A line goes through the points (8,11) and (-2,7). What is the slope of the line? Show your work. Write the equation of the line in point-slope form. Show your work. Write the equation of the line in slope-intercept form. Show your work.

Answer:

E

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let the diagonal ( hypotenuse ) be d , then

d² = 5² + 5² = 25 + 25 = 50 ( take square root of both sides )

d = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex] → E

Step-by-step explanation:

remember the domain is the interval or set of valid input (x) values. the range is the interval or set of the valid result (y) values.

so, the given domain tells us the interval to look at.

what are the functional values of the function between 0 and 50 ?

since the function is continuous (there are no gaps) in this interval, we can safely assume that all values between f(0) and f(50) are valid y values.

f(0) = 4×0 + 5 = 5

f(50) = 4×50 + 5 = 205

so, the range is 5 <= y <= 205

Answer:

1/3x+7=26

Step-by-step explanation:

1/3 of a number which could anything so mark as X

add 7

equals 26

1/3x+7=26

Answer:

I can't explain this discrepancy other than to suggest that they are talking about 2 different groups.  The boss has included his salary in the average, but the employee is only concerned about the wage of the average worker.

Step-by-step explanation:

Answer:  See below.

Step-by-step explanation:

We'll assume the top and bottom lines are parallel.  That means angles 4 and 5 are 90 degrees since the line coming down is perpendicular to the parallel line.  The sum of angles 1 and 2 is also 90°.  The interior angles of a triangle must add to 180°. So far we have two:  90° and 60°.  The third must therefore be 30°(angle 2).  Angle 3 must be 120° since it shares a straight line with the 60° angle and the straight line is 180° from one side to the other.  Angle 1 must be (90°- angle 2), which makes it 60°.  

1.  60°

2. 30°

3.  120°

4.  60°

5.  90°

Answer: Alex has $77 more than Amy

Explanation:

Draw a vertical number line. Plot -28 and 45 on this number line. Also, plot the number 0. Note the distance from -28 to 0 is 28 units. Then from 0 to 45 is another 45 units.

Overall, the distance is 28+45 = 77 units. This is the distance between the points -28 and 45 on the number line. It indicates Alex has $77 more compared to Amy. Effectively, Amy has $0 right now, but she's in debt $28. If we ignored the debt temporarily, then Alex has $45 more compared to Amy's balance of $0. Then we tack on the debt of 28 to bump to $77.

Another way to see this is to consider that Amy somehow gets $28. That 28 dollars is then immediately paid back to bring the balance back to $0. Then we'll tack on the $45 to get to 45+28 = 77.

Answer:

the factored form is 5(y + 8z)

Step-by-step explanation:

Because 5 divides evenly into both 5y and 40z, the GCF is 5 and the factored form is 5(y + 8z)

Answer:

k = 7

Step-by-step explanation:

The median is the middle value of the data arranged in ascending order.

If there is no exact middle value then the median is the average of the 2 values either side of the middle.

5 , k + 3 , 2k + 1 , 3k - 2 , 26 , 31

                          ↑ middle

Then

[tex]\frac{2k+1+3k-2}{2}[/tex] = 17 ( multiply both sides by 2 to clear the fraction )

5k - 1 = 34 ( add 1 to both sides )

5k = 35 ( divide both sides by 5 )

k = 7

The value of k is 7 if 5, k+3, 2k+1,3k-2, 26, and 31 are in ascending order and the median of the data set is 17.

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

We have:

5, k+3, 2k+1 ,3k-2, 26 and 31 are in ascending order

The median of the data set is 17.

The mid-terms are 2k+1 ,3k-2

(2k + 1 + 3k - 2)/2 = 17

5k -1 = 34

5k = 34 + 1

5k = 35

k = 35/5

k = 7

Thus, the value of k is 7 if 5, k+3, 2k+1,3k-2, 26, and 31 are in ascending order and the median of the data set is 17.

Learn more about the median here:

brainly.com/question/21396105

#SPJ5

Answer:

It's x² -12xi-12x

Step-by-step explanation:

You always do ax²+bx+c

Answer:

Length is 30ft, area is 600ft squared

Step-by-step explanation:

Answer:

y = (4/3)x - 2/3

Step-by-step explanation:

From (-6, -2) to (-3, 2) we see the x-component changing by 3 units and the y-component by 4 units.  Thus, the slope of this new line is

m = rise / run = 4/3.  

Let's focus on the point (-3, 2).  Here x = -3 and y = 2.  Plugging these three values into the slope-intercept form of the equation of a line, we get:

2 = (4/3)(2) + b.

Then 2 = 8/3 + b, or 6/3 = 8/3 + b.  Thus, b = 6/3 - 8/3, or -2/3.

The equation of the desired line is y = (4/3)x - 2/3

Answer:y=4/3x+6

Step-by-step explanation:

Step-by-step explanation:

if I understand your text right, we are looking at the line going through the points (0, 2) and (5, 3).

the slope is in a line equation always the factor of x.

anyway, it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point on the line to another.

so, we are simply going from (0, 2) to (5, 3).

x changes by +5 (from 0 to 5).

y changes by +1 (from 2 to 3).

so, the slope is y/x = 1/5.

Answer:

B. [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

Lets solve for x:

We know the ratio is 1:3

1x+3x = 52

4x = 52

x = 13

Since the ratio is 1:3:

13(3) = 39

13:39

Which makes 39 the larger number

Answer:

16/3

Step-by-step explanation:

formula :

p = kq

k = 8/3

so that is k

it will be like this "p = 8/3 x"

p = 8 × 2 / 3

p = 16/3

cant divide 3 with 16.

so, "p = 16/3" is the answer

.,........................

========================================================

Explanation:

Angles A and B are supplementary which mean they combine to form a straight line. This further means the angles add to 180.

A+B = 180

(8x-27) + (4x+3) = 180

(8x+4x) + (-27+3) = 180

12x-24 = 180

12x = 180+24

12x = 204

x = 204/12

x = 17

Use this x value to find angles A and B

Note how A+B = 109+71 = 180 to help verify the answer.

Answer:

109

Step-by-step explanation:

supplementary angles equals 180 degrees

8x-27+4x+3=180

12x-24=180

12x=204

x=17

Then you put the 17 where the x is

8(17)-27=109

Answer:

4.5 + 19.75 = 24.25

Find your missing digits with the equation above

Answer:

(4w+1)-(8w+6)

Step-by-step explanation:

Hope this helps :)

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

The distance between points, P and Q can be evaluated by the Pythagoras theorem as follows;

Therefore, a point whose distance from both P and Q is exactly 13 is the midpoint of PQ.

Therefore,

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

Read more:

https://brainly.com/question/18049211

Answer:

33

Step-by-step explanation:

3*4*2.75=33

Answer:

(-9, 5)

Step-by-step explanation:

1. Find the equations of both lines (y = mx +b).

For the table on the left, we can see that the y-intercept is 23 (at x=0, y=23). Hence, b = 23. We can also see that the y-value for the left table increases by increments of 2, meaning that the slope (m) will be 2. Thus:

f1(x) = 2x + 23

For the right table, do the same thing. The table tells us that when x = 0, y = -58 (so b = -58). We also see that the y-value DECREASES in increments of 7, meaning that the slope, m = -7. Thus,

f2(x) = -7x - 58

2. Set the equations equal to each other to find the x-value at which the two equations will intersect.

2x + 23 = -7x - 58

9x = -81

x = -9

3. Plug your newfound x-value into any of the two equations to find the y-value at which both equations will intersect.

y = 2x + 23

y = 2(-9) + 23

y = 5

OR

y = -7x - 58

y = -7(-9) - 58

y = 5

ANSWER: At the point (-9, 5), the two lines intersect. Hence, the solution to the equation is (-9, 5).

Answer:

x = -9 and y =. 5

Step-by-step explanation:

(-2, 19) and (-1, 21)

Slope: (21-19)/(-1- -2) = 2

y-intercept = 21 - (2)(-1) = 23

a) y =2x + 23

(-2,-44) and (-1,-51)

Slope: (-51- - 44)/(-1- -2) = -7/1 = -7

y-intercept: -44-(-7)(-2)=-58

b) y = -7x - 58

Substitute y in equation a.

-7x-58 = 2x + 23

-9x = 81

x = -9

Substitute X by -9 in equation b: y = -7(-9) - 58= 5

y = 5

Answer:

the answer is c and the entire equation means that the tickets each cost $15 and the service fee is $12

Answer:  x = 200 km

Step-by-step explanation:

Distance(x) = Speed(s) x Time(t)

t is in hours

x=s*t

At 75km/h:  75*t = x

At 80km/h:  80*(t-(10/60)) = x  [the -(10/60) is the 10 minutes saved, in hours]

We know the distance, x, is the same, so we can set these equal to each other:

75*t = 80*(t- (10/60))

75*t = 80*t - 13.3333

-5*t = -13.3333

t = 2 2/3 hours

Both situations should give the same distance with 2 2/3 and 2 2/3 - :

x = (75 km/hr) x ( 2 2/3 hr)= 200 km

x = (80 km/hr) x (2 2/3 - 1/6 hr) = 200 km

Answer:

6.8h

Step-by-step explanation:

5 tasks in 34h

So 1 task is taking 34/5 h

34/5 = 6.8h

1 task is taking 6.8h to complete

Answer:

only D as the correct answer

Step-by-step explanation:

The correct quadratic could not be B or C, because the negative sign in each indicates that the parabola opens down, which is not what we see here.

A is not appropriate either, because of the (x + 2)^2; that + sign tells us that the vertex lies 2 units to the left of the y-axis.

This leaves only D as the correct answer.