Find the distance between two points.
P(5\sqrt{x} 3,7\sqrt{x} 5),Q(\sqrt{x} 3,-\sqrt{x} 5)

The miles for which  Austin drove the truck  is 141 miles

It is given that Austin rents a truck for one day

The daily rental base fee of the truck is $17.99

It is also given that additional charge of 73 cents per mile is charged.

It is also to be noted that 1$ =100 cents

Therefore, 73 cents in the form of dollar is 0.73$

Now it is given that total bill that is paid is $120.92

Now the total number of miles travelled by Austin is total bill minus the base fee and 73 cents multiplied by miles

Let the miles travelled by Austin be 'x'

Therefore, Miles travelled by Austin = 120.92$-17.99$

                                     0.73 x =(120.92 -17.99)  $                      

                                     x= 102.93 / 0.73

                                     x=141

Hence, the miles for which Austin drove the truck is 141 miles

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Answer:it's the second option

Step-by-step explanation:

-x is already -1 so why would factoring it make it -1 again

The nth term of the given sequence is 4n - 1.

So,

Therefore, the nth term of the given sequence is 4n - 1.

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There are 5 possible arrangements to make seat all 22 children.

The smallest number of tables Ms. Francis is 10 tables.

Total number of children at the party = 22

When we picturize the scenario, each child need to get a side of the table.

So at least 22 sides should be there after arranging it into rectangles. Also the square card tables are arranged side to side to get rectangle rows.

It is also said that there can be multiple rows. So combining all these points, we can consider a row of 10 tables. Then the the squares on the ends contribute a total of 6 sides and the remaining 16 seats can be arranged by 8 square tables in between the end square tables. So a total of 10 square table is required to make a rectangle in one row.

For making 22 seats in 2 rows, the 4 square tables on the ends contribute 8 seats. For the remaining 12 seats add 7 square tables in each row, that is a total of 14 square tables. That is, for 2 rows, the square tables required is 14 + 4 = 18.

Similarly, for 3 rows, a total of 24 square tables are required.

For 4 rows, a total of 28 tables and for 5 rows, a total of 30 tables are needed.

We cannot make a 6 row because it will be same as a 5 row.

So 5 different arrangements can be made to seat all 22 children.

They are:

1 row → 1 x 10 = 10 tables

2 rows → 2 x 9 = 18 tables

3 rows → 3 x 8 = 24 tables

4 rows → 4 x 7 = 28 tables

5 rows → 5 x 6 = 30 tables

The smallest number of tables that Ms. Francis needs to rent is, therefore, 10 tables.

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Answer:

hello

Step-by-step explanation:

hi

MSA

my milkshake brings all the boys to the yard yeah right its better than yours yeah right its better than yours

[tex]scale \: from \: b \: to \: a = \frac{3}{2} \\ x = \frac{2}{3} \times 10.5 = 7[/tex]

Figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

If a figure is the scale copy of another figure, the corresponding side lengths of both figures would be proportional to each other, which means their ratios would be the same.

From the figure given, the ratios of their side lengths are:

18/9 = 2

12/12 = 1

30/15 = 2

This shows that their ratios are not the same.

Therefore, we can conclude that figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

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The length of BE is 15 cm.

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Answer:

(-1, 0) and (8, 9)

Step-by-step explanation:

x² - 6x-7 = x + 1

x² - 7x - 8 = 0

(x - 8)(x + 1) = 0

x = -1, 8.

When x = - 1, y = 0

and x = 8, y = 9

Answer:

3×a-3×2=3a-6

3a-6=3a-6 proved

Answer:

One could be: 8*8 times 4*4

Another could be: 8 to the second power times 4 to the second power

A third way to write this could also be: 8*4*8*4

Step-by-step explanation:

Hope its helpful

Answer:

A

Step-by-step explanation:

43987-32650= 11337

And it’s more

plss give your self a answer

Answer:

X = 9287.5

Step-by-step explanation:

Solving steps

7.5+ 9287=x+7

Calculate

9294.5=x+7

Move the terms

-x=7-9294.5

Calculate

-x=-9287.5

Change the signs

Solution

X = 9287.5

The price of the jacket is $23.75

Let m be the price of a jacket and n be the price of pair of pants.

The total cost of a jacket and a pair of pants was $52.37

So, we get an equation,

m + n = 52.37              ................(1)

Also, the price of the jacket was $4.87 less than the pair of pants

So, we get an equation,

m = n - 4.87               .............(2)

Substitute above value of m in equation (1)

⇒ (n - 4.87) + n = 52.37

⇒ 2n - 4.87 = 52.37

⇒ 2n = 52.37 + 4.87

⇒ 2n = 57.24

⇒ n = 28.62

This means, the cost of a pair of pants is $28.62

Substitute above value of n in equation (2)

⇒ m = n - 4.87

⇒ m = 28.62 - 4.87

⇒ m = 23.75

This means, the cost of a jacket is $23.75

Therefore, the price of the jacket is $23.75

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The term containing b^6 is -210 a^6 b^6

The given expansion can be solved by using the Binomial expansion

The binomial expansion for two terms (a + b)  raised to the power n is given by

(a+b)^n = Σ[tex]a^{n-k} * b^k[/tex] * n!/k!(n-k)!

To find term contain b^6 we use the formula

Use the formula T r+1 =(−1) ⁿCr [tex]a^{n-r} * b^r[/tex]

Putting n=10,

we get 10-r=6

             r=4

Therefore,

it is the fourth term ,

T = (-1)^3  10!/4!6! [tex]a^{10-6} * (b^2)^4[/tex]

   = -1  x   10x9x8x7/4x3x2=-210 [tex]a^6 b^6[/tex]

Hence the term containing b^6 is -210 a^6 b^6

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Answer:

Hello,

Step-by-step explanation:

a)

[tex]x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\[/tex]

b)

[tex]x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\[/tex]

Answer:

Step-by-step explanation:

You want the speed and speed multiplier for Jet B given that it makes a journey in 5 minutes that takes Jet A 2 hours for half the journey.

For the same distance, speed is inversely proportional to time.

  speed multiplier = (speed B)/(speed A) = (time A)/(time B)

  speed multiplier = ((2 h)/(1/2))/(5 min)

  speed multiplier = (240 min)/(5 min) = 48

The speed of Jet B is 48 times that of Jet A:

  48(417 mph) = 20016 mph . . . . speed of Jet B

__

Additional comment

The time for the full trip by Jet A can be found using the proportion ...

  partial time/partial distance = total time/total distance

If the total distance is "1 unit", then this proportion is ...

  (2 h)/(1/2) = t/1 . . . . . where t/1 = t is the time for the full trip by Jet A

You will recognize the value (2 h)/(1/2) as the time value we used for Jet A in the above solution.

Answer:

500

Step-by-step explanation:

3+6=9
10-9=1

They sell 9 out of the 10 boxes. if each box has 500 balloons, then they have 500 left

Answer: 500 balloons

Step-by-step explanation: if you do 500 x 10 you get 5000 and then you do 3 x 500 + 6 x 500 then you get 4500 then subtract that from 5000

Answer:

I think Dessicant

Step-by-step explanation:

i hope it helped you if I'm right :D

The value of x is 3 and  -3 respectively.

Given that;

From equation (1)

4x+60 < 72  

First, collect like terms

4x < 72 - 60

subtract like terms

4x < 12

Make 'x' the subject

x < 12/ 4

x < 3

For equation (2)

14x +11 <-31

collect like terms

14x < -31 - 11

14x < -42

Make 'x' the subject

x < -42/ 14

x < -3

Thus. the value of x is 3 and  -3 respectively.

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3(n-10)=-7

Solve the equation in 2 step equation.

n=18.5

Given that 3(n-10)=7

step1: multiplication

Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.

3n-30=7

step2: adding 30 on both sides of the equation.

When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.

2n-30+30=7+30

2n=37

step3: divide the equation by 2.

Basically, dividing is the act of dividing anything into equal sections or groups.

[tex]\frac{2n}{2} =\frac{37}{2}\\ n=\frac{37}{2} or 18.5[/tex]

Therefore, n=18.5

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The probability that no Tails is achieved on flipping a fair coin for three consecutive times is [tex](\frac{1}{8})[/tex].

As per the question statement, we are to flip or toss a fair coin thrice consecutively.

We are required to calculate the probability that no Tails is achieved during the above mentioned event.

To solve this question, first let us calculate all the possible outcomes of flipping a fair coin thrice consecutively. [We will denote a Heads outcome as "H" and a Tails outcome as "T"]

The total number of outcomes can be given by the formula [tex](2^{n})[/tex], where "n" is the number of times, the coin is tossed.

Here, (n = 3), therefore, total number of outcomes in our case [tex]=(2^{3})=8[/tex].

These 8 outcomes can be listed as [tex][{(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}][/tex]

And among the above listed 8, our favorable outcome is (H, H, H), i.e., 1 favorable outcome of 8.

Hence, probability that no Tails is achieved on flipping a fair coin thrice consecutively = [tex]\frac{1}{8}[/tex].

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a dot plot can easily show all the data.

Step-by-step explanation:

In this example, a dot plot can easily show all the data. If the data set is very large (more than 100 values, for example) or if there are many different values that are not exactly the same, it may be hard to see all of the dots on a dot plot.

The cardinal number of (2, 4, 6, ..., 106) is 53.

The cardinal number of a set is the number of elements in the particular set.

We are given the set (2, 4, 6, ..., 106). As we can can clearly see, it is forming an Arithmetic Progression (AP).

Hence, let the number of elements or the cardinal number of the set be n.

Hence, according to the formula of AP, we can write,

2 + (n-1)(2) = 106

2(n-1) = 106 - 2

2(n-1) = 104

n - 1 = 104/2

n - 1 = 52

n = 52 + 1

n = 53

Hence, the cardinal number of the set is 53.

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((9×7)÷9−6)+13

(63÷9−6)+13

(7−6)+13

1+13

14

Answer:

9 X 7 / 9 - 6 + 13

we can cut 9

=7-6 + 13

=1+13

=14

As Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).

As given,

Regular working hours =40 hours

Overtime at the rate of (1.5 of regular hours) = 6 hours

Gross pay =$650

Let 'h' be the hourly rate

Required equation

40h + 6(1.5h) =650

⇒ 40h +9h=650

⇒49h=650

⇒h=$13.27(approximately)

Therefore, as Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).

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Answer:

What do you need help with?

Step-by-step explanation:

Answer: Our carpet calculator will help you determine your approximate floor area in square metres. Simply measure the length and width of each room to the nearest 10cm, i.e. 5.4m x 3.7m, then enter your totals into the calculator and hit the 'calculate' button at the bottom.  

For awkwardly shaped rooms (such as an L shape) divide the room into blocks, measure them separately and add them in as individual rooms.

Step-by-step explanation: