How much tip should you leave if you want to tip 23% at Applebee's on a $27.31 bill?

Angle APR is vertical with Angle SPL. If Angle APR = 13x - 30, and Angle SPL = 3x + 70, what is the value of x?

Luba_88 [7]

Answer:

The value of $x$ is 10.

Step-by-step explanation:

If APR and SPL are vertical angles, then we get that $\angle APR = \angle SPL$ . Given that $\angle APR = 13\cdot x -30$ and $\angle SPL = 3\cdot x + 70$ , we find that the value of $x$ is:

$13\cdot x - 30 = 3\cdot x +70$

$10\cdot x = 100$

$x = 10$

The value of $x$ is 10.

6 0

3 years ago

Two car washes charge a basic fee plus a fee based on the number of extras that

mezya [45]

Answer:

a. The first car wash charges more for the basic fee

b. 6 extras must be chosen for the total cost to be the same

Explanation:

The complete question is shown in the attached diagram

The general form of the linear equation is:

y = mx + c where m is the slope and c is the y-intercept

The y-intercept represents the initial value which, in the given problem, is the basic fee

For the first car wash, we are given the equation:

y₁ = x + 9

Now, we will start by getting the equation for the second car wash:

1- getting the slope:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{12-9}{4-2}=1.5$

The equation now is: y = 1.5x+c

2- getting the y-intercept:

To get the y-intercept, we will simply choose a point, substitute with it in the equation from 1 and solve for c. I will use point (2,9)

y = 1.5 x + c

9 = 1.5 (2) + c ............> c = 6

The equation for the second car wash is:

y₂ = 1.5x + 6

Part 1:

As mentioned above, the y-intercept represents the basic fee

For the first car wash:

y₁ = x + 9 ................> The basic fee is $9

For the second car wash:

y₂ = 1.5x + 6 ..............> The basic fee is $6

It is clear that the basic fee for the first car wash charges more for the basic fee

Part 2:

In both equations, x represents the number of extras. We want the total cost to be the same. So, we will simply equate y₁ and y₂ and solve for x

x + 9 = 1.5x + 6

1.5x - x = 9 - 6

0.5x = 3

x = 6

Let's verify:

For x = 6:

y₁ = x + 9 = 6 + 9 = $15

y₂ = 1.5x + 6 = 1.5(6) + 6 = $15

Total cost is the same. This means that 6 extras must be chosen for the total cost to be the same

Hope this helps :)

6 0

3 years ago

What is the next number on sequence 2 7 8 3 12 9

Kamila [148]

The term of this sequence is:
-(17/30)n^5+(113/12)n^4-(173/3)n^3+(1915/12)n^2-(5813/30)n+85 
Therefore,term number 7 is:-146/1=-146

8 0

3 years ago

Ajay bought a fan and a heater for rs 4000. He sold the fan at a profit of a 25% and the heater at a loss of 5%. If he gained 7%

Alborosie

Answer: Heater -Rs 2400; Fan- Rs 1600

Step-by-step explanation:

Given

Ajay bought a fan and a heater for Rs 4000

Suppose the price of fan is x and that of heater is 4000-x

Profit on the fan is $0.25x$

Loss on heater is $0.05\times (4000-x)$

Total profit is 7% i.e. $0.07\times 4000$

$\therefore 0.07\times 4000=0.25x-0.05(4000-x)\\\Rightarrow 280=0.25x-200+0.05x\\\Rightarrow 480=0.3x\\\Rightarrow x=1600$

Thus, the price of heater is $4000-1600=Rs.\ 2400$

Price of fan is $Rs.\ 1600$

Price of heater is $Rs.\ 2400$

8 0

3 years ago

There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 4 books are selected at random without r

mixer [17]

Answer:D

Step-by-step explanation:

This is combination.

If 4 books selected out of eight book in the shelf:

(4 combination 8)= 70

For hardback selection:

Then selection of 4 books out of the hardback, it means there is no paperbach will be:

(4 combination 6)= 15

So , if at least one paperback selected will be : 70-15

That is 55

4 0

3 years ago