Assuming that you want the product of the two factors given in each problem:
⇒ we solve this problem by timing each unit of a factor to every unit
of the other factor
⇒then add each one of them who shares a common like-term
⇒to get the answer
Let's solve:
Question 9:[tex](4m+n)(m-2n)=4m*m+(-2n)*4m+n*m+n(-2n)\\=4m^2-7nm-2n^2[/tex]
Question 12[tex](2a-4b)(7a-2b)=2a*7a+(-2b)(2a)+(-4b)7a+(-4b)(-2b)\\=14a^2-4ab-28ab+8b^2\\=14a^2-32ab+8b^2[/tex]
Question 15[tex](4m+1)^2=(4m+1)(4m+1)=4m*4m+4m*1+1*4m+1\\=16m^2+4m+4m+1\\=16m^2+8m+1[/tex]
Question 18[tex](2w+1)(2w-1)=2w*2w+2w(-1)+1*(2w)+1(-1)\\=4w^2-1[/tex]
Question 21:[tex](m+3)(m^2+4m+7)\\=m*m^2+m*4m+m*7+3m^2+3*4m+3*7\\=m^3+4m^2+7m+3m^2+12m+21\\=m^3+7m^2+19m+21[/tex]
Question 24:[tex](3x+2)(5x^2-12x-2)\\=3x*5x^2+3x(-12x)+3x(-2)+2(5x^2)+2(-12x)+2(-2)\\=15x^3-36x^2-6x+10x^2-24x-4\\=15x^3-26x^2-30x-4[/tex]
Hope that helps!
You are in charge of purchasing breakfast for an upcoming service activity involving about 50 people.
You have the choice to pick one of the following food items:
donuts ($0.30/each)
muffins ($0.50/each)
bagels ($0.40/each)
You have the choice to pick one of the following drinks:
individual cartons of milk or chocolate milk ($0.50/each)
individual bottles of orange juice or apple juice ($0.75/each)
You must stay within a budget of $100.
Write the following in your notebook.
What food item did you choose? What drink did you choose? Why?
Write an inequality to represent the cost of the items (less than or equal to $100) in standard form. Use x to represent the number of food items and y to represent the number of drinks.
Solve the inequality for y (slope-intercept form). Interpret the slope in context of the drinks and food items that are being purchased.
Graph the inequality and describe your graph and the process you used; for example, is your line dotted, solid, or shaded up or down? What does the shaded region represent?
What are the x and y-intercepts? Explain what these would represent in this situation.
What are the domain and range in this problem? Explain why you would or would not use the minimum and maximum values of the domain and range. How are the domain and range in the context of this problem different from the domain and range of any linear equation? What are the limits?
The limits of the domain and the range are 0 to 200, respectively; and you would use the minimum and maximum values of the domain and range because the graph of the inequality uses a solid line.
The items chosenThe items selected here could be any of the listed drinks and food items.
To solve this question, we use the following selection:
Muffins ($0.50/each) -- xindividual cartons of milk or chocolate milk ($0.50/each) -- yBudget of $100The inequality of the cost of itemsIn this case, we use the less than or equal to inequality.
So, we have:
0.5x + 0.5y ≤ 100
Solve the inequality for y (slope-intercept form).In (b), we have:
0.5x + 0.5y ≤ 100
Subtract 0.5x from both sides
0.5y ≤ -0.5x + 100
Divide through by 0.5
y ≤ -x + 200
This means that the slope is -1, and it means that for every food item bought, there is a decrement of 1 in the drink.
The graph of the inequalitySee attachment for the graph of the inequality
The features of the graph include
Straight and solid lineIt is shaded downThe shaded region represents the acceptable solutionsWhat are the x and y-intercepts?From the attached graph, we have:
x-intercept = 200y-intercept = 200This means that you can buy 200 food items, when you buy no drinks or buy 200 drinks when you buy no food item
What are the domain and range in this problem?These are the acceptable x and y values of the graph.
From the attached graph, we have:
Domain: 0 ≤ x ≤ 200Range: 0 ≤ y ≤ 200The domain and range are different from the domain and range of any linear equation because the domain and the range of a linear equation is the set of all real numbers, while this domain and range are limited to 0 to 200
Read more about linear inequality at:
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A box is shaped like a rectangular prism. the base area of the box is 630 square centimetres, and the height is 20 centimetres. determine the volume of the box.
Answer:
12600 cm³
Step-by-step explanation:
The volume of a prism is the product of its base area and height:
V = Bh
__
For your prism, this product is ...
V = (630 cm²)(20 cm) = 12600 cm³
The volume of the box is 12600 cm³.
Is 1000 a sequence in 50 65 80 95
Answer: yes
Step-by-step explanation:
it’s the 41st term
PLEASE HELP ASAP!!!!!!!!!
The diameter of a circle is 7 cm, What is it's area/circumference????!
HELP!!!!
Answer:
Below in bold.
Step-by-step explanation:
Circumference = π * diameter
= π * 7
= 20.99 cm to nearest hundredth.
Radius of the circle = 1/2 * diameter = 7/2
= 3.5cm.
Area = π r^2
= π * 3.5^2
= 38.48 cm^2 to nearest hundredth.
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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]
◈ The diameter of a circle is 7 cm. What is its area? How about its circumference?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]
We're asked to find the circle's circumference, which can be found using the formula below:-
[tex]\textsf{Formula for Circumference of a Circle:- \boxed{\bold{C=\pi d}}}[/tex]
Where:-
[tex]\bold{C=Circumference}[/tex][tex]\pi[/tex] = pi [3.14][tex]\bold{d=diameter}[/tex]As per provided information (d=7cm), we can easily find the circumference by substituting 7 for d:-
↬ [tex]\sf{C=\pi (7)}[/tex]
On simplification,
↬ [tex]\sf{C=7*3.14}[/tex]
Remember, 3.14 is pi.
On further simplification,
↬ C=21.98 cm.
So we conclude that the circumference of the given circle is:-
C=21.98 cm.
Now, how about the area?
[tex]\textsf{Formula for Area of a Circle:-\boxed{\bold{A=\pi r^2}}}[/tex]
Where:-
A=arear=radius (it's squared, which means it's multiplied times itself)Notice that we only have the diameter and not the radius.
We can easily find the radius by dividing the diameter by 2:-
3.5
So the radius is 3.5.
Substitute the value of r into the formula, which results in:-
↬ [tex]\sf{A=\pi (3.5)^2}[/tex]
On simplification,
A=12.25πOn further simplification,
A=12.25•3.14 (3.14 is pi)
On further simplification,
A=38.465 cm²
Good luck.-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(3x+8) (x + 4) need help solving the problem
Answer:
3x^2 [squared] + 20x + 32 (If your factoring)
Step-by-step explanation:
3x X x = 3x^2
3× X 4 = 12x
8 X x = 8x
8 X 4 = 32
Mrs. Purdue needs to pick three random students in her class to be representatives on the student council. Explain how Mrs. Purdue could use slips of paper to generate a random sample.
Answer:
See below
Step-by-step explanation:
She could have each student in the class write his or her name on a slip of paper and put it in a bowl. Then, she could shake the bowl and pull out any slip of paper with a student's name on it. After 3 times, the random sample would be over, and Mrs. Purdue would have her 3 representatives.
Ade think of a number.he double it and then subtract five.the results cannot less than 100 . find the range of value of x
Answer:
[tex]x > \frac{105}{2}[/tex]
Step-by-step explanation:
Let's say that the number is [tex]x[/tex].
He doubles the number and then subtracts five to get the number to be [tex]2x - 5[/tex]. If the result cannot be less than 100, then we can write the inequality [tex]2x - 5[/tex] > [tex]100[/tex]. Now, solving for x, we get [tex]x > \frac{105}{2}[/tex].
A campaign manager is creating campaign signs that advertise his political candidate. The campaign manager would like to maximize the surface area of the signs so that passersby have the greatest chance of seeing them. In keeping with local campaign laws, the campaign signs must have a perimeter of 160 inches. Explain how the campaign manger can find the width and height of the signs that maximize area. Round your values to the nearest tenth of a square inch.
Will mark brainliest please help!!
So if length be L and width be B
We know
Perimeter
2(L+B)So if he wants to create a rectangle advertisement
2(L+B)=160L+B=80The sum of length and breadth must be 80
If it's square
4S=160S=40inIt should have side as 40in
Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?
The values of n does either player have a winning strategy is; Player B has a winning strategy for all n ≥ 2.
How to predict winning probability?Let us use an example to solve this question. The game is played on the complete graph Kₙ (n ≥ 2), which consists of n vertices, each pair of vertices joined by an edge.
Now, Initially all edges are unpainted. At each turn, A chooses an edge, which B paints blue or red. Now, B will win if, after the last edge is painted, there is a vertex which is joined to all other vertices by blue edges. If that doesn't happen, then A wins.
The winning strategy of B is described by 3 rules which are;
Rule 1; Paint the last edge blue.Rule 2. Never paint an edge red if that would result in two red vertices being joined by an unpainted edge.Rule 3. Use red paint whenever permitted by Rules 1 and 2.Thus, if n >2, the first edge will always be painted red, the second will always be painted blue.
In conclusion, when we apply that same scenario to our question it is the same result and as such Player B has a winning strategy for all n ≥ 2.
Read more about probability at; https://brainly.com/question/24756209
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Can someone help please
Answer:
-18a⁸
Step-by-step explanation:
-2a²(-3a³)²
-2a²*9a⁶ (Opening the square)
-18a⁸
Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
Answer:
[tex]29i[/tex]
Step-by-step explanation:
From this information, we can write the following equation: [tex](2-5i)(2 + 5i)(i)[/tex]
We can see that there is the factorization of the difference of squares, so we can first expand that. The equation will become the following: [tex](4+25)(i)[/tex]
= [tex]29i[/tex]
hope this helped! :)
Solve for x in the equation -2/5 x = 12
Answer:
x= -30
Step-by-step explanation:
What is the value of x?
Answer:
x = 52°
Step-by-step explanation:
The angles add up to 360°.
x + 98 + x + 91 + x + 15 = 3603x + 204 = 3603x = 156x = 52°Divide. 12.92/105 please
Answer:
0.2584
Step-by-step explanation:
First off 10 to the 5th power is 10 x 5 = 50, so 12.92 / 50 is 0.2584.
which of the following is a true statement
Answer:
b
Step-by-step explanation:
[tex] = \frac{68}{5} - \frac{18}{5} \\ [/tex]
[tex] = \frac{50}{5} \\ [/tex]
Change into lowest term
[tex]10...[/tex]
Find the MAD:
98, 140, 220, 150
Answer:
I'm not too sure but I think It's 34
Step-by-step explanation:
Rusty in that particular area of math
PLEASE HELP!!
(look at picture!)
Answer:
a. 35, 34
b. 25, 18
Step-by-step explanation:
Find the lateral surface area of the triangular prism.
Answer:
672
[tex]A_L = (a+b+c)h = (12+10+20)*16 = 672[/tex]
What is the slope of a line that goes through (2, -2) and (5, 6)
8/3
4/3
3/4
3/8
Answer:
correct option is A i.e. 8/3
Can the volume of a cone with the same size base as a cylinder ever have a bigger volume? Explain
Answer:
No, because if a cone and a cylinder have bases with equal areas, and both have identical heights, then the volume of the cone is one-third the volume of the cylinder.
Evaluate the indefinite integral.
Answer:
[tex]\frac{1}{3} x^3 - x^2 + 4x[/tex]
Step-by-step explanation:
All this takes is the use of the power rule, which, for integrals, says that
∫[tex]x^n[/tex] = [tex]\frac{1}{n+1}x^{n+1}[/tex].
With this in mind, we can integrate:
∫[tex]x^2 - 2x + 4[/tex]
= [tex]\frac{1}{3} x^3 - x^2 + 4x[/tex].
We can also check our answer by differentiating our answer:
[tex]\frac{d}{dx} (\frac{1}{3}x^3 - x^2 + 4x)\\\\ = x^2 - 2x + 4[/tex]
so we are correct!
hope this helped!
A soup can, shaped like a cylinder, has a diameter of 3.5 inches and a height of 5 inches. Each serving of soup is 15 cubic inches. If a can of soup this size costs $1.99, what is the cost for each serving of soup? Round to the nearest cent.
Answer: The answer to your question is Cost of a serving = $0.62
Step-by-step explanation:
Data
diameter = 3.5 in
height = 5 in
each serving = 15 in³
Cost of the can = $1.99
Process
1.- Calculate the volume of the can
Volume = πr²h
-Substitution
Volume = (3.14)(3.5/2)²(5)
-Simplification
Volume = (3.14)(3.062)(5)
-Result
Volume = 48.08 in³
2.- Use proportions and cross multiplication to find the cost of a serving.
48.08 in³ ---------------- $1.99
15 in³ ---------------- x
x = (15 x 1.99)/48.08
x = 29.85/48.08
x = $0.62
Write this percentage as a fraction in its simplest form. 50 %
Answer:
1/2
Step-by-step explanation:
50/100 = 5/10 =1/2
in it's simplest form
;)
How many participants will make 45 handshakes in total
NEED ASAP PLS HELP ILL MARK BRAINLIEST IF CORRECT
(06.02 MC)
A line is drawn on a scatter plot, as shown below:
Which statement best describes the line?
(A) It can be the line of best fit because it shows a positive linear association between x and y.
(B) It can be the line of best fit because it closely fits the data points.
(C) It cannot be the line of best fit because it does not pass through all the data points.
(D) It cannot be the line of best fit because it shows a negative linear association.
Answer:
B
Step-by-step explanation:
The diameter of a ceiling fan, blade tip to blade tip, is 120 centimeters.
a) about how many whole revolutions does it take for the fan to move 1000 meters?
_______
b) if the fan rotates at 40 revolutions per minute, about how long does it take to move 1000 meters? round to the nearest minute.
_______
The number of whole revolutions for 1000 meters is 265, while the time taken to move 1000 meters with a speed of 40rev/min is 7minutes.
What is a revolution?This is the number of times a body moves round a circular path.
A revolution is equal to the circumference of a circle.
Analysis:
r = 120/2 = 60cm
1 revolution of a circle = 2πr
Let n be the number of revolutions
so that 2πr x n = 1000 x 100 since 100 cm = 1 m
n = 100000/2πr = 265 revolutions
If the Fan turns 40 rev / minute
Then it 265 revolutions = 1000 meters, 265/40 = 7 minutes
In conclusion, the number of revolutions for 1000 meters is 265 and the time taken for 265 revolutions is 7 minutes.
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Carson grew up to be one of Texas most prominent real estate investor. Carson took $32,500 he made on the sale of a home and placed it in a new account that earns 6% compounded annually. Find the total amount after 5 years.
ps (delta math)
Answer:
$44,492.33
Step-by-step explanation:
Compound Interest Formula
A = P (1 + r/n)^(nt)A = amount of interestP = Principalr = interest rate (in decimals)n = number of times interest is compoundedt = number of yearsSolving
A = (32,500)(1 + 0.06/1)⁵A = (32,500)(1.06)⁵A = (32,500)(1.33822558)A = $44,492.33 (nearest cent)Can anyone tell me the formula or way to solve this problem
[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]
please help me It's pythagorean theorem
Answer: 4
Step-by-step explanation:
3^2 + b^2 = 5^2
9 + b^2= 25
b^2 = 16
b = ±4
Answer:
The simple answer is 4 inches for steps look below
Step-by-step explanation:
According to pythagoras theorem
[tex] {5}^{2} = {3}^{2} + {x}^{2} \\ \\ \\ 25 - 9 = {x}^{2} \\ \\ x = 4[/tex]
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
A bag contains 7 red marbles, 12 orange marbles, 18 yellow marbles, and 5 purple marbles. a marble is drawn at random from the bag. what is the probability that the marble drawn will not be orange? 130 112 27 57
Answer:
its 5/7
Step-by-step explanation:
no of marbles that r not orange = 30
no of total marbles = 42
probability = 30/42
= 15/21
= 5/7
I hope my answer is helpful