A family eats at a restaurant and the meal is $65, and they leave a tip of 20% of the price of the meal. What is the total with the meal and the tip?

Answer:

a) x = 14

b) The perimeter of △QRS is 77 units.

Step-by-step explanation:

a) Due to the question asking for a solution using the Triangle Proportionality Theorem, it is assumed that △RQS is similar to the smaller triangle inside it.

Let us define the point at which the line inside △RQS meets line RQ as T, and the point at which that same line meets line RS as V.

Hence, △RTV ~ △RQS.

According to the Triangle Proportionality Theorem:

[tex]\frac{RT}{RQ} = \frac{TV}{QS} = \frac{VR}{SR}[/tex]

Hence, we can substitute all values that we know from the diagram:

[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{TV}{17} = \frac{21 - 7}{21}[/tex]

After getting this information, all we have to do is simplify and solve the equation:

[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{21 - 7}{21}[/tex]

[tex]\frac{2x - 2}{2x + 11} = \frac{14}{21}[/tex]

[tex]\frac{2x - 2}{2x + 11} = \frac{2}{3}[/tex]

[tex]3(2x - 2) = 2(2x + 11)[/tex]

[tex]6x - 6 = 4x + 22[/tex]

[tex]6x - 4x = 22 + 6[/tex]

[tex]2x = 28[/tex]

[tex]x = 14[/tex]

To verify this answer, we can plug in the value of x into the equation:

[tex]\frac{2(14) - 2}{2(14) - 2 + 13} = \frac{2}{3}[/tex]

[tex]\frac{26}{39} = \frac{2}{3}[/tex]

[tex]\frac{2}{3} = \frac{2}{3}[/tex]

Hence, after verification, we can get the answer: x = 14.

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b) To find the perimeter of △QRS, all we have to do is to add all the lengths of the sides of △QRS together.

Hence, 2(14) - 2 + 13 + 17 + 21

= 28 - 2 + 13 + 17 + 21

= 77 units

Therefore, the perimeter of △QRS is 77 units.

Hope this helped!

Answer:

the answer is 4!!!!!!!!!!!!!!

Answer:

4

Step-by-step explanation:

LOL

Answer:

x  <  15

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

6

Step-by-step explanation:

6 inches of snow is an amount above ground, so it is represented by a positive integer.

Answer: 6

Answer:

Firstly, it was 4 inches

After snowing it becomes (4+6)= 10 inches;

From ground it is 10 inches of snow

So, 10 inches is the right answer.

Answer:

 x • (3x + y)

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x to the power of to +xy= x (3x+y)

Answer:

Yes, Sample information does indicate that a 2-liter bottle of Pepsi contains more than 250 calories  

Step-by-step explanation:  

Null Hypothesis [H0] : u < 250  

Alternate Hypothesis [H1] : u > 250 {One Tail}  

t = (x' - u) / [ sd / √n ]  

= (255 - 250) / (5.6 / √20)  

5 / (5.6 /√20)  

= 3.99  

As t ie 3.99 > t value 1.65 ie for one tail 95% confidence level. So, we reject the null hypothesis & conclude that it contains more than 250 calories.  

Answer:u have to be missing something

Step-by-step explanation:

Answer:

does the question have a graph or is it just the word problem?

here is the answer if its just the word problem

Step-by-step explanation:

y= -5x+4

hope I helped :)

Answer:

3(-4x+8)= now distribute it -12 x+24 so the answer will be that

Answer:

if you Simplify the expression it is 112x

(or 120-8x if 30x 24 is multiplication)

Answer:

It is also not B.

Step-by-step explanation:

I think that it might be D then.

50% chance lol

Answer:

x = 12

Step-by-step explanation:

5x - 30 = 2x + 6

3x = 36

x = 12

Answer:

x=12

Step-by-step explanation:

1) distribute values:

5x-30=2x+6

2) add 30 to both sides

5x=2x+36

3) subtract 2x from both sides

3x=36

4) divide by 3

x=12

Answer: 381

Step-by-step explanation:

Lets solve this in two parts, first the bottom one, then the upper one

Bottom one is a rectangle so 3*7*16=336

The one above is a triangular prism or something. You use base times height to find it. The base is 3*5/2=7.5

7.5 times height of 6 is 45.

Now add the 2 together to get 381

Answer:

Brand A price per diaper: 0.3

Brand B price per diaper: 0.3

Brand B is the better buy.

This can be found by taking the price of each brand and dividing it by the amount of diapers in each pack.

ex:

$11.49 / 36 = $0.32 (then round to nearest tenth)

Answer:

Step-by-step explanation:

Well since the polynomial is of not an even or odd sequence like the polynomial in the question is

[tex]3x^6+2x^4-x^3+7\\[/tex]

like the degree 6 is even the degree 4 is even but the degree 3 is odd so since the sequence breaks the polynomial above has no real x-intercepts meaning it has complex roots.

Answer:

D

Step-by-step explanation:

i think the 4th is the answer

Answer:

48

Step-by-step explanation:

12*4=w=48

Step-by-step explanation:

2800/7 = 400, ,

please you can see the upper paper which

can to solve this division math

Answer: 25x+10?

Step-by-step explanation:

Answer:

uikjhukcopllpp

Step-by-step explanation:

pp98ii9ijjhhhjigctuicico8

9514 1404 393

Answer:

  π/3

Step-by-step explanation:

The given integral does not exist. We assume there is a typo in the upper limit, and that you want the integral whose upper limit is (√3)/2.

It is convenient to make the substitution ...

  x = sin(y) . . . . so, y = arcsin(x)

 dx = cos(y)·dy

Then the integral is ...

  [tex]\displaystyle\int_0^{\sqrt{3}/2}{\dfrac{\cos{y}}{\sqrt{1-\sin^2{y}}}}\,dy=\int_0^{\sqrt{3}/2}{dy}=\left.\arcsin{x}\right|\limits_0^{\sqrt{3}/2}\\\\=\arcsin{(\sqrt{3}/2)}=\boxed{\dfrac{\pi}{3}}[/tex]

Answer:

108 votes

Step-by-step explanation:

There were 180 votes in the election and Jordan received 10% of them.

180 × 0.10 = 18

Jordan received 18 votes the first time. This year, he received 6 times as many votes.

18 × 6 = 108

Jordan received 108 votes this year.

Hope that helps.

Step-by-step explanation:

sqrty = y^(0.5)

1 / sqrty = y^(-0.5).

-1/5 = -0.2.

Therefore we have (1 / sqrty)^(-1/5)

= [y^(-0.5)]^(-0.2)

= y^[(-0.5)(-0.2)] (Law of indices)

= y^0.1

= 10th square root of y. (2nd option)

Answer:

1/sqrt 10th y

Step-by-step explanation:

1/(sqrt9)

19/76sprt

Answer: x= 1/2y+2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

Answer:

you should multiply 2 by 2.1 with that you would get the width of the dog run.

The width would be 4.2

Step-by-step explanation:

Answer:

W = 4.2 ft

Step-by-step explanation:

By what number must we multiply 5 to get the actual length 10.5 feet?

5x = 10.5 ft, or x = 2.1 ft, where x is the length

The following is true:  5 : 2 = L : W, or

  5      L

----- = -----

  2       W

Since we have L (10.5 ft) and need W, we solve the above equation for W:

5W = 2L, so that W = (2/5)L

Since L = 10.5 ft, W must be W = (2/5)(10 1/2 ft)

                    2           21

Then W = --------- * -------- ft = 21/5 ft = 4.2 ft                W = 4.2 ft

                     5           2

Answer:

1/3

Step-by-step explanation:

Answer:

m=3

Step-by-step explanation:

m= 7-1= 6

    5-3= 2

then you simplify    

    3

m= 1 which also equals 3

I am not very good at explaining on this but i hope this helps :)

Answer: D

Step-by-step explanation:

The best use of the associative and commutative properties to simplify the expression 2.4 + 13 - 5 + 3.6 + 7 would be:

D. (2.4 + 3.6) + [13 + 7 + (-5)]

By applying the associative property, we can group the numbers in a way that allows for easier computation.

Here, we group 2.4 and 3.6 together and 13, 7, and -5 together. This allows us to simplify each group separately and then add the results together.

Calculating the groups:

(2.4 + 3.6) = 6

[13 + 7 + (-5)] = 15

Now, we add the results together:

6 + 15 = 21

So, the simplified expression is 21. Therefore, option D provides the best use of the associative and commutative properties to simplify the given expression.

Learn more about the associative and commutative properties here:

https://brainly.com/question/29279825

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