Find the greatest possible x-coordinate of point A such that for any point B on the y-axis between (-24) and 25, the segment AB has a common point with the line segment PQ, where P(5, -12), Q(5, 9).

Step-by-step explanation:

you can see that answer directly at x = 0. because y is then exactly the missing "?".

and that is 4.

so,

? = 4

Answer:

Equation is [tex]a_n = 2.50n + 2.50[/tex]

This is discrete

=======================================================

Explanation:

There are n = 12 months in a year.

[tex]a_1[/tex] = first term = x

d = common difference = 2.50, which is the amount the allowance is increasing month to month.

[tex]S_n = \text{Sum of the first n terms of an arithmetic sequence}\\\\S_n = (n/2)*(2a_1 + d(n-1))\\\\S_{12} = (12/2)*(2\text{x} + 2.50(12-1))\\\\S_{12} = 6(2\text{x} + 27.5)\\\\S_{12} = 12\text{x} + 165\\\\[/tex]

The sum of the first n = 12 terms of the arithmetic sequence is 12x+165, where x is the first term (i.e. the allowance on January 1st).

We're told that this total is $225. We'll set the value of [tex]S_{12}[/tex] equal to 225 and solve for x.

[tex]S_{12} = 225\\\\12\text{x} + 165 = 225\\\\12\text{x} = 225 - 165\\\\12\text{x} = 60\\\\\text{x} = 60/12\\\\\text{x} = 5[/tex]

Therefore, you got $5 on January 1st. Then 5+2.50 = 7.50 dollars on February 1st. Then 7.50+2.50 = 10 dollars on March 1st. And so on, until reaching December. All of those dollar amounts then should add to $225 to help confirm the answer.

This equation is discrete because the terms are finite from n = 1 to n = 12. We can't have a midpoint of say between months 3 and 4. It doesn't make sense to have month 3.5 for instance. There's only a set amount of payments.

--------

Now that we know [tex]a_1 = 5[/tex] is the first term, we can then determine the value of any allowance value for any given value of n.

[tex]a_n = \text{nth term of arithmetic sequence}\\\\a_n = a_1 + d(n-1)\\\\a_n = 5 + 2.50(n-1)\\\\a_n = 5 + 2.50n-2.50\\\\a_n = 2.50n + 2.50\\\\[/tex]

Let's see what the allowance would be for month n = 2

[tex]a_n = 2.50n + 2.50\\\\a_{2} = 2.50(2) + 2.50\\\\a_{2} = 5 + 2.50\\\\a_{2} = 7.50\\\\[/tex]

The allowance for month n = 2  (aka February) is $7.50, which was mentioned earlier in the previous section. I'll let you confirm the other values of n.

Keep in mind that n is a positive whole number in the set {1,2,3,...,10,11,12}. It might help to make a table of values.

The word problem of swimming pool resulted to a simultaneous equation and the solution is

the number of adults in the pool is 242

the number of children in the pool is 317

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let the number of adults in the pool be x

let the number of children in the pool be y

559 people used the public swimming pool

559 = x + y

The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $1001.25

1.25y + 2.50x = 1001.25

Hence:

x + y = 559

1.25y + 2.50x = 1001.25

solving the equation gives

y = 317

x = 242

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Answer:

(X−6)(X+8)

Step-by-step explanation:

The restaurant delivery service cover the area 113.04 miles².

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A fast-food restaurant offers delivery service anywhere within a 6-miles radius.

Now,

The area cover by delivery service = πr²

Here, r = 6 miles

Thus, The area cover by delivery service = πr²

                                                                 = 3.14 x 6²

                                                                 = 3.14 x 36

                                                                 = 113.04 miles²

Therefore, The restaurant delivery service cover the area 113.04 miles².

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Answer:

Step-by-step explanation:

You wire be able to put out

month, for 25 years.

$2307.94 each

All the steps given are take to ensure fairness when collecting data.

What is data analysts?

A data analyst examines data to find significant customer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information.

You need excellent quantitative and analytical skills to succeed as a data analyst.

To answer problems logically, you must be able to pay attention to detail. Additionally, you must be able to articulate your conclusions clearly to people who will base choices on them.

Therefore, all the steps given are take to ensure fairness when collecting data.

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The inequality to represent the problem is x - 78.50 ≤ 61.50.

Joy can sped at most 140 dollars.

Joy went to a sporting goods store and bought a tennis racket for $78.50. To stick to her budget, she knows she can spend up to $61.50 on new tennis shoes.

The inequality that can be used to represent the problem is as follows;

Therefore,

x = total money Joy wants to spend in all

Hence, the inequality is x - 78.50 ≤ 61.50

x - 78.50 ≤ 61.50

x ≤ 61.50 + 78.50

x ≤ 140

Therefore, she wants to spend at most 140 dollars.

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The remainder when the polynomial  P(x)=x3-x2-2x+8 is divided by (x+2) is 0

Remainder Theorem

From the definition of remainder theorem which stated that , if a polynomial f(x) is divided by a binomial (x−a), then the remainder is f(a)

Using the remainder theorem, P(x)=x3-x2-2x+8 is divided by (x+2).

binominal (x-a)

Step 1: We divide  p(x) by (x + 2)            

P(x)=x3-x2-2x+8  and X = -2

therefore, Remainder = p(-2)

Step 2: Substitute the value of the remainder into p(x)

P(-2) =[tex](-2)^{3}[/tex] -( [tex]-2^{2}[/tex] ) - 2([tex]-2[/tex]) + 8

P(-2) = -8 - 4  + 4 + 8

P(-2) = -12+12

P(-2) =0

Therefore, from the remainder theorem, the remainder when P(x) is divided by (x+2) is 0

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If she uses 32 spacers, plus 7 beads per inch of necklace length. The equation to find how many beads Li has" will be,y=32+7x

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable. A linear equation has the form y = mx + b in the slope-intercept format

It is given that, for each necklace, she uses 32 spacers, plus 7 beads per inch of necklace length.

If x is the length in inches, of the necklace. The equation to find how many beads Li has" will be,

y=32+7x

Thus, if she uses 32 spacers, plus 7 beads per inch of necklace length. The equation to find how many beads Li has" will be,y=32+7x.

The question is incomplete. The complete question is"Li is making beaded necklaces. For each necklace, she uses 32 spacers, plus 7 beads per inch of necklace length. Where is x the length in inches, of the necklace? Write an equation to find how many beads Li has"

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Answer:

-2x + 15.

Step-by-step explanation  Perpendicular lines have slopes that are opposite reciprocals of each other. Therefore, the slope of the line is -2. When we solve for the y-intercept, the result is 15.

Answer: the answer to this is true

If Bisector BD bisects ∠ABC. and  ∠ABD= 67°, m∠CBD= 67°then m∠ABC= 134

As given, bisector BD bisects the angle ABC so this means, the angle ABC is divided into two halves. We need to find ∠ABC

So,

angle ABD= angle CBD.

and ∠ABD= (8x + 35)° (i)

∠CBD= (11x + 23)° (ii)

So,

(8x + 35)° = (11x + 23)°

On solving the above equation, we have

3x= 12

x= 4.

Putting x=4 in (i) we have,

∠ABD= 8(4) + 35

∠ABD= 67°

As ∠ABD = ∠CBD, we have

∠CBD= 67°

Now,

∠ABC= ∠ABD + ∠CBD

∠ABC= 67° + 67°

∠ABC= 134°.

Hence, If Bisector BD bisects ∠ABC. and  ∠ABD= 67°, m∠CBD= 67° then m∠ABC= 134

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Disclaimer

The question given is incomplete as the diagram is missing, so a similar question has been solved here.

Answer:

5

Step-by-step explanation:

Since we have given that

As per given relation about the height of the buildings , the height of building A is 655 feet and height of building B is 855 feet.

As given in the question,

Let us consider height of building A is equal to x feet.

According to given condition height of building A is 200 feet shorter than building B.

Height of building B is equal to ( x + 200 ) feet.

Total height of building A and building B is equal to 1510 feet

Required equation is :

x + x + 200 = 1510

⇒ 2x + 200 = 1510

⇒ 2x = 1510- 200

⇒ 2x = 1310

⇒ x = 655 feet

Height of building B is :

x+ 200 = 655 + 200

            = 855 feet

Therefore, for the given relation about the height of the buildings , the height of building A is 655 feet and height of building B is 855 feet.

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a.) Expression for the amount of money is 75+18n

b.) money spend in 12 months is $291

From the question, we have

Buy a network router for $75.00. The fee for internet service is $18.00 per month.

a.) Expression for the amount of money (y) is,

y = 75+18n

b.) money spend in 12 months = 75+18*12

= $291

Addition:

The phrase "the addition" refers to the combining of two or more integers. Three is written as three plus three since the plus sign (+) signifies the sum of two integers. The frequency with which the plus symbol (+) is used is likewise under your control. for example, 3 + 3 + 3 + 3. The teaching of addition in math to children is crucial. In primary school, students learn fundamental addition sums, such as one-digit facts, math addition sums, and double-digit arithmetic addition sums. One of the most fundamental and exciting Math concepts for primary school children is sums in addition. Because math is a fascinating subject, children begin learning basic mathematical concepts like adding numbers in their early years.

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The equation, 3·x - 13 = 7·(x + 2) - 4·(x - 7), has no solution

An equation can have no solution, infinitely many solutions or one solution

The equation is; 3·x - 13 = 7·(x + 2) - 4·(x - 7)

Expanding the left and right expressions of the equation, gives;

3·x - 13 = 7·x + 7×2 - 4·x + 4 × 7

Collecting like terms gives;

3·x - 13 = 7·x + 14 - 4·x + 28 = 7·x - 4·x + 14 + 28

3·x - 13 = 7·x - 4·x + 14 + 28 = 3·x + 42

3·x - 13 = 3·x + 42

3·x - 13 + 13 = 3·x + 42 + 13 = 3·x + 55

3·x + 0 = 3·x + 55

3·x = 3·x + 55

3·x - 3·x = 55

3·x - 3·x = 0 = 55 (No solution for x)

Therefore, the value of x in the equation, 3·x - 13 = 7·(x + 2) - 4·(x - 7) has no solution as the left and right expressions are not the same

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Answer: $56.25

Step-by-step explanation:

x = cost to make the shirt

x + 75(0.25) = 75

x = 75 - 18.25 = 56.25

Step-by-step explanation:

1. Draw x y plane

2. Identify where x = -5, 1, 7 on x plane

3. Identify where y = 3, 1, -1 on y plane

4. Mark the intersection point

5. Draw the line

The value o f c based on The Mean Value Theorem is 1

The Mean Value Theorem stated that if f(x) is a continuous on [a,b] and differentiable on (a,b) then there is a c such that:

f'(c) = [tex]\frac{f(b)-f(a)}{b-a}[/tex] ... (i)

Based on the question, we got equations:

f(x) = 1 + x + x² ... (ii)

By using derivative, we get:

f'(x) = 1 + 2x ... (iii)

From the question, we get:

f(a) = f(0)

f(b) = f(2)

Then we need to find the value of both f(0) and f(2):

f(0) = 1 + (0) + (0)²

f(0) = 1 ... (iv)

f(2) = 1 + (2) + (2)²

f(2) = 7 ... (v)

We also need to find the equation for f'(c) based on equation (iii):

f'(x) = 1 + 2x

f'(c) = 1 + 2c ... (vi)

We will input equations (iv) and (v) into equation (i) to find another equation of f'(c):

f'(c) = [tex]\frac{f(2)-f(0)}{2-0}[/tex]

f'(c) = [tex]\frac{7-1}{2-0}[/tex]

f'(c) = [tex]\frac{6}{2}[/tex]

f'(c) = 3 ... (vii)

Then we will subtitute the equation (vi) with equation (vii) to find the value of c:

f'(c) = 1 + 2c

3 = 1 + 2c

2c = 2

c = 1... (viii)

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The simplified value of the expression (x³ + 9x²+ 26x + 24), when divided by (x + 3), is: the quotient will be x^2 + 6x + 8 and the remainder will be 0. (x + 3) will be a factor of (x³ + 9x²+ 26x + 24).

Let us solve the given algebraic expression by the long division method:

We are given the expression:

(x³ + 9x²+ 26x + 24) and (x + 3)

We need to perform the division of the given algebraic expression:

x + 3  ) x^3 + 9x^2 + 26x + 24 ( x^2 + 6x + 8

           x^3 + 3x^2

         -         -                            

                    6x^2 + 26x + 24

                    6x^2 + 18x

                     -        -                  

                                 8x + 24

                                 8x + 24

                               -       -          

                                     0

So,

quotient = x^2 + 6x + 8

remainder =  0

As the remainder is 0.

So, (x + 3) will be a factor of (x³ + 9x²+ 26x + 24)

Thus, the simplified value of the expression (x³ + 9x²+ 26x + 24), when divided by (x + 3), is: the quotient will be x^2 + 6x + 8 and the remainder will be 0. (x + 3) will be a factor of (x³ + 9x²+ 26x + 24).

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Answer:

  28

Step-by-step explanation:

You require a teacher : children ratio of at least 1 : 4 for the activity of climbing, and you want to know the greatest number of children that can go climbing with 7 teachers.

We can describe this problem by the inequality ...

  teachers/children ≥ 1/4

  7/children ≥ 1/4 . . . . . for 7 teachers

multiplying by (4·children) gives ...

  28 ≥ children

At most, 28 children can go climbing.

Answer:

4 x y

Step-by-step explanation:

y x y x y x y = y

2 x 2 = 4

4 x y

Using the volume formula, the height of the cylinder is [tex]h = \frac{v}{\pi r^{2} }[/tex]

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

In other words, a cylinder is a geometric solid with two circular bases joined by a curved surface.

The volume of a cylinder can be represented as follows:

The formula to calculate volume of a cylinder is given by the product of base area and its height

where

Therefore, the question asked us to solve for height, h.

Hence, let's make height the subject of the formula.

v = πr²h

divide both sides by πr²

[tex]\frac{v}{\pi r^{2} }=\frac{\pi r^{2} h}{\pi r^{2} }[/tex]

Therefore,

[tex]h = \frac{v}{\pi r^{2} }[/tex]

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Answer:

yes

Step-by-step explanation:

A cat is a domestic species of small carnivorous mammal. It is the only domesticated species in the family Felidae and is often referred to as the domestic cat to distinguish it from the wild members of the family. A cat can either be a house cat, a farm cat or a feral cat; the latter ranges freely and avoids human contact.

So, it will be considered as a yes.

Answer:

4th option

Step-by-step explanation:

216p³ + 125q³ ← is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

then

216p³ + 125q³

= (6p)³ + (5q)³ → with a = 6p and b = 5q

= (6p + 5q)((6p)² - 6p(5q) + (5q)² )

= (6p + 5q)(36p² - 30pq + 25q²)

Yes, there is enough weight of plastic pellets in a full barrel for the machine to make trash bags for 5 minutes.

It is given that the factory makes trash bags using plastic pellets. The plastic pellets are placed in barrels. The barrels containing the plastic pellets are then poured into a machine. When the machine is operating, the change from a barrel of pellets to the trash bags is 3 kg per minute. Each full barrel contains 18 kg of plastic pellets.

We need to check if there are enough pellets in a full barrel for the machine to make trash bags for 5 minutes. Let the time for which the machine can make the bags from a single barrel of plastic pellets be denoted by the variable "t". The time taken by the machine to fully convert a barrel full of plastic pellets into trash bags is the ratio of the total weight of plastic pellets in the barrel to the rate of conversion of the plastic pellets into trash bags.

t = 18/3

t = 6

Hence, the machine can convert a barrel of plastic pellets into trash bags in a time duration of 6 minutes. So, there are enough pellets in a full barrel for the machine to make bags for 5 minutes.

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The expression for the rectangular prism's base area is 11x² + 7x + 5.

Given;

The volume of rectangular prism = 33x³ + 43x² + 29x + 10

The height of the prism = 3x + 2

We know that, the area of the prism = length * breadth

where as, volume = length * breadth * height

So, area = volume / height

Using synthetic division, dividing volume by height, we get;

3x+2  ) 33x³ + 43x² + 29x + 10 ( 11x² + 7x + 5

            33x3 + 22x2

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

                        21x² + 29x

                        21x² + 14x

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

                                  15x + 10

                                   15x + 10

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

                                       x

Quotient is 11x² + 7x + 5 which is equal to expression for the area of the base of the rectangular prism.

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