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3 years ago

Complete the equation of the line through (6,-6) and (8,8)

Mathematics

1 answer:

noname [10]3 years ago

6 0

Answer:

y = 7x - 48

Step-by-step explanation:

To find the equation of the line

y = mx + c

Step 1 : find the slope

( 6, -6) ( 8, 8)

x_1 = 6

y_1 = -6

x_2 = 8

y_2 = 8

Insert the values into

m =( y_2 - y_1) /( x_2 - x_1)

m - slope

m = (8 - (-6)) / (8 -6 )

m = 8 +6 / 8 - 6

m = 14 / 2

m = 7

Step 2: substitute slope into intercept form equation

y = mx + c

y = 7x + c

Step 3: substitute either point into the equation in step 2

y = 7x + c

Let's pick point ( 8,8)

y = 8

x = 8

y = 7x + c

8 = 7(8) + c

8 = 56 + c

8 - 56 = c

c = 8 - 56

c = -48

Substitute the value of c back into the equation

y = 7x + c

y = 7x - 48

The equation of the line is

y = 7x - 48

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Maximizing revenue. Edwards University wants to determine what price to charge for tickets to football games. At $18 per ticket,

Papessa [141]

Answer:

New price is $12.75

New attendance is 57500

Step-by-step explanation:

For starters, we use the relation.

18 - 3x

Since we don't know the number of times we're expected to deduct $3 from the price.

Again, we have 40000 + 10000x on another hand. Question says to add 10000 people everytime $3 is deducted.

Since (40000 + 10000x) is the number of people, we multiply it by $4.50, the average amount each person spends is then gotten to be

(18 - 3x) (40000 + 10000x) + (40000 + 10000x) (4.5) = 0

Expanding the bracket, we have

[720000 + 60000x - 30000x²] + [180000 + 45000x] = 0, solving further, we have

900000 + 105000x - 30000x² = 0 or

-30000x² + 105000x + 900000 = 0

Then, we find the maximum of a quadratic, by finding the axis of symmetry. Use x = -b/2a

x = -105000 / 2 * -30000

x = -105000 / -60000

x = 1.75

From our earlier equations, the new price then is

18 - 3(1.75) = 18 - 5.25 = $12.75

The new attendance also is

40000 + 10000(1.75) =

40000 + 17500 = 57500

7 0

3 years ago

Please Help Me!

alex41 [277]

Answer:

✔️2 sets of corresponding angles

<D and <S

<R and <L

✔️2 sets of corresponding sides

DR and SL

RM and LT

Step-by-step explanation:

When two polygons are congruent, it implies that they have the same shape and size. Therefore, their corresponding angles and sides are congruent to each other.

When naming congruent polygons, the arrangement of the vertices are kept in a definite order of arrangement.

Therefore, Given that polygon DRMF is congruent to SLTO, the following angles and sides correspond to each other:

<D corresponds to <S

<R corresponds to <L

<M corresponds to <T

<F corresponds to <O

For the sides, we have:

DR corresponds to SL

RM corresponds to LT

MF corresponds to TO

FD corresponds to OS.

We can select any two out of these sets of corresponding angles and sides as our answer. Thus:

✔️2 sets of corresponding angles

<D and <S

<R and <L

✔️2 sets of corresponding sides

DR and SL

RM and LT

4 0

3 years ago

Given f of x equals 5 times x minus 6 for x less than 3, equals x squared for x between 3 and 5 inclusive, and equals 2 times x

konstantin123 [22]

Answer:

D. 5 for x less than or equal to 4, equals 2x for x between 4 and 6 including 6, and equals 4 for x greater than 6 Domain: All real numbers.

Step-by-step explanation:

Find the complete diagram attached

First we need to get the derivative of the functions

For the function f(x) = 5x - 6

Using the formula

If f(x) = axⁿ

f'(x) = naxⁿ⁻¹

For the function f(x) = 5x - 6

f'(x) = 1(5)x¹⁻¹

f'(x) = 5x⁰

f'(x) = 5

For the function f(x) =x²-2

f'(x) = 2x²⁻¹

f'(x) = 2x

For the function f(x) = 4x+10

f'(x) = 1(4)x¹⁻¹

f'(x) = 4x⁰

f'(x) = 4

Get the domain

The domain is the value of the input variable x for which the functions exists. For the functions given, the domain will be on all real numbers i.e the functions will exists for any value of x on the number line.

Hence Option D is correct

7 0

3 years ago

Trapezoid WKLX has vertices W(2, −3), K(4, −3), L(5, −2) , and X(1, −2) . Trapezoid WKLX is translated 4 units right and 3 uni

guapka [62]

Okay, so first of all, if the trapezoid was translated right 4,
Then all the (x)'s should be 4 more than the original value
For example: (2,-3) → (6,-3)
Now since the Trapezoid was translated down 3,
Then all the (y)'s should be 3 less than the original value
For example: (2,-3) → (2,-6)
Now do this to all the Vertices
 $(6,-6)(8,-6)(9,-5)(5,-5)$
Final Answer: Option 2

7 0

3 years ago

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Convert $98.60 to pounds

MariettaO [177]

Answer:

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Step-by-step explanation: HOPE THIS HELPS

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