Answer:
The dimensions of the rectangle are length 25 feet and width 15.92 feet
Step-by-step explanation:
Let L be the length of the rectangle and w be the width.
The area of the rectangular part of the shape is Lw while the area of the two semi-circular ends which have a diameter which equals the width of the rectangle is 2 × πw²/8 = πw²/4. The area of each semi-circle is πw²/4 ÷ 2 = πw²/8
So, the area of the shape A = Lw + πw²/4.
The perimeter of the shape, P equals the length of the semi-circular sides plus twice its length. The length of a semi-circular side is πw/2. So, both sides is 2 × πw/2 = πw
P = πw + 2L
Since the perimeter, P = 100 feet, we have
πw + 2L = 100
From this L = (100 - πw)/2
Substituting L into A, we have
A = Lw + πw²/4.
A = [(100 - πw)/2]w + πw²/4.
A = 50w - πw²/2 + πw²/4.
A = 50w - πw²/2
Now differentiating A with respect to w and equating it to zero to find the value of w which maximizes A.
So
dA/dw = d[50w - πw²/2]/dw
dA/dw = 50 - πw
50 - πw = 0
πw = 50
w = 50/π = 15.92 feet
differentiating A twice to get d²A/dw² = - π indicating that w = 50/π is a value at which A is maximum since d²A/dw² < 0.
So, substituting w = 50/π into L, we have
L = (100 - πw)/2
L = 50 - π(50/π)/2
L = 50 - 50/2
L = 50 - 25
L = 25 feet
So, the dimensions of the rectangle are length 25 feet and width 15.92 feet
Which expression is equivalent to squareroot 100?
A10
B10^2
C50
D50^2
Answer:
10^2=100
because all u would do is put down 10 two times and then u just multiply those 2 numbers
Step-by-step explanation:
Elizabeth earned $150 a week tutoring . If he saved $75, what percent of the money he earned did he save
Answer:
50%
Step-by-step explanation:
Cuz 75 is 1/2 of 150, so 1/2 is equal to 50%.
QUICK! (100 POINTS) Answers All of this question fast i beg yall
Answer:
5: 4
6: 20
7: $3.20
8: 92
9: 22
10: $11.60
Step-by-step explanation:
6. remove 3 from 83, you will have 80 and then divide by 4 = 20 students in a class.
7. Subtract 8.80 from 24.80, you will get 16 dollars. Do 16 ÷ 5 = 3.2 as the cost of each pencil.
9. 94- 6 = 88 so, 88 ÷ 4 = 22.
10. 13.40 -7.60 = 5.8 as his weekly allowance.
I hope it helps.
write a polynomial function of least degree with integral coefficients that has the given zeros 0,-2,4
Answer:
[tex]x^3-2x^2-8x[/tex]
Step-by-step explanation:
[tex]x(x+2)(x-4)[/tex]
[tex]x(x^2-2x-8)[/tex]
[tex]x^3-2x^2-8x[/tex]
26.
ndicate which student has the higher z score.
Art Major
I-46 T-50.5 :- 5.2
Theater Major X - 70 T-75.1 :-7.3
Answer:
boom bam ba boom bam ba
This is the question but thank you
Answer:
8200/1000 = 8.2 so each time a class sells 8.2 bars, they receive 1 dollar.
If a class sold 16 bars, the class receives 2 dollars, if it sold 82 bars, it receives 10 dollars and so on.
how long did it take for Car A to travel 10 meters
Answer:
isnt it 5 seconds?
its quite blurry but i think its 5
It took car A five seconds to travel 10 meters. The 5 on the x-axis aligns with the 10 meters on the y-axis.
HELPPPPP please its worth 50
[tex](3 {m}^{6} {n}^{2} ) ^{3} .2m {n}^{4} \\ = {3}^{3} {m}^{6 \times 3} {n}^{2 \times 3} \times 2 m{n}^{4} \\ = 27 {m}^{18} {n}^{6} \times 2m {n}^{4} \\ = (27 \times 2) {m}^{18 + 1} {n}^{6 + 4} \\ = 54 {m}^{19} {n}^{10} [/tex]
Answer:
[tex]54 {m}^{19} {n}^{10} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
Solution given:
[tex]\bold{(3m^6n²)³.2mn⁴}[/tex]
distribute power
[tex]3³m^{6*3}n^{2*3}.2mn⁴[/tex]
[tex]27m^{18}n^6.2mn⁴[/tex]
multiply like terms and add or subtract power in multiplication
[tex]27*2.m^{18+1}n^{6+4}[/tex]
[tex]\large{\bold{54m^{18}n^{10}}}[/tex] is a required answer
I need help with this math problem
Step-by-step explanation:
that is just a complicated way to ask, at what values of x is the functional value infinite ? or directly, for what values of x is the denominator of that fraction 0 ?
it is zero, if just one of the 3 factors is 0.
and that would happen for
x = 0
x = -6
x = 1
so, A, D and E are correct.
A sandwich costs $4.25 and a fruit drink costs $1.85. How much change will you get from a $10 bill?
Follow: Maddie Edits
Answer:
3.90
Step-by-step explanation:
4.25
+1.85=6.10
10-6.10=3.9
======================================================
Work Shown:
4.25+1.85 = 6.10
It costs $6.10 to get the sandwich and drink.
If the customer pays with a $10 bill, then they get 10.00 - 6.10 = 3.90 dollars in change.
One way to represent $3.90 is to have:
3 dollar bills = 3 dollars3 quarters = 3*25 = 75 cents1 dime = 10 cents1 nickel = 5 centsThe coins add up in value to 75+10+5 = 90 cents.
Or another option is to have 9 dimes and no other coins. Or perhaps you could have nothing but nickels and you'd need 18 nickels. There are a few ways to determine what coins to use.
c. What is located at the reflection of (3,1) across
the y-axis? What are the coordinates of this
location?
Check the picture below.
The equation of the blue line is y=-x+ 5. Manipulate the orange line by setting the sliders so its slope, m, is -1 and its y-intercept, b, is 5. Which statement describes the system after the changes? O The lines intersect at the same point as before the changes. O The lines intersect at a different point than before the changes. O The lines do not intersect. 0 The lines overlap.
Answer:
D
Step-by-step explanation:
[tex]5/4+3/4+1/4=[/tex]
A construction company needs to remove 2 5/6 tons of dirt from a construction site. They can remove 3/10 tons of dirt each hour. What is the total amount of hours it will take to remove the dirt?
Answer:
Here is a generic way to set up this type of algebra problem.
d = total amount of dirt at the site (tons)
r = rate or removal (tons/hr)
t = time it takes to remove all of the dirt (hr)
d = rt
The total amount of dirt equals the removal rate times hours spent removing all the dirt.
Since you want to solve for t, divide both sides by r
t = d/r
Last week a candle store received $515.90 for selling 30 candles. Small candles sell for $11.25 and large candles sell for $22.40. how many large candles did the store sell?
Answer:
16
Step-by-step explanation:
x+y=30 solve for x x=30-y
substitute x with 30-y and solve
11.25x+22.4y=515.9
11.25(30-y)+22.4y=515.9
337.5+11.15y=515.9
11.15y=178.4
y=16
since we're solving for just large candles it's 16
if need small cangle number 30-16=14
I am confused in these problems ?
8. 9.
Answer:
8. 14
9. 720
Step-by-step explanation:
Both questions are asking you to find the GCD (Greatest Common Divisor) and LCM (Lowest Common Multiple).
8. Find the greatest number that can divide 392 and 462 exactly.
Find the GCD of 392 and 462:
1. Find the prime factorization of 392
2^3 × 7^2 (2 × 2 × 2 × 7 × 7)
2. Find the prime factorization of 462
2 × 3 × 7 × 11
3. To find the GCD, multiply all prime factors common to all numbers
GCF = 2 × 7, therefore GCD = 14.
9. What is the smallest number that is divisible by 20, 48, and 72?
Find the LCM of 20, 48, and 72:
1. Find the prime factorization of 20
2^5 (2 × 2 × 5)
2. Find the prime factorization of 48
2^4 x 3 (2 × 2 × 2 × 2 × 3)
3. Find the prime factorization of 72
2^3 x 3^2 (2 × 2 × 2 × 3 × 3)
4. To find the LCM, multiply all prime factors
LCM = 2^4 × 3^2 × 5 (2 × 2 × 2 × 2 × 3 × 3 × 5), therefore GCF = 720
Calculator Input:
The easiest way to find the GCD or LCM of 2 or more numbers is by using a scientific calculator. Input GCD(x,y) or LCM(x,y) for the answer. This will work for any amount of numbers as long as the input is logical.
For questions 8 and 9, you would type in GCD(392,462) and LCM(20,48,72).
Not all calculators are made the same, so other labels might be GCF or HCF instead of GCD, and LCF instead of LCM. I use GCD and LCM because that's how it is on my calculator. There isn't any difference, so using any label is fine.
What is the answer for 6 7/16 - 4 1/2?
Answer:
1.9375
Step-by-step explanation:
used a clacalator
Answer:
31/16 or 1.9375 or 1 and 15/16
Step-by-step explanation:
Is 111111 divisible by 37?
Answer:
Yes
Step-by-step explanation:
3003 woooow
Answer:
yes
Step-by-step explanation:
A is divisible by B, if after dividing them, A ÷ B, the remainder is zero.
Expand & simplify
(x +3) (x-3)
Answer:
x^2 - 9
Step-by-step explanation:
Multiply parenthesis
x × x = x^2
x × -3 = -3x
3 × x = 3x
3 × -3 = -9
x^2 - 3x + 3x - 9
= x2 - 9
A scale drawing for a backyard is shown below.
In the drawing, 1 cm represents 4 m.
Assuming the patio is rectangular, find the area of the real patio.
-6 cm
-3 cm-
Patio
2 cm
Lawn
2 cm
Answer:
The area of real patio is 50m².
Step-by-step explanation:
Given,
Length of patio = 3 cm
Width of patio = 6 cm
According to scale =
3 cm = 5m
1 cm = \frac{5}{3}\ m35 m
6 cm = \frac{5}{3}*6 = 10\ m35∗6=10 m
Real length of patio = 5 m
Real width of patio = 10 m
Area = Length*width
\begin{gathered}Area=5*10\\Area=50\ m^2\end{gathered}
Area=5∗10Area=50 m2
The area of real patio is 50m².
A provisional license holder under 18 may not drive without special permission _____________________ .
A between 8:00 a.m. and 9:00 pm
B between 12:00 am and 5:00 am
C between 5:01 am and 11:59 pm
D between 6:00 a.m. and 6:00 pm
Answer:
C
Step-by-step explanation:
A provisional license holder under 18 may not drive without special permission between 5:01 am and 11:59 pm.
plssssssssssssssssssssss help me i will mark you the brainlyest Graph.
y= –34x–1
Answer:
the x-axis is 0,1
the y -axis is -1, - 35
sorry if im rong
Step-by-step explanation:
Answer:
look at explanation
Step-by-step explanation:
the first thing to do when graphing is to look at your y coordinate, the last number without a variable behind it. this would be (-1).
mark -1 on your graph, which should be one slot to the left of zero.
the slope (the number with the variable behind it) can be read as rise/run. turn -34 into a fraction by simply putting it over 1. this will give you -34/1.
your rise in this case would be -34, which means from -1, go down 34 slots and put a nother dot. your run(denominator in fraction) is where you move horizontally. since the run is 1, move over 1 spot from where your last dot is and that is your final plot. connect the first dot you made tot he third dot you made and you have officially graphed it.
ean is comparing prices on ground beef. Store A is selling 5 pounds of ground beef for $23.49. Store B is selling 8 pounds of ground beef for $36.96.
Which store is offering the better deal on ground beef? Show your work.
Find the x-intercept(s) and the coordinates of the vertex for the parabola =y−x2−2x3. If there is more than one x-intercept, separate them with commas.
Answer:
Step-by-step explanation:
Your equation makes no sense.
I will ASSUME you mean
y = -x² - 2x + 3
which can be factored
y = (x + 3)(-x + 1)
x intercepts occur when y = 0
0 = (x + 3)(-x + 1)
which means either
x + 3 = 0
x = -3
or
-x + 1 = 0
x = 1
x intercepts are (-3, 0) and (1, 0)
The vertex will occur halfway between these point
x = (-3 + 1) / 2 = -1
so vertex = y = -(-1)² - 2(-1) + 3 = 4
(-1, 4)
Choose the true statement about virtue-based ethics.
i. According to the principles of virtue-based ethics, character is more important than actions.
ii. According to the principles of virtue-based ethics, right and wrong are assessed using culture as a guide.
iii. According to the principles of virtue-based ethics, the consequences of actions are very important.
iv. According to the principles of virtue-based ethics, rules are used to evaluate actions.
Virtue based ethics holds that character is more important than actions.
Virtue based ethics is the aspect of ethics that holds that the moral character of a person if of more paramount importance than the person's actions and its consequences.
Hence, the true statement about virtue based ethics from the options is that; "according to the principles of virtue-based ethics, character is more important than actions."
Learn more about ethics: https://brainly.com/question/25784680
Please help me!!! I will try to give brainliest
Answer:
Slope-intercept form: y = -3x/5 - 3
Point slope form: y = -3/5 (x + 5)
Standard form: 5y + 3x = -15
Step-by-step explanation:
Using points (-5, 0) and (0, -3)
Gradient of the line = (-3-0)/(0+5)
= -3/5
Slope intercept form; y = mx + c
when x= 0 , y = -3
therefore intercept on y axis = - 3
y= -3x/5 - 3
Point slope form: y - y1 = m (x - x1)
y - 0 = -3/5 (x + 5)
y= -3/5 (x+5)
Standard form: ax + by = c
y= -3/5 (x + 5)
5y = -3(x + 5)
5y= -3x - 15
5y + 3x = -15
Someone Help?
Find the problem:
22 + 53x + x = -20 + 60x
22+ 54x = -20 + 60x
22= -20+ 6x
2= 6x
x = 1/3
Fix the problem (Rewrite and solve):
If a spherical tank 6 m in diameter can be filled with a liquid for $600, find the cost to fill a tank 12 m in diameter.
The cost to fill the 12 m tank is $__
The amount of money, y, pizzeria J makes by
selling x pizzas can be modeled by the equation
y = 14x. The relationship of the amount of money
pizzeria W makes is shown in the following graph.
Which pizzeria makes more money per pizza?
Answer:
Pizzeria J
Step-by-step explanation:
Pizzeria J makes
y = 14x
Let x = 1, for 1 pizza. Then,
y = 14 × 1
y = 14
At pizzeria J, 1 pizza costs $14.
In the equation y = 14x, the slope, 14, is the cost per pizza.
Now we find the slope of the graph for pizzeria W.
The x-axis is the number of pizzas.
For x = 1, y = 11.
The slope is 11, so the price per pizza is $11.
Answer: Pizzeria J
3. Write an equation in slope-intercept form for the line with a slope of 5/4 and a
y-intercept of 2.
Answer:
y = [tex]\frac{5}{4}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{5}{4}[/tex] and c = 2 , then
y = [tex]\frac{5}{4}[/tex] x + 2 ← equation of line
