Point (8 5) was translated as follows (8 5) (2.9) A student wrote the algebraic rule to desenbe the translation

What is a solution to the system? y = x^2 + 2x - 15 y – 4x = -12

astra-53 [7]

9514 1404 393

Answer:

(x, y) = (-1, -16) or (3, 0)

Step-by-step explanation:

Perhaps you want to solve the system of equations ...

y = x^2 +2x -15
y -4x = -12

Substituting the first expression for y into the second equation gives ...

x^2 +2x -15 -4x = -12

x^2 -2x -3 = 0 . . . . . . . . add 12

(x -3)(x +1) = 0 . . . . . . . factor

Solutions are the values of x that make the factors zero: x = 3, x = -1.

The corresponding values of y are ...

y = -12 +4x

y = -12 +4{-1, 3} = -12 +{-4, 12} = {-16, 0}

The solutions to the system are ...

(x, y) = (-1, -16) or (3, 0)

5 0

3 years ago

A Best Eastern Motel is a regional motel chain. Its rooms rent for $90 per night, on average. The variable cost is $40 a room pe

Vlad1618 [11]

Answer: break even point (y) = 24000

Step-by-step explanation:

This is quite simple to solve,

We will take a step by step calculation.

let us begin;

Given that the Room rent per night is = $90

Also the variable cost per night = $40

Total fixed cost = $1200,000

Now we are asked to solve for the Break even point;

Remember that at break even point, the Revenue = cost

Say the required revenue from renting y rooms R = $90y

The cost of renting y rooms = C = $ (40y + 1200,000)

therefore from this we have the Break even point as

$90y = $ (40y + 1200,000)

where y = 24000

cheers i hope this helps!!!!!!

4 0

3 years ago

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Danny charges $40 for 4 hours of swimming lessons, Martin charges $85 for 5 hours of swimming lessons. Who offers a better deal?

Ratling [72]

Answer:

Danny does

Step-by-step explanation: 40 / 4 = 10

85 / 5 = 17

10 is less than 17 meaning that Danny is offering a better deal.

Hope this helps!

4 0

3 years ago

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Which two numbers add up to ___ and multiply to ___?

Assoli18 [71]

1. multiply to -18 add to -17 = Multiplying -18 and 1 will give -18 as the result and then on adding -18 and + 1 the result comes to -17
2. multiply to 36 add to -13 = Multiplying -9 and -4 will give -36 as the result and then on adding -9 and -4 the result comes to -13
3. multiply to -24 add to -5= Multiplying -8 and +3 will give -24 as the result and then on adding -8 and +3 the result comes to -5
4. multiply to -18 add to 7= Multiplying +9 and -2 will give -18 as the result and then on adding +9 and -2 the result comes to 7
5. multiply to -36 add to 9= Multiplying +12 and -3 will give -36 as the result and then on adding +12 and -3 the result comes to 9
 6. multiply to 24 add to 10= Multiplying +6 and +4 will give 24 as the result and then on adding +6 and +4 the result comes to 10
 7. multiply to 18 add to -9= Multiplying -6 and -3 will give -18 as the result and then on adding -6 and -3 the result comes to -9
 8. multiply to -36 add to -16= Multiplying -18 and +2 will give -36 as the result and then on adding -18 and +2 the result comes to -16

3 0

3 years ago

Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negati

IceJOKER [234]

Answer:

The correct option is;

A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25

Please find attached the graphs of the table data

Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x, -3, -1, 2, 5, 10

y, -4.5, -3.0, -1.5, 0.0, 1.5

-4.5/-3 = 1.5 ≠ -3.0/-1 = 3

No direct variation

Table 2

x, -5.5, -4.5, -3.5, -2.5, -1.5

y, 10, 8, 6, 4, 2

10/(-5.5) = -20/11 ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3

x, -5.5, -5.5, -5.5, -5.5, -5.5

y, -3, -1, 2, 5 , 10

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x, -3, -1, 2, 5, 10

y, -7.5, -2.5, 5.0 , 12.5, 25

-7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists

8 0

3 years ago

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