Answer:
61.5
Step-by-step explanation:
61.5 + 8.1 + 7.4 = 77
you're welcome
Complete the Statement
triangle JKL is congruent to triangle TRS
An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is 400 meters. What dimensions for the rectangular region maximize the area of the rectangular region?
Answer:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
Step-by-step explanation:
The distance around the track (400 m) has two parts: one is the circumference of the circle and the other is twice the length of the rectangle.
Let L represent the length of the rectangle, and R the radius of one of the circular ends. Then the length of the track (the distance around it) is:
Total = circumference of the circle + twice the length of the rectangle, or
= 2πR + 2L = 400 (meters)
This equation is a 'constraint.' It simplifies to πR + L = 400. This equation can be solved for R if we wish to find L first, or for L if we wish to find R first. Solving for L, we get L = 400 - πR.
We wish to maximize the area of the rectangular region. That area is represented by A = L·W, which is equivalent here to A = L·2R = 2RL. We are to maximize this area by finding the correct R and L values.
We have already solved the constraint equation for L: L = 400 - πR. We can substitute this 400 - πR for L in
the area formula given above: A = L·2R = 2RL = 2R)(400 - πR). This product has the form of a quadratic: A = 800R - 2πR². Because the coefficient of R² is negative, the graph of this parabola opens down. We need to find the vertex of this parabola to obtain the value of R that maximizes the area of the rectangle:
-b ± √(b² - 4ac)
Using the quadratic formula, we get R = ------------------------
2a
-800 ± √(6400 - 4(0)) -1600
or, in this particular case, R = ------------------------------------- = ---------------
2(-2π)
-800
or R = ----------- = 200/π
-4π
and so L = 400 - πR (see work done above)
These are the dimensions that result in max area of the rectangle:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
f(x-1)=3x²-7x+8, find f(x)
Answer:
f(x) = 3x² -x +4
Step-by-step explanation:
Use (x+1) for x and simplify.
f((x+1) -1) = 3(x +1)² -7(x +1) +8
f(x) = 3(x² +2x +1) -7x -7 +8
f(x) = 3x² -x +4
Need help! attachment below. will give brainlist
Answer:
In the graph locate the point (3,0) and draw a line parrallel to Y-axis passing through (3,0) .
Then your line will cut the graph of f(x) at some point, that point's y-coordinate will be your value of f(3).
Step-by-step explanation:
Hope it helps!
Circle the multiplication problem that does not belong with the other three. explain 12×8=,22×4=,42×2=,33×3=
Answer: 12 x 8
Step-by-step explanation: The other three are not the basic multiplication facts from 0 - 12.
At the math store each circle costs one amount and square cost anthor. 5 circles +1 square =20 cents, two circles +3 square=21 cents . At these prices how many cents does 12 circles + 5 squares cost?
Answer:
61 cents
Step-by-step explanation:
We can create 2 equations.
5C + (1)S = 20
2C+ 3S = 21
We can alter the first equation below
S = 20 - 5C
Now we replace S with 20 - 5C into the second equation as shown
2C + 3(20 - 5C) = 21
Simplify:
2C + 60 - 15C = 21
Combine Like Terms:
-13C = -39
C = 3
Now we can calculate S
S = 20 - 5(3)
S = 5
12(3) + 5(5) = 36+25 = 61
guys please help this is graded
For the number line shown, which statement is not true?
Answer:
The first one is incorrect
Step-by-step explanation:
|a| would still be less than b, because you are mirroring a on the other side of b.
The diagram shows where |a| would lie.
-Chetan K
QUICKEST 100 POINTS EVER!
Answer:
D. 25x⁴ + 30x³ + 29x² + 12x + 4Step-by-step explanation:
(5x² + 3x + 2)² = (5x² + 3x + 2)(5x² + 3x + 2) = 5x²(5x² + 3x + 2) + 3x(5x² + 3x + 2) + 2(5x² + 3x + 2) =25x⁴ + 15x³ + 10x² + 15x³ + 9x² + 6x + 10x² + 6x + 4 = 25x⁴ + 30x³ + 29x² + 12x + 4Correct choice is D
Answer:
D. 25x⁴ + 30x³ + 29x² + 12x + 4
Step-by-step explanation:
(5x² + 3x + 2)² =
(5x² + 3x + 2)(5x² + 3x + 2) =
5x²(5x² + 3x + 2) + 3x(5x² + 3x + 2) + 2(5x² + 3x + 2) =
25x⁴ + 15x³ + 10x² + 15x³ + 9x² + 6x + 10x² + 6x + 4 =
25x⁴ + 30x³ + 29x² + 12x + 4
Estimate the product.
627x 3.73
2,520
Estimate 627 to 630
3.73's closest estimate is 4
So, 630*4=2,520
Find the median for the following group of data items.
36, 33, 32, 31, 37, 34, 30, 32
Answer:
32.5
Step-by-step explanation:
order the numbers) 30, 31, 32, 32, 33, 34, 36, 37
cancel the numbers from each side to the middle) 32 and 33
add the values together and divide by two) [32+33] divide by 2=65/2=32.5
Roger’s office building has a $320,000 value, a 2 rating, and a B building classification. The contents in the building are valued at $105,000. Calculate his total annual premium.
Answer:
2,230
Step-by-step explanation:
Estimate 5,924 ÷ 33 =
please this is all I ask is what is this?
I need it ASP
Answer:
179.6 (Estimated)
Step-by-step explanation:
5,924 ÷ 33 = 179.6 (Estimated)
Hoped this helped.
Answer:
5,924 ÷ 33 = 179.6 (in estimated form)
Step-by-step explanation:
5,924 divided by 33 equals 179.515151515.
Since 179.515151515 is not in estimated form, this can't be the correct answer.
Since we see that 51 is repeating, this allows us to determine whether we can round this up or not.. And we can!
179.515151515 → 179.6
Since 51 was repeating, we could round it up.
Therefore, 179.6 is your final answer.
Hope this helps! :D
(Can you mark me brainliest? It is greatly appreciated!)
- ♥ 7272033Alt ♥
In one week, a computer shop sold 13 laptop computers and
7 desktop computers. What was the ratio of laptop computers to all
computers that were sold in the week? Describe the ratio using words.
Answer:
13:7
Step-by-step explanation:
This ratio would be 13 laptop computers for every 7 desktop computers; 13:7
Five more than the difference of two numbers
Answer: (x - y) + 5
Step-by-step explanation: Difference of two numbers means subtraction so we know its x - y. Then, we need five more so addition which means (x - y) + 5.
Would appreciate brainly <3
okay this is what i need help with its kinda easy
Answer:
B is the answer .......+4+$#88#!$
The sixth number 20210A is prime for only one digit A. What is A?
9514 1404 393
Answer:
A = 9
Step-by-step explanation:
Beyond the first few primes, all prime numbers end in one of the odd digits, 1, 3, 7, or 9. We can reduce this list by using a couple of simple divisibility rules.
The sum of the digits is 2+0+2+1+0+A = A+5. The number will be divisible by 3 if A+5 is divisible by 3. That will be the case for A=1 and A=7.
The sum of odd digits is A+1+0 = A+1. The sum of even digits is 0+2+2 = 4. When these sums are equal, the number is divisible by 11. That will be the case for A=3.
So, we have ruled out all digits except 9. If the number is prime it must be ...
202109
A = 9
_____
Additional comment
To make sure the number is prime, we would need to check divisibility by all primes less than √202109 ≈ 449.
Answer: 9
the answer is 9 because if i root 202109 i get about 446 and if its decimal it prime
its a joke but how come hotdog buns are pact in 8 and hotdog meat is pact in 10
Answer:
every 5 bun packs : 4 hotdog meat pack
5:4
Step-by-step explanation:
7x when x=3
Please help
Answer:
21
Step-by-step explanation:
7x, x=3. Plug x in as 3. 7x3=21.
Which equations and/or functions represent the graphed line? Select three options.
i included the graph and choices in the attachment (;
Answer:
1,3,4
Step-by-step explanation:
hope this helped
3x + 5.5 < 20.5
please help
Answer:
x < 5
Step-by-step explanation:
[Given] 3x + 5.5 < 20.5
[Subtract 5.5 from both sides] 3x < 15
[Divide both sides by 3] x < 5
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
25 + -100 = 25 - n solve the equation mentally
Answer:
n = 100
Step-by-step explanation:
25 + -100 = 25 - n
=> -100 = -n
=> n = 100
Hoped this helped.
[tex]25-100 = 25 -n\\\\\implies -100 = -n\\\\\implies n = 100[/tex]
HELP FAST, I'LL GIVE BRAINLIEST, 50 POINTS!!!
-2.25+0.4x=-2.8
Solve and show your steps in both fraction form, and decimal form
Answer:
Decimal = -1.375, Fraction = -11/8
Step-by-step explanation:
Decimal:
-2.25 + 0.4x = -2.8
0.4x = -0.55
x = -1.375
Fraction:
-9/4 + 2/5x = -14/5
-45/20 + 8/20x = -56/20
8/20x = -11/20
x = -11/8
Hopefully this helps!
Brainliest please?
Hey I just wanted to know if anyone could help me out with this, I really would love the help.
Thank you :)
Answer:
3x-6 A.
Step-by-step explanation:
I would glady help anyone.
You welcome.
Help! This assignment is due at 7:00 and this is the last question!
Solve for all values of b in simplest form (delta math)
|6-3b|=4
Answer:
b=2/3, b=10/3
Step-by-step explanation:
first equation
6-3b=4
6=4+3b
3b=2
b=2/3
second equation
6-3b=-4
10=3b
b=10/3
Can some help please
Answer:
9×10^16
Step-by-step explanation:
Only if the power is the same, you can just add the first numbers
You just need to combine.
The rule (a) = a tells us we can just remove the parenthesis.
2*10^16 + 7*10^16
That would equal to 9 x 10^16 because when adding exponents, you keep them the same.
what is the slope of the line of (8,10) (-7,14)
The answer is : -4/15
Answer:
-4/15
Step-by-step explanation:
slope is simply the rise over the run which is the change in y over the change in x.
( (y_2) - (y_1) ) / ( (x_2) - (x_1) )
if you plug in your variables that gives you
(14-10) / (-7-8)
which equals
4/-15
- (4/15)
During a hurricane in Central Florida, the amount of rainfall R, in centimeters, is a function of time. Let R = f(t) define the amount of rain recorded by meteorologists beginning at midnight. Give an interpretation of the statements below, using the appropriate units.
A. (6) = 4.8
B. f'(6)=0.5
C. f(-1)(5) = 14
D. f(-1)'(5) = 1.5
The amount of rainfall is an illustration of inverse functions, and rates.
The function is given as: R = f(t)
(a) Interpret f(6) = 4.8
This means that:
The amount of rainfall at 6 seconds is 4.8 cm
(b) Interpret f'(6) = 0.5
f'(6) represents the rate of the function
So, this means that:
The rate at which rain falls at 6 seconds is 0.5 cm per second
(c) Interpret f^-1(5) = 14
f^-1(6) represents the inverse function
So, this means that:
The time at which 5 cm of rain falls, is 14 seconds
(d) Interpret f^-1'(5) = 1.5
f^-1'(5) represents the rate of the inverse function
So, this means that:
The rate of time when 5 cm of rain falls is 1.5 seconds per cm
Read more about functions, inverse and rates at:
https://brainly.com/question/15634149
A collection of 77 quarters and dimes is worth $12.50. How many quarters are in the collection? PLS HELP ILL GIVE YOU BRAINLEST ANSWER
Answer:
32
Step-by-step explanation:
77 quarters and dimes
q + d = 77
subtract q from both sides
d = 77 - q
---------------------------
A collection of quarters and dimes is worth $12.50 (1250 cents)
25q + 10d = 1250
substitute for d
25q + 10(77 - q) = 1250
distribute
25q + 770 - 10q = 1250
Combine like terms
15q + 770 = 1250
subtract 770 from both sides
15q = 480
divide both sides by 15
q = 32
What is three times a number is increased by 11 ,the result is 32
Answer:
7
Step-by-step explanation:
let x be the number
3x + 11 = 32
3x = 21............subtract both sides by 11
x = 7................divide both sides by 3
Answer:
Expression-
3×r+11=32
r=7
Step-by-step explanation:
I have run this answer the calculator a million times so trust me on this one
How would the numbers -40, 0, and 40 appear on a horizontal number line?
A. 0 on the left end, -40 in the middle, and 40 on the right end
B. 0 on the left end, and both 40 and -40 on the right end
C. 40 on the left end, 0 in the middle, and -40 on the right end
D. -40 on the left end, 0 in the
middle, and 40 on the right end
SUBMIT
Check the picture below.