Point A is at (-7, 5) and point B is at (7,3).
What is the midpoint of line segment AB?

Answer:

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

Step-by-step explanation:

The sum of 2 numbers is 96, this can be expressed as

The larger number is 9 less than 4 times the smaller, this can be expressed as

Now, we replace the second equation in the first one

We use this number to find x.

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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The number of runs that Jack must score will be 90.

It should be noted that the mean score from 8 matches is 45. Therefore, the total score will be:

= 8 × 45

= 360

When the coach says that he must increase the mean to 50 in the next match, the total score will be:

= 50 × 9

= 450

Therefore, the number of points that must be scored will be:

= 450 - 360

= 90

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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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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)

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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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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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

Answer:

1594

Step-by-step explanation:

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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The inequality is (3,∞) < x < 4.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Given Data

x is a number less than 4

x<4

Numbers which are less than 4 are 3 to infinity

So,

The inequality is:

(3,∞) < x < 4

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Answer:

circle is 22

Triangle is 34

Step-by-step explanation:

22 + 22 + 22 = 66

22 + 34 + 34 = 90  

Take 90 - 22 = 68

Divide 68 by 2 to get 34

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)

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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The inequality that represents the number of minutes of calls made in the United States and in France, can be presented as follows:

An inequality expresses the relationship between two or more values that are not equal.

The value of the calling card = $25

The cost of calls made in the United States = $0.10

Cost of calls made in France = $0.25

The number of minutes that can be used for calls in the U.S. = x

The number of minutes that can be used for making calls in France = y

The duration of calls that can be made in the United states is therefore:

[tex]x_{max} = \dfrac{\$25}{\$0.10} = 250[/tex]

The inequality that represents the number of calls that can be made in the United States is therefore: 0 ≤ x ≤ 250

The duration of calls that can be made in France with the $25 calling card is therefore: [tex]y_{max}=\dfrac{\$25}{\$0.25} = 100[/tex]

The inequality that represents the number of minutes the calling card can be used in making calls in France is: 0 ≤ y ≤ 100

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Answer:

11 hours

Step-by-step explanation:

let x represent the hours worked

26(x) + 80 = 366

26(x)=366-80

26(x)=286

x=11

.˙. the plumber worked 11 hours

Answer: C

Step-by-step explanation:

- 5/8k -8 + 2 + 1/3k

-5/8 = -15/24

1/3 = 8/24

-15/24k -8 + 2 + 8/24

-7/24k -6

Answer:

400

Step-by-step explanation:

the volume of a pyramid with a square base is [tex]\frac{lwh}{3}[/tex] so the volume is 12*10*10 divided by 3, which is 1200/3, or 400

Answer:

A= 5000 e

A= 39,624.12

Step-by-step explanation:

Answer:

no round to the nearest cant and do no

Zander downloaded a total of 19 Songs and 8 Games.

In the given question, it is stated that Zander's downloads had a combination of 30 games and songs in which he downloaded 8 songs more than games. The equation representing the given situation is g + (8 + g) = 30. Here, g represents Games, and (g+8) represents songs.

Now, to find out the number of games and songs, we need to calculate the value of g by the equation.

=> g + (8 + g) = 30

=> 2g + 8 = 30

=> 2g = 22

=> g = 11

We get value of g = 11, So, downloaded games will be 11 and songs will be 19

Hence, the number of Games and Songs will be 11 and 19 respectively.

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A cucumber seed needs to be planted 1 inch deep for optimal growth. the plant grows an average of 3 inches every 2 weeks. then the slope in the situation is 2

How do you find the slope of a line?

We need to find the ratio of the difference between the y-coordinates and x-coordinates of the two points, that form the line. The resulted value is the slope of the line. It shows the rise of the line along the y-axis over the run along x-axis.

since seed planted 1 inch deep then y1 = -1 and initial x1 =0

the plant grow an average of 3 inches every 2 weeks then y2 =3 and x2=2

putting in the formula

slope= y2 -y1 /x2 -x1

       = 3-(-1)/2-0

      = 4/2

      =2

thus the slope in this situation is 2

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The sequence 7, 5, 2, 1, then the

( i ) . The general term d = 2

( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]

( iii ) . The 25th term [tex]a_{25}[/tex] = 55

The sequence is,

⇒ 7, 5, 2, 1

[tex]a_{1} ,a_{n+1} ,a_{n+2} ,a_{n+3} = 7 , 5 , 2 , 1[/tex]

( i ) . The general term,

Let us assume general term = d

We can use this formula,

d = [tex]a_{n+1} -a_{n}[/tex]

where,

[tex]a_{n+1} = 5\\a_{n} = 7[/tex]

d = 7 - 5

d = 2

So,

The general term d = 2

( ii ) . The next three terms, [tex]a_{5} ,a_{6} ,a_{7}[/tex]

We can use this formula,

[tex]a_{n+1} =a_{n} +d[/tex]

[tex]a_{5} =a_{4} +d ;\\a_{6} = a_{5} +d ;\\a_{7} = a_{6} +d[/tex]

[tex]a_{5} = 1+2\\a_{5} = 3[/tex]

[tex]a_{6} = 3+2\\a_{6} = 5[/tex]

[tex]a_{7} = 5+2\\a_{7} = 7[/tex]

So,

The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]

( iii ) .  The 25th term

We can find nth term,

We can use this formula,

[tex]a_{n} =a_{1} +(n-1)d[/tex]

[tex]a_{n} = 7+(n-1)2[/tex]

[tex]a_{n} =7+2n-2\\a_{n} = 2n+5[/tex]

Then, 25th term is,

We can substitute n = 25

[tex]a_{25} = 2(25)+5\\a_{25} =50 + 5\\a_{25} = 55[/tex]

So,

The 25th term [tex]a_{25}[/tex] = 55

Therefore,

( i ) . The general term d = 2

( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]

( iii ) . The 25th term [tex]a_{25}[/tex] = 55

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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

Using  division we can infer that 50 pages will not be enough.

Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number.

Timmy has 810 stamps.

Now each page can hold 16 stamps and he has 50 pages.

Now we will divide 810 by 16 to calculate the number of pages required to put all the stamps.

∴ 810 ÷ 16 = 50 remainder 10.

Therefore after completing the 50 pages there are 10 stamps left.

Hence from division we can infer that 50 pages will not be enough.

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Timmy has 810 stamps. He wants to organize them on pages that hold 16 stamps each. He has 50 pages. Does Timmy have enough pages to organize all his​ stamps?

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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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