The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.
What is the area of a rectangle?The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:
Area of a rectangle = length(x) × breath(y)
1000000 sq.ft = (x) × (y) ---- (1)
However, to determine the fencing, we have:
Length of fencing = 2x + 2y
since the rectangle has four sides and opposite sides are equalSuppose we use the x-direction to estimate the region where the fencing is located, we have:
Length of fencing = 2x + 2y + x
Length of fencing = 3x + 2y ---- (2)
From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)
The Length of fencing is:
[tex]\mathbf{L = 3x - 2( \dfrac{1000000}{x})}[/tex]
[tex]\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}[/tex]
[tex]\mathbf{ x^2= \dfrac{2000000}{3} }[/tex]
[tex]\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }[/tex]
[tex]\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}[/tex]
Now, if we replace the value with equation (1), then y will be:
[tex]\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\ \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}[/tex]
[tex]\mathbf{x =500\sqrt{6}}[/tex]
Now, the shortest length of the fencing can be computed by using the equation (2):
L = 3x + 2y
[tex]\mathbf{L = 3( \dfrac{1000 \sqrt{6}}{3}) + 2(500 \sqrt{6})}[/tex]
[tex]\mathbf{L =1000 \sqrt{6} + 1000 \sqrt{6}}[/tex]
[tex]\mathbf{L =2000 \sqrt{6} }[/tex]
[tex]\mathbf{L \simeq 4899 \ ft}[/tex]
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The circumference of a circle is 18π ft. What is the area, in square feet? Express your answer in terms of \piπ.
HELp pls
Answer:
A = 81 pi ft^2
Step-by-step explanation:
We know the circumference of a circle is given by
C = 2 * pi *r
18 pi = 2 * pi *r
Divide each side by 2 pi
18 pi / ( 2pi) = 2 pi r / ( 2pi)
9 = r
We can find the area by
A = pi r^2
A = pi ( 9)^2
A = 81 pi ft^2
Factor out the following:
-x^5+9x^3
Answer:
x^3(-x+3)(x+3)
Step-by-step explanation:
-x^5 + 9x^3
factor out x^3
x^3(-x^2+9)
9 and -x^2 are perfect squares so we can factor out a 3 and an x to get (-x+3)(x+3)
the fully factored form would be x^3(-x+3)(x+3)
Answer:
-x^3(x - 3)(x + 3).
Step-by-step explanation:
-x^5+9x^3
the greatest common factor = x^3 so we can write it as
x^3(-x^2 + 9)
= -x^3(x^2 - 9)
The expression in the parentheses is the difference of 2 squares so we have:
-x^3(x - 3)(x + 3) Answer.
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!
Find the mode of the data
Answer:
shoe size (US) 6
Step-by-step explanation:
Mode = most frequently occurring data value
From inspection of the table, we can see that the highest frequency (most number of women) is 20, so therefore the modal class of the data is shoe size (US) 6.
Answer:
Shoe Size (US) = 6Step-by-step explanation:
The mode of the data is the modal class with the highest frequencyIt is 20, present in the 4th columnIts corresponds with the modal class : Shoe Size (US) = 68 + (7 + 1) 2 ÷ 4 ⋅ 1 over 2 whole to the power of 4
Answer:24divided by 16/64
Step-by-step explanation:
8x[7+1]2/4x4/16
8x8/2/4x4/16
48/2/4x4/16
48/2/16/64
24/16/64
How to solve 16x-8y=72
**Kind note:
Since there are two variables in one equation, it is impossible to determine a specific value for x and y. (Unless the trial-and-error method is used).
How to determine the value of x using the equation (16x - 8y = 72)?
To determine the value of "x", we need to isolate the x-variable on one side. The value (or expression) obtained on the opposite side of the x-variable will be the value of x.
How to determine the value of y using the equation (16x - 8y = 72)?
To determine the value of "y", we need to isolate the y-variable on one side. The value (or expression) obtained on the opposite side of the y-variable will be the value of y.
Determining the x-variable:
⇒ 16x - 8y = 72
⇒ 16x = 72 + 8y [Adding 8y to both sides of the equation]
⇒ 16x/16 = (72 + 8y)/16 [Dividing 16 to both sides of the equation]
⇒ x = 9/2 + y/2 [Simplifying both sides of the equation]
⇒ x = (9 + y)/2 [Combining the denominators]
Determining the y-variable:
⇒ 16x - 8y = 72
⇒ 16x - 8y - 16x = 72 - 16x [Subtracting 16x both sides of the equation]
⇒ -8y = 72 - 16x [Simplifying both sides of the equation]
⇒ -8y/-8 = (72 - 16x)/-8 [Dividing -8 to both sides of the equation]
⇒ -8y/-8 = 72/-8 - 16x/-8
⇒ -8y/-8 = -72/8 + 16x/8
⇒ y = -9 + 2x [Simplifying both sides of the equation]
First simplify it to suitable form of slope intercept then you can get values
16x-8y=722x-y=9y=2x-9The pairs are
(1,-7)(2,-5)(3,-3)(4,-1)(5,1)And so on
The Egyptian pyramids have square bases and are roughly twice as wide as they are tall. If a miniature model of the pyramid is 3 inches wide, what is the volume of the model
If a miniature model of the pyramid is 3 inches wide. The volume of the model is 4.5.
Volume of the modelPyramids square bases are twice as wide as they are tall
Model of pyramid=3 inches wide
First step is to find the model height
Let Model height=x
2 × height=weight
2x=3
x=3/2
x=1.5
Second step is to calculate the volume of model:
Volume of model=3×3×1.5×1/3
Volume of model=4.5
Therefore the volume of the model is 4.5.
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Please show the work thank you!
Answer:
a= 1/4 , h=8 , k = -12
Step-by-step explanation:
There is really not much to say.
[tex]y=\frac{1}{x}[/tex] , [tex]y=\frac{1}{4x-32}-12[/tex]
Factor the denominator by 1/4.
[tex]y=\frac{1}{4(x-8)}-12[/tex]
You got your formula: [tex]y=\frac{a}{x-h}+k[/tex]⇒[tex]y=a\frac{1}{x-h}+k[/tex]
a= 1/4 means to shrink due to it being fraction.
h=8 means 8 right
k = -12 means 12 down.
what is 20% by 37 decreased
Answer:
37 decreased by 20% is 29.6.
Step-by-step explanation:
To do this, what we do is simply take 20% of 37 and subtract it from 37.
20% of 37. A trick to easily figure this out is multipling 37 by 20 and dividing by 100.
37*20 = 740
740 / 100 = 7.40
37 - 7.40 = 29.6
37 decreased by 20% is 29.6.
Tristan needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.75 hours and charged him $50 for parts. The total was $643.75. What was the cost of labor, per hour?
Answer:
its $125
thank me later <3
The cost of labor, per hour, will be equal to $125.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Tristan needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.75 hours and charged him $50 for parts.
The cost for labor per hour is,
TC = 50 + 4.75x
643.75 = 50 + 4.75x
x = ( 643.75 - 50) / 4.75
x = $125
Therefore, the cost of labor, per hour, will be equal to $125.
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A wall in Alex and Carla Dinu's garden is to be built using brick that is 5 3/8 inches wide and a mortar joint that is 3/4
inch wide. Using the diagram, what is the height of the wall?
Answer: 29 7/8
Step-by-step explanation:
The height of wall will be 29.875 inch.
How to measure height of the wall?The height of the wall can be measured by the sum of total height of bricks and the height of mortar joint between the bricks.
According to question there is 4 mortar joint and 5 rows of bricks.
How to determine the no. of mortar joint?1 mortar joint is situated between 2 bricks. So, if the no. of bricks is n, then mortar joint between them will be n-1.
So, width of one mortar joint is= 3/4 inch
Width of 4 mortar joints = (3/4)*4=3 inch
width of one brick is= 5.375 inch
Width of 5 bricks = 5.375*5=26.875 inch
Height of the wall
= width of 4 mortar joints + width of 5 bricks
= 3+26.875
=29.875inch or 29 7/8 inch
Therefore, the height of wall will be 29.875 inch.
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giving 50 points it's grade 9 algebra 1 help please
Answer:
(a) y = 34.27 + 7.79x
(b) r = 0.98 (nearest hundredth)
(c) strong, positive correlation - as the students spends more time studying, their test scores increase.
Step-by-step explanation:
Correlation measures how closely two variables are linked.
If two variables are correlated, you can draw a line of best fit on the scatter plot.
Explanatory (independent) variable is drawn on the x-axisResponse (dependent) variable is drawn on the y-axis.Linear regression is a method for finding the equation of a line of best fit on a scatter plot.
The regression line of y on x is: y = a + bx
where a = y-intercept and b = gradient
If b is positive, the variables are positively correlated.
If b is negative, the variables are negatively correlated.
Part (a)Inputting the data from the table into a calculator and using the statistical function:
a = 34.27272727
b = 7.792207792
Therefore, the linear equation is:
y = 34.27 + 7.79x
Part (b)The correlation coefficient is the Product Moment Correlation Coefficient (r) and measures the strength of the linear correlation between two variables.
Again, inputting the data from the table into a calculator and using the statistical function:
r = 0.9815741571
⇒ r = 0.98 (nearest hundredth)
Part (c)The r value is always between +1 and -1. The closer it is to +1 or -1, the stronger the correlation between the two variables.
Values close to +1 mean a strong, positive correlation.Values close to -1 mean a strong, negative correlation.Values close to zero mean a weak correlation.Therefore, as r is very close to +1, the correlation coefficient suggests a strong, positive correlation. In the context of the problem, this suggests that as the students spends more time studying, their test scores increase.
cylinder:
diameter = 6 mm
height = 18 mm
Answer:
508.9
Step-by-step explanation:
What is the volume of Trisha's
pyramid. in cubic inches?
9 in
6 in
8 in
Answer:
its 72 in cubed because you do the base area/2 x the height divided by 3 so the base area is 48 and divide by 2 is 24 and then multiply by the height of the pyramid which is 9 and that will give you 216 and divide by 3 which is 72
Step-by-step explanation:
please mark as brainliest
Can anyone help me with this?
Answer:
a. x=4 or x=−10
b. x= 3/2 or x= −8
Step-by-step explanation:
(FOR LETTER A)
Step 1: Factor left side of equation.
(x−4)(x+10)=0
Step 2: Set factors equal to 0.
x−4=0 or x+10=0
x=4 or x=−10
(FOR LETTER B)
Step 1: Factor left side of equation.
(2x−3)(x+8)=0
Step 2: Set factors equal to 0.
2x−3=0 or x+8=0
x= 3/2
or x= −8
Family B lives in Boise, Idaho. Their total household monthly income is $4,675.
Use the graph to calculate the central angle of each section for Family B. Then, complete the following table. Note: Express each angle measure as a number, rounded to the nearest tenth of a degree.
Family B
1. Housing
° ____
2. Food
° ____
3. Childcare
° ____
4. Transportation
° ____
5. Insurance
° ____
6. Other Needs
° ____
7. Taxes
° ____
Best answer gets brainliest!
Answer:
See below
Step-by-step explanation:
The pie chart gives the percentage of the $ 4675 that goes to each expense
Housing 16 % .16* 4675 = $ 748
Food 16% .16 * 4675 = $748
Childcare 18% .18 * 4675 = $ 841.50
Trnsport 13% .13 * 4675 = $ 607.75
etc I think you can do the others---- right ?
how do calculate probablility
Answer:
Let me get my notes real quick. Give me a few seconds. Ok, in order to dermine propability you first do:
1: Determine the event (Like picking out 2 red marbles from a bag.) with 1 outcome (In this case, getting the marbles.)
2: Find the total amount of outcomes, like 1 7 2 9 1 2 2 2, (Example: What is the propability of geeting a 2? 4/8/50%)
3: Divide the number of events (How many times you've done it.) by the number of possible outcomes.
That's all there is.
My coach bought 88 cupcakes to split with 11 people, What would my fair share be??
( 1 Person. )
Answer:
You would get 8 cupcakes
Step-by-step explanation:
Since we're splitting C (cupcakes) with P (people) and we know that c = 88 and p = 11 we have to do the equation c / p or 88 / 11 which equals 8.
can you help me please.
Answer:
Step-by-step explanation:
-x + 2y = 16
y = mx + 8
Start with the top equation. Add x to both sides.
-x + 2y + x = x + 16 Combine the left
2y = x + 16 Divide by 2
2y/2 = (1/2)x + 1/2(16)
y = 1/2 x + 8
If m = 1/2, both equations together will give an infinite number of solutions.
Evaluate cos 300' without using a calculator,
2
O A. 1 /
O B. 1
о
c
va
Answer:
[tex]Cos \ 300 = \dfrac{1}{2}[/tex]
Step-by-step explanation:
[tex]\sf \boxed{Cos \ (2\pi - \theta) = Cos \ \theta}[/tex]
Cos 300 = Cos ( 360 - 60)
= Cos 60
[tex]\sf = \dfrac{1}{2}[/tex]
A bag contains 5 marbles. There are 3 yellow marbles and 2 red marbles.
Suppose that Glen chooses a marble first and then Kris chooses one.
Answer the questions to show the probability that Kris will get a yellow marble if Glen chooses a yellow one first.
1. What is the probability that Glen will get a yellow marble? Show how you calculated this probability.
2. After Glen chooses a marble, how many are left in the bag?
3) If Glen chooses a yellow marble, how many yellow marbles are left?
4. If Glen chooses a yellow marble first, and does not put it back in the bag, what is the probability that Kris chooses a yellow marble?
If the hypotenuse of a right triangle has length 9 feet and one of the other sides has length 2 feet, what is the length of the remaining side, in feet?
[tex]\sf A) \sqrt{11}[/tex]
[tex] \sf B) \sqrt{7}[/tex]
[tex]\sf C) \sqrt{85}[/tex]
[tex]\sf D) \sqrt{77}[/tex]
[tex]\sf E) 7[/tex]
Apply Pythagorean theorem
P²=H²-B²P²=9²-2²P²=81-4P²=77P=√77Option D
Answer:
[tex]\sf D) \sqrt{77} \: ft [/tex]
Step-by-step explanation:
Given that,
→ Perpendicular (x) = ?
→ Hypotenuse (h) = 9 feet
→ Base (b) = 2 feet
Now by using the Phythagoras theorem,
→ (Hypotenuse)² = (Perpendicular)² + (Base)²
→ (h)² = (x)² + (b)²
→ (9)² = (x)² + (2)²
→ 81 = (x)² + 4
→ (x)² = 81 - 4
→ (x)² = 77
→ [ x = √(77) ]
Thus, length of remaining side is √(77) ft.
HELP URGENT!!! The surface area of a globe is about 1018 in^2. What is the diameter of the globe? Round to the nearest whole number.
PLS EXPLAIN THE STEPS
The diameter of the spherical globe that has a surface area of about 1018 in.² is: 18 inches.
What is the Surface Area of a Sphere?Surface area = 4πr², where r is the radius, which is half of the diameter.
The globe is a sphere with a surface area of 1018 in.².
1018 = 4πr²
Solve for r
1018 = 4πr²
1018/4π = r²
81.0 = r²
r = √81.0
r = 9 in.
Diameter = 2(r) = 2(9)
Diameter of the sphere = 18 in.
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Solve the equation 7=-10s-3
Answer:
s= -1
Step-by-step explanation:
I believe 7=-10s-3
(s=-1)
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
2 1/2
Step-by-step explanation:
Turn both fractions into improper fractions, multiply the whole number by the denominator and add the numerator.
4 3/4
4 * 4 + 3 = 19
19/4
2 1/4
2 * 4 + 1 = 9
9/4
Now since she drank 2 1/4 gallons of juice, subtract 9/4 from 19/4.
19/4 - 9/4 = 10/4
Now turn back into a mixed fraction, do this by putting 4 into ten twice and taking the remainder and putting it as numerator:
4 * 2 = 8
10 - 8 = 2
2 1/2
Quadratic function h can be used to model the height in feet of a rocket from the ground
t seconds after it was launched. The graph of the function is shown.
Answer:
t = -b 2a = -120/(-32) = 3.75 The height of the rocket is a maximum 3.75 seconds after its launch. To find the height we only need to plug into the model: s(3.75) = -16(3.752) + 120(3.75) + 80 = 305 The maximum height of the rocket is 305 feet.
Step-by-step explanation:
The maximum value of graph of function is (3.75,225).
How to build the equation and find value of x-axis ?
We consider, the equation is y=a(x-0)(x-7.5)
Now, when x=6 and y = 144
144=6a(-1.5)
⇒a= - 144/9
⇒a= -16
Now, y= -16(x-0)(x-7.5)
⇒ y= -16[tex]x^{2}[/tex]+120x
∴ x = -b/2a = -120/(-32) = 3.75
How to find y co-ordinate ?When x=3.75, then the value of y is maximum.
∴ [tex]y_{max}[/tex] = [tex]-16(3.75)^{2}+120*3.75[/tex]
= 225
Hence, the maximum value of y is 225.
So, the required co-ordinate is (3.75,225).
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A bowl of cereal weights 60g.Is that more or less than 1 kg?
Answer:
Less than 1 kg
Step-by-step explanation:
1 gram = 0.001kg
So 60g = 0.06kg
Which is a factor of x2 + 5x – 24?
(xO
(x-6)
O (x + 6)
(8 - x) O
(8 + x) O
Answer:
D.) (x + 8)
Step-by-step explanation:
Which two values multiply to (-24) and add to (5)?
These values are (-3) and (8):
-3 x 8 = -24
-3 + 8 = 5
As such, the factors include these two values. One of the factors (x + 8), is one of the answer choices.
x² + 5x - 24 = (x - 3)(x + 8)
What are the solutions to this quadratic equation?
x^2 + 13= 8x +37
A. X = 4 V10
B. X = –2 + 4v10
C. X = –4 4/10
D. X= 4 2V10
Answer:
B.
Step-by-step explanation:
x² + 13 = 8x + 37
HELPPP frenss!!! HURRY j
Answer:
(2, -7)
x = 2
y = -7
Step-by-step explanation:
Let's solve this system of equations by elimination.
Start by multiplying the first equation by 2:
[tex]2(4x)+2(3y)=2(-13)\\8x+6y=-26[/tex]
Next, multiply the second equation by 3:
[tex]3(-5x)+3(2y)=3(-24)\\-15x+6y=-72[/tex]
Notice that both equations now have a "6y", meaning we can subtract both equations and thereby eliminating the variable "y" from the equation:
[tex]8x+6y-(-15x+6y)=-26-(-72)\\8x+6y+15x-6y=-26+72\\23x=46[/tex]
Divide both sides by 23
[tex]x=2[/tex]
Substitute 2 for "x" to solve for "y".
[tex]4x+3y=-13\\4(2)+3y=-13\\8+3y=-13[/tex]
Subtract 8 from both sides:
[tex]3y=-21[/tex]
Divide both sides by 3:
[tex]y=-7[/tex]
Therefore the answer is:
[tex](x, y)=(2, -7)[/tex]
Additional Comments:
Note that we can only divide, subtract, multiply, or add both sides of the equation by the same quantity due to the Division, Subtraction, Multiplication, or Addition Property of Equality. These properties state that if you divide/subtract/multiply/add one side of the equation by one quantity, you must do the same to the other side of the equation so that it remains an equation.
need help please :,)
Answer:
x>=324
Step-by-step explanation:
sqrt(x) > = 18 square both sides of the equation
x >= 324