Answer:
a) length x = 45ftb) maximum area = 4050 ft²Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
Hence the length of the building that should border the yard to maximize the area is 45 ft
To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
Hence the maximum area of the yard is equal to 4050 ft²
PLEASE HELP
You have to create 3 functions to make hills on a grap
Requirements are in the photo.
(ignore graphs)
4. Write equations for three hills that do meet the requirements. Sketch them on one axis. (For the
purposes of this exercise, this is a sketch, so the steepness and minimums and maximums of the
graphs do not need to be exact). (6 points: 1 point for each equation, 1 point for each sketched curve)
Answer:
Hill 1: F(x) = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)
Hill 2: F(x) = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)
Hill 3: F(x) = 4(x - 2)(x + 5)
Step-by-step explanation:
Hill 1
You must go up and down to make a peak, so your function must cross the x-axis six times. You need six zeros.
Also, the end behaviour must have F(x) ⟶ -∞ as x ⟶ -∞ and F(x) ⟶ -∞ as x⟶ ∞. You need a negative sign in front of the binomials.
One possibility is
F(x) = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)
Hill 2
Multiplying the polynomial by -½ makes the slopes shallower. You must multiply by -2 to make them steeper. Of course, flipping the hills converts them into valleys.
Adding 3 to a function shifts it up three units. To shift it three units to the right, you must subtract 3 from each value of x.
The transformed function should be
F(x) = -2(x +1)(x)(x -2)(x -3)(x - 6)(x - 7)
Hill 3
To make a shallow parabola, you must divide it by a number. The factor should be ¼, not 4.
The zeroes of your picture run from -4 to +7.
One of the zeros of your parabola is +5 (2 less than 7).
Rather than put the other zero at ½, I would put it at (2 more than -4) to make the parabola cover the picture more evenly.
The function could be
F(x) = ¼(x - 2)(x + 5).
In the image below, Hill 1 is red, Hill 2 is blue, and Hill 3 is the shallow black parabola.
Part of the population of 6,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 6 of them are infected. How many elk are likely to be infected? Based on the sample, there will likely be infected elk in the wildlife preserve.
====================================================
Explanation:
6 in the sample of 50 are infected, so 6/50 = 12/100 = 12% are infected in the sample. We expect this percentage to carry over to the entire population assuming we picked a representative random sample that isn't biased.
12% of 6250 = 0.12*650 = 750 is the expected number of infected individuals in the population.
----------
Here's an alternative way you can solve through a proportion
(number infected)/(total) = (number infected)/(total)
6/50 = x/6250
6*6250 = 50x ... cross multiply
37500 = 50x
50x = 37500
x = 37500/50 ... divide both sides by 50
x = 750
Find the mode for the data set 18 24 24 24 25 37 37 46
Answer:
the mode would be 24
Step-by-step explanation:
it is what numbers appears most often
What is the simplest form of this expression? 3x(-x2 + 2x + 12)
Answer:
-3x³ + 6x² + 36x
Step-by-step explanation:
3x(-x² + 2x + 12)
3x*-x² + 3x*2x + 3x*12)
-3x³ +6x² + 36x
how many five card hands that contain all 4 aces can be dealt from a standard pack of 52 cards
Answer:
48
Step-by-step explanation:
52-4=48
hope this helps
if f(x)=x-6 and g(x)=x^1/2(x+3), find g(x) X f(x)
Answer:
[tex]\bold{f(x)\cdot g(x)=\big x^\frac52-3\big x^\frac32-18\big x^\frac12}[/tex]
Step-by-step explanation:
[tex]f(x)=x-6\ ,\qquad g(x)=\big x^\frac12(x+3)\\\\\\f(x)\cdot g(x)=(x-6)\cdot\big x^\frac12(x+3)=\big x^\frac12(x^2-3x-18)=\big x^\frac52-3\big x^\frac32-18\big x^\frac12[/tex]
plz help me f(x) = 2x – 2 , find f(– 1)
Answer:
-4
Step-by-step explanation:
f(-1) = 2(-1) - 2 = -4
I NEED HELP ASAP FOR THIS MATH QUESTION
Answer:
The answer is C.
Step-by-step explanation:
First, you want to isolate the variable you are look for, 'l'. First subtract [pi]L from both sides. Then subtract S from both sides.
-[pi]L+S=[pi]r(superscript)2 ->
-[pi]L=[pi]r(superscript)2-S
Now, since you have your variable 'l', you want to remove the [pi] away from your variable. To do this, multiply by negative 1 divided by pi, or -1/[pi].
L=S-r(superscript)2.
Therefore, the answer is C.
Answer:
C
Step-by-step explanation:
[tex]s = \pi .l \: + \pi. {r}^{2} [/tex]
Make the term including 'l' stand alone.
[tex]s - \pi. {r }^{2} = \pi.l[/tex]
Now make L stand alone by dividing through by pi.
[tex] \frac{s - \pi. {r}^{2} }{\pi} = l[/tex]
This is the same as
[tex] \frac{s}{\pi} - {r}^{2} = l[/tex]
a 6 meter pole is supported by guy wires that are anchord to the ground as shown. what is sin d?
Answer:
6/6.71
Step-by-step explanation:
If you are given a 6-meter pole that is supported by guy wires that are anchored to the ground, you can create a relationship with respect to sin theta. sin theta is equal to the 6 meters over the slant line supported by the pole. as shown.
jack has 13 lengths of rope. Each is 6 3/4 meters long. How much rope does Jack have to divide amond 20 people
Hey there! I'm happy to help!
First we multiply the the length of each length of rope by the number of lengths of rope (try saying that five times fast).
6 3/4×13=87 3/4
Now, we divide this by 20 to see how much rope each person gets.
87 3/4÷20= 4 31/80
Therefore, each person has 4 31/80 or 4.3875 meters of rope.
I hope that this helps! Have a wonderful day! :D
The sum of Rhonda and her daughter Tenica’s age is 64. The difference in their ages is 28. How old is each person?
Answer:
The mother (Rhoda) is 46 years old.
The daughter (Tenica) is 18 years old
Step-by-step explanation:
Let the age of the mother (Rhoda) be m
Let the age of the daughter (Tenica) be d.
The sum of Rhonda and her daughter Tenica’s age is 64. This can be written as:
m + d = 64 ... (1)
The difference in their ages is 28. This can be written as:
m – d = 28 ... (2)
From the above illustrations, the equation obtained are:
m + d = 64 ... (1)
m – d = 28 ... (2)
Solving by elimination method:
Add equation 1 and 2 together
. m + d = 64
+ m – d = 28
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
2m = 92
Divide both side by 2
m = 92/2
m = 46
Substitute the value of m into any of the equation to obtain the value of d. Here, we shall use equation 1
m + d = 64
m = 46
46 + d = 64
Collect like terms
d = 64 – 46
d = 18
Therefore, the mother (Rhoda) is 46 years old and the daughter (Tenica) is 18 years old.
math now..!! Help..?
Answer:
2p + 12
2 (p = +6) + 12 = 20
Answer:
I think its 6
Step-by-step explanation:
because you have to add 9 and 3 together then you get 12 and you have to divide 2p with 12 and you'll get 6
cuantos son 4 elevado a 4???
Answer:Answer and Explanation:
When a number is said to be 'to the fourth power,' that just means that you need to multiply the number by itself four times. For example, 7 to the...
Step-by-step explanation:
If you invest $600 at 5% interest compounded cptinuously, how much would you make after 6 years?
Answer:
180
Step-by-step explanation:
1) 600 % 100 = 6 (to get 1% of 600)
2) 6 x 5 = 30 (to get 5% pf 600)
3) 30 x 6 =180 (to get the amount of profit per the 6 years)
please give brainliest if this helps
A baby weighs 100 ounces. Find the baby's weight in pounds and ounces.
Work Shown:
1 pound = 16 ounces
100/16 = 6.25
100 ounces = 6.25 pounds
100 ounces = 6 pounds + 0.25 pounds
-------
1 pound = 16 ounces
0.25*1 pound = 0.25*16 ounces
0.25 pounds = 4 ounces
------
100 ounces = 6 pounds + 0.25 pounds
100 ounces = 6 pounds + 4 ounces
100 ounces = 6 pounds, 4 ounces
please help me answer this in variable terms and constant terms -5.6x + 7 + 24y - 9
Answer:
Variable terms:
x and y
Constant terms:
7 and -9
Coefficient terms:
-5.6 and 24
9=m/3=4 please help!!
Answer:
Step-by-step explanation:
9 = m/3 + 4
5 = m/3
m = 15
Answer: m=15
Step-by-step explanation:
[tex]9=\frac{m}{3}+4[/tex]
subtract 4 on both sides
[tex]\frac{m}{3}+4-4=9-4[/tex]
[tex]\frac{m}{3}=5[/tex]
multiply 3 on both sides
[tex]\frac{3m}{3}=5\cdot \:3[/tex]
[tex]m=15[/tex]
Find the equation of the line with a slope of − 1/2 through (4, 5)
Answer: Hello:
Slope - intercept form is y = mx + b.
Since -1/2 is your slope and 5 is your y - intercept, all you need to do is substitute those values into the equation:
y = -1/2 + 5
Hope this helps!
acute angle between the hours hand and the minute hand at 1pm
Answer: 30 degrees
Step-by-step explanation:
1 hour = 60 min = 360 degree
1 min = 360/60 degree
1 min = 6 degree
and the gap of hour hand and minute hand at 1pm, is of 5 min
therefore acute angle formed is 5 X 6 = 30 degrees.
:-)
Answer:
30 degrees
Step-by-step explanation:
1 hour = 60 min = 360 degree
1 min = 360/60 degree
1 min = 6 degree
and the gap of hour hand and minute hand at 1pm, is of 5 min
therefore acute angle formed is 5 X 6 = 30 degrees.
Solve for 'x' in both of the following problems. Show all your work/explanations on your own paper and then submit a picture of your work and answers in the dropbox below.
Answer/Step-by-step explanation:
1. <B is an inscribed angle in a circle which intercepts arc AC.
Therefore, m<B = ½ of m<AC
B = ½ * 128° = 64°
x = 180 - (64 + 43)
x = 180 - 107 = 73°
2. The circle given shows two chords intersecting at point H.
According to intersecting chords theorem, the products of the segments formed by one chord equals the product of the segments formed by the other.
Therefore,
[tex] 10*x = 14*5 [/tex]
Solve for x
[tex] 10x = 70 [/tex]
Divide both sides by 10
[tex] x = 7 [/tex]
What are the zeros of this function?
A. X= 2 and x = -6
B. x= 0 and x = -6
C. X= 0 and x = 5
D. X = 0 and x= -5
Answer:
I think its C because if I remember correctly zero of the function is just the x intercept
If the amount of VAT paid for an item at 13% was Rs 390, at what price was the item sold?
Answer:
Step-by-step explanation:
Let the price of the item = Rs x
13% of x = 390
[tex]\frac{13}{100}*x=390\\\\\\x = 390*\frac{100}{13}\\\\\\[/tex]
x = Rs. 3000
A sequence of transformations is described below. A reflection over a line \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point PPP Another reflection over \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point QQQ Which of the following must be preserved under this sequence of transformations? Choose 1 answer: Choose 1 answer: (Choice A) A Angle measures only (Choice B) B Segment lengths only (Choice C) C Both angle measures and segment lengths (Choice D) D Neither angle measures nor segment lengths
Answer:
The correct option is;
(Choice C) Both angle measures and segment lengths
Step-by-step explanation:
The given transformations are;
The reflection over the line, [tex]\overleftrightarrow{PQ}[/tex], with, A rotation about the point P. Another reflection over [tex]\overleftrightarrow{PQ}[/tex]. A rotation about the point Q, we have;
The transformations involve changes only in the orientation and location of the pre-image, which remain rigid, therefore, there are no changes in the segment lengths or angle dimensions
Therefore, the correct option is, both angle measures and segment lengths.
(Choice C) C Both angle measures and segment lengths
Simplify 3(2x - 5). 1)-6x - 15 2) 6x - 15 3) 6x - 8 4) 5x - 2
Answer:
[tex] \boxed{ \bold{ \: 6x - 15}}[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \mathsf{3(2x - 5)}[/tex]
Distribute 3 through the parentheses
⇒[tex] \mathsf{3 \times 2x - 3 \times 5}[/tex]
Calculate the product
⇒[tex]6x - 15[/tex]
Hope I helped!
Best regards!!
-k^2-(7k-5n)+9n
k= -1
n= -2
Answer:
-k² - (7k - 5n) + 9n
-(-1)² - [7(-1) - 5(-2)] + 9(-2)
-1 - [-7 - (-10)] - 18
-1 - 3 - 18
= -22
Which item is more economical?
Answer:
what are the items
Step-by-step explanation:
Given that p=x^2-y^2/x^2+xy
I. Express p in the simplest form
ii. Find the value of p, if x=-4 and y=-6
Answer:
When x = -4 and y = -6, p = 37.75
Step-by-step explanation:
Given that p = x² - y²/x² + x·y, we have;
p = (x² × x² -y² + x·y×x²)/x²
p = (x²⁺² - y² + x¹⁺² × y)/x²
p = (x⁴ - y² + x³·y)/x²
Therefore, p in the simplest form is given as follows;
[tex]p = \dfrac{x^4 - y^2 + x^3 \cdot y }{x^2}[/tex]
To find the value of p when x = -4 and y = -6, we plug in the value of x and y into the above equation to get the following equation;
[tex]p = \dfrac{(-4)^4 - (-6)^2 + (-4)^3 \cdot (-6) }{(-4)^2} = 37.75[/tex]
Therefore, the value of p when x = -4 and y = -6 is equal to 37.75.
Which theorem or postulate proves the two triangles are similar?
AA Postulate
SSS Theorem
AS Postulate
SAS Theorem
Answer:
AA Postulate
Step-by-step explanation:
The bottom lines are parallel. In this case they are also congruent. Combined with the top angle this makes in AA postulate
I need help answering this
Answer:
100 degrees
Step-by-step explanation:
Sondra receives an allowance of $10 per week, plus an additional $5 for each chore she completes. Which graph represents Sondra's earnings?
Answer: I know this is a bit late but for anyone looking the answer to this question, i got it right here :D.
Step-by-step explanation: I guessed and got it correct.
The graph representing Sondra's weekly earnings is plotted and attached.
What is a expression? What is a mathematical equation? What is Equation modelling ?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Sondra receives an allowance of $10 per week, plus an additional $5 for each chore she completes.
Assume that her weekly earnings is $y. Assume she does [x] extra chores in a week. Then, we can model her earnings by the equation -
y = 5x + 10.
Refer to the graph attached.
Therefore, the graph representing Sondra's weekly earnings is plotted and attached.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
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