Answer: B: complementary
Step-by-step explanation: :)
PLSSS HELP WIL REWARD BRAINLIEST!!
You may begin by calculating the slope's angle, then marking the slope's midway point, or 0, then the left end, -1, and finally the right end, 1.
3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of
cardboard that is 10 inches by 18 inches. The box will be formed by making cuts as shown in
the diagram and folding up the sides.
a) Write a function that models the volume of the box.
b) What are the dimensions of the box with the maximum volume? Round to the nearest tenth.
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c) What is the maximum volume of the box?
The volume of the box is the amount of space in it.
The dimension of the postcard is:
[tex]\mathbf{Length = 10}[/tex]
[tex]\mathbf{Width = 18}[/tex]
Let x represents the length of the cut.
So, the dimension of the box is:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
(a) The function that represents the volume of the box
This is calculated as:
[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]
So, we have:
[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]
Expand
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
(b) The dimension that maximizes the volume
We have:
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]
Set to 0
[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{x = 7.3,2.1}[/tex]
The value x = 7.3 is greater than the dimension of the box.
So, we have:
[tex]\mathbf{x = 2.1}[/tex]
Recall that:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, we have:
[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]
[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]
[tex]\mathbf{Height = 2.1}[/tex]
Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1
(c) The maximum volume
This is calculated as the product of the dimension of the box
So, we have:
[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]
[tex]\mathbf{Volume = 168.1}[/tex]
Hence, the maximum volume of the box is 168.1 cubic inches
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please help me!!!! trying to catch up over break :P
Answer:
Fast Freddy can go 15 miles per hour which is 4 minutes per mile
Speedy Sam can go 7.5 miles per hour which is 8 minutes per mile
Fast Freddy ran faster because he went 15 mph which is double the speed of Speedy Sam.
Step-by-step explanation:
Speedy Sam: So, we can find how fast per mile, by multiplying 4 by 2 because, it takes 4 minutes to go 1/2 of a mile, so double it to make a full mile. So the rate is 8 minutes per mile for Speedy Sam. If you wanted to calculate miles per hour, it would be 7.5 miles per hour because, you would simply take 60 minutes, an hour, and divide it by 8 minutes per mile, to get 7.5 miles per hour.
Fast Freddy: We can right away notice that after one mile, it hits 4 minutes. Making the rate 4 minutes per mile. To find the miles per hour, we would do, 60 minutes divided by 4 minutes per mile to get 15. Meaning fast freddy goes 15 miles per hour
The first truck carries 35 tons less rice than the second truck. The number of paddy in the first truck is 2/3 of the amount in the second truck. How many tons of paddy does each cart hold?
Answer:
First truck = x
Second truck = y
x + 35 = y
x = 2/3y
So
2/3y +35=y
1/3y = 35
y = 35*3
y = 105
And ,
x = 2/3y = 70
The first truck carry 70 tons while the second carry 105 tons
Let the amount the first truck can carry be xLet the amount the second can carry be y
If the first truck carries 35 tons less rice than the second truck, then;
x = y - 35
If the number of paddy in the first truck is 2/3 of the amount in the second truck
x = 2/3 y
Equate both to have:
2/3 y = y - 35
2/3y - y = -35
-y/3 = -35
y = 105
Since x = 2/3 y
x = 2/3 * 105
x = 70
Hence the first truck carry 70 tons while the second carry 105 tons
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PLZ HELP I NEED IT
Find the length for X
Answer:
Step-by-step explanation:
[tex]\frac{6}{4.5}=\frac{4}{x}[/tex]
6x = 4 × 4.5
6x = 18
x = 3
I need help on this pls
[1] Complementary means the angles will add up to 90 degrees
() Blank one is BOC
() Blank two is 90
() Reason blank I am unsure as I do not know the wording that is being looked for, but it is either "given," "complementary angles" or something similar
[2] Since AOC is equal too BOC + 30, we can decide the following is true
() First blank is BOC
() Second blank is 30
[3] 30°
() BOC + BOC + 30 = 90 [Given]
2(BOC) = 60 [Subtract 30 from both sides & combine like terms]
BOC = 30 [Divide by 2]
[4] 60°
() 90 - 30 = 60
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
which one is the answer? Please i need this quick
Answer:
Step-by-step explanation:
what is the question
A closed circular cylinder has a diameter of 21 cm and height of 14.5 cm find it total surface area
Answer:
this is the correct answer happy
3n - 31 = 8 + 7 ( 1 + 7n)
[tex]n = - 1[/tex]
hope it helpsIf a local tax rate is 4% and you are taxed on your $6000 purchase,
1)what is the tax?
2)What will final bill be?
Answer: Tax(240), Total cost(6240)
Step-by-step explanation:
6000 x .04 =240
240 +6000 = 6240
Which direction does the decimal point move in when you divide by powers of 10 greater than 0?
Answer:
the left side is the answer
A satellite’s original velocity is 40000
m/s. After 10 minutes, the velocity of
the satellite is 4000 m/s. What is the
satellite’s acceleration?
Answer:
-60m/s²
Step-by-step explanation:
The first thing to do is know the equation:
(Final velocity - initial (original) velocity) / time (seconds)
Next you check the units:
10 minutes = 600 seconds
Then you use the equation to solve the problem:
(4000 - 40000) = -36000
-36000 / 600 = -60
Units for acceleration = m/s²
Answer = -60m/s²
The value is negative because the satellite's velocity has decreased
Hope this helps.
how many times can 14 go into 97
Answer:
6 time
Step-by-step explanation:
97÷14=6•928
=6 or round it up to 7
Answer:
6
Step-by-step explanation:
97÷14=6.928
6 or round it up to 7
(x^2+ 6x + 9) / (x-3)
Answer:
Simplify:
[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]
Factoring:
[tex] {x}^{2} + 6x + 9[/tex]
The first term is, x2 its coefficient is 1 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
-9 + -1 = -10
-3 + -3 = -6
-1 + -9 = -10
1 + 9 = 10
3 + 3 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3
[tex] {x}^{2} + 3x + 3x + 9[/tex]
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
3 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x+3)
Which is the desired factorization.
Multiply (x+3) by (x+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+3) and the exponents are :
1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]
and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]
The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]
A true/false test consists of 100 questions. A student knows the correct answer to 40 of the questions. She guesses each of the other answers independently based on the toss of a coin.
Answer:
whats the question
Step-by-step explanation:
Use angle relationships to complete the top equation. Then, solve for x and find the measure of both angles.
Question.[Mathematics]
6³ + 6³ =
[tex] \: \: \: \: \: \: [/tex]
[tex] = 432[/tex]
Step-by-step explanation:
[tex] {6}^{3} + {6}^{3} [/tex]
collect like terms[tex]2 \times {6}^{3} [/tex]
evaluate the power[tex]2 \times 216[/tex]
multiply the number[tex] = 432[/tex]
hope it helps[tex] \: \: \: \: \: \: [/tex]
1. ) Find the mean for each data set. ROUND FINAL ANSWERS TO THE TENTHS PLACE.
Answer:
710
Step-by-step explanation:
81+74+72+66+67+72+66+66+72+65+71= 701
701 rounded to the nearest tenth is 710
The age of father is 30 yeays more than that
of hs Son. Aller 5 years.Fother's age will be thrice of his
Find thiey present age
Step-by-step explanation:
check the attached file
According to the Rational Root Theorem, the following are potential roots of f(x)=9x2−3x−2.1,
−1,23,19
Which is an actual root of f(x)?
Step-by-step explanation:
9x2 -3x -2 factors to (3x-2)(3x +1)
solve 3x-2 =0 and 3x+1=0
making the roots -1/3 and 2/3
if 8 boxes contain 480 pins how many pin will there be in 3 boxes
Answer:
180
Step-by-step explanation:
help me plz.......................
Answer:
B
Step-by-step explanation:
-16x - 32
We can factor out -16 from the -16 and -32 which leads us to this equation:
-16 (x + 2)
Meaning B would be the correct answer
Answer: B. -16(x + 2)
Step-by-step explanation:
The GCF, or greatest common factor, of -16 and -32, is -16.
Thus, distribute out -16 to get -16(x + 2)
Hope it helps :) and let me know if you want me to elaborate.
find the measure of the indicated angle that makes lines u and v parallel
Answer:
55 degrees
Step-by-step explanation:
if u and v are parallel and cut by the transversal in the middle the two angles would be congruent or equal to each other , therefore the angle in question is also 55
If sin(0) > 0, then in which quadrants could 0 lie? Select all correct answers.
Select all that apply:
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer:
I and IV
Step-by-step explanation:
based on the unity circle 0 and 360 is on the same plane..hope it's answerd
Part 2
Directions: Use the information in the charts to answer the questions.
Type of Fruit Cost
Estimated
Cost
apple
$1.75/pound
orange
$2.35/pound
banana
$1.50/pound
Answer:
i think you need to add all that up
Step-by-step explanation:
what is the product of... see attachment below
The answer is -7 (option A)
Steps are in the attachment.
_________
Hope it helps ✌
Susan has a collection of 90 nickels and dimes. If the number of nickels is five times the number of dimes, how many nickels and how many dimes does she have?
Answer:
15 Dimes and 75 Nickles
Step-by-step explanation:
N = Nickles
D = Dimes
5D + D = 90
6D= 90
D= 15
90 - 15 = 75
N = 75
There are 75 nickels and 15 dimes does she have.
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;
Susan has a collection of 90 nickels and dimes.
And, The number of nickels is five times the number of dimes.
Now,
Since, The number of nickels is five times the number of dimes.
Let number of dimes = x
Then, Number of nickels = 5x
Since, Susan has a collection of 90 nickels and dimes.
Hence, We can formulate;
⇒ 5x + x = 90
⇒ 6x = 90
⇒ x = 15
Thus, The number of dimes = 15
And, Number of nickels = 5 × 15 = 75
Therefore, There are 75 nickels and 15 dimes does she have.
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round 4,204 to the nearest hundred
Answer:
4200
hope helpful <3 !!!!!!!!!!!!!
The video suggests you consider these 4 things before deciding to take out a loan: Is it necessary? Do the monthly payments fit in your budget? Could you save instead of borrow? Is it worth the added interest?
1. If you were trying to decide whether to take out an auto loan for $6500 to buy your first car, thereby allowing you to commute for an impressive summer internship program next year, would that loan meet the requirements?
Answer:
The requirements for taking out a loan tend to be very strict, and therefore, an impressive internship program would not be something that can meet the requirements to obtain a loan of $6500.
Step-by-step explanation:
1. If you were trying to decide whether to take out an auto loan for $6500 to buy your first car, thereby allowing you to commute for an impressive summer internship program next year, that loan would not meet the requirements.
Is it necessary?
No, travelling can be done by other means.
Do the monthly payments fit in your budget?
Maybe
Could you save instead of borrow?
Yes saving for the whole year is better than borrow.
Is it worth the added interest?
No, its not worth the added interest.
All of the answers indicate that the loan does not meet the requirements.
Paying a huge amount of interest for something which is not that necessary is useless.
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solve pls brainliest
$200
Step-by-step explanation:Simple interest is the same value of interest each year. It is based on the original value. The original value here is $5000.
You must find 2% of the $5000 dollars. This is 0.02 * 5000, or $100.
The question asks for the value after two years, so you must double this to $200.
The question asks how much interest he is paid, which does not include the original $5000. The answer is therefore $200.