9514 1404 393
Answer:
58.5 ft by 39 ft
Step-by-step explanation:
Let x represent the length of the two horizontal segments. Then the three vertical segments will be ...
(234 -2x)/3
The total enclosed area is the product of these dimensions:
A = (x)(234 -2x)/3
A = (2/3)(x)(117 -x)
This is the equation of a downward-opening parabola with zeros at x=0 and x=117. The maximum of the parabola will be on the line of symmetry, halfway between these zeros. The value of x there is ...
x = (0 +117)/2 = 58.5
The lengths of the vertical segments are ...
(2/3)(117 -58.5) = 2/3(58.5) = 39
The dimensions of the region enclosing the maximum area are 58.5 ft by 39 ft. The additional vertical segment is 39 ft.
_____
Comment on maximum area problems
You may have noticed that the total length of the fence allocated to the long sides (2×58.5 = 117) is half the total length of fence and is equal to the total length of fence allocated to the short sides (3×39 = 117).
This relationship is true in all rectangular fencing problems where the area is being maximized for a given total fence length. It doesn't matter how many partitions there are in either direction: the total of horizontal lengths is equal to the total of vertical lengths.
Angle AOC has the measure of 87°, determine the measure of the angle in radians.
Answer:
1.518 radians is the answer.
Step-by-step explanation:
Degree to radian conversion = 1° × [tex]\frac{\pi }{180}[/tex]
87° × [tex]\frac{\pi }{180}[/tex]
1.518 radians
Find the area of the figure. 8.5 cm 9.5 cm 24 cm The area of the figure is_______cm2
Answer:
432 is the blank
Step-by-step explanation:
I just did this problem
if sinθ = A, find cos(π/2-θ)
(using trigonometric identities to fine the value)
Answer:
Cos(π/2 - θ) = A
Step-by-step explanation:
We know that:
Sin(θ) = A
And we want to find the value of Cos(π/2 - θ)
Here we can use the cosine relationship:
Cos(a - b) = Cos(a)*Cos(b) + Sin(A)*Sin(B)
Then:
Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ)
We know that:
Cos(π/2) = 0
Sin(π/2) = 1
Then:
Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ) = 0*Cos(θ ) + 1*Sin(θ)
= 1*Sin(θ) = A
Cos(π/2 - θ) = A
if y=10 when x=5 what does y equals when x=0.2
Answer:
.4
Step-by-step explanation:
y=2x
y=2(.2)
y=.4
there is your answer
A physical examination was used to screen for breast cancer in 7600 women with biopsy proven adenocarcinoma of the breast and in 11,000 age and race matched control women. The results of the physical examination were positive (i.e. a mass was palpated) in 5,500 cases and 1,700 control women (who showed no evidence of cancer at biopsy). The total population is 18,600. The sensitivity of the physical examination was:______.
Answer:
72.37%
Step-by-step explanation:
Calculation for what The sensitivity of the physical examination was
Using this formula
Sensitivity=Positive physical examination cases/Physical examination screening for breast cancer
Let plug in the formula
Sensitivity=5,500 cases / 7600 women
Sensitivity=0.7237*100
Sensitivity=72.37%
Therefore The sensitivity of the physical examination was 72.37%
Answer:
72.37% is the answer for this
1+1=???????????????????
Answer:
I.d.k I think 1 :)
Step-by-step explanation:
have a great day
Assessment timer and count
Assessment items
Item 1
A scientist studied the replication of bacteria in a lab environment. This table gives the bacteria count for the first 12 hours. The table can be modeled using an exponential function.
Hours 2 4 6 8 10 12
Bacteria count 1,240 5,100 20,990 86,520 365,520 1,469,170
What function best represents the data?
y=300+4x
y=1240⋅2.03x
y=4x
y=300⋅2.03x
Answer: y=300⋅2.03x
Step-by-step explanation:
Answer:
D.) y = 300 ⋅ 2.03x
Step-by-step explanation:
By using the plug-in method, you use "Hours" as the X in this question.
If you plug in 2, 4, 6, 8, 10, and 12 to y = 300 ⋅ 2.03x, you will get the closest answers to "Bateria Count"
1,236.27 = 300 ⋅ 2.03^2
5,094.54= 300 ⋅ 2.03^4
2,0994.11 = 300 ⋅ 2.03^6
86,514.63 = 300 ⋅ 2.03^8
and so on- all are the closest to the chart.
Hope this helped! :)
explain how you know plz
Answer:
this is a nonlinear function because the point do not have a steady rate of change for example y went up one and x went up 1 but from the next set of pairs y went up one and x went up three so this is a nonlinear function
If the sales tax rate is 8.5%, how much would you pay for an item that costs $26.00?
Answer:
23.79
Step-by-step explanation:
PLZZ help middle school math you just have to explain how to solve it. please don't put big words so I can understand and my teacher will think its me...lol
Answer:
tell her you don't understand it and she'll help you ok good luck
A? is a graphical display of a set of data where each separate piece of data is shown as a
mark above a number line.
Answer:
dot plot a visual display in which each piece of data is represented by a dot above a number line.
Step-by-step explanation:
Jason launched a rocket for a physics experiment. This equation can be used to find
the height (h), in feet, of the rocket after t seconds.
h = -16t2 + 288t + 8
How many seconds will it take for the rocket to reach a height of 1,304 feet?
Answer:
5.063 seconds
Step-by-step explanation:
Use a graphing calculator to graph, then use the table functions to solve for 1304
or say
1304= rest of equations and solve for X
Find the surface area and volume of the prism
Answer:
I only know the first one.
The surface area of the prism is 900 cm2
Step-by-step explanation:
To solve the surface area, we need to find the area of the SURFACE not the inside of the cube. Lets do the rectangles first.
28 x 13 = 364
28 x 5 = 140
28 x 12 = 336
1 1
336
+ 140
364
-------------
8 4 0
Now lets do the triangles.
Remember! To find the area of a triangle, you have to do Base x Height x 1/2 because it's half a rectangle.
(The triangles have the same area)
12 x 5 x 1/2 = 30
12 x 5 x 1/2 = 30
30
+ 30
--------
60
The last step is to add the areas of the triangles and the rectangles.
1
840
+ 60
------------
900 cm2
The answer is 900cm2
This Is not copy pasted, I actually put in all this effort.
Hope this helps :) And have a wonderful day! :D
Please verify the following trigonometric identities.
1. [tex]\frac{\tan x + \tan y}{\cot x + \cot y} = \tan x + \tan y[/tex]
2. [tex]\frac{\sin^3x + \cos^3x}{\sin x + \cos x} = 1 - \sin x \cos x[/tex]
3. [tex]\tan(\frac{x}{2}) + \cos x \tan(\frac{x}{2}) = \sin x[/tex]
Seems like there is a correction in the first question (RHS is tanx.tany)
(i) For convenience: let tanx = a ; tany = b
Thus, tanx + tany = a + b
Moreover, cotx = 1/tanx = 1/a ; coty = 1/b
Thus,
cotx + coty = 1/a + 1/b = (a + b)/ab
Hence,
=> (tanx + tany)/(cotx + coty)
=> (a + b) / { (a + b)/ab }
=> ab(a + b)/(a + b)
=> ab => tanx.tany , proved.
(ii) For convenience: let sinx = a ; cosx = b
As we know, sin²x + cos²x = 1 => a²+b²=1
=> (a³ + b³)/(a + b)
=> (a + b)(a² + b² - ab) / (a + b)
=> (a² + b² - ab)
=> 1 - ab => 1 - sinx.cosx , proved
(iii): let x/2 = A
=> tan(x/2) + cosx.tan(x/2)
=> tanA + cos2A.tanA
=> tanA [1 + cos2A]
=> tanA (2cos²A) {1+cos2A = 2cos²A}
=> (sinA/cosA) (2cos²A)
=> sinA (2cosA)
=> 2sinAcosA
=> sin2A
=> sin2(x/2)
=> sinx proved
Letting x/2 = A is not mandatory. I did it to decease words*(in a line).
Indentities used:
• sin²A + cos²A = 1
• (a³ + b³) = (a + b)(a² + b² - 1)
• 1 + cosA = 2 cos²(A/2)
• tanA = sinA/cosA.
• 2sinAcosA = sin2A
What number should
be added to both sides of the equation to complete the square?
x2 + 8x = 4
4
8
16
O 32
WILL GIVE BRAINLST
HAVE A AMAZING DAy !!
Answer:
u 2
and stay positive :)
Step-by-step explanation:
Hello! I do not know if you meant to put up a question, but I also hope that you have an amazing day! :)
Write an equation from a real life situation
1. A membership at a yoga studio costs $35 per month, m. Write an equation to find the final cost, c?
2. After you wrote your equation, answer this question. Show your work.
" You attended the yoga studio for 20 months. What was the final cost?
Answer:
1. C=35m?
2.C=700 or $700
Step-by-step explanation:
1. Total Cost= Rate x Number of Months
2. C=35m
Cost=rate x number of months
C=35(20)
C=700 or Total Cost=$700
Answer:
1. c = 35m
2. c = 35 · 20
20 · 35 = $700
Step-by-step explanation:
A 80-ounce bottle of apple juice contains 32 ounces of water. Which juice has the greater percent of water? What percent of the bottle of apple juice is water
Answer:
Only 1 juice is listed.....
So apple juice has the greatest percent of water
40%
Step-by-step explanation:
Answer:
40%
Step-by-step explanation:
Just did it on iready
Simplify 3^2 ⋅ 3^5
^ = are exponents
A 3^7
b
3^10
c
9^7
d
9^10
Answer:
B
Step-by-step explanation:
when simplifying base stays the same we only deal with exponent I think I need help too
Turner’s backyard deck cost $38.31 per square meter to build. The deck is 9 meters wide and 11 meters long. How much did it cost to build the deck?
Answer:
$3792.69
Step-by-step explanation:
First, we would find the area,
Area = width x length
Area = 9 x 11
Area = 99[tex]m^{2}[/tex]
Since each square meter costs $38.31, we would multiply the cost with the area,
Total Cost = 99 x 38.31
Total Cost = $3792.69
(Anyone can correct me if I'm wrong)
3/5 x ?/? = 3/5 plz im on a test!
Answer:
Dont say its a test youll get reported and banned by brainly
Step-by-step explanation: also the answer is: 3/5 x 3/5 = 925 = 0.36
Answer: 1/1
Step-by-step explanation:
1/1 because it = 1 so that means 3/5 x 1/1 is 3/5
Mitch has 2 cups of unpopped popcorn. He uses
1/4 cup to make 1 bowl of popcorn. How many bowls of
popcorn can he make?
I really need help Will give brainyest!!!
Answer:
C.
Step-by-step explanation:
The median is the middle line of the box. 30 is for Town A and 40 is for Town B. 30 is less than 40
Asim mixed 5 gallons of paint.
Which of the following can be used to
find the number of pints of paint that
Is Asim mixed?
a.5 × 4 × 2
b. 5 × 4 , 2
c.5 × 2 × 2
d.5 , 2 × 2
is it a.b.c.d?
Answer:
5 × 4 × 2
Step-by-step explanation:
5 gallons
4 quarts per gallon
2 pints per quart
which expression is equivalent to 8(5x-3)
13x-11
13x-24
40x11
40x-24
Answer:
The last answer option.
What is the volume of the cone to the nearest cubic millimeter (use pi)
If DB = 18cm and AC = 24cm, Use the properties of rhombus to find the length of one side of the rhombus please helppp!!!!
Answer:
15 cm
Step-by-step explanation:
You need to remember 2 theorems about a rhombus.
1. The diagonals of a rhombus bisect each other
2. The diagonals of a rhombus are perpendicular to each other
In other words, the diagonals of a rhombus are perpendicular bisectors.
BE = 9 and AE = 12
ΔAEB is a right triangle. So, the Pythagorean theorem says
[tex]9^{2} + 12^{2} = AB^{2}[/tex]
[tex]AB^{2}[/tex] = 81 + 144
= 225
AB = [tex]\sqrt{225} = 15[/tex] cm
PLEASE HELP NO WRONG ANSWERS
Answer:
I believe it's C
Step-by-step explanation:
[tex]\\ \sf\longmapsto Area=30x^2-53x+12[/tex]
[tex]\\ \sf\longmapsto Area=30(3)^2-53(3)+12[/tex]
[tex]\\ \sf\longmapsto Area=30(9)-159+12[/tex]
[tex]\\ \sf\longmapsto Area=270-159+12[/tex]
[tex]\\ \sf\longmapsto Area=111+12[/tex]
[tex]\\ \sf\longmapsto Area=123[/tex]
And
[tex]\\ \sf\longmapsto Base=4x-6[/tex]
[tex]\\ \sf\longmapsto Base=4(3)-6[/tex]
[tex]\\ \sf\longmapsto Base=12-6=6[/tex]
Now
[tex]\\ \sf\longmapsto Area=\dfrac{1}{2}bh[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{2}6h=123[/tex]
[tex]\\ \sf\longmapsto 3h=123[/tex]
[tex]\\ \sf\longmapsto h=\dfrac{123}{3}[/tex]
[tex]\\ \sf\longmapsto h=41[/tex]
Determine the domain and range of each graph. Use inequalities to write your answer.
Answer: Domain is [3,∞), The range is All real numbers.
Step-by-step explanation:
There are five blue crayons, seven yellow crayons, and eight red crayons in a box. If one is randomly drawn and replaced 15 times, find the probability of drawing exactly four blue crayons.
0.2252
(Please mark me brainliest! thank you in advance!!)