The pairs of whole numbers which have 40 as a sum is 21
What is Whole numbers ?
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.
For finding the term we use Arithmetic Progression which is :
a(n) = a + (n - 1)d
where,
a(n) = the nᵗʰ term in the sequence
a = the first term in the sequence
d = the common difference between terms
Given,
The first term a₁ = 0
The common difference d = 1 (from 1 - 0, 2 - 1, etc.)
The last term aₙ = 20
Putting the values in the formula we get,
20 = 0 + (n - 1)1
20 = 0 + n- 1
20 + 1 = n
21 = n
Hence, there are 21 pairs of whole numbers that have a sum of 40
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area of composite figures worksheet #1 (don’t mind the pen it’s a mistake)
Answer:
Given that,
Rectangular room is of the dimension 12 feet by 18 feet
To find the number of square feet of carpet needed.
Explanation:
Area of the rectangle is,
[tex]\text{ length}\times\text{ breadth}[/tex]Area of the rectangular room is,
[tex]12\times18[/tex][tex]=270\text{ ft}^2[/tex]Area of the rectangular room is 270 square feet.
Therefore, 270 square feet of carpet are needed to cover the room.
we know that,
[tex]1\text{ yard }=3\text{ feet}[/tex]Using this conversion we get,
[tex]270\text{ ft}^2=270(\frac{1}{3}\text{ yd})^2[/tex]A monument is made in the form of a right pyramid with a regular hexagon as a base. each base side is 5 meters and the slant height is 30 meters. if only the sides (and not the base) of the monument is to be covered by metal, how many square meters of metal are needed to cover the sides of the pyramid?
A. 450 m 2
B. 300 m 2
C. 75 m 2
D. 150 m 2
450 m² of metal are needed to cover the sides of the pyramid.
The correct answer is an option (A)
In this question, a monument is made in the form of a right pyramid with a regular hexagon as a base. each base side is 5 meters and the slant height is 30 meters.
If only the sides (and not the base) of the monument is to be covered by metal, we need to find the amount of metal needed to cover the sides of the pyramid.
Since the base of the pyramid is hexagon, there are 6 triangular sides of the pyramid.
We need to find the area of 6 triangular surfaces.
The base of the triangle b = 5 meters and the height of the triangle is the slant height of the pyramid.
h = 30 meters
So, area of the one triangular surface would be,
A1 = 1/2 × b × h
A1 = 1/2 × 5 × 30
A1 = 5 × 15
A1 = 75 square meters
And the area of the 6 triangular surfaces would be,
A = 6 × A1
A = 6 × 75
A = 450 square meters
Therefore, 450 m² of metal are needed to cover the sides of the pyramid.
The correct answer is an option (A)
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Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 4 hours of work from
Carlo and 4 hours from Anita. Each toy requires 2 hours of work from Carlo and 4 hours from Anita. Carlo cannot work
more than 20 hours per week and Anita cannot work more than 28 hours per week. If each mailbox sells for $15 and
each toy sells for $24, then how many of each should they make to maximize their revenue? What is their maximum
revenue?
Answer:
7 toys and 0 mail boxes
Step-by-step explanation:
Answer:
Given that:!
Carlo mailbox = 1
Anita mailbox = 3
Carlo toy = 1
Anita toy = 4
Carlo work = 7 hours per week
Anita work= 24 hours per week
mailbox sells = $8
toy sells $14 =
solution
we consider here number of mailboxes is m
and m≥0
and
number of toys is t
and t≥0
so we can say equation will be
1m + 1t ≤7
3m+ 4t≤ 2
solve these equation 1,2,3 and 4 in graph and we will get graph that is attach here
we get here are 4 corner that is
The corner points are: (0, 0), (7, 0), (4, 3), (0, 6)
so objective revenue function is
F(m, t) 8m + 14t =
put here all value of corner
F(0, 0) = $0
F(7, 0) = 7×8 = $56
F(4, 3) = 4×8+ 3×14= $74
F(0, 6) = 6×14 = $84
so here maximize the revenue they should make 6 toys
The maximum revenue is $84If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°, how high above his starting level is the skier?
If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°, how high above his starting level is the skier is 2350 feet.
HeightGiven data:
Distance = 4700 feet
Angle of inclination = 30°
Now let determine the height by formulating an equation which will help us to find the height
4700 × sin 30°
Where:
Sin 30° = 0.5 or 1/2
Hence,
Height :
Height = 4700 feet × 0.5
Height = 2350 feet
So,
Height = 2350 feet above the starting level
Therefore we can conclude that the skier is 2350 feet above the starting level.
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Bernie is making wooden stools for a local charity. He has 12 1/2 feet of wood. The instructions call for 2 1/2 feet of wood to make two stools. Which of the following correctly shows the total number of complete stools that Bernie can make?
The most appropriate choice for fraction will be given by -
Bernie can make 10 stools
What is a fraction?
Suppose there is a collection of objects and a part of collection has been taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of fraction is called numerator and the lower part of fraction is called denominator.
[tex]2\frac{1}{2}[/tex] feet = [tex]\frac{5}{2}[/tex] feet of wood can be used to make 2 stools
1 feet of wood can be used to make [tex]2 \div \frac{5}{2}[/tex] stools
[tex]2 \times \frac{2}{5}[/tex] stools
[tex]\frac{4}{5}[/tex] stools
[tex]12\frac{1}{2} = \frac{25}{2}[/tex] feet of wood can be used to make [tex]\frac{4}{5} \times \frac{25}{2}[/tex] stools
= 10 stools
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Step-by-Step Example: Sketch a graph for a situation.
A carnival game booth begins the evening with 40 prizes.
In the first 30 minutes that the booth is open, no one wins
a prize. In the next hour, 8 prizes are won. In the next 45
minutes, 10 prizes are won. During the next 45 minutes,
the booth owner brings in 16 additional prizes. In the next
2 hours, 12 prizes are won. An hour later, 4 prizes are
won, and the carnival closes for the evening.
Sketch a graph that shows the number of prizes the booth
had over the time it was open.
By using the method subtraction, Total prizes are left over are 52- 34= 18
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
A carnival game booth begins the evening with 40 prizes.
In the first 30 minutes that the booth is open, no one wins
a prize.
In the next hour, 8 prizes are won. In the next 45
minutes, 10 prizes are won.
During the next 45 minutes, the booth owner brings in 16 additional prizes.
In the next 2 hours, 12 prizes are won.
An hour later, 4 prizes are won, and the carnival closes for the evening.
Total prizes are 52 prizes.
Total prizes given are 34 prizes
Total prizes are left over are 52- 34= 18
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write x<19 in interval notation
The inequality x<19 is the unbounded interval
answer:____
The resulting inequality equation in interval form is (-∞, 19).
Interval form of an inequalityThe range of values that might result in an inequality being true can be represented using interval notation.
There are two kinds of intervals, called open and closed (explained below), and each has a unique manner to notate it so we can distinguish between the two.
Given the inequality expression x < 19. This means that the interval must contain values that are less than 19 (19 excluded.)
The inequality x<19 as an unbounded interval is given as (-∞, 19).
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What is 2M?
M=[3 5
-4 0]
The value of matrix 2M is [tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]
What is matrix ?A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics. The representation of rotations and other picture changes has been accomplished using matrices, which have significant uses in computer graphics.
How to do Matrix Multiplication ?Multiplication of matrices, often known as matrix multiplication, is one of the operations that can be carried out on matrices in linear algebra. If the two matrices given, A and B, are compatible, then matrix A and matrix B can be multiplied. The binary operation of multiplying matrices produces a matrix from two input matrices.
M = [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]
2M = 2 [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]
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(2y-1)+3y+5
please help
Answer:
5y + 4; y = -4/5
Step-by-step explanation:
combine like terms
add 2y+3y together, and -1+5
5y+4=0
-4 -4
5y= -4
/5 /5
y= -4/5
18. Convert the following base-ten number to a number in the indicated base.
130 to base six
130=_____six
Please show work.
The result of converting the number 130 base 10 to the base six is [tex]334_{6}[/tex]
Given the number 130 base 10
Here we have use base conversion 130 base 10 to the number base six
.Here we have to follow 2 steps
In first step : Converting 130 to base 10
1 × [tex]10^{2}[/tex] = 100
3 × [tex]10^{1}[/tex] = 30
0 × [tex]10^{0}[/tex] = 0
Add of the result together
100 + 30 + 0 = [tex]130_{10}[/tex]
In second step : Converting [tex]130_{10}[/tex] to base 6
We can solve it by using the method
6 | 130
6 | 21 | 4
6 | 3 | 3
6 | 3 | 3
Then the result will be [tex]334_{6}[/tex]
Hence, the result of converting the number 130 base 10 to the base six is [tex]334_{6}[/tex]
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Can someone help with this question?✨
The equation of the line parallel to y = 4x - 2 and passes through (1, 8) is
y = 4x + 4
How to find equation for a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slope of the linesb = y-interceptTherefore, the equation of a line is parallel to y = 4x - 2 and passes through (1, 8)
Parallel lines have the same slope.
Therefore,
y = 4x + b
let's find y-intercept using (1, 8)
8 = 4(1) + b
b = 8 - 4
b = 4
Therefore,
the equation of the line is y = 4x + 4
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I inserted a picture of a question please state whether the answer is a b c or d
Given:
[tex]\begin{gathered} y=x^2 \\ y=\mleft(\frac{1}{3}x\mright)^2 \end{gathered}[/tex]The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 3.
ption D is the final answer.
Let f(x)=x − 3 and g(x)=x2−x. Find and simplify the expression. (f+g)(−6)
Answer: 33
Step-by-step explanation:
(f+g)(−6)=
f(-6)+g(-6)=
-6-3 + (-6)^2-(-6)=
-(6+3) + 36+6=
-9+42=
42-9=33
Use 3.1 < sqrt 10 <3.2 to find the possible values of each expression. 2-sqrt 10
Thanks for the response.
i did the same for 2-square root 10, for 2 - 3.1 < 2 - sqrt 10 < 2 - 3.2 and thought 2 -3.1 < 2 -sqrt 10 < 2 -3.2,
-1.1<< 2 - sqrt 10 < -1.2 will be the answer but doesn't look like its right. Appreciate your help for this. thanks
Think of -1.1 as -11
Think of -1.2 as -12
I moved the decimal points to the right for each value
Then on a vertical number line, notice how -12 is below -11, so -12 < -11
If we divide both sides by 10, then we go from -12 < -11 to -1.2 < -1.1
In short, the final expression you have -1.1 < middleStuff < -1.2 is in the wrong order.
It should be -1.2 < 2 - sqrt(10) < -1.1
I swapped the places of -1.1 and -1.2
If you were to use a calculator, then 2-sqrt(10) = -1.162 approximately which fits the description of being between -1.2 and -1.1; this helps confirm we have the correct upper lower and upper bounds.
------------------------------------
Here's another way to look at it
3.1 < sqrt(10) < 3.2
-1*3.1 > -1*sqrt(10) > -1*3.2 ............ see note1 below
-3.1 > -sqrt(10) > -3.2
-3.1+2 > -sqrt(10)+2 > -3.2+2 ....... see note2
2-3.1 > 2-sqrt(10) > 2-3.2
-1.1 > 2 - sqrt(10) > -1.2
-1.2 < 2 - sqrt(10) < -1.1 ........... see note3
Footnotes
note1: For this step I multiplied all three sides by -1. Multiplying by a negative will flip the inequality signsnote2: I added 2 to all three sides. This does not flip any of the inequality signs.note3: We go from the form a > b > c to c < b < a. The outer sides 'a' and 'c' swap places while b in the middle stays where it is. The inequality signs flip. It might help to think of something like 3 > 2 > 1 flipping to 1 < 2 < 3.Which pair of similar triangles can be mapped from one to the other by dilation with scale 3 and center of dilation (0,0) followed by the translation (x,y) (x -6, y -6)
Triangles P is equal to triangle v and triangles A is equal to triangle J.
Consider the unit of the scale on the X-axis is 1 unit. and
Consider the unit at Y-axis is 1 unit.
Take a triangle p and measure each unit.
1/2 + 1/2 + 1/2 + 1 + 1 + 1 = 9/2
=4.2
Take a triangle V and measure each unit.
1/2 + 1/2 + 1/2 + 1 + 1 + 1 = 9/2
=4.2
∴ The calculation is too same.
Here, ΔP=ΔV
Take a triangle I and measure each unit.
unit of I is 1.
Take a triangle J and measure each unit.
unit of J is 1.
∴ ΔI=ΔJ
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I need Help!!!!!!!!!
Answer: The photo below will show you how to do the problem. (i used 2 as an example)
Step-by-step explanation:
: Find the x- and y- intercepts. ...
Step 2: Find at least one more point. ...
Step 3: Plot the intercepts and point(s) found in steps 1 and 2. ...
Step 4: Draw the graph. ...
Step 1: Find the x- and y- intercepts.
Step 2: Find at least one more point. ...
Step 3: Plot the intercepts and point(s) found in steps 1 and 2.
Chris bought 18.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline Chris bought? Question 1 options: 6.21 L 14.6 L 4.84 L 69.92 L
The measurement that is closest to the 18.4 gallons of gasoline that Chris bought is 69.92 liters , the correct option is (d) 69.92 L .
In the question ,
it is given that ,
number of gallons that Chris bought = 18.4 gallons
also given that 1 gallon = 3.8 liter
Using the conversion , 1 gallon = 3.8 liter ,
we get ,
18.4 gallons = 3.8 × 18.4
= 69.92
hence, 18.4 gallons = 69.92 liters
Therefore , the measurement that is closest to the 18.4 gallons of gasoline that Chris bought is 69.92 Liters, the correct option is (d) 69.92 L .
The given question is incomplete , the complete question is
Chris bought 18.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline Chris bought?
(a) 6.21 L
(b) 14.6 L
(c) 4.84 L
(d) 69.92 L
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Solve the equation.
−3=z−8
Answer:
add -8 to -3 so thats 5 and your answer is 5=z
Step-by-step explanation:
what is the domain of the relation shown below?
what is the slope of 10x + 5y = 30
Answer:
[tex]y=-2x+6[/tex]
So, the slope is -2.
Step-by-step explanation:
Solve the literal equation for y and use the slope value formed.
[tex]10x+5y=30\\5y=-10x+30\\\frac{5y}{5}=\frac{-10}{5}x+\frac{30}{5}\\y=-2x+6[/tex]
So, according to [tex]y=mx+b[/tex], the slope is -2 where m is the slope.
Answer:
i swear your going to give a head ack i told you the answer
Step-by-step explanation:
Plot the image of point P under a translation by 4 units to the left and 3 units down.
We are given the following point:
[tex]P=(-2,-4)[/tex]The given transformation is the following:
[tex](x^{\prime},y^{\prime})=(x-4,y-3)[/tex]Replacing the values:
[tex]\begin{gathered} P^{\prime}=(-2-4,-4-3) \\ P^{\prime}=(-6,-7) \end{gathered}[/tex]Therefore, the image is (-6,-7)
-2(x-1)+4x=10
What is the answer to this question
Answer:
4
Step-by-step explanation:
to solve this equation you should add the values on the left side then divide 10 by whatever value you get
-2(x-1)+4x=10
-2x+2+4x=10
2x+2=10
2x=10-2
2x=8
x=4
A container has a capacity of 2/3 gallons. How many gallons are there in six of these containers in each container is filled to capacity.
The number of gallons in 6 containers is 4
How to determine the number of gallons?The statement is given as
A container has a capacity of 2/3 gallons
This means that
1 container = 2/3 gallons
Multiply both sides of the equation by 3/2
So, we have
3/2 * 1 container = 2/3 gallons * 3/2
Evaluate the products
So, we have
3/2 containers = 1 gallon
Multiply both sides by 4
So, we have
4 * 3/2 containers = 4 gallons
This gives
4 gallons = 6 containers
Hence, the number of gallons is 4
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Population of Arkansas is currently 3 million people. If it grew by just 5%, what would the new population be?
Please mark me brainliest. please
Population of Arkansas is currently 3 million people. If it grew by just 5%, what would the new population be?
Answer : 3,150,000 people
Step-by-step explanation:
3,000,000 + 5% = 3,150,000
Help 4567778776655555
In order to calculate the function (f/g)(x), we need to divide f(x) by g(x).
First, let's find the zeros of the function f(x), so we can write it in the factored form:
[tex]\begin{gathered} f(x)=-10x^2+30x+40\\ \\ a=-10,b=30,c=40\\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{-30\pm\sqrt{900+1600}}{-20}\\ \\ x_1=\frac{-30+50}{-20}=-1\\ \\ x_2=\frac{-30-50}{-20}=4 \end{gathered}[/tex]So the factored form is:
[tex]\begin{gathered} f(x)=a(x-x_1)(x-x_2)\\ \\ f(x)=-10(x+1)(x-4) \end{gathered}[/tex]Now, calculating the composite function, we have:
[tex]\frac{f(x)}{g(x)}=\frac{-10(x+1)(x-4)}{-5x-5}=\frac{-10(x+1)(x-4)}{-5(x+1)}=2(x-4)=2x-8[/tex]Are the lines created using the given points perpendicular?L1: (1,2), ( 3,1) and L2: (0,-1), (2,0)
Answer:
[tex]No,\text{ they are not}[/tex]Explanation:
To check for this, we have to get the slope of the two lines
The slope of a line can be calculated using the formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) are the coordinates of the first point and (x2,y2) are the coordinates of the second
Mathematically, we have the slope of the first as follows:
[tex]m\text{ = }\frac{1-2}{3-1}\text{ = -}\frac{1}{2}[/tex]For the second line, we have it that:
[tex]m\text{ = }\frac{0+1}{2-0}\text{ = }\frac{1}{2}[/tex]When two lines are perpendicular, the product of their slopes is equal to -1
We have it that:
[tex]\frac{1}{2}\times(-\frac{1}{2})\text{ = -}\frac{1}{4}[/tex]This shows that the two lines are not perpendicular
A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?
A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?
Let n be the number of pieces. He sold n - 2 pieces
Let p be the original price. His selling price = p + 4
Then n · p = 70.00
And (n - 2) · (p + 4) = 70.00+18.00 ---> np + 4n - 2p - 8 = 88.00
---> np + 4n - 2p = 96.00
---> 70.00 + 4n - 2p = 96.00
4n - 2p = 26.00
2n - p = 13.00
Trying some possibilities (7 & 1), (8 & 3), (9 & 5), and (10 & 7), finally gets us to the answer: n = 10 and p = 7.00.
therefore
the number of pieces was 10Part I
Find the domain and the range of the following function.
f(x)=
x+3, for x≤ -3
1, for -3
1/2x, for x ≥4
The domain of the function is
(Type your answer in interval notation)
Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
What Separates a Function's Domain from its Range?
A function's domain and range are its constituent parts. In contrast to a function's range, which is the set of all potential outputs, a function's domain is the set of all possible inputs.
All real numbers fall under the expression's domain, with the exception of cases where it is undefined. No real number exists in this situation, rendering the statement undefinable.
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Please help I’ll mark you as brainliest if correct!
Answer: a = 30
d = 4
c = 18
b = 6
Step-by-step explanation:
9(x)=1/4x+1
What is g(-16)?
G(-16)=
Answer:
1; 4/35
2; -16g
sorry if wrong