A poster is to have an area of 200 square inches with 1 inch margins on the left and right sides, and 2 inch margins on the top and bottom. Varying the dimensions of the poster changes the area of the region inside the margins. What is the maximum area inside the margins?.

The equation in slope-intercept form of line k is y = - x + 5.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of a line in slope- intercept form is

y = mx + c

where,

   m is the slope and c the y- intercept.

We have,

y = x - 3

∴  It is in the slope intercept form.

with slope m = 1

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular} = -\frac{1}{m} = -\frac{1}{1} = -1[/tex] ,

The partial equation of line j is,

y = - x + c

By substituting (2, 0) into the partial equation we get, c

0 = - 2 + c

c = 0 + 2 = 2

∴ c = 2

The equation of line j is y = - x + 2.

Similarly,

The slopes of parallel lines are the same.

The partial equation of line k is,

∴ y = - x + c

By substituting (- 1, 6) into the partial equation we get, c

6 = 1 + c

c = 6 - 1 = 5

∴ c = 5

The equation of line k is y = - x + 5.

Therefore, the equation in slope-intercept form of line k is y = - x + 5.

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The inequality that would represent the possible values for the number of hours babysitting and landscaping is b + l ≤ 14.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, Alexander can work a maximum of 14 hours altogether between both jobs in a given week. This will be illustrated as:

b + l ≤ 14

b = babysitting

l = landscaping

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Answer:

[tex]\left(m+2\right)\left(n^2+2n+m+1\right)[/tex]

Step-by-step explanation:

Hoooo boy.

This is a long one.

But let's do it!!!!

Apply exponent rule: [tex]\:a^{b+c}=a^ba^c[/tex]

Answer:

9

Step-by-step explanation:

(2(-3)+3)^2

(-6+3)^2

(-3)^2

since the power of 2 is even it will be a positive result (if its a odd number like 3 it will be a negative result)

3^2

=9

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 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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The greatest amount of sap collected from any one tree is ?

times as great as the least amount of sap collected from

any one tree. = 2 times

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)

The values of ∠PQR = 45° and ∠POR = 90°.

The circumference of a circle is defined as its linear distance around it. In other words, if a circle is opened to form a straight line, the length of that line equals the circumference of the circle.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually denoted by the letters 'R' or 'r'.

Given that

O is the center of the circle, if ∠OPQ = 25° &∠ORQ = 20°

We have to determine the values of ∠PQR and ∠POR

Sol. OP = OQ

⇒∠OQP = ∠OPQ = 25° [Radii of the same circle]

Similarly, ∠OQR = 20°

∠PQR = 25° + 20°

∠PQR = 45°

Furthermore ∠POR = 2 ∠PQR [the angle at the centre is twice the angle at the circumference].

⇒∠POR = 2 × 45°

∠POR = 90°.

Therefore the values of ∠PQR = 45° and ∠POR = 90°.

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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

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

Answer:

(X−6)(X+8)

Step-by-step explanation:

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.

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:

-4

Step-by-step explanation:

m= y2-y1/x2-x1

m= 11-3/0-2

m= 8/-2

m= -4

Answer: The slope is -4

Step-by-step explanation: The general formula for calculating the slope is  [tex]\frac{y2-y1}{x2-x1}[/tex].

x1 = 2, y1 = 3, x2 = 0, y2 = 11

So we have [tex]\frac{11-3}{0-2}[/tex] = [tex]\frac{8}{-2}[/tex] = -4.

Answer:

x = 2.875

Step-by-step explanation:

1 1/3 (9 - 6x) = -11

        12 - 8x = -11

            - 8x = -23

                x = 2.875

5761.4 feet is the height of the mountain prior to construction

Given: 1.1h – 622.5 = 5,675

This is an algebraic equation, we need to solve for h

1.1h – 622.5 = 5675

collect like terms:

1.1h =  5675 + 622.5

Add like terms:

1.1h = 6337.5

Divide both sides by 1.1:

h = 6337.5/1.1

h = 5761.4 feet

Therefore,  the height of the mountain prior to construction is 5761.4 feet

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Answer: My answer is 4. You may want another answer.

Step-by-step explanation:

visual studying

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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Answer:

Answer is x = 9                                                                

Answer: the answer to this is true

Answer:

Step-by-step explanation:

You wire be able to put out

month, for 25 years.

$2307.94 each

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 sine function is  y = 5 sin ([tex]16\pi x[/tex] ) + 3.

The function y =[tex]sin x[/tex] defines a sine wave as a geometric waveform that oscillates (moves up, down, or side to side) frequently.

It is an s-shaped, smooth wave that oscillates above and below zero, to put it another way.

In its most general form, the sine wave can be described using the function y=[tex]a sin (bx)[/tex]

Given:

Amplitude = 3

midline= 5

As, we know

General sine function:  a sin b[tex](x- c)[/tex] + d

and, amplitude = absolute value of a

b = 2π / period

c = phase shift (horizontal shift)

d = vertical shift  (i/e., midline is  y = d)

So,

a = 5, d = 3, and b = 2π / (1/8) = 16π, c = 0

Substituting the above value in Sine function we get

Thus, y = 5 sin ([tex]16\pi x[/tex]) + 3

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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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By writing both variables in the same side of the linear equation, we will get the standard form:

2y + (-1)*x = 4

A linear equation between two variables x and y written in standard form is:

a*x + b*y = c

Where the coefficients a, b, and c, are all real numbers.

In this case, we have the linear equation:

2 + (1/2)*x = y

If we multiply both sides by 2, we get:

2*(2 + (1/2)*x) = 2*y

4 + x = 2y

Now we subtract x in both sides to get:

4 + x - x = 2y - x

4 = 2y - x

This is the linear equation in standard form:

2y + (-1)*x = 4

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The 65 represents the speed.

97.5 miles covered in 1.5 hours.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given: d= 65t

We know the Formula of Speed- distance

speed= Distance / time

and, distance = speed x time

So, comparing it with given equation

distance =d , time= t and speed= 65

Now, t=1.5 hours

Distance = 1.5 x 65 = 97.5 miles

and, d= 26 miles

t= 26 / 65

t= 0.4

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The height is either 10 cm,12 cm,14 cm.

Given:

The base of the parallelogram has a length of 10 cm.

Here area is not given so the height may be anything.

suppose h = 10

area = base * height

= 10 * 10

= 100 cm^2

if h = 12

area = 10 * 12

= 120 cm^2

if h = 14

area = 10 * 14

= 140 cm^2

Therefore the height is either 10 cm,12 cm,14 cm.

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