Three friends have dinner at a restaurant. The total bill for dinner is $41. The friends want to leave a 15% tip, how much money do they need to leave including tip?

Answer:

hot dog= $2.25

juice= $1.50

Step-by-step explanation:

Let the price of a hot dog be $H and that of a juice be $J.

H +J= 3.75 -----(1)

2H +3J= 9 -----(2)

(1) ×2:

2H +2J= 7.5 -----(3)

(2) -(3):

2H +3J -(2H +2J)= 9 -7.5

Expand:

2H +3J -2H -2J= 1.5

J= 1.5

Substitute J= 1.5 into (1):

H +1.5= 3.75

H= 3.75 -1.5

H= 2.25

∴ The price of a hot dog and a juice is $2.25 and $1.50 respectively.

Answer:

[tex]a=60\\b=44\\c=76[/tex]

Step-by-step explanation:

You can write these equations to represent the problem:

[tex]a+b+c=180\\b+c=2a\\b=c-32[/tex]

Now, just solve it as a system of equations. I'll solve by substitution, starting from the bottom as b is already defined there.

[tex]b=c-32\\b+c=2a\\(c-32)+c=2a\\c+c-32=2a\\2c-32=2a\\a=c-16[/tex]

That's the middle equation done, now I'll do the top one:

[tex]b=c-32\\a+b+c=180\\a+(c-32)+c=180\\a+2c-32=180\\a+2c=212\\a=-2c+212[/tex]

Now we have just 2 equations with 2 variables. That's another system of equations, but this one is much easier to solve. Using substitution again:

[tex]a=c-16\\a=-2c+212\\c-16=-2c+212\\3c-16=212\\3c=228\\c=76[/tex]

Finally, we have one variable solved. Using the value of C, now we can solve for A:

[tex]c=76\\a=c-16\\a=76-16\\a=60[/tex]

Thats 2 done. Now, pick any equation that has all 3 variables and solve for B:

[tex]a=60\\c=76\\a+b+c=180\\60+b+76=180\\b+136=180\\b=44[/tex]

All 3 variables done.

[tex]a=60\\b=44\\c=76[/tex]

Now, we can confirm that they're correct by checking with the original equations:

[tex]a+b+c=180\\60+44+76=180\\180=180\\\\b+c=2a\\44+76=2(60)\\120=120\\\\b=c-32\\44=76-32\\44=44[/tex]

They all work fine.

Answer:

56

Step-by-step explanation:

Let the angle be " x ".

Complement of the angle = ( x - 22 )

To find : x = ?

x + x - 22 = 90

2x - 22 = 90

2x = 90 + 22

2x = 112

x = 112 / 2

x = 56

Therefore, the angle is 56.

Adjacent angles will be same

[tex]\\ \sf\longmapsto <N=<P[/tex]

[tex]\\ \sf\longmapsto 6y=8y-16[/tex]

[tex]\\ \sf\longmapsto 8y-6y=16[/tex]

[tex]\\ \sf\longmapsto 2y=16[/tex]

[tex]\\ \sf\longmapsto y=8[/tex]

Answer:

[tex]y = 8[/tex]

Step-by-step explanation:

If two sides of a triangle is equal the opposite interior angles are also equal.

Therefore,

[tex]6y = 8y - 16 \\ 16 = 8y - 6y \\ 16 = 2y \\ \frac{16}{2} = \frac{2y}{2} \\ 8 \degree = y[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

kikjnknj

Step-by-step explanation:

Answer:

2b + 3n = £15.50

4b + 1n = £13.50

2 ( 2b + 3n =  15.50 )

4b + 6n = 31.00

    4b + 6n =  31.00

-    4b +  1n = 15.50

            5n  = 15.50

              n  =  3.1

subtitue n in to the equation

2b + 9.3 = £15.50

2b          = £6.20

b             = 3.10p

Step-by-step explanation:

both the bracelets and necklace cost £3.10

The cost of one bracelet is $2.50

b = cost of the bracelet

n = costs of necklace

⇒ 2b + 3n = 15.50

⇒ 4b+1n = 13.50

Multiply the first equation by -2

⇒ -4b - 6n = -31

⇒ 4b + n = 13.50

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

-5n = -17.50

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

Divide each side by -5

⇒ -5n / -5 = -17.5 / -5

⇒ n = 3.50

Now we can find b

⇒ 4b + n = 13.50

⇒ 4b + 3.50 = 13.50

⇒ 4b + 3.50 - 3.50 = 13.50 -3.50

⇒ 4b = 10

Divide by 4

⇒ 4b / 4 = 10/4

⇒ b = 2.50

The cost of one bracelet is $2.50.

A system of equations comprises two or more equations and seeks common solutions to the equations.

Learn more the system of equations about here: brainly.com/question/14323743

#SPJ2

Part A.)

12.1 / 2.2 = 5.5

So, the elevation of Winston's house is 5.5 times greater than the elevation of the ocean at 2 p.m.

Part B.)

My apologies if any of the following equations is not the right number, I had looked up the equation for the right number.

12.1 x 3.5 = 42.35

So the elevation of Tammy's house is 42.35.

Part C.)

42.35 / 2.2 = 19.25

the elevation of Tammy's house is 19.25 times greater than the elevation of the ocean.

Part D.)

Had to look for the number again. Next time, could you possibly make sure that all of the numbers are here? It makes it a lot easier.

-2.5 x 20.2 = -50.5

Winston reached an elevation of -50.5 feet.

Part E.)

-50.5 / 2 = -25.25

He had stopped at -25.25.

Again, my apologies if some numbers are incorrect. You did not give them, so I went looking for them.

Answer:

-4/9

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

C: 16 is a constant

B:3

A: 4

Answer: C: 16 is a constant

B:3

A: 4

Step-by-step explanation:

Answer:

A)

6x - y = 8

3x + 2y = 9

(Graph is attached for you⤴⤴⤴)

Step-by-step explanation:

Line m ordered pairs = (-4,-32), (2,4),

(5, 22)

Line n ordered pairs = (-5,12), (1,3), (5,-3)

Use this formula⤵⤵⤵

[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]

For line m, we'll use (2,4) and (5,22):

22 - 4 = 18

5 - 2 = 3

18 ÷ 3 = 6

Slope of line m = 6

For line n, we'll use (1,3) and (5,-3):

-3 - 3 = -6

5 - 1 = 4

Slope of line n = -6/4 or -3/2

We'll turn all the options to slope-intercept form, so we can tell which has the slopes we need.

A) - Subtract 6x on both sides to get

-y = -6x + 8, then flip all the signs to get y = 6x - 8.

- Subtract 3x on both sides to get 2y = -3x + 9, then divide 2 on both sides to get y = -3/2 x + 9/2.

B)

- Subtract 6x on both sides to get

y = -6x - 8.

- Subtract 3x on both sides to get

-2y = -3x + 9, then divide -2 on both sides to get y = -3/2 x - 9/2.

C)

- Add 6x on both sides to get -y = 6x - 8, then flip all signs to get y = -6x + 8.

- Add 3x on both sides to get 2y = 3x + 9, then divide 2 on both sides to get

y = 3/2 x + 9/2.

D)

- Subtract 6x on both sides to get

-y = -6x - 8, then flip all signs to get

y = 6x + 8.

- Add 3x on both sides to get -2y = 3x + 9, then divide -2 on both sides to get

y = -3/2 x - 9/2.

Hope this helps :)

Answer:

9

Step-by-step explanation:

Well since 11 of the pirates had eyepatches, and 11 is greater than 9, all 9 of the pirates that had cutlasses had eyepatches as well. I don't know if this is completely correct but it's the only thing that makes sense to me.

Answer:

5/16

Step-by-step explanation:

Answer:

what is it

Step-by-step explanation:

Answer:

317 is the finally awnser

Answer:

Step-by-step explanation:

g(3)= (3+1)/(3-1)= 4/2= 2

f(2)= 3(2)-7 = 6 - 7 = -1

answer is a. -1

We know that f(x) = 12x + 12

f(1) = 12 * 1 + 12= 24

f(0) = 12*0 + 12 = 12

The formula of the average rate of change is : f(1) - f(0)  /  (1 - 0)

(24 - 12) / 1 = 12/1 = 12

So the average rate of change is 12

Good Luck

9514 1404 393

Answer:

  n = 3

Step-by-step explanation:

In order for 3 × 3 = 9 to be a factor of both numbers, we must have ...

  n = 3

D. x>1 or x<7

all the others don't fit

Answer:

9a+18=9

9a=-9

a=-1

Step-by-step explanation:

Y-intercept - 4

Slope - 3

Slope intercept form - y=3x + 4

Hope it's correct and it helped:)

Answer:

around 5 books

Step-by-step explanation:

hope this helpsss :D

Answer:

Step-by-step explanation:

given A(-1, 2), B(-3, 4), C(-2, 5)

after translating by (4, 4)

points are A(-1 + 4, 2 + 4),  B(-3 + 4, 4 + 4), C(-2 + 4, 5 + 4)

A(3, 6), B(1, 8), C(2, 9)

to rotate 90° counter clockwise (x, y) ----> (-y, x)

now it is rotated around point A(3, 6).That means A remains same and we need to find new coordinates of B and C.  To find B and C let us make origin as A and find B ,C coordinates from it.

B'(1 - 3, 8 - 6) = (-2, 2)

C'(2 - 3, 9 - 6) = (-1, 3)

now it becomes (-y, x)

B'(-2, -2)

C'(-3, -1)

now we have to move origin from (3,6) to (0,0) again.

so B'(-2 + 3, -2 + 6) = (1, 4)

C'(-3 + 3 , -1 + 6) = (0, 5)

now reflection over y axis means (x, y) --> (-x, y)

A'(-3, 6)

B'(-1, 4)

C'(0, 5)

it is different from the options

but this is the process, tell me if you find any step different from the question

see the figure below

Answer:

g(x) = (x - 1)³

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

Here g(x) is the graph of f(x) shifted 1 unit to the right , then

g(x) = (x - 1)³

Answer:

x = 20

Step-by-step explanation:

The 2 given angles are adjacent on a straight line and sum to 180° , then

123 + 2x + 17 = 180

140 + 2x = 180 ( subtract 140 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Slope:

M = -1

Slope intercept-form:

y = -x + 1

Answer:

18 = 2 x 3²

Step-by-step explanation:

Factors of 18: 1, 2, 3, 6, 9, 18

Prime factorization: 18 = 2 x 3 x 3

Answer:

55

Step-by-step explanation:

You multiply 5 on both sides of the ratio, and you get 40 children : 15 adults. Adding that up, you would get 55 people.

Answer:

Step-by-step explanation:

Write and solve an equation of ratios.  The given ratio is 8:3.  The number of children is 40 and that of adults is 40 - c.  Note that c + (40 - c) = 40.

Solve the following equation of ratios for c:         8        40

                                                                               ---- = ----------

                                                                                3          a

Cross multiplying, we get 8a = 120, of 15.  Then a = number of adults = 24.

Here a = 15 and c = 40.  Check the ratio 40/15; does it equal 8/3?  YES

The total number of people at the pool is 40 + 24, or 64