the lines shown below are parallel. if the green line has a slope of -1, what is the slope of the red line

[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{17})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-17}{1-8}\implies \cfrac{-13}{-7}\implies \cfrac{13}{7} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{17-4}{1-8}\stackrel{\leftarrow \textit{atop she used }y_1-y_2}{\frac{}{}}~\hfill[/tex]

For this case we have that by definition, the slope of a line is given by:

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

According to the data we have the following points:

[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 8,17)[/tex]

Substituting we have:

[tex]m = \frac {17-4} {8-1}\\m = \frac {13} {7}[/tex]

So, the slope is [tex]\frac {13} {7}[/tex]

ANswer:

The student's mistake was to erroneously subtract the "x" coordinates from the points

Answer:

x = 98°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle and 53° and 45° are the opposite interior angles, hence

x = 53° + 45° = 98°

Answer:

(1.6, -1.6)

Step-by-step explanation:

We have the following system of equations:

[tex]y=1.5x - 4[/tex]

[tex]y=-x[/tex]

We have the following system of equations:

To solve the system substitute the second equation in the first one and solve for x

[tex]y=1.5x - 4[/tex]

[tex]-x=1.5x - 4[/tex]

[tex]4=2.5x [/tex]

[tex]2.5x =4[/tex]

[tex]x =\frac{4}{2.5}[/tex]

[tex]x = 1.6[/tex]

Now replace the value of x in one of the two equations and solve for y

[tex]y=-x[/tex]

[tex]y=-1.6[/tex]

The solution is:

(1.6, -1.6)

Answer:

I believe its true

Answer:

A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex]

Step-by-step explanation:

First, we have to turn 4x - 3y = -12 into slope-intercept form (y = mx + b). To do this, we first have to isolate 3y.

4x - 3y = -12

    +3y    +12     Add 3y to both sides and add 12 to both sides

4x + 12 = 3y

3y = 4x + 12

Isolate y by dividing 3 from both sides.

y = [tex]\frac{4}{3}[/tex]x + 4

The graph that is parallel will have the same slope as this equation, which is [tex]\frac{4}{3}[/tex].

Therefore, A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex] would be the correct answer.

Answer:

A

Step-by-step explanation:

Solve for y.

4x – 3y = -12

4x + 12 = 3y

y = 4/3 x + 4

The slope of the line is 4/3.  So you need another line with the same slope.  So the answer is A.

Adam earned approximately 12.48% interest on his savings account over 10 years.

To find the rate of interest (r) earned by Adam, we can use the formula for compound interest:

A = P * (1 + r[tex])^{t}[/tex]

where:

A = ending amount ($1649 in this case)

P = principal (initial amount) ($100 in this case)

r = interest rate (what we want to find)

t = time (in years) (10 years in this case)

We know the values of A, P, and t, so we can plug them into the formula and solve for r:

1649 = 100 * (1 + r)¹⁰

Divide both sides of the equation by 100:

16.49 = (1 + r)¹⁰

Now, let's isolate (1 + r) by taking the 10th root of both sides:

(1 + r) = √(16.49)

(1 + r) ≈ 1.12479

Now, subtract 1 from both sides to find the value of r:

r ≈ 1.12479 - 1

r ≈ 0.12479

Finally, convert the decimal to a percentage to get the interest rate:

r ≈ 0.12479 * 100

r ≈ 12.48%

So, Adam earned approximately 12.48% interest on his savings account over 10 years.

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Answer:

C

Step-by-step explanation:

So I'm going to subtract (x+7)/(x+3) on both sides:

(x-6)/(x+5)-(x+7)/(x+3)>=0

Now I'm going to find a common denominator which is (x+5)(x+3).

[(x-6)(x+3)-(x+7)(x+5)]/[(x+5)(x+3)]>=0

Now I just have a lot of simplifying to do:

[x^2+3x-6x-18-(x^2+5x+7x+35)]/(x^2+3x+5x+15)>=0

[-3x-18-12x-35]/(x^2+8x+15)>=0

[-15x-53]/[x^2+8x+15]>=0

Probabilities are used to determine the chance of events

The value of [tex]\mathbf{P(A\ or\ B) }[/tex] is 0.75

The given parameters are:

[tex]\mathbf{P(A) = 0.50}[/tex]

[tex]\mathbf{P(B) = 0.40}[/tex]

[tex]\mathbf{P(A\ and\ B) = 0.15}[/tex]

The required probability is calculated using:

[tex]\mathbf{P(A\ or\ B) = P(A) + P(B) - P(A\ and\ B)}[/tex]

So, we have:

[tex]\mathbf{P(A\ or\ B) = 0.50 + 0.40 - 0.15}[/tex]

[tex]\mathbf{P(A\ or\ B) = 0.75}[/tex]

Hence, the value of [tex]\mathbf{P(A\ or\ B) }[/tex] is 0.75

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Answer:0.75

Step-by-step explanation:

did it

Answer:

-32x

Step-by-step explanation:

Combine like terms (terms with the same amount of variables).

First, subtract 7x from 15x:

15x - 7x = 8x

Next, subtract 40x from 8x:

8x - 40x = -32x

-32x is your answer.

~

Answer:

D. 12

Step-by-step explanation:  

We have been given a diagram of a triangle. We are asked to find the value of y for our given triangle.

First of all, we will find 3rd side of larger triangle using Pythagoras theorem.

[tex]\text{3rd side}^2=16^2-8^2[/tex]

[tex]\text{3rd side}^2=256-64[/tex]

[tex]\text{3rd side}^2=192[/tex]

[tex]\text{3rd side}^2=192[/tex]  

We will use geometric mean (leg) theorem to solve our given problem.

[tex]\text{3rd side}^2=y\times 16[/tex]  

[tex]192=y\times 16[/tex]  

[tex]\frac{192}{16}=\frac{y\times 16}{16}[/tex]  

[tex]y=12[/tex]  

Therefore, the value of y is 12 and option D is the correct choice.

Answer:

3 and 9

Step-by-step explanation:

The factors of 18 can be listed as

1, 2, 3, 6, 9, 18

The two which sum to 12 are 3 and 9

Answer:

The correct answer option is D. (-2, 1).

Step-by-step explanation:

We are given the coordinates of the square A"B"C"D" after the rule is applied and we are to find the coordinates of the vertex A.

For that, we will reverse the rule.

A" = (-5, -3)

x: - 5 + 4 = -1

y: - 3 + 1 = -2

Now we will reverse the 90 degrees counter in counter clockwise rotation:

(x, y) ---> (y, -x)

(-1. -2) ---> (-2, -(-1)) = (-2, 1)

Answer:

4.0616 seconds approximately

Step-by-step explanation:

We are looking for how long it takes the ball to hit the ground. h is 0 then.

So we are looking to solve -16t^2+64t+4=0

Divide both sides by -4 to make the numbers a little simpler to work with.

4t^2-16t-1=0

You could aim for completing the square or quadratic formula here.

I'm going for quadratic formula.

a=4

b=-16

c=-1

So the discriminant=b^2-4ac=(-16)^2-4(4)(-1)=16^2+16=16(16+1)=16(17)=272

You could have just put (-16)^2-4(4)(-1) into your calculator.

The quadratic formula says to do:

-b plus or minus square root (discriminant)

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

                             2 times a

=

16 plus or minus sqrt(272)

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

                   8

=(approximately)

16 plus or minus 16.4924

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

                  8

=

16+16.4924                            16-16.4924

----------------             or            ----------------

        8                                          8

=

32.4924                                  -0.4924

-------------                 or              -----------

     8                                               8

=

4.0616                    or             -0.062

So the baseball hits the ground 4.0616 seconds approximately after the ball has been hit.

Answer: 2 plus or minus square root of 17 end root over 2

Answer:

C)

Step-by-step explanation:

The first thing you want to do is add x to both sides (add one positive x-tile):

2x+5=-x-1

+x       +x

2x+x+5=-x+x-1

combine like terms

3x+5=-1

Answer:

d)  1

Step-by-step explanation:

3a = –2b – 7

We have the point (a, -5) so b = -5

Substituting in

3a = -2(-5) -7

3a = 10-7

3a = 3

Divide each side by 3

3a/3 = 3/3

a =1

To find the value of a in the equation 3a = -2b - 7, substitute the coordinates of the given point and solve for a. The value of a is -5.

In this given equation 3a = -2b - 7, o find the value of a, we can substitute the coordinates of the given point into the equation and solve for a. Let's substitute the value of a as -5:

3(-5) = -2b - 7

Simplifying the equation:

-15 = -2b - 7

Adding 7 to both sides:

-8 = -2b

Dividing both sides by -2:

b = 4

So, the value of a is -5.

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Answer:

supplementary

Step-by-step explanation:

Consecutive angles in a parallelogram sum to 180°

That is they are supplementary.

Answer:

q = [tex]\frac{4+3p}{5}[/tex]

Step-by-step explanation:

Given

5(q + p) = 4 + 8p ← distribute the left side

5q + 5p = 4 + 8p ( subtract 5p from both sides )

5q = 4 + 3p ( divide both sides by 5 )

q = [tex]\frac{4+3p}{5}[/tex]

The equation in its simplest form and q as subject is q = (1/5)(4+3p)

Reducing any fraction or equation to its simplest form means to to reduce it to a form from where no more factors can be taken common from the numerator and denominator , or the equation is in the form where no more simplification can be done.

An equation is given in the question .

5(q+p) = 4+8p

To reduce it in the simplest form and making q as the subject ,

then p will be the subject .

5q+ 5p = 4+8p

5q = 4 + 8p - 5p

5q = 4 +3p

q = (1/5)(4+3p)

Therefore the equation in its simplest form and q as subject is q = (1/5)(4+3p)

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Answer:

The answer is B. the diameter of the base

Step-by-step explanation:

Just got it right on edg! Have a great day!

Answer:

16

* usually means multiplication

If you have an open circle there instead, please inform me.

Step-by-step explanation:

* usually means multiplication

If you had an open circle there, please let me know.

Find h(10) and then multiply that answer to itself.

h(10)=6-10=-4

So the answer is -4*-4=16

Answer:

Option C : y = -4x+10

Step-by-step explanation:

Given equation of line is:

[tex]y = -4x-1[/tex]

Comparing it with standard form

y=mx+b

m = -4

As the slopes of parallel lines are equal, the slop of other line will also be -4.

Now, to find the value of b

[tex]2 = -4(2) + b\\2 = -8 + b\\2+8=b\\b=10[/tex]

Putting the values of b and m in standard form

[tex]y=mx+b\\y = (-4)x+10\\y= -4x+10[/tex]

Hence,

Option C is the correct answer ..

For this case we have that the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal.

So, if we have:

[tex]y = -4x-1[/tex]

A parallel line has slope [tex]m = -4[/tex]

y = -4x + b

We substitute the point (2,2) to find "b":

[tex]2 = -4 (2) + b\\2 = -8 + b\\b = 2 + 8\\b = 10[/tex]

Finally we have:

[tex]y = -4x + 10[/tex]

Answer:

Option C

Answer:

7

Step-by-step explanation:

2x² - 28x + 98 = 0

x² - 14x + 49 = 0

(x - 7)² = 0

x = 7

To solve the equation 2x^2 - 28x + 98 = 0, we can use the quadratic formula. After substituting the values into the formula, we simplify the equation and solve for x. The solution is x = 7.

To solve the equation 2x2 - 28x + 98 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -28, and c = 98. Substituting these values into the formula:

x = (-(-28) ± √((-28)^2 - 4(2)(98))) / (2(2))

Simplifying the equation gives:

x = (28 ± √(784-784)) / 4

Since the term inside the square root is zero, we have:

x = (28 ± √0) / 4

The square root of zero is zero, so:

x = (28 ± 0) / 4

Simplifying further:

x = 28 / 4

x = 7

Therefore, the solution to the equation 2x2 - 28x + 98 = 0 is x = 7.

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Answer:

[tex]g(x)=(x-3)^{2}[/tex]

Step-by-step explanation:

Options 2 and 3  are discarded because those are traslations to up and down.

Now, the point (0,0) is in the function [tex]f(x)=x^{2}[/tex] and after being traslated it needs to be (3,0). The option [tex]g(x)=(x+3)^{2}[/tex] doesn't satisfice that because the image of 3 is 36 and needs to be 0. On the other hand, [tex]g(x)=(x-3)^{2}[/tex] is the only option that contains the point (3,0) so it is the correct answer.

Answer..

D) g(x) = (x − 3)2

Answer:

B) 54 inches

Step-by-step explanation:

2*3 = 6

3*3 = 9

A= l*w

6*9=54

Answer:

b 54 inches^2

Step-by-step explanation:

2 inches by 3 inches  gets scaled by 3

it becomes 2*3   by 3*3

6 inches by 9 inches

The area is

A = l*w

A = 6*9

A = 54 inches^2

Answer:

-2

Step-by-step explanation:

The equation of a line in slope intercept form is

y = mx +b where m is the slope and b is the y intercept

y = -2x+4

The slope is -2 and the y intercept is 4

Answer:

Square root 9x + 7 + square root 2x = 7

Step-by-step explanation:

Square root 9x + 7 + square root 2x = 7, if i could put the square root symbol in I would.

Hope my answer has helped you and if not i'm sorry.

Answer:

Step-by-step explanation:

Look at the picture.

Coordinates of a point (x, y)

x - from x-axis

y - from y-axis

Answer:

Because the sectors are of equal size, each sector has the same probability of happening.

So for every number, you have a probability of 0.2 of it appearing.

Because you have three odd numbers, the probability to land on an odd number on each spin is 0.6. You can also say that the probability to not have an odd number is 0.4.

So what is the probability to have 0 odd number in two spins?

What is the probability to have 1 odd number in two spins? You can have one odd number on the first or one odd on the second spin, that is why we add the probabilities.

What is the probability to have 2 odd numbers in two spins?

To verify if we did a good job, we add all the probabilities. We should get 1.

.

So to slide your bars, you slide them up to the number I gave you for each case.

Hope this helps!

The likelihood of spinning a 3 on an equal-segment spinner is 1/5 per spin. When spun twice, the probability of getting 3 both times is 1/25. The variable x, which represents how many times 3 is spun, can therefore be 0, 1, or 2.

Your inquiry is related to probability.

Each spin of the spinner is an independent event. This means that the result of the first spin does not influence the result of the second spin. Since the spinner is equally likely to land on any of the 5 sectors, the probability of it landing on 3 (or any given number) is 1 out of 5 or 1/5.

Since the spinner is spun twice, we multiply these probabilities together to find the total probability of spinning a 3 both times. Therefore, the total probability of spinning a 3 twice would be (1/5) * (1/5) = 1/25.

Thus, the variable x, representing the number of times 3 is spun in these two attempts, can be 0, 1, or 2. These are the possible outcomes.

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Hello There!

.84 ÷ .02 ≈ 42

WORK SHOWN IN IMAGE ATTACHED

Answer:

= 26x3 − 12x2 + 5x + 7

Step-by-step explanation:

Use the FOIL method to multiply the two binomials. Then distribute the negative sign. Finally, order like terms from highest degree to lowest degree and combine.

(2x3 − 3x + 11) − (3x2 + 1)(4 − 8x)

= (2x3 − 3x + 11) − (12x2 − 24x3 + 4 − 8x)

= 2x3 − 3x + 11 − 12x2 + 24x3 − 4 + 8x

= 2x3 + 24x3 − 12x2 − 3x + 8x + 11 – 4

= 26x3 − 12x2 + 5x + 7