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Answer: 2x(3x−1)(x+2)

Step-by-step explanation:

Answer: 2x(3x-1)(x+2)

Step-by-step explanation:

6x^3 + 10x^2 - 4x=

2x(3x^2 + 5x - 2)=

2x(3x^2 + 6x - x - 2)=

2x(3x(x+2) - 1(x+2))=2x(3x-1)(x+2)

Starting with part a, question (i):

Find the average rate of change in both populations between 2002 and 2012.

Recall that the average rate of change of a function f(x) in the interval [ a, b] is given by the quotient:

rate of change = ( f(b) - f(a) ) / (b - a)

Therefore, for our population P1 case on the years 2002 and 2012 we have:

[ P1(2012) - P1(2002) ] / (2012 - 2002) = [62 - 42] / 10 = 20 / 10 = 2

for population P2 we have:

22 [72 - 82] /10 = -10/10 = -1

You can proceed doing the same process for the other cases (ii) and (iii).

Case (ii)Now part b of the problem:

Rate of change between 2002 and 2019:

99 [ 76 - 42] / ( 17) = 534 / 17 = 2

2(929 9[ 65 - 82] / 17 = -17 / 17 = -1

Case (iii)

Rate of change between 2007 and 2019:

9797 [76 - 52] / 12 = 24/12 = 2

22 [65 - 77] / 12 = -12 / 12 = -1

We see that the rates of change for each population remained constant over the years.

What we noticed in the table regarding both populations, is that while population P1 is increasing over the years, population P2 is going down in numbers year after year.

We can say therefore that P1 is INCREASING, while P2 is DECREASING. And that the rate of change they experienced was constant over the years.

Answer:

D. 12(2x − 3) > 60

Step-by-step explanation:

Area of rectangle = length x width

The length of the rectangle is 12 feet, and the width is (2x - 3) feet.

Area = 12 x (2x - 3)

= 12(2x - 3)

From the given question,

area of rectangle > 60 square feet

So that;

12(2x - 3) > 60

24x - 36 > 60

24x > 60 + 36

24x > 96

Divide both sides by 24, to have;

=

x > 4

Therefore,

width = (2x -3)

since x > 4, then;

width > (2x4 - 3)

> 8 -3

width > 5 feet

Thus,

length x width > 60

Square root 12+Square root 6/Square root 3+1. After Rationalize the denominator we got 4.68.

Given that,

Square root 12+Square root 6/Square root 3+1

​We have to Rationalize the denominator.

If the denominator's radical is a square root, multiply by a square root that, when multiplied by the denominator, produces a perfect square beneath the radical.

The square root of a number is the element that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents.

[tex]\sqrt{12}+\sqrt{6} /\sqrt{3+1}[/tex]

Square root of [tex]\sqrt{12} is 2\sqrt{3}[/tex]

[tex]2\sqrt{3}+\sqrt{6}/\sqrt{4}[/tex]

Square root of [tex]\sqrt{4} is 2[/tex]

[tex]2\sqrt{3}+\sqrt{6}/2[/tex]

Calculating the terms

3.46+2.44/2

3.46+1.22

4.68

Therefore, After Rationalize the denominator we got 4.68.

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Answer:

1594

Step-by-step explanation:

     In a point-to-point graph, also known as a line graph, particular values of a function are represented graphically by dots on a coordinate plane. Straight lines connect adjacent pairs of dots.

    Choose x and work out the equation for y, or, to locate points on the line y = mx + b. Decide on y, then find x.

         Depending on your preference, you can plot points one at a time, a few on a line, or all at once in a table. Start with the video on the right before continuing to the resources and challenges below to learn more.

          The point (-4, 482) is located on the y=6f[-(x-5)] graph. -4 What is the fundamental idea behind y=f(x).

  If x=-4 and y=482 are subtracted from y=6f[-(x-5)],

I obtain the result f=9 at -4.

When I adjust the slider to f=9 and enter y=6f[-(x-5)]-4 into Demos, the line goes through the point (-4,482)

Does this imply that y=9x is the solution.

None of this actually makes sense to me. I don't understand a single thing. Just rearranging the numbers is all. There were NO examples in the lessons of an equation with a "y". Additionally, the left side of the equation in each example contained "f(x)" or "g(x)".

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∠GML ≅ ∠HMJ by the Vertical Angles Congruence Theorem.

∠GMH ≅ ∠LMJ by the Vertical Angles Congruence Theorem.

∠GMK ≅ ∠JMK by the Right Angles Congruence Theorem. They form a linear pair which means they are supplementary by the Linear pair Postulate and because one is a right angle so is the other by the Subtraction Property of Equality.

According to the congruence theorem of vertical angles or angles that are vertically opposing, two opposing vertical angles that are created when two lines intersect one other are always equal.

So from the figure, we can determine the vertically opposite angles,

∠GML ≅ ∠HMJ

Similarly, ∠GMH ≅ ∠LMJ

The angles ∠GMK and ∠JMK form a linear pair and are supplementary by the linear pair postulate which states that the two angles in the linear pair add up to 180°.

We know that all right angles are congruent from the Right Angle Congruence Theorem.

Hence,∠GMK ≅ ∠JMK

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In ascending order the integers are arranged from the left to right of the integer line. The arrangements are shown below.

The arrangement of the set of integers in increasing order is as follows:

Every positive integer is greater than a negative integer. Zero is less than every positive integer. Zero is greater than every negative integer. The greater the number, the lesser its opposite,i.e., If a and b are two integers such that a>b, then -a<-b.

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Answer:

23) D

24) A

25) C

26) B

Step-by-step explanation:

23)

4x + 4y = -8  Let's find the intercepts.  The x intercept is when y = 0 and the y intercept is when x = 0

Let y = 0

4x + 4y = -8

4x = -8

x = -2

(-2,0)

4x + 4y = -8

Let x = 0

4y = -8

y = -2

(0,-2)

We are looking for the line that goes through the points (-2,0) and (0,-2)  That is line D.

24)

3x -2y = -6

Let y = 0

3x = -6

x = -2

(-2,0)

Let x = 0

-2y =-6

y = 3

(0,3)

We are looking for the line that goes through the points (-2,0) and (0,3).  That is line A.

25)

x + 2y = 2

Let y = 0

x = 2

(2,0)

Let x = 0

2y = 2

y = 1

(0,1)

We are looking for the line that goes through the points (2,0) and (0,1).  That is line C

26)

3x - y = 3

Let y = 0

3x = 3

x= 1

(1,0)

Let x  = 0

-y = 3

y= -3

(0, -3)

we are looking for the line that goes through the points (1,0) and (0, -3) which is line B

Answer: 23. D   24. A   25. C   26. B

Step-by-step explanation:

                              y=mx+b

The intersection of the straight line with the y-axis equals b

23.

4x+4y=-8

Divide both parts of the equation by 4:

x+y=-2

x+y-x=-2-x

y=-x-2

⇒b=-2 (D)

24.

3x-2y=-6

3x-2y+2y=-6+2y

3x=2y-6

3x+6=2y-6+6

3x+6=2y

Divide both parts of the equation by 2:

1,5x+3=y

⇒ b=3  (A)

25.

x+2y=2

x+2y-x=2-x

2y=-x+2

Divide both parts of the equation by 2:

y=-0.5x+1

⇒ b=1  (C)

26.

3x-y=3

3x-y+y=3+y

3x=y+3

3x-3=y+3-3

3x-3=y

⇒ b=-3  (B)

The dimensions of the fenced-in area is given as

either length is 35 yards and width is 80 yards ,  

or length is 40 yards and width is 70 yards .

In the question ,

given that the total length of the fence (perimeter) = 150 yards

let L be the length of the portion to be fenced

let B be the width of the house

Given that , one side of the portion is fenced using the back side of the house

So, the perimeter of the portion to be fenced is 2L+B

equating both the perimeter ,we get

2L+B=150

B=150-2L       ....(i)

Also , given that the area of the  fenced-in portion = 2800 yards

also the formula for area of fenced-in portion = L×B

hence

L*B=2800

Substituting the values of B from equation(i) , we get

L*(150-2L)=2800

150L - 2L² = 2800

2L² - 150L + 2800 = 0

simplifying further , we get

L² - 75L + 1400 = 0

L² -40L -35L +1400 = 0          .....using splitting the middle term

L(L-40) -35(L-40) = 0

(L-35)(L-40) = 0

So , L = 35 yards or L = 40 yards

Using L = 35 yards , we get B = 150-2(35) = 80 yards

and using L =40 yards , we get B = 150-2(40) = 70 yards .

Therefore , the dimensions of the fenced-in area is given as

either length is 35 yards and width is 80 yards ,  

or length is 40 yards and width is 70 yards .

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Ila invested $42,000 into an account earning 4% compounded annually. She makes no other deposits and does not withdraw any money, the balance of Ila's account in 5 years is $510,99.42.

Compound interest is when you receive the interest on both your interest income and your savings.

For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest. Compound interest allowed you to earn 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.

The yearly interest rate is raised to number of compound periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from loan's entire original amount.

The formula is

A=[tex]p (1+r)^t[/tex]

A= future value?

P= present value 42000

R= interest rate 0.04

T= time 5years

A=[tex]42,000*(1+0.04)^5[/tex]

A=51,099.42

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There are 9 cans of soup and the 4 frozen dinners that were purchased.

Let x = the number of cans of soup purchased.

Let y = the number of frozen dinners purchased.

Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that

x + y = 13 ..... i

x = 13 - y

The equation will be illustrated as

250x + 550y = 4450 .... ii

Substituting x = 13 - y into equation ii, it becomes

250(13 - y) + 550y = 4450

3250 - 250y + 550y = 4450

- 250y + 550y = 4450 - 3250

300y = 1200

y = 1200/300

y = 4

4 frozen dinners

Substituting y = 4 into x = 13 - y, it becomes

x = 13 - 4 = 9

9 cans of soup.

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Answer:

3x^6-15x^3+2x^4-10x

Step-by-step explanation:

The expression to represent the number of hours Erica babysits  each week is 7x .

In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number) .

Erica works x hours each day and there are 7 days in a week.

Hence Erica works 7x hours in a week

Therefore the expression to represent the number of hours Erica babysits  each week is 7x .

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Answer:

x = 0, y = - 4

Step-by-step explanation:

7x + 3y = - 12 → (1)

2x - 5y = 20 → (2)

multiplying (1) by 5 and (2) by 3 and adding will eliminate y

35x + 15y = - 60 → (3)

6x - 15y = 60 → (4)

add (3) and (4) term by term to eliminate y

41x + 0 = 0

41x = 0 ⇒ x = 0

substitute x = 0 into either of the 2 equations and solve for y

substituting into (2)

2(0) - 5y = 20

0 - 5y = 20

- 5y = 20 ( divide both sides by - 5 )

y = - 4

A function in the mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as function's domain and codomain, respectively. Here f(x)= 60.

A function in the mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as function's domain and codomain, respectively.

Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, the functions represented the idealized relationship between two changing quantities. A planet's position, for the instance, depends on time. In the past, idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity). The realms of application of the concept of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

The most common letters used to represent functions are f, g, and h. A function's value at an element of its domain x is denoted by the symbol f(x), and the numerical value obtained by evaluating the function at a specific input value is denoted by replacing x with that value. For example, the value of f at x = 4 is denoted by the symbol f(x) (4). The value of the function at, say, x = 4 may be denoted by E|x=4 when the function has no name and is represented by the expression E.

if, f(x)= (-8),

f(-8)= (-9)*(-8)-12 = 60

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A graph's correlation between two variables reveals the relationship between them. The correlation is given a name based on the characteristics of the variables represented on the graphs.

What does the term correlation mean?

The data points of a person with two different factors are related in a scatterplot. The term "correlation" refers to this connection.

A correlation is the relationship between any two variables represented on any graph.

The correlation is divided into three main categories based on the sort of relationship between the variables. Those are

i) Positively correlation

ii) Negative correlation

iii) No correlation

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The sentence for 4x-9 = 19 is "when 9 is subtracted from 4 times a number, it equals 19."

Definition. A conditional statement is one that has the syntax "If P then Q," with P and Q denoting sentences. P is referred to as the hypothesis and Q is referred to as the conclusion for this conditional statement. The implication of "If P then Q" is that whenever P is true, Q must also be true.

We have a conditional statement, for instance. In the event of rain, we will not play. Let's say A: It's raining and B: We're not going to play. If A is true—that is, if it is raining—and B is false—that is, if we played—then A implies that B is untrue.

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39 pounds of type coffee were used.

Type a coffee costs, Kira, $5.85 per pound, and type b coffee cost $4.20 per pound.

let, A pound of type a coffee,

B pounds of type b coffee.

according to the question;

this month's blend used 3 times as many pounds of type B coffee as type A coffee.

Total pounds of coffee =  x + 3x

The total cost then is:

(cost for Type A)(x) + (cost for Type B)(3x) = 717.60

=>5.65x + 4.25(3x) = 717.60

=>5.65x + 12.75x = 717.60

=>18.40x = 717.60

x = 39 pound

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Answer: 4 : 9

Step-by-step explanation:

Total number of blue shirts purchased by Alice = 4

Total number of yellow shirts purchased by Alice = 5

Hence, total number of shirts purchase by her = 4 + 5

= 9

Therefore, Ratio of number of blue shirts to the total number of shirts

[tex]=\frac{Total~number~of~blue~shirts}{Total~number~of~shirts}[/tex]

[tex]=\frac{4}{9}[/tex]

Hence, Ratio = 4 : 9

Answer:

Rotate AEFB 180 degrees counterclockwise around point G

Rotate AEFB 180 degrees clockwise around point G

Translate AEFB by the directed line segment from F to E, and then rotate 180 degrees clockwise around point E.    

Step-by-step explanation:

Answer:

x = 40 in

Step-by-step explanation:

the missing angle in the triangle on the left is

180° - (74 + 51)° = 180° - 125° = 55°

the missing angle in the triangle on the right is

180° - (74 + 55)° = 180° - 129° = 51°

the 2 triangles have 3 pairs of congruent angles and are therefore congruent.

Corresponding sides and angles are then congruent

consider the corresponding sides opposite 74° , that is x and 40 in , so

x = 40 in

The four students; Michal, Hypatia, clodoveo and Jamal's attempt to explain the expression "3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³" is incorrect

This means to make simpler, either by reducing in complexity, reducing to component parts, or making easier to understand.

3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³

Using PEMDAS

Correct workings:

3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³

3 - 5 × (1 × 2)² - 1 + 2(-1)³

= 3 - 5 × (2)² - 1 + 2(-1)

= 3 - 5 × (4) - 1 - 2

= 3 - 20 - 3

= - 20

In conclusion, the correct simplification of the expression "3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³" is -20

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For v = -4, 0, and 8 are not solutions of the equation 1 - 7v = - 69. The solution of the equation is v = 10.

Consider the equation,

1 - 7v = - 69

For the value of v = - 4,

1 - 7v = - 69

1 - 7 × - 4 = - 69

1 + 28 ≠ - 69

29 ≠ - 69

Hence, v = - 4 is not a solution.

For v = 10,

1 - 7v = - 69

1 - 7 × 10 = - 69

1 - 70 = - 69

- 69 = - 69

Therefore, v = 10 is a solution.

For the value of v = 0,

1 - 7v = - 69

1 - 7 × 0 = - 69

1 ≠ - 69

Hence, v = 0 is not a solution.

For the value of v = 8,

1 - 7v = - 69

1 - 7 × 8 = - 69

1 - 64 ≠ - 69

- 63 ≠ - 69

Hence, v = 8 is not a solution.

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Answer:

4/5 cup

Step-by-step explanation:

Answer: 1 1/2

Step-by-step explanation:

1/2 divided 1/3  = 3/2 = 1 1/2

1/2 divided 1/3

= 1/2 x 3/1

1 × 3

2 × 1

= 3/2

= 1 1/2

The population of the town in the year 1995 will be 61415.

From the information, the population of a town was 980 in 1970 and the population has been growing at a rate of 18% each year.

Therefore, it should be noted the difference in the number of years will be:

= 1995 - 1970

= 25 years

Therefore, the population of the town in the year 1995 is:

= 980 × (1 + 18%)^25

= 980 × (1.18)^25

= 980 × 66.6686

= 61415

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