7/12

5/12 of the pan is left

Answer:

1/2x42 = 21

42-21= 21x1/3= 7

21-7= 14

14-8= 6

santa got 6 cookies

option c is the answer....

Answer:

48

Step-by-step explanation:

80% = .8

60 x .8 = 48

Answer: 48

Step-by-step explanation:

80% of 60 or 80/100 x 60 = 48

Answer:

-17\12

Step-by-step explanation:

Answer:

y = (1/4)x + 1

Step-by-step explanation:

The points mentioned are (-4,0) and (4,2).

We can find the slope m:

(2-0)/(4-(-4)) = 2/8 = 1/4

We now have the equation y = (1/4)x + b

Now we must find the y-intercept.

Plugging in the first point:

0 = (1/4)*(-4) + b

0 = -1 + b

1 = b

y = (1/4)x + 1

Answer:

A' = (-2, -3)

B' = (0, -3)

C' = (-1, 1)

I did this on edg

Step-by-step explanation:

Since it's a reflection over the x axis, the x coordinates will stay the same while the y coordinates will be opposite of what they are.

After reflected: A'(-2,-3), B'(0,-3), C'(-1,1)

Answer:

QS=23.32

Step-by-step explanation:

by Pythagorean theoremh square is equal to p square + b square

Buddy mark me as a brainlist

Answer: no? because the comma goes after every three numbers.

Answer:

Step-by-step explanation:

(a)

From the given information:

Let An denote the amount in the account at the end of n month

Thus,

[tex]A_o[/tex] =1000

After the first month ends, interest = [tex]=A_o \times \dfrac{3}{100} \times \dfrac{1}{12}[/tex]

= [tex]0.0025A_o[/tex]

Additional deposit = $200

Now,

[tex]A_1 = A_o + 0.0025A_o + 200[/tex]

[tex]=1.0025A_o + 200 --- eqn(1)[/tex]

Interest after 2nd month, = [tex]A_1 \times \dfrac{3}{100} \times \dfrac{1}{2}[/tex]

Additional deposit = $200

[tex]A_2 = A_1 + 0.0025A_1 + 200[/tex]

[tex]=1.0025A_1 + 200 --- eqn(2)[/tex]

Thus:

[tex]A_n = 1.0025A_{n-1} +200[/tex]

(b)

From above;

[tex]A_1 = 1.0025A_ 0+ 200[/tex]

Thus;

[tex]A _2 = 1.0025A_ 1+ 200[/tex]

[tex]A_2 = 1.0025( 1.0025A_ 0+ 200)+ 200[/tex]

[tex]A_2 = 1.0025^2A_o +200 ( 1+1.0025)[/tex]

[tex]A _3 = 1.0025A_ 2+ 200[/tex]

[tex]A _3 = 1.0025( 1.0025^2A_o +200 ( 1+1.0025))+ 200[/tex]

[tex]A _3 = 11.0025^3A_o +200 ( 1+1.0025 + 1.0025^2)[/tex]

To continuity...

[tex]A_n = 1.0025^n A_o + 200 (1+1.0025 +1.0025^2 +...+ 1.0025^{n-1} ) ---- (3)[/tex]

Thus, we have a geometric term [tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1}[/tex]

where:

a = 1 (first term)

r = 1.0025>1 (common ratio)

Thus;

[tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1} = \dfrac{a(r^n -1)}{r-1}[/tex]

[tex]= \dfrac{1(1.0025^n -1)}{1.0025-1}[/tex]

[tex]= 400(1.0025^n -1)[/tex]

From equation(3)

[tex]A_n = (1.0025^n \times 1000) + 80000(1.0025^n -1)[/tex]

[tex]A_n = 1.0025^n \times 81000-80000[/tex]

Answer:

4h

2d

Step-by-step explanation:

Answer:

2 m/s

Step-by-step explanation:

Answer:

2m/s²

Step-by-step explanation:

acceleration= v-u/t

=3-1/1

=2m/s²

Answer:

$2.35 per quart (rounded to nearest cent)

Step-by-step explanation:

6 quarts --- $14.12

1 quart --- [tex]\frac{1}{6}[/tex] × $14.12 = $2.35 (rounded to nearest cent)

Answer:

-9

Step-by-step explanation:

here is your answer pls check it

Answer:

5. Use the race times to calculate the mean time for each team. Show your work. (3 points: 1 point for each team)

Red

45.6

Yellow

47

Blue

42.8

6. How do the three teams rank based on mean times? List them in order from fastest to slowest, and explain your ranking. (1 point)

From fastest to slowest the teams rank

Red

Yellow

Blue

7. How do the three teams rank based on median times? Explain your ranking. (1 point)

Based on median times the teams rank from fastest to slowest

Red and yellow tie for the first place

Blue

8. What statistic should you use if you wish to compare the spreads? Explain your reasoning. (1 point)

The interquartile range would be the best option for measuring the spread of these statistics.

Step-by-step explanation:

Sorry, this is the best I can do I need help with the rest of the questions.

Answer:

The equation of the line is y= -2/5x+156/5

Step-by-step explanation:

y=mx+b

m= -2/5 ( 23,22)

y-y=m(x-x¹)

y-22=-2/5(x-23)

y-22=-2/5x+46/5

+22 +22

y= -2/5x+156/5

Answer:

Her rate of change is 75 ft/h

Step-by-step explanation:

Rate of Change

It measures how one quantity varies with respect to another. The second variable usually is the time.

The climber is hiking. We are given two points of her progress: At 2 hours, she is at 400 ft. This corresponds to the point (2,400).

At 6 hours, she is at 700 ft. This is the point (6,700)

The rate of change is the slope between these two points or the quotient of the variations of each variable:

[tex]\displaystyle m=\frac{700\ ft-400\ ft}{6\ h-2\ h}[/tex]

[tex]\displaystyle m=\frac{300\ ft}{4\ h}[/tex]

[tex]m=75\ ft/h[/tex]

Her rate of change is 75 ft/h

Answer:

B

Step-by-step explanation:

4x+2y=6

6x-4y=-12

2y=6-4x

y=3-2x

6x-4(3-2x)=-12

6x-12+8x=-12

2x-12=-12

2x=0

x=0

4(0)+2y=6

2y=6

y=3

(0,3)

Answer:

Please check the explanation.

Step-by-step explanation:

Given that

|v|=38

Ф = 120°

Finding the horizontal component

The horizontal component can be obtained using the formula

Vx = |v| cos Ф

     = 38 cos 120°

     = 38 (-0.5)

      = -19

Thus, the  horizontal component is:

Vx = -19

Finding the vertical component

The vertical component can be obtained using the formula

Vy = |v| sin Ф

    = 38 sin 120°

    = 38 (0.86)

    = 32.68

Thus, the vertical component is:

Vy = -19

v = |v| cos Ф i + |v| sin Ф j

As

|v|=38

Ф = 120°

Thus, the vector is

v = 38 cos 120° i + 38 sin 120° j

or

v = -19 i + 32.68 j

Answer:

0

Step-by-step explanation:

We're given the ODE,

y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) - (9t + 6)

(where I denote exp(x) = eˣ )

First determine the characteristic solution:

y'' + 4y' + 3y = 0

has characteristic equation

r ² + 4r + 3 = (r + 1) (r + 3) = 0

with roots at r = -1 and r = -3, so the characteristic solution is

y = C₁ exp(-t ) + C₂ exp(-3t )

For the non-homogeneous equation, assume two ansatz solutions

y₁ = (at ² + bt + c) exp(-t )

and

y₂ = at + b

• y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) … … … [1]

Compute the derivatives of y₁ :

y₁ = (at ² + bt + c) exp(-t )

y₁' = (2at + b) exp(-t ) - (at ² + bt + c) exp(-t )

… = (-at ² + (2a - b) t + b - c) exp(-t )

y₁'' = (-2at + 2a - b) exp(-t ) - (-at ² + (2a - b) t + b - c) exp(-t )

… = (at ² + (b - 4a) t + 2a - 2b + c) exp(-t )

Substitute them into the ODE [1] to get

→   [(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c)] exp(-t ) = 8t exp(-t ) + 6 exp(-t )

(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c) = 8t + 6

4at + 2a + 2b = 8t + 6

→   4a = 8   and   2a + 2b = 6

→   a = 2   and   b = 1

→   y₁ = (2t ² + t ) exp(-t )

(Note that we don't find out anything about c, but that's okay since it would have gotten absorbed into the first characteristic solution exp(-t ) anyway.)

• y'' + 4y' + 3y = -(9t + 6) … … … [2]

Compute the derivatives of y₂ :

y₂ = at + b

y₂' = a

y₂'' = 0

Substitute these into [2] :

4a + 3 (at + b) = -9t - 6

3at + 4a + 3b = -9t - 6

→   3a = -9   and   4a + 3b = -6

→   a = -3   and   b = 2

→   y₂ = -3t + 2

Then the general solution to the original ODE is

y(t) = C₁ exp(-t ) + C₂ exp(-3t ) + (2t ² + t ) exp(-t ) - 3t + 2

Use the initial conditions y (0) = 2 and y' (0) = 2 to solve for C₁ and C₂ :

y (0) = C₁ + C₂ + 2 = 2

→   C₁ + C₂ = 0 … … … [3]

y'(t) = -C₁ exp(-t ) - 3C₂ exp(-3t ) + (-2t ² + 3t + 1) exp(-t ) - 3

y' (0) = -C₁ - 3C₂ + 1 - 3 = 2

→   C₁ + 3C₂ = -4 … … … [4]

Solve equations [3] and [4] to get C₁ = 2 and C₂ = -2. Then the particular solution to the initial value problem is

y(t) = -2 exp(-3t ) + (2t ² + t + 2) exp(-t ) - 3t + 2

Given:

Two cards are drawn from a standard deck of 52 cards without replacement.

To find:

The probability that both cards selected for black.

Solution:

We know that,

Total number of cards = 52

Total number of red cards = 26

Total number of black cards = 26

[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

Probability of selecting first black card is

[tex]\text{Probability}=\dfrac{26}{52}[/tex]

[tex]\text{Probability}=\dfrac{1}{2}[/tex]

Number of remaining total cards = 52-1 = 51

Number of remaining black cards = 26-1 = 25

Probability of selecting second black card is

[tex]\text{Probability}=\dfrac{25}{51}[/tex]

So, the probability that both cards selected for black is

[tex]\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}[/tex]

[tex]\text{Probability}=\dfrac{25}{102}[/tex]

Therefore, the required probability is [tex]\dfrac{25}{102}[/tex].