Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
evaluate: (_1_i)^(5/3)
Answer:
(
1
)
(
5
/
3
)
Step-by-step explanation:
The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?
Answer:
formula for the area A of a circle in terms of its radius r:
A = πr2
It is important to remember that both r, and hence, A are functions of time, t. Take the derivative of both sides with respect to t and obtain
dA/dt = 2πr(dr/dt)
Note that we are using implicit differentiation here, since A and r are (implicit) functions of t. Now we can find the required answers.
r = 5 inches.
Substitute r = 5 and dr/dt = 3 to get
dA/dt = 2π5·3 = 30π ≅ 95.25
(the units are in2/min.)
r = 22 inches
dA/dt = 2π22·3 = 132π ≅ 414.69
Hope that helps.
What does MIJ equal ?
Line u has a slope of Line v is parallel to line u. What is the slope of line v? v יל Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
I have no idea what the answer is because I am in 6th grade but good luck
Step-by-step explanation:
I don't know
The diameter of each circular hole in a paint palette is 42 millimeters.
Find the circumference of each hole. Use 3.14 as an approximation for .
A 128 millimeters
B 131.88 millimeters
C 120 millimeters
D 42 millimeters
Answer:
B
Step-by-step explanation:
The circumference is just diameter x π (3.14 in this case) so 42 x 3.14 = 131.88
Answer:
B
Step-by-step explanation:
the circumference of a circle is
2×pi×r
with r being the radius (half the diameter).
2r is then the diameter.
so, in our case the circumference is
42×pi = 42 × 3.14 = 131.88 mm
Find the value of Y helpppp
Answer:
y = 4
Step-by-step explanation:
Both the triangles are congruent by SSS postulate.
Therefore,
[tex]4y + 8 = 24 \\ (corresponding \: sides \: of \: \\ congruent \: \triangle s) \\ 4y = 24 - 8 \\ \\ 4y = 16 \\ \\ y = \frac{16}{4} \\ \\ y = 4[/tex]
Find the quotient of 376 divided by 4
Answer:
94
Step-by-step explanation:
Jonathan went shopping for a new pair of pants. Sales tax where he lives is 4.75%. The price of the pair of pants is $20. Find the total price including tax. Round to the nearest cent.
Answer:
20.95$
Step-by-step explanation:
To find the total price we need to find 4.75% of the 20 and to do that we need to multply 20 with 4.75 and divide it by 100
20 × 4.75 ÷ 100 = 0.95
20$ + 0.95$ = 20.95$
5+6(2x-1)
i need this like now pls
Answer:
Step-by-step explanation:
5 + 6 = 11 x 2 - 1 = 21 therefore its 21
Class intervals in a grouped frequency distribution are given as 4−11, 12−19, 20−27, 28−35, 36−43. Write the next two class intervals.
i) what is the each class interval?
ii) write the class boundaries of all classes?
iii) what are the class marks of each class?
Answer:
{44-55}{52- 59 } are the last two interval sStep-by-step explanation:
To get the class boundaries deduct 0.5 from the first number and add 0.5 to the second number = 4-0.5 = 3.5 = 11.5 + 0.5 = 11.5 = 3.5 -11.5 as in the fish class boundary .same for all other boundariesGiven the graph below, which of the following statements is true?
Answer:
A. the graph represent a one - to - one function because every x-value is paired with only y-value
Step-by-step explanation:
that's it
50+12÷3×5−2 do this for 25 points fast please (use PEMDAS)
Answer:
68
Step-by-step explanation:
Alexis has a bag of starbursts. After giving half of the candy to her best friend, she ate 6 starbursts.
Now, she only has 10 starbursts left. How many starbursts did Alexis start with?
Answer: 22
Step-by-step explanation:
Janie ordered boxed lunches for a student advisory committee meeting. Each lunch costs $4.25. The total cost of the lunches is $53.75, including a $7 delivery fee.
Part A
Which equation will help you find x, the number of boxed lunches Janie ordered?
a 4.25x = 60.75
b 4.25 + 7x = 53.75
c 4.25x + 7 = 53.75
d 4.25(x + 7) = 53.75
Part B
Solve the equation from Part A to find x.
x = _____
Answer:
Part A: c. 4.25x+7=53.75
Part B: 11
Step-by-step explanation:
4.25x+7=53.75
4.25x=46.75
x=11
Determine which point is part of the solution set to the following
system of inequalities: f(x) < x + 4; f(x) > - X-3; and f(x) < 5.
(0,0)
(-60)
(-3, 4)
(4,6)
Find the area of the composite figure?
Answer:
400
Step-by-step explanation:
25*35=700
10*30=300
700-300=400
what is a square unit
Answer:
A square unit is a small area of a square used to find a total.
Step-by-step explanation:
HELP PLEASEEEEEE IM BEGGING YOUUU (question): Linda is making a line plot of the data below.
11.25, 12.5, 11.25, 14.125, 10.5, 11.25, 12
Which line plot represents the data correctly?
A.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 12.5 has 1 dot. 14.125 has 1 dot.
B.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 2 dots. 12 has 1 dot. 12.5 has 1 dot. 14.125 has 1 dot.
C.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 12.5 has 1 dot. 13.75 has 1 dot.
D.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 14.125 has 1 dot. ( PLEASE ANSWER ASAP) (i already made this question once pls dont get it wrong again) ill give 60 if correct!!
The answer is D ...........
Answer:
the answer is Actually A believe me i did the test
Step-by-step explanation:
What is the volume of a sphere with the diameter = 10 cm and the height = 200 cm
A picture of Margo's garden is shown below. It is made of 2 rectangular prisms. She wants to
-10 feet -
1 foot
3 feet
7 feet
3 feet
7 feet
2 feet
09 cubic feet
O 10 cubic feet
0 98 cubic feet
0 107 cubic feet
The Volume of dirt required for the Margo's garden which is made of 2 rectangular prisms is, 107 cubic feet, So option D is correct
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within closed region of every three dimensional objects.
In given problem, we have two rectangular prisms
One has sides (1 feet, 3 feet, 3 feet)
Another one has sides (2 feet, 7 feet, 7 feet)
Volume of a rectangular prism = Length×Height×Width
Volume of a rectangular prism 1 = 3×1×3 = 9
Volume of a rectangular prism 2 = 7×2×7 = 98
Total Volume = 107
Hence, Total dirt required 107 cubic feet
To know more about Volume check:
https://brainly.com/question/13338592
#SPJ1
Please answer look at pitot
Answer:
z = 7
Step-by-step explanation:
Based on the midsegment theorem of a triangle, the length of the midsegment of the triangle (z) = ½ of the length of the 3rd side of the triangle (14)
Thus:
z = ½(14)
z = 7
Pls help 10 ptsssssssssssss
NO LINKS
Answer: If m=2, then 28 divided by 2 equals 14. Plug m into the equation.
What is the volume, in cubic centimeters, of a cube with an edge length of 15 centimeters?
Answer:
3375cm
Step-by-step explanation:
because it is asking for volume it is cubed
wich 15 x 15 x 15 3 times equals volume of cube hope that makes sense
HELP ASAP!! I will give brainlist!! THANK YOU!
Answer:
dont trust me but i think its subtraction or division
Step-by-step explanation:
Please help givin brainliest
Answer:
Answer H
Step-by-step explanation:
A 32 ft board is cut into three pieces at a sawmill. The second piece is 5 ft longer than the first and the third piece is 1 ft longer than the second.
What are the lengths of the three pieces?
Answer:
The first piece is 7 ft long, the second piece is 12 ft long, and the third piece is 13 ft long
Step-by-step explanation:
Let x represent the length of the first piece.
Since the second piece is 5 ft longer than the first, it can be represented by x + 5
Since the third piece is 1 ft longer than the second, it can be represented by x + 6
Create an equation that adds all of these terms up to 32, and solve for x
(x) + (x + 5) + (x + 6) = 32
3x + 11 = 32
3x = 21
x = 7
So, the first piece is 7 ft long.
Using the expressions we created, solve for the lengths of the second and third pieces.
x + 5
7 + 5 = 12
x + 6
7 + 6 = 13
The first piece is 7 ft long, the second piece is 12 ft long, and the third piece is 13 ft long
I need help on homework its due tomorrow
Paula kitten weighs 3 1/2 pounds write this weight in the boxes using pounds and ounces.
Answer:
Step by step explanation
First, we have to convert 3 1/2 into a decimal, so we have to do the following:
1/2 = 1 divided by 2 3 1/2 = 3 + (1÷2) = 0.5 (1 ÷ 2 done by long division)
Then we add the whole number.
3 + 0.5 = 3.5
Next, we multiply
3.5 x 16 = 56 ounces.
Answer:
3 pounds and 8 ounces
Step-by-step explanation:
1 pound (lbs) = 16 ounces (oz)
Using both pounds and ounces, the problem is asking us to eliminate the decimal and substitute it for the number of ounces (a smaller unit than pounds)
So we know it is 3 pounds, but what is half a pound equal to in terms of ounces?
Remember 1 lb = 16 oz, so 1/2 of a lb = half of 16 oz
Half of 16 (or 16 ÷ 2) equals 8
Therefore, half a pound equals 8 ounces
Combining the two units together means the boxes weigh 3 pounds and 8 ounces
SALE
75% off
original price!
The original price of a red clay pot is $40. What is the sale price?
Find the measurement of the angle labeled X
PLEASE IM REALLY BAD AT THESE QUICK!!!!!!!!!!!!!
Answer:
b.
42+x+90+8=180° linear pair
x=180-140=40°
x=40°
c.
10+x+90+3x=180 linear pair
4x=180-100
x=80/4=20
x=20°