The dimension of pen that maximize the area is 150 ft by 150 ft.
What is the dimension of a area?
In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
Given the perimeter of the rectangular is 600 ft.
Assume that the length of the rectangular be l and the breadth be b.
The perimeter of the rectangular is 2(l+b).
According the question:
2(l+b) = 600
Divide both sides by 2:
(l+b) = 300
l = 300 - b
The area of rectangular is A = lb
Substitute the value of l in the above equation:
A = (300 - b) b
A = 300b - b^2
The maximum value of a quadratic polynomial Ax^2+BX+C is at x = - B/(2A).
Compare Ax^2+BX+C with 300b - b^2:
A = -1 and B = 300.
Putting A = -1 and B = 300 in b= - B/(2A).
b= - 300/(2×(-1))
b = 150.
Putting b =150 in l = 300 - b
l = 300 - 150
l = 150
The dimension is 150 ft × 150 ft.
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if m angle 1 =3x +15 and m angle 2 = 6x+3 find x
Answer:
x=27 I think
Step-by-step explanation:
1 = 3x + 15
2 = 6x + 3
We can solve by putting both equations together.
Let's multiple the top equation by -2
-2(1 = 3x + 15)
-2 = -6x - 30
2 = 6x + 3
0=x - 27
27=x
5. A road has a 6% downgrade (meaning for every 100 feet you could go horizontally, you go down 6
feet). What is the angle the road makes?
The angle the road makes is 3.43°
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
A 6% downgrade means that for every 100 units of horizontal run.
The vertical height decreases by 6 units.
The grade has a downward angle of
tan⁻1(6/100) = 3.43°
Hence, the angle the road makes is 3.43°
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Choose the equation that represents the line that passes through the point (6, -3) and has a slope of. 1/2
y-2x+6
y-1x-6
y=2x-3
y=x+3
Answer:
The line meeting the criteria is y = (1/2)x + 6 does not match any of the answer options.
Step-by-step explanation:
Let's use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0). We are given the slope, (1/2), so let's put that into the equation:
y = (1/2)x + b
It is the value we choose for b that will make the line pass through point (6,-3). We can determine that value by entering the given point in the equation and then solving for b:
y = (1/2)x + b
-3 = (1/2)*(6) + b for point (6,-3)
-3 = 3 + b
b = -6
The full equation is thus y = (1/2)x + 6
See the attached graph.
===
The `list of options doesn't have an equation that matches this conclusion. The first two aren't even equations. Assuming for the moment they are mistyped and should have an "=" sign after the y, we will change the list as follows:
Original New
y-2x+6 y=2x+6
y-1x-6 y=1x-6
y=2x-3 y=2x-3
y=x+3 y=x+3
The slopes are either +1 or +2. None have the required slope of (1/2)
What is the answer to this question?
We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.
Given that,
The linear equation is y=-9x-10.
We have to fill the table given in the question.
First,
Taking x value is -8
We get y value as,
y=-9(-8)-10 (multiply -9 and -8)
y=72-10 (Subtracting 72 and 10)
y=62
When x is -8 y is 62.
Taking y value is -73
We get x value as,
-73=-9x-10
-73+10=-9x
-63=-9x
63=9x
x=63/9
x=7
When y is -73 x is 7.
Taking x value is 3.
We get y value as,
y=-9(3)-10
y=-27-10
y=-37
When x is 3 y is -37.
Therefore, We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
In words, describe the graph of the proportional relationship.
A line from (0, 0) going through (22.25, 25) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (25, 22.25) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
Answer:
(B) A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
Step-by-step explanation:
You want a description of the graph showing the proportional dependency of cost on weight if a couple of (weight, cost) points are (25, 22.25) and (41, 36.49).
GraphThe independent variable is weight, so the x-axis will be labeled Weight (in pounds). The dependent variable is cost, so the y-axis will be labeled Cost (in dollars). The two given points can be plotted on the graph.
The description from the available answer choices is ...
A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
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Determine which set of side measurements could be used to form a triangle.
A. 13, 19, 7
B. 25, 12, 13
C. 18, 2, 24
D. 3, 1, 5
Option A. The set of side measurement that can be used to form a triangle is given as A. 13, 19, 7
What is a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
How to get the measurement that can produce a triangle.
a + b > c = 13 + 19 > 7
a + c > b = 13 + 7 > 19
b + c > a = 7 + 9 > 13
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D. 4. A Jamaican Airline plane flew 1,200 miles southeast from Freeport Bahamas to San Juan Puerto Rico. The plane then flew 800 miles west to Montego Bay, Jamaica. The plane then flew north back to Freeport. To the nearest whole mile, how far did the plane fly from Montego Bay to Freeport? Bermada 1,200 miles Hast Dominican Bers 800 miles CARII WorldA Atlantic Ocean TUK
The flight of plane from Montego bay to freeport is 894 miles.
To solve this we use Pythagoras theorem.
What is Pythagoras theorem?
The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem.
Main Body:
Formula for Pythagoras theorem = [tex]P^{2} +B^{2}[/tex]= [tex]H^{2}[/tex]
here H = 1200
B= 800
P =?
solving this equation
1200² = 800²+P²
P²= 800000
P=[tex]\sqrt{800000}[/tex]
P ≈ 894 miles
Hence the distance of flight from Montego Bay to Freeport is 894 miles.
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Tommaso and Pietro have each been given 3,818 euro to save for college.
Tommaso wants to invest his money in an account such that his investment
will increase to 1.6 times the initial amount in 6 years. Assume the account
pays a nominal annual interest of r % compounded quarterly.
Determine the value of r. Give your answer as a percentage number, not as
a decimal equivalent. Round to two decimal places.
Assume the account pays a nominal annual interest of r% compounded quarterly, the value of the interest rate (r) is equal to 7.87%.
How to determine the value of r?Mathematically, compound interest can be calculated by using this formula:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Substituting the given parameters into the formula, we have;
1.6(3,818) = 3,818(1 + r/8)^{8 × 6}
1.6 = (1 + r/8)^{48}
Taking the 48th root of both sides of the equation, we have:
[tex]\sqrt[48]{1.6} = \sqrt[48]{(1 + \frac{r}{8} )^{48} }[/tex]
1.00983983823726 = 1 + 0.125r
0.125r = 1.00983983823726 - 1
0.125r = 0.00983983823726
Interest rate, r = 0.00983983823726/0.125
Interest rate, r = 0.0787
Interest rate, r = 7.87%
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We know that the diretrix is at x = 5 and that h = 2. This would make p =
When the directrix is at x = 5 and point in the vertex is at h = 2. Then P would be -3
What is P in parabolic equation?In the equation of parabola, P is defined as the distance between the directrix and the vertex
The vertex is defined by the points V ( h, k )
h is for the x coordinate
k is for the y coordinate
when the directrix is given in the x, we solve for P using h
P = h - point given for directrix
P = 2 - 5
P = -3
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y=5/x. Make x the subject of the formula
Solve in terms of x.
[tex]y=\frac{5}{x}[/tex]
Multiply by x on both sides to remove it from the denominator.
xy =5
Divide by y to get x by itself
[tex]x=\frac{5}{y}[/tex]
Answer:
x=5/y
Step-by-step explanation:
y=5/x
cross multiplying
yx=5
x=5/y
The sum of the two numbers is -34 and their difference is 5. Find the numbers.
Answer:
y = -19.5, x = -14.5
Step-by-step explanation:
We can form equations from this statement:
x + y = -34
x - y = 5
If we rearrange the second equation, we get:
x - y = 5
x = 5 + y
Then, we substitute this value into the other equation to get the answer.
x + y = -34
5 + y + y = -34
Then solve:
2y + 5 = -34
2y = -39
so, y = -19.5
now we can find x with y:
-19.5 + x = -34
-34 + 19.5 = x
x = - 14.5
The sum of thrice a number and 5 is greater than or equal to the sum of twice a number and 1. Write down the inequality and solve it..
Answer:
May be helpful.
thx.......
Find the length of X using law of cosines.
The length of the X using law of cosine is 34.30yd.
What is cosine?
In a right angled triangle, the cosine of an angle is:
The length of the adjacent side divided by the length of the hypotenuse.
The abbreviation is cos
cos(θ) = adjacent / hypotenuse
Consider that;
[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex] (using law of cosine)
[tex]X = \sqrt{21^2+18^2-2\times 21\times 18\times cos(123 ^\circ)}[/tex]
[tex]X = \sqrt{441+324-756\times (-0.5446)}[/tex]
X = 34.30 yd
If A, B, and C are the measures of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite the corresponding angles, then the square of a side of the triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.
[tex]c^2 = a^2+ b^2- 2abcos C[/tex]
We have to the value of X which is present on the side c,
so, from the above formula we modified for the X,
and the formula become,
[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex](using law of cosine)
rest of the solutions are only calculation which is elaborated above which provide us the value of X = 34.30 yd.
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How many solutions does the
equation have?
3(d + 11) = 6(d + 33)
a. 0
b. 1
c. infinitely many
Answer: 1 solution
Step-by-step explanation:
3(d+11)=6(d+33)
simplifing the above equation
3d+33=6d+198
3d-6d=198-33
-3d=165
d= -165/3
d=-55
Answer:
b. 1
Step-by-step explanation:
3d + 33 = 6d + 198
3d - 6d = 198-33
-3d = 165
thus, d = -165/3
= -55
Triangles geometry . PLS
Step-by-step explanation:
Angle BAC = angle BCA
as sum of angles in triangle = 180
49 + 49 + ABC = 180
180 - 49 - 49 = ABC
ABC = 82°
some answer?
4. Look at the functions that describe the profits of each business. Why do you think the a-value of the lawn care business is negative while the a-values of the dog walking and housesitting businesses are positive?
The a-values of the business are classified as follows:
Dog walking and house-sitting: positive because they are represented by increasing functions.Lawn care: negative because it is represented by a concave down parabola.How to obtain the a-value of a business?The a-value of a business depends on the behavior of the earning function for these business, as follows:
The a-value is positive if the function is increasing.The a-value is negative if the function has decreasing points.From the table given by the image at the end of the answer, for the lawn care business, a concave down parabola represents the situation, as the earnings start increasing but then during the 3rd month they start to decrease. Hence, the a-value of the business is negative.
For the dog walking and for the house-sitting business, the values are always increasing over the time interval of the table, hence the a-value of these two businesses is positive.
Missing InformationThe table is given by the image at the end of the answer.
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a sock drawer contains 10 white socks, 6 black socks , and 8 blue socks if 2 socks are chosen at random, without replacement
calculate the probability she chooses 2 socks of the same colour
Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
calculate the probability she chooses 2 socks of the same colour ?I clarify this because the question uses plural “drawing white socks”. Ok, in our language practice one does usually say socks instead of sock because they usually come in pair.
If it means 1 draw of 1 sock then the probability is 6out of 21. Or about 28.57%
But if it is to draw twice with one sock being drawn in each draw to get a pair of white socks then the probability is 6/21 * /20 = 30/420 = 1/14 or about 7.14%
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a telephone call arrived at a switchboard at random within a one-minute interval. the switch board was fully busy for 15 seconds into this one-minute period. what is the probability that the call arrived when the switchboard was not fully busy?
The chance that the call arrived when the switchboard was not completely busy is 0.75.
Probability is a branch of mathematics that studies the likelihood of a random event occurring.
It is given that the switchboard is fully busy for the first 15 seconds, that means it is not busy for the next 15 seconds to 60 seconds
Therefore the probability that calls arrived when the switchboard was not fully busy is
P(15< x < 60) = ∫_15^60▒f(x)dx
= ∫_15^60▒〖1/60 dx〗
=1/60 ∫_15^60▒〖1.dx〗
= 1/60 [ x ]6015
= (60 – 15)/60
= 45/60
= ¾
= 0.75
Therefore the probability that the call arrived when the switchboard was not fully busy is 0.75
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there have been 2 earthquakes in the magnitude range 6.0-7.0 in the san francisco area over the past 30 years. what is the mean recurrence interval of earthquakes in this magnitude range?
The mean recurrence interval between earthquakes of this magnitude range over the previous 30 years essentially has been 4.769230 in a basically sort of big way in a subtle way.
Given, the earthquake's magnitude literally basically is between 6.0 and 7.0 in a very definitely big way, or so they for all intents and purposes thought. occurrences = 2 earthquakes
Duration: 30 years
particularly Mean Earthquake Recurrence Interval,
T=(n+1) / m
Where m = 6+7 / 2 = 6.5 , n = 30
T = ( 30+1)/6.5
= 31/6.5
= 4.769230
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What’s the exact value of sin,cos,tan.
Answer:
a) 1
b) 0.5
c)0
Josiah read 28 pages in 1 3/5 hours. At what rate, in pages per hour, did he read?
PLEASE HELP!!!!
Josiah read at the rate of 17.5 pages per hour.
What is the speed of reading?Speed of reading is the number of pages read per hour.
Given here, Josiah read 28 pages in 1 ³/₅ hours which is in mixed fraction
now 1 ³/₅ = ⁸/₅ = 1.6 hours
therefore the speed of reading is = 28 / 1.6 = 17.5 pages hour.
Hence, Josiah's the speed of reading is 17.5 pages hour.
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Graph the line with slope 1 passing through the point -2, -5 .
~Shown Graph and Question~
Answer: y = x - 3
Step-by-step explanation:
Answer:
y = x+3
Step-by-step explanation:
First of all we have to find the equation of the line
Slope-intercept form is:
[tex]y=mx+b[/tex]
Putting the value of slope
[tex]y=x+b[/tex]
Putting the point in the equation
(-4,-1)
[tex]-2=-5+b\\b=-2+5\\b=3[/tex]
So the equation is:
[tex]y=x+3[/tex]
The graph is attached with the answer
Keywords: Equation of line, slope
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Kaela wants to purchase a pair of shoes at Macy’s that cost $80. If Macy’s charges a
6% sales tax, how much will Kaela pay for the shoes, including tax?
Answer: $84.80
Step-by-step explanation:
The actual sales tax was 4.80 because 6% of 80 is 4.80
Then add the 4.80 to the 80 to get your total
Hope this helped :)
Jorge ha 173 fih for hi dog led team that he want to divide into maller piece how many piece of fih would there be if jorge divided eachfih into thenth
If the fishes are divided to be in tenths, then the total pieces of fishes that would be available would be 1730
How to solve for the pieces of fishIt is assumed that Jorge has 173 fish that he intends to cut up into smaller portions for his dog sled team.
The amount of fish pieces that would remain if Jorge divided each fish into tenths must be determined.
We are aware that there are 10 pieces to every fish.
There are a total of 173 fish available for the dog.
The product of the number of fish that are available and the number of pieces that each fish is divided into results in the total number of fish.
173 * 10
= 1730 pieces of fish.
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Complete question
Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
Weekly
wages at a certain factory
are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
[ ? ]%
The probability that a worker selected at random makes between $350 and $400 = 0.34134
What is a z score formula?
The standard score represents how far a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Positive standard scores are assigned to raw scores that are greater than the mean, while negative standard scores are assigned to raw scores that are less than the mean.
By using the z score formula:
z = (x - μ) / σ
Where,
x = raw score
μ = mean
σ = Standard deviation
We are told in the question to find the probability that a worker selected at random makes between $350 and $400
Consider, x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.
z1 = (x1 - μ) / σ = (350-400) / 50 = -1
z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0
From tables, P(z <= -1) = 0.15866
P(z <= 0) = 0.5
Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134
Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134
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Does the series shown below converge or
diverge?
If convergent, find its sum.
Answer: Diverge Reasoning I took the test
degree and real roots of (x-3)(x+1)(x-1)=0
Step-by-step explanation:
at first multiply the factors
[tex] ({x}^{2 } + x \: - 3x \: - 3)(x - 1) = 0[/tex]
[tex] {x}^{3} - {x}^{2} - 3 {x}^{2} - \: 3x - {x}^{2} - x \: + 3x + 3 = 0[/tex]
[tex] {x}^{3} - 5 {x}^{2} - x + 3 = 0[/tex]
Here we see the highest power is 3 so the degree of the equation is 3
As for the real roots, the factors each as in (x-1), (x-3) & (x+1) can be considered zero each to find the real roots because for the value of x to be zero any of the multiplied factors must be zero.
either, x-1=0
=> x = 1
or, x+1=0
=> x = -1
or, x-3=0
=> x = 3
real roots of x are: 1, -1 and 3
Vivian and Kyle each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Vivian has 18 signatures, and Kyle has 14. Vivian is collecting signatures at an average rate of 1 per day, whereas Kyle is averaging 3 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?
The number of days it take the same number of signature will be 2 days.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Vivian has 18 signatures, and Kyle has 14.
Vivian is collecting signatures at an average rate of 1 per day, whereas Kyle is averaging 3 signatures every day.
Now,
Since, Vivian has 18 signatures, and Kyle has 14.
And, Vivian is collecting signatures at an average rate of 1 per day, whereas Kyle is averaging 3 signatures every day.
Let number of days it take the same number of signature = x
So, We can formulate;
⇒ 18 + x = 14 + 3x
Solve for x as;
⇒ 18 + x = 14 + 3x
⇒ 18 - 14 = 3x - x
⇒ 4 = 2x
⇒ 2x = 4
⇒ x = 2
Thus, The number of days it take the same number of signature will be 2 days.
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pls help me wit this
Take 16 objects (pieces of paper, coins, plums, checkers) and put them in four
rows of 4 each. Remove 6, leaving an even number of objects in each row and each
column. (There are many solutions.)
There can be different possible ways in which we can remove the objects and can form possibilities within the rows and columns
What are rows and columns?
Rows and columns are used to properly distinguish categories, classifications, types, etc., when they occur in matrices, spreadsheets, etc. The usage of these words is a bit confusing for most. Rows are a group of cells arranged horizontally to provide uniformity. Columns are a group of cells aligned vertically, and they run from top to bottom. Although the main reason for both rows and columns is to bifurcate groups, categories, and so on,
In the question, It is given that:
There are 16 objects.
and Number of rows = 4;
Number of column = 4;
The task to do is to remove 6, leaving an even number of objects in each row.
So, we can do that in the following manner;
So, we can remove the 2nd object, 4th object, 6th object,8th object,10th object, and 12th object. when we are dealing with rows.
So, we can remove the 2nd object, 4th object, 6th object,8th object,10th object, and 12th object. when we are dealing with the column.
Hence,
There can be different possible ways in which we can remove the objects and can form possibilities.
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