Answer:
Example 1
A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4th side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length
L.
In a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable,
W, to represent the side of fencing parallel to the 4th side or backyard fence.
Since we know we only have 80 feet of fence available, we know that
L + W + L = 80, or more simply, 2L + W = 80. This allows us to represent the width, W, in terms of L: W = 80 – 2L
Now we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so
A = LW = L(80 – 2L)
A(L) = 80L – 2L2
This formula represents the area of the fence in terms of the variable length
L.
Example 2
Returning to our backyard farmer from the beginning of the section, what dimensions should she make her garden to maximize the enclosed area?
Earlier we determined the area she could enclose with 80 feet of fencing on three sides was given by the equation
A(L) = 80L – 2L2. Notice that quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.
In finding the vertex, we take care since the equation is not written in standard polynomial form with decreasing powers. But we know that
a is the coefficient on the squared term, so a = -2, b = 80, and c = 0.
Finding the vertex:
h
=
−
80
2
(
−
2
)
=
20
,
k
=
A
(
20
)
=
80
(
20
)
−
2
(
20
)
2
=
800
The maximum value of the function is an area of 800 square feet, which occurs when
L = 20 feet. When the shorter sides are 20 feet, that leaves 40 feet of fencing for the longer side. To maximize the area, she should enclose the garden so the two shorter sides have length 20 feet, and the longer side parallel to the existing fence has length 40 feet.
Example 3
A ball is thrown upwards from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation
H(t) = –16t2 + 80t + 40.
What is the maximum height of the ball?
When does the ball hit the ground?
To find the maximum height of the ball, we would need to know the vertex of the quadratic.
h
=
−
80
2
(
−
16
)
=
80
32
=
5
2
,
k
=
H
(
5
2
)
=
−
16
(
5
2
)
2
+
80
(
5
2
)
+
40
=
140
The ball reaches a maximum height of 140 feet after 2.5 seconds.
To find when the ball hits the ground, we need to determine when the height is zero—when
H(t) = 0. While we could do this using the transformation form of the quadratic, we can also use the quadratic formula:
t
=
−
80
±
√
80
2
−
4
(
−
16
)
(
40
)
2
(
−
16
)
=
−
80
s
q
r
t
8960
−
32
Since the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions:
t
=
−
80
−
s
q
r
t
8960
−
32
a
p
p
r
o
x
5.458
The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds.Step-by-step explanation:
i need help with part a and b. sorry its kind of hard to read
Answer:
A) 4900
B) How far above she is before she starts hiking/the distance she is from the canyon floor.
Step-by-step explanation:
Since it's linear, it will follow the formula y=mx+c.
We can sub in the values to get:
3500=m(1)+c → 3500-m=c
2100=m(2)+c → 2100 = 2m+c
Sub '3500-m' in for c:
2100=2m+3500-m
m= -1400
c=3500-m=3500-(-1400)=3500+1400=4900
∴equation is: y= -1400x+4900
To find the initial value, ie when the number of hours = 0, we sub in zero for x:
y = -1400(0) + 4900
PART A ANS: 4900
PART B ANS: Since the number of hours passed is zero, the value represents how far above she is before she starts hiking/the distance she is from the canyon floor.
Shikita borrowed money from her brother and paid back a set amount each week. The table shows how much she owed in a given week.
Let x represent the number of weeks and y represent the amount owed. Write an equation in slope-intercept form to model the amount Shikita owed each week. Do not leave any empty spaces in your answer.
Answer:
y= -2.5x+40
Step-by-step explanation:
Sarah brought a box of salt water taffy with 25 vanilla and 25 strawberry flavored pieces . What is the number of the possible outcome if she picks out 2 pieces of taffy
Answer:
The answer is 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Which of the following tables represents a function
Answer:
d is the answer of the question
Select all the correct answers.
63. 26
Which expressions are equal to
23 ?
Answer: The first option and the third option
Step-by-step explanation: You are not supposed to find something equivalent to the fraction, you have to divide the fraction.
13824 ÷ 8 = 1728
Then it is when you try to find a number equivalent to 1728. 12 to the power of 3 equals 1728
12×12=144
144×12=1728
12 to the power of 3 is equivalent to 1728
These are wrong: 2 to the power of three is unequivalent and so is 12 to the power of 6 and 6 to the power of 3
2 to the power of 6 is 64
2×2=4
4×2=8
8×2=16
16×2=32
32×2=64
3 to the power of 3 is 27
3×3=9
9×3=27
64 times 27 equals 1728 so it's equivalent and that means that our answers are A, the 1st option , and C, the 3rd option
The equivalent expression will be;
⇒ 12³
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;
The expression is,
⇒ 6³ × 2⁶ / 2³
Now,
Since, The expression is,
⇒ 6³ × 2⁶ / 2³
Solve as;
⇒ 6³ × 2⁶ × 2⁻³
⇒ 6³ × 2⁶⁻³
⇒ 6³ × 2³
⇒ (6 × 2)³
⇒ 12³
Thus, We get;
⇒ 6³ × 2⁶ / 2³ = 12³
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Carlos rode the elevator up 4 floors, then down 2 floors. He then rode down 5 more floors and got off on the first floor. Where was Carlos when he began his elevator ride?
Answer:
fourth floor
Step-by-step explanation:
Solve for w.
4 = 2w − 4
w =
What is the slope and what does the slope represent in this situation
Answer:
Step-by-step explanation:
slope is -60
it's the rate of change... in the distance to the destination
Neil is completing a 10 km run in 4 months’
time. His personal best for 10 km is 55 minutes
and he wants to complete this run in less than
45 minutes.
Identify the components of health-related
fitness that Neil will have to develop to try and
achieve this. Justify your choices.
Answer:
Hello There!!
Step-by-step explanation:
There are five components of physical fitness:
1. Body composition
2.Flexibility
3. Muscular strength
4. Muscular endurance
5. Cardiorespiratory endurance
I think he will have to develop Flexibility,Muscular Endurance and also Cardiorespiratory Endurance.
hope this helps,have a great day!!
~Pinky~
If 11 yards of carpet weighs 240 pounds, which formula can be used to determine x, how much 17 yards of carpet weighs?
Answer:
cross multiplication
Step-by-step explanation:
[tex]\frac{11}{240}[/tex] x [tex]\frac{17}{x}[/tex]
[yards/weight x yards/unknown weight]
11x = 4080
x = 370.9 or 371 pounds
Answer Choice
A)Sophomore Class
B) P.E. Classes
C)Math CLub members
D)entire student body
Harrison has 40 CDs in his music collection.
If 30% of the CDs are country music and 50% are pop music, how many CDs are other types of music?
There are____ CDs that are other types of music.
Answer:
20 of the cds are pop
12 are country
That leaves 8 cds that are other types of music.
Step-by-step explanation:
Answer:
There are 8
Step-by-step explanation:
Since the percentage of pop music is 50, and there are 40 CDs, we can see that 20 are pop
if we do 40(.30) we get 12
12+20=32
40-32=8
please choose the correct answer due at 11:59
Answer:
B
Step-by-step explanation:
if you line up the months (x) with the money (y) evrything lines up correctly whe you look at the points on the graph
hope this helps <3
share 1200kg in the ratio 3:37
Answer:
3+37=40
3/40×1200=90kg
37÷40×1200=1110kg
Step-by-step explanation:
''.''
Answer:
[tex]3x+37x=40x\\40x=1200kg\\x=\frac{1200}{40} \\x=30kg\\[/tex]
[tex]3x=30kg*3=90kg\\37x=30kg*37=1110kg[/tex]
The number of of petals in a daisy garden is proportional to the number of daisies in the garden, as shown in the graph.
Answer: There are 200 petals on 25 daisies, so the constant of proportional is 8
Answer: the constant of proportionality is 8
Step-by-step explanation:
Help pls thank you !!
Answer:
B is correct 4⁷ is the final answer
HELPPppPpPPpppppppp BRAINLIESTTTT
Choose the inequality symbol (>,
<
=
5x + 4y=-14
3x + 6y = 6
Find the value of the variable(s) in each figure. Explain your reasoning
Answer:
x=14 and y=37
Step-by-step explanation:
Help me please
Ayudame por favor
In their stamp collections, Marlee has 62 stamps, Xavier has 56 stamps, Nicki has 48 stamps, and Cameron has 89 stamps. Estimate how many stamps they would have if they combined their collections by rounding to the nearest ten first and then adding the rounded numbers.
Answer:260 is the answer
Step-by-step explanation:
marlee=60 xavier=60 nicki=50 cameron=90 60+60=120 120+50=170 170+90 =260
Drag graphs to show a group of each equation in the table
Answer:
y=5x = 1/5 is bottom middle
y= -1/5x + 5 is top middle
y= -5x - 1/5 bottom left
y= 1/5x - 5 top left
Step-by-step explanation:
A bowling alley and a skating rink both offer birthday party rentals. The bowling alley costs $5 per person plus a $15 room rental fee. The skating rink costs $3 per person plus a $20 room rental fee. You have $50. If you want to invite as many people as possible, which location should you choose?
how many degrees is the measurement of angle 1? show you work GVING BRAINLY
Answer:
m<1 = 79°
Step-by-step explanation:
12x + 19 + 22x - 9 = 180
add the numbers
34x + 10 =180
minus 10
34x = 170
divide by 34
x = 5
plug 5 into the equation of angle 1
12(5) + 19 =
79
give answer plzzz fast...
it's very important for me...
Answer:
the required answers will be
a) -48b) -3c) 72d) 2Step-by-step explanation:
for explanation see the attached picture
okay
HELP PLEASE I HAVE 2 HOURS TO FINISH THIS:
match the given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
Answer: ↓↓↓
Step-by-step explanation:
Slope intercept formula: y = mx + b
Slope, m = 2, y-intercept, b = 5 ---> y = 2x + 5
Slope, m = 3, y-intercept, b = 5 ---> y = 3x + 5
Slope, m = 5, y-intercept, b = 4 ---> y = 5x + 4
Carla and Andrew have 29 chocolate chip cookies. Andrew has 8 more than twice Carla’s cookies. How many cookies does each person have?
Step-by-step explanation:
29 cookies
Carla has X cookies
Andrew has 8+ 2X cookies
x + 8 + 2x = 29
3x = 29-8
3x= 21
x = 7 / Carla has 7 cookies
8+ 2x = 8+2•7= 8+14=22 / Andrew has 22 cookies
Can someone help me !!!
Answer:
101 sq. ft
Step-by-step explanation:
This shape can be divided into 4 parts (see picture). Recall that the formula for rectangles and squares is length * width.Also note that triangles are half a square, meaning if you divide the formula of a square's area by two (length* width), then you'll get the area of a triangle.Rectangle: 16 * 5 = 80 sq.ftRectangle: 6 * 2 = 12 sq.ftRectangle: 2 * 3 = 6 sq.ftTriangle: [Assume that it is a full square with a length of 2 and with of 3, then divide that by 2] (3*2)/2 = 3 sq.ft.Lastly add all your values together: 80 + 12 + 6 + 3 = 101Don't forget to add units!Answer: 101 sq. ftPlease help! In desperate need :(
y=6
[tex]z=3\sqrt{13} \\x=2\sqrt{13}[/tex]
What is the function that is represented by the graph shown:
Answer:
I believe its the second one