Part 1 of 2
Find the numerical value of the rational expression when x = 2 and x = -3.
11x+6
2
2x + 28x + 48

Answer:

5:6

Step-by-step explanation:

The entire class is 11/11.

Girls: 5/11 of the class.

Boys: 11/11 - 5/11 = 6/11

Ratio of girls to boys:
5/11 / 6/11 = 5/11 × 11/6 = 5/6

Answer: 5:6

Answer:

The rate of change is -2

Step-by-step explanation:

formula we will use: G(x)= [tex]\frac{f(b)-f(a)}{b-a}[/tex]  [-1,2]

g(x)= [tex]x^3[/tex]-5x

g(-1)=[tex]-1^3[/tex]-5(-1)

g(-1)=-1+5

g(-1)=4

g(2)=[tex]2^3[/tex]-5(2)

g(2)=8-10

g(2)=-2

so g(x)= [tex]\frac{(-2)-(4)}{(2)-(-1)}[/tex]

g(x)= [tex]\frac{-6}{3}[/tex]

g(x)=-2

The missing reasons used in solving the given inequality are;

Reason 2; Subtraction property

Reason 3; Subtraction property of order

Reason 5; Division property of order.

There are different properties of algebra such as distributive property, commutative property, associative property, addition property, division property e.t.c

We are given the inequality as;

−2(x + 3) − 4 > 4x + 30

Step 1;

-2x - 6 - 4 > 4x + 30

Reason 1; Distributive property

Step 2; -2x - 10 > 4x + 30

Reason 2; Subtraction property

Step 3; -6x - 10 > 30

Reason 3; Subtraction property of order

Step 4; 6x > 40

Reason 4; Addition property of order

Step 5; x < -20/3

Reason 5; Division property of order.

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If function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35

The function is

f(x) = (x+3)(3x-5) - 4

We have to find the value of f(3) - f(-2) ,to find that find the value of f(3) and f(-2) separately.

The function is

f(x) = (x+3)(3x-5) - 4

Substitute the values in the equation

f(3) = (3+3)(3×3 - 5) - 4

= (6) × (9-5) - 4

= 6 × 4 -4

= 24 - 4

= 20

The value of f(3) = 20

f(-2) = (-2+3)(3×-2 - 5) - 4

= 1 × (-6-5) -4

= 1 × (-11) - 4

= -11 - 4

= -15

The value of f(-2) = -15

Then,

f(3) - f(-2) = 20 - (-15)

= 20 + 15

= 35

Hence, if function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35

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A possible perimeter for the rectangular table that was built by Irene is 50 inches.

My thinking was gotten by getting the dimensions and then using the perimeter formula to solve it.

From the information given, it should be noted that the area of the rectangle is given as 114 square inches. A dimension that can give this is 19 inches and 6 inches

The perimeter of a rectangle is calculated as:

= 2(Length + Width)

= 2(19 inches + 6 inches)

= 2(25 inches)

= 2 × 25

= 50 inches

The perimeter is 50 inches.

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The total fencing material required to fence the playground and both flower beds is

Information from the question

The boundary of a park is shaped like a circle

The length of the rectangular playground is / and its width is w

The length of each side of the square flower beds is a

The problem is asking for the perimeter of a rectangle and 2 squares

perimeter of a rectangle is 2( /  + w)

perimeter of a square is 4a

If there was no over lap the expression will have no reduction and hence the quantity of material required for the fencing is equal to their respective perimeters

The flower beds are two so the perimeter will be multiplied by 2 to give 8a

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Answer:

$420

Step-by-step explanation:

multiple 10.50 by 40 to get 420

The fraction in their simplest form will be:

9. 12/15 = 4/5

10. 6/8 = 3/4

11. 25 / 100 = 1/4

12. 5 / 40 = 1/8

13. 7/77 = 1 / 11

14. 4 / 36 = 1/9

15. 18/20 = 9/10

16. 100/1000 = 1/10

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

It should be noted that in order to divide a fraction in their simplest form, the equivalent numbers must be used.

For example, 100/1000 will be:

(100 ÷ 100) / (1000 ÷ 100)

= 1 / 10

25 / 100 has a common factor of 25 as.this gives 1/4.

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Equation of the line in standard form is 6x + y + 4 = 0.

Slope-intercept form of equation -> y = mx + c

Given in question,

Slope = m = -6

y-intercept = c = -4

Putting values of m and c in Slope-intercept form of equation,

y = -6x - 4

Standard form :

6x + y + 4 = 0

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The probability that George will win is 1/10 and the probability that Julia will win is 1/20.

So, calculate the probability as follows:

We know,

(A) George's probability of winning:

(B) Julia's probability of winning:

Therefore, the probability that George will win is 1/10 and the probability that Julia will win is 1/20.

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A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

example :

y=4+2x+x

y = 3x + 4

y = 3x + 4 is a polynomial that has exponent equal to 1.

Therefore A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

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Answer:

-2x^2  - 43x - 343 - 2393/x-7

The total cost for the appliances plus interest is 4330.

What is an interest rate?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR.

Here, we

Cost of the appliance = $3725

Neema paid $700 so amount financed = $3725 - $700 = $3025

Interest rate on the loan = 3025*0.05*4 = $605

Total cost of the appliance = $3725 + 605 = $4330

Hence, the total cost for the appliances plus interest is 4330.

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The mistakes that Claire made in solving the equation are;

1) She did not use distribution property correctly in step 1 as 2(8) = 16 and not 10.

2)  - (2+5x) should have been simplified to -2 - 5x and not -2 + 5x

3) 10 + 56x = 8x - 2 should have been 12 = -64x and not 12 = 64x

We want to solve the equation 8(2 + 7x) = 3x - (2 + 5x)

Step 1; Expand the bracket on the left hand side and right hand side to get; 16 + 56x = 3x - 2 - 5x

Step 2; Simplify the right hand side to get;

16 + 56x = -2x - 2

Step 3; Rearrange to get;

16 + 2 = -58x

Step 4; Add up the left hand side to get;

18 = -58x

Step 5; Divide both sides by -58 to get;

x = -9/29

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Complete question is;

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It

turns out Clare's work has three mistakes!

find all three mistakes explain the below

8(2 + 7x) = 3x - (2+5x)

10 + 56x = 3x - 2 + 5х

10 + 56x = 8x - 2

10 = 64x - 2

12 = 64x

x = 3/16

Answer:

                             y = (-1/4)x + 9/4

Step-by-step explanation:

i got u

The value of g(x) is √2x.

What is a composite function?

A function whose values are obtained from two given functions by first applying one to an independent variable and then using the result to apply the second, and whose domain is made up of those independent variable values for which the first function's result falls within the second function's domain.

Here, we have

g(f(x)) =x√6.

f(x) = 3x²

By applying a composite function

g(f(x)) =√6x

g(3x²) = x√6

g(x) must be √(2x)

because if we  substitute  x = 3x² in this we get

= (√2(3x^2))

= √2√3√(x²)

= √6 x

Hence, the value of g(x) is √2x.

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Using mathematical operations, the amount that would be saved by buying 3 dresses instead of buying per piece is $3.40.

The mathematical operations include the following basic operations: addition, subtraction, division, and multiplication.

Mathematical operations determine the results of mathematical expressions and problems.

Cost of a dress = $6.20

Cost of 3 dresses = $15.20

Cost per dress if 3 dresses were bought = $5.067

Amount saved for buying 3 dresses instead of one = $3.40 ($6.20 x 3 - $15.20)

Thus, mathematically, the customer would save $3.40 by buying 3 dresses for $15.20 instead of buying at $6.20 per unit.

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The percent of error is 15%. The correct option is B.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Alton estimated that 230 people attended the band concert.

The actual count for attendance was 200 people.

To find the percent of error:

230 - 200 / 200

= 30 / 200

= 0.15

0.15 decimal to the percentage is 15%.

Therefore, the error is 15%

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The bookcases that Deion will be able to paint is 16.

It should be noted that a fraction is a part of a whole number that has a numerator and denominator.

In this case, Deion has 3 1/5 gallons of paint and all of the bookcases are the same size and each requires 1/5 gallon of paint.

The number of bookcase needed will be:

= Total gallons / Gallons for each

= 3 1/5 ÷ 1/5

= 16/5 ÷ 1/5

= 16/5 × 5/1

= 16

He can paint 16 cases.

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By solving a system of equations, we will see that the equation is:

-4*x - 3*y = -18

We know that the linear equation:

A*x + B*y = -18

We know that this linear equation passes through the points (-3, 10) and (6, -2), then replacing these values in the equation we will get two equations:

A*-3 + B*10 = -18

A*6 + B*-2 = -18

So we have a system of equations:

-3A + 10B = -18

6A - 2B = -18

if we add the two times the first equation and the second one we get:

2*(-3A + 10B) + 6A - 2B = 2*(-18) - 18

18B = -3*18

B = -3

by replacing that value of B in one of the equations we will be able to solve it for A.

6*A - 2*(-3) = -18

6*A + 6 = -18

6*A = -18 - 6 = -24

A = -24/6 = -4

The equation is:

-4*x - 3*y = -18

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By taking the product between the combinations of possible groups fo men and women we will see that the number of different committees is:

392

For a set of N elements, the number of different sets of K elements that can be formed is:

C(N, K) = N!/(K!*(N - K)!)

Here we have 8 men and 7 women, and we want to make a committee of 5 men and 6 women

Then the total number of different committees is given by the product between the different sets of 5 men and the different sets of 6 women, these are:

for men:

C(8, 5) = 8!/( 5!*(8 - 5)!) = (8*7*6)/(3*2*1) = 56

for women:

C(7, 6) = 7!/(6!*(7 - 6)!) = 7

Then the total number of different committees is:

C = 56*7 = 392

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Answer:

B

Step-by-step explanation:

the two angles lies on the same lines and they have the same vertex

Total number of postage stamp having total mass 1 kg = 50000 stamps

Unitary Method: What is it?

The unitary method involves first establishing the value of a single unit, followed by the value of the required number of units. What can be numbers and units?

Let's say you go to the store to purchase six apples. You are told by the shopkeeper that he is selling 10 apples for Rs 100. In this example, the value and the units are the cost of the apples. Understanding the units and values is crucial when using the unitary technique to a problem.

Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.

Given That :

1 postage stamp is = 1 cg

now we will convert cg into g

1 cg = 0.01g

1 postage stamp is = 0.02g

now we will convert g into kg

1 g = 0.001 kg

0.01g = 0.00001kg

1 postage stamp is = 0.00002kg

so now

total number of stamp in 1 kg = 1/0.00002 = 50000

Hence the ans is 50000 stamps

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The simplified expression of the expression given as -3x+16+5x+8 is 2(x + 12)

From the question, the equation is given as

-3x+16+5x+8

To start with, we need to rewrite the expression

So, we have the following representation

-3x + 16 + 5x + 8

The above expression is not an equation

Instead, it is an expression

This is so because there is no equality symbol i.e. = in the expression

So, we collect the like terms

-3x  + 5x + 8 + 16

Solving further, we need to evaluate the like terms

So, we have the following equation

-3x  + 5x + 24

Evaluate the like terms again

So, the equation becomes

2x + 24

The above expression cannot be further simplified, however, it can still be factored

Factor out 2 from the expression

This gives

2(x + 12)

Hence, the solution is 2(x + 12)

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The area of the plot is 193 sq.yd.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, A developer buys an empty lot to build a small house.

To find the area, we need to be divided the figure into triangles and rectangles

Area of the first triangle = (1/2) * base * height

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5=85 sq. unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq. unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

Adding all the areas to get the area of the plot = 85+36+63+9

Hence, Area of the plot = 193 sq.yd.

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Answer:

p < -15

Step-by-step explanation:

[tex]4 - \frac{1}{6} (p - 3) > 7[/tex]

[tex] - \frac{1}{6} (p - 3) > 3[/tex]

[tex]p - 3 < - 18[/tex]

[tex]p < - 15[/tex]

Answer:

The answer should be 13.928

Step-by-step explanation:

You do A square + B square = C square

Answer:

1024

Step-by-step explanation:

8 times 2 to the 7th power

2 by the 7th power 128 times 8 1024