Using the Optimization problem solving strategy, the maximum area inside the margins is 108 inch².
Firstly , we can develope a function of two variables. let the length of poster be x inch and width be y inch.
total Area of poster (A ) = x × y = 200 inch² ---(1)
we have provided that bottom and top margin is 2 inch each and right -left margin is 1 inch each.
So, length of poster inside margin (l) = (x-4 ) inch
width of poster inside the margin (w) = (y-2) inch
Area inside the margins = l × w sq. inch
= (x-4)(y-2) sq.inch ---(2)
from (1) we can find out the value of one variable and put in equation (2) ,
from( 1), y = 200/x
Area inside margins= (x-4)(200/x - 2) = 2(x -4)( 100/x - 1) = 2( 100 - x - 400/x + 4)
Area inside margins = 2 ( -x - 400/x + 104)
To minimize the area inside the margins we take first order derivative of it
dA/ dx = d/dx[ 2( -x - 400/x + 104) ]
= 2 d/dx ( -x - 400/x +104) = 2 ( -1 + 400/x² )
critical points occurs when dA /dx = 0
2 ( -1 + 400/x² ) = 0 => 800/x² = 2
=> x² = 400 => x = 20
putting value of x in equation (1) we get ,
x×y = 200 = 20× y => y = 10
so, length of poster is 20 inch and width is 10 inch.
Now, length of poster inside margin (l) = 16 inch
width of poster inside margin (w) = 8 inch
maximum area inside margin is 108 inch².
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what steps do data analysts take to ensure fairness when collecting data? select all that apply. 1 point clean the data provided use an inclusive sample population understand the social context include data self-reported by individuals
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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She uses 32 spacers, plus 7 beads per inch of necklace length. Where is x is the length in inches, of the necklace
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
What is a linear equation?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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Complete the equation describing how
x and y are related.
X
y
-2 -1 0
1
2 3 4 5
2
3
6 7
y = x + [?]
Enter the answer that belongs in [?].
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
m(x) = -2/3x + 8; m(x) = 2
Answer:
Answer is x = 9
O is the center of the circle, if ∠OPQ = 25° & ∠ORQ = 20°, find ∠PQR and ∠POR
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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19. Linej passes through point (2, 0)
and is perpendicular to the graph
of y=x-3. Line k is parallel to
line j and passes through point
(-1, 6). What is the equation in
slope-intercept form of line k?
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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true or false: the quantity represented by θ is a function of time (i.e., is not constant).
Answer: the answer to this is true
Building A is 200 feet shorter than Building B. The total height of the two buildings is 1510 feet. Find the height of each building.
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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then m = -3,
(2m + 3)² =?
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
The base of the parallelogram has a length
of 10 cm. What is the height?
10 cm
12cm
14cm
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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You have $300,000 saved for retirement. Your account earns 8% interest.
How much will you be able to pull out each month, if you want to be able to
take withdrawals for 15 years?
Answer:
Step-by-step explanation:
You wire be able to put out
month, for 25 years.
$2307.94 each
Write a sine function that has an amplitude of 3, a midline of 5 and a period of pie
The sine function is y = 5 sin ([tex]16\pi x[/tex] ) + 3.
What is Sine function?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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Find m/ABC and mZCBD if mLABD = 120°.
m/ABC=(5x-6)
m/CBD =2x
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.
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.
Let x represent how much money Joy wants to spend in all. Which inequality describes the problem?
The inequality to represent the problem is x - 78.50 ≤ 61.50.
Joy can sped at most 140 dollars.
How to represent problems with inequality?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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HEY 55 POINTS!!!!
Complete the sentence.
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.
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
Write the linear equation in standard form. Do not use any spaces in your answer.
2 + (1/2)x = y
By writing both variables in the same side of the linear equation, we will get the standard form:
2y + (-1)*x = 4
How to write the linear equation in standard form?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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Pls help due tomorrow!!!!!
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 the problems shown
The 65 represents the speed.
97.5 miles covered in 1.5 hours.
What is Algebra?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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Find the length x.
HELPPP PLSSSS
Answer: My answer is 4. You may want another answer.
Step-by-step explanation:
visual studying
what is the remainder when P(x)=x3-x2-2x+8 is divided by (x+2)
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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Sally earns $37.00 for 4 hours of babysitting. At this rate, how much more would she eam for 9 hours of babysitting? 6.RP.3 Step 1: Find the Unit rate of how much Sally makes per hour?
Alexander is working two summer jobs, babysitting and landscaping. He can work a maximum of 14 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours babysitting, b, and the number of hours landscaping, ll, that Alexander can work in a given week.
The inequality that would represent the possible values for the number of hours babysitting and landscaping is b + l ≤ 14.
What is an inequality?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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Today, the mountain that contains Mount Rushmore is approximately 5,675 feet high. The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.
The equation to find the height of the mountain prior to construction, represented by the variable h, is
1.1h – 622.5 = 5,675
Solve an equation to find the height of the mountain prior to construction, represented by the variable h.
h =
feet
5761.4 feet is the height of the mountain prior to construction
How to solve an equation to find the height of the mountain?
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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What is the slope of the line that passes through the points (2, 3) and (0, 11)
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.
In a cookie recipe, 1 2/3 cups of milk makes 16 cookies. How many cups of milk are needed to make 24 cookies?
how many soluitons does 3x - 13 = 7(x + 2) - 4(x - 7) have?
The equation, 3·x - 13 = 7·(x + 2) - 4·(x - 7), has no solution
What are the types of solutions of an equation?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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how to solve and answer:1
1/3(9-6x)=-11
Answer:
x = 2.875
Step-by-step explanation:
1 1/3 (9 - 6x) = -11
12 - 8x = -11
- 8x = -23
x = 2.875
pls help. It will make my day even better
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)
A line goes through (-5,3), (1,1) and (7,-1)
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
factorize X² + 2X - 48
Answer:
(X−6)(X+8)
Step-by-step explanation: