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Math!!

Answer:

a = 6

b = 2

Step-by-step explanation:

Here, we want to take all values of p up and all values of q down

From the division, 9

goes up and the term above comes down

We have all the following indices rule to use;

(a^x)^y = a^xy

a^x * a^y = a^x + y

a^x / a^y = a^x-y

Let us evaluate all p terms;

p^12/p^4 = p^8

Let us evaluate all q terms

q^16/q^10 * 1/q^2

= q^6/q^2 = q^4

Let us evaluate all number terms

We have;

2^4/-3^2 * 9/4^2

= 16/9 * 9/16 = 1

All

number terms canceled out

Now, let us work with the exponents;

For the p terms;

p^8 = p^a+b

a + b = 8 •••••••••(i)

For the q terms;

q^4 = q^a-b

a-b = 4 ••••••••••(ii)

Add both equations

2a = 12

a = 12/2 = 6

For b;

a-b = 4

6-b = 4

b = 6-4

b = 2

Answer:

3(3a-6b+7c)

Step-by-step explanation:

Answer:

A. £147.10

B. 17 children

Step-by-step explanation:

Let

Number of children = x

Cost of hiring a bouncy castle = £4.70 * x + £86

What is the cost of the bouncy castle for 13 children

Cost of hiring a bouncy castle = £4.70 * 13 + £86

= £61.1 + £86

= £147.10

How many children went to the party when cost of hiring bouncy castle = £165.90

Cost of hiring a bouncy castle = £4.70 * x + £86

£165.90 = £4.70 * x + £86

165.90 = 4.70x + 86

165.90 - 86 = 4.70x

79.9 = 4.70x

x = 79.9/4.70

= 17

x = 17 children

Given:

[tex]R^2=0.92,a=8000,b=0.9[/tex].

Exponential regression model is

[tex]y_1\sim a(b)^{x_1}[/tex]

To find:

The exponential regression representing the population of Lazy Town as a function of time in years.

Solution:

Exponential regression model is

[tex]y_1\sim a(b)^{x_1}[/tex]       ...(i)

We have, [tex]a=8000,b=0.9[/tex].

Substituting [tex]a=8000[/tex] and [tex]b=0.9[/tex] in (i), we get.

[tex]y_1\sim 8000(0.9)^{x_1}[/tex]

Therefore, the exponential regression representing the population of Lazy Town as a function of time in years, is [tex]y_1\sim 8000(0.9)^{x_1}[/tex].

Answer:

3y+7x+3

Step-by-step explanation:

3y+2x+5x-4+

=3y+7x+3

Answer:

54

Step-by-step explanation:

.......................

Answer:

54

Step-by-step explanation:

Answer:

138.16 cm

Step-by-step explanation:

Recall that the formula for calculating the circumference is pi times diameter.

Circumference = 44 x 3.14 cm = 138.16 cm.

Answer:

264 pine trees

Step-by-step explanation:

Calculation for How many pine trees does the nursery plant in all?

Pine trees=(6 rows*32 pine trees)+(3 rows*24 pine trees)

Pine trees=192 pine trees+72 pine trees

Pine trees=264 pine trees

Therefore the numbers of pine trees that the nursery plant in all is 264 pine trees

Answer:

For this scenario, I used the elimination method. Organize the equations, so it's easier to subtract from each other. My x-variable will represent the number of hot dogs and my y-variable will represent the number of sodas.

3x+2y=213

x  + y =87

We need to make sure one of the monomials are alike in each equation, so we can eliminate a variable. Distribute 3 to each number/variable in the second equation.

3x+2y=213

3(x+y=87) --> 3x+3y=261

Now we can eliminate x.

  3x+2y=213

-  3x+3y=261

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

        -y=-48  

Divide -1 to both sides to get y=48. So, you sold 48 cans of soda. Now, we can find the number of hot dogs by substituting 48 into the second equation to get x+48=87. Subtract 48 to both sides to result with x=39. So, you sold 39 hot dogs.

Answer: the m in in the equation y = mx + b represents the slope of the graph of y = mx + b.

Answer:

y= -2x +11

Step-by-step explanation:

the 2 points: (-2,15) and (1,9)

find the slope: 6/ -3 = -2

find y-intercept: 9 = -2 + b       b=11

Answer:

Tom had 5 friends with him at the beach.

John came by with out his shirt on, showing his muscles.

2 of Tom's friends left with John

What fraction of Tom's friends were left with Tom?

Step-by-step explanation:

Expression: Jacob shared 3 pizzas with four of the friends. And each of them get 3/5 pizzas.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Expression is 3/5.

To write a division number story with an answer of 3/5:

Jacob and his 4 friends went to pizza house.

That means, the total number of people = 5.

Jacob bought 3 pizzas and share with his friends.

So, each of them get 3/5 pizzas.

Therefore, required expression is, Jacob shared 3 pizzas with his 4 friends.

To learn more about the division;

brainly.com/question/13263114

#SPJ2

Answer:

3) yes by AA~...

Step-by-step explanation:

ALTERNATE INTERIOR ANGLES

[tex]( {n}^{2} - 6n) + 6 = - 2[/tex]

[tex]( {n}^{2} - 6n + 9) + 6 - 9 = - 2 \\ {(n - 3)}^{2} - 3 = - 2 \\ {(n - 3)}^{2} = 1[/tex]

[tex] \sqrt{ {(n - 3)}^{2} } = + \sqrt{1} \\ \sqrt{ {(n - 3)}^{2} } = - \sqrt{1} \\ n - 3 = 1 \\ n - 3 = - 1[/tex]

[tex]n - 3 = 1 \: \: \: or \: \: \: n - 3 = - 1 \\ n = 1 + 3 \: \: \: or \: \: \: n = - 1 + 3 \\ n = 4 \: \: \: or \: \: \: n = 2[/tex]

[tex] \large \boxed {n = 4,2}[/tex]

Answer:

$24.00 dollars. The problem is confusing, so sorry if this is wrong.

Step-by-step explanation:

Step-by-step explanation:

distance around a circle- like middle of an apple

Answer:

The circumference is defined as the distance around something round or rounded, especially the distance around the edge of a circle. An example of circumference is the distance around the outer boundary of a circle. The line bounding a circle, a rounded surface, or an area suggesting a circle.

Answer:

Yes

Step-by-step explanation:

29-18=11

c=11

18+2(11)=40

Answer:

30

Step-by-step explanation:

If A+B is 18, A and B should equal 9.

A+B+C=29, that should mean C=6.

A+B+2C=9+9+2(6)

9+9+2(6)=30

Answer: Andre subtracted 3x from both sides

Answer:

B

Step-by-step explanation:

Answer:

Weight of large box = 18.75 kg

Weight of small box = 6.5 kg

Step-by-step explanation:

a fruit company delivers its fruit in two types of boxes : large and small. a delivery of 6 large boxes and 5 small boxes has a total weight of 145 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 57 kilograms. how much does each type of box weigh?

Let

Weight of large box = x

Weight of small box = y

6x + 5y = 145 (1)

2x + 3y = 57 (2)

Multiply (2) by 3

6x + 9y = 171 (3)

6x + 5y = 145 (1)

Subtract (1) from (3)

9y - 5y = 171 - 145

4y = 26

y = 6.5 kg

Substitute y = 6.5 kg into (2)

2x + 3y = 57

2x + 3(6.5) = 57

2x + 19.5 = 57

2x = 57 - 19.5

2x = 37.5

x = 37.5/2

x = 18.75 kg

Weight of large box = 18.75 kg

Weight of small box = 6.5 kg

Answer: Yes. They'll both make 4 apple pies.

Step-by-step explanation:

Jennifer makes 13 apple pies using 338 apples. The fraction of apple pies made based on the number of apples will be:

= 13 / 338

= 0.03485

Mateo used 9 apple pies using 216 apples. The fraction of apple pies made based on the number of apples will be:

= 9 / 216

= 0.0417

When they each have 105 apples, the number of apple pies that Mateo will make will be:

= 0.03485 × 105

= 3.65925

= 4 apple pie approximately

Jennifer will make:

= 0.0417 × 105

= 4.3785

= 4 apple pie approximately

Answer:

You will select both x = 1 + 5sqrt(2) and x = 1 - 5sqrt(2)

Step-by-step explanation:

Firstly you have to take the square root of both sides to get rid of the exponent. (x - 1)^2 = 50 becomes x - 1 = +- sqrt(50)

Then you simplify the right. x - 1 = +- 5sqrt(2)

The answer is both the positive and negative versions.

Answer: 237.160283353

Step-by-step explanation:

Answer:

the answer is 237.1602834

source: Calculator