Answers
9514 1404 393
Answer:
b. A × B = GCF(A, B) × LCM(A, B)
c. 15 = GCF × LCM / 20
Step-by-step explanation:
b. The products of the numbers in the table are 80, 108, 216, 45.
The products of the corresponding GCF and LCM are 80, 108, 216, 45.
Conjecture: the product of the numbers is equal to the product of the GCF and LCM.
__
c. GCF×LCM = 5×60 = 300 = A×B = 20×B
B = 300/20 = 15
The other number is 15, found by using the conjecture of part b.
_____
Additional commentIf you think for a minute about what the GCF and LCM are, you realize the relationship discussed in this problem must be the case. Consider the factors of two numbers A and B:
A = (factors in common with B) × (factors unique to A)
B = (factors in common with A) × (factors unique to B)
The GCF, by definition, are (factors in common between A and B).
The LCM, by definition, is the product of unique factors:
(common factors) × (factors unique to A) × (factors unique to B)
__
Then the product of the LCM and the GCF is ...
GCF × LCM =
(factors in common) × ((factors in common) × (unique to A) × (unique to B))
Using the associative and commutative properties of multiplication, we can rearrange this product to be ...
((factors in common)×(unique to A)) × ((factors in common)×(unique to B))
= A × B
__
Personally, I use a kind of diagram to represent the factorization of A and B and their LCM and GCF:
[unique to A (common] unique to B)
Then A = factors in [ ], and B = factors in ( ). The stuff in (common] is the GCF, and the overall product is the LCM.
Using the example of part c, this would look like [4 (5] 3), so A = 4·5 = 20 and B = 5·3 = 15. The GCF is 5, and the LCM is 4·5·3 = 60.
The end parts [unique to A( and ]unique to B) can have no common factors. Any common factors must reside in the (common] part.
Related Questions
Given f(x)=3x(to the scnd power)−5x−2. What is the value of f(−2/3)? 1 8/3 3 10/3
Answers
Given:
[tex]f(x)=3x^2-5x-2[/tex]; find f(-2/3)
Answer:
[tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
Step-by-step explanation:
1. Insert [tex]-\frac{2}{3} \\[/tex] as X; [tex]f(-\frac{2}{3}) = 3 (-\frac{2}{3} )^2 - 5 (-\frac{2}{3}) - 2[/tex]
2. Solve equation; [tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
Identify the independent and dependent variables in the following situation: Julie notices that her plant grows one inch for every liter of water that it receives. Question 17 options: The independent variable is the type of tap water used, and the dependent variable is the amount of water the plant receives. The independent variable is the amount of water the plant receives, and the dependent variable is the height of the plant. The independent variable is the height of the plant, and the dependent variable is the number of pieces of fruit the plant produces. The independent variable is the height of the plant, and the dependent variable is the amount of water the plant receives.
Answers
Determine the independent variable and dependent variable in the situation
The independent variable is the "amount of water the plant receives", and the dependent variable is the "height of the plant".
An independent variable is a the variable which causes a change.A dependent variable is the result or effect of a change.Therefore, the independent variable from the phenomena is "amount of water" and the dependent variable is the "height of the plant".
Read more:
https://brainly.com/question/23700645
Adjoa’s gross salary for last month was Ghc4,687.24. If Ghc421.78 was deducted from Adjoa’s salary pay, how much take-home pay did Adjoa earn this past month?
Answers
Adjoa's got 4265.46 Ghc as his take home pay for the past month.
The question gave us his gross salary, which means everything he earned. At the same time, giving us a particular number as deduction. To calculate the net salary, all we have to do is to subtract the deduction from the gross salary, And thus;
4687.24 - 421.78 = 4265.46 Ghc
to learn more, see here https://brainly.com/question/16688602
HELPPP!!! WILL MARK BRAINLIEST!!!
Graphing Asymptotes for Rational Functions
Two copies of the same Rational Functions are shown below.
On the graph on the left, draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
On the graph on the right, draw the Vertical Asymptote and write the equation for the Vertical Asymptote underneath.
Answers
Answer:
Horizontal Asymptote: y=2
Vertical Asymptote: x=3
Step-by-step explanation:
One way: Look at graph
Look at for a horizontal or vertical line that both lines don't touch.
Second Way:
When you look for vertical asymptotes, you set the denominator equal to zero and solve.
For example, the second question has a denominator of x-3.
x-3=0
x=3 (This is the vertical asymptote)
When you look for horizontal asymptote, you do long division.
For example, the first question [tex]f(x)=\frac{2x}{x-3}[/tex]
The answer will be 2. 2 is the quotient. You only want quotient not remainder.
y=2.
Classify each number as an integer or not -32/4 yes or no -27/9 yes or no 5/11 yes or no -73.27 yes or no -36 yes or no
Answers
Answers:
-32/4 = yes-27/9 = yes5/11 = no-73.27 = no-36 = yes=====================================================
Explanation:
Use long division or a calculator to find that -32/4 turns into -8. This is an integer because it's a negative whole number.
The same goes for -27/9 because it turns into -3
The value -36 is also an integer as well
Something like 5/11 is not an integer because 5/11 = 0.4545 approximately which isn't a positive whole number. Integers are either positive or negative whole numbers, or 0.
For similar reasons, we can see that -73.27 isn't an integer either because it's not a negative whole number.
solve pls branliest !
Answers
Answer:
72
Step-by-step explanation:
8×3²
=8×9
=72
so it is the answer
Premier Consulting’s two consultants, Avery and Baker, can be scheduled to work for clients up to a maximum of 160 hours each over the next four weeks. A third consultant, Campbell, has some administrative assignments already planned and is available for clients up to a maximum of 140 hours over the next four weeks. The company has four clients with projects in process. The estimated hourly requirements for each of the clients over the four-week period are as follows:
Client Hours
A1 180
B2 75
C3 100
D4 85
Hourly rates vary for the consultant–client combination and are based on several factors, including project type and the consultant’s experience. The rates (dollars per hour) for each consultant–client combination are as follows:
Client
Consultant A B C D
Avery1 100 125 115 100
Baker2 120 135 115 120
Campbell3 155 150 140 130
a. Develop a network representation of the problem.
b. Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing?
c. New information shows that Avery doesn’t have the experience to be scheduled for client B. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revised schedule?
Answers
Answer:
The correct network diagram is the first one.
Step-by-step explanation:
Max 100 x 11 + 115 x 23 + 125 x 12 + 120 x 24 + 1 x 12 + 120 x 21 + 140 x 33 + 135 x 22 + 130 x 34 + 115 x 13 + 155 x 31 + 1
Excel formulation:
А B с D E F G H 1 1 2 2 3 4 5 6 7 Flow RHS Avery =SUM(C3:06) 160 Baker =SUM(C7:C10) 160 Campbell =SUM(C11:C14) 140 A =SUM(C3,
Solver inputs:
Set Objective: $D$15 To: Max Min O Value Of: 0 By Changing Variable Cells: $C$3:$C$14 + Subject to the Constraints: $G$3:$G$5
Solution:
Amount Billing
Avery-Client A 0 0
Avery-Client B 40 5000
Avery-Client C 100 11500
Avery-Client D 0 0
Baker-Client A 40 4800
Baker-Client B 35 4725
Baker-Client C 0 0
Baker-Client D 85 10200
Campbell-Client A 140 21700
Campbell-Client B 0 0
Campbell-Client C 0 0
Campbell-Client D 0 0
Total Billing 57925
Make 'Avery to B' zero in the solver entry and run the model again:
Amount Billing
Avery-Client A 0 0
Avery-Client B 0 0
Avery-Client C 100 11500
Avery-Client D 40 4000
Baker-Client A 40 4800
Baker-Client B 75 10125
Baker-Client C 0 0
Baker-Client D 45 5400
Campbell-Client A 140 21700
Campbell-Client B 0 0
Campbell-Client C 0 0
Campbell-Client D 0 0
Total Billing 57525
will you please help me
Answers
Answer:
sure if im able, with what?
Step-by-step explanation:
Zahin has 4/6
kg of rice. She divides it into 5 equal portions to cook for dinner. How much rice, in kilograms, does she use to cook one portion for dinner?
fraction word problem
Answers
Answer:
2/15 or 0.13
Step-by-step explanation:
first you multiply 2/3 and 1/5 which gets you 2/15
If this is the graph of f(x)= a(x+h) +k, then:
Answers
Answer:
The forth one as both are positive the domain = x ascending = + h and the range = y where y = k the vortex and both include infinity
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Apie
Jane paid $110 for an item at 40% off. What was the original price?
Answers
Answer:
$183.33
Step-by-step explanation:
Please help me help please help
Answers
Answer: 1/2
Step-by-step explanation: it is 1/2 because the 2 points are 2 away on the x an is 1 on the y so it is 1/2.
A rectangular cake pan has a volume of
234
cubic inches. If the length of the pan is
9
inches and the width is
13
inches, what is the height of the pan?
Answers
Step-by-step explanation:
volume of a rectangular pan = length of the pan × width of the pan × height of the pan
V=l.b.h
234=9.13.h
h=234/9×13
h= 2in.
hope this helps you.
Answer:
2 inches
Step-by-step explanation:
V= 234, L=9, W=13, H=?
V= LxBxH
234= 9x13xH
234= 117H
divide through by 117
234/117 = 117H/117
H= 2inches
A) HL
B) Not enough information
C) AAS
D) SAS
Answers
The 90° angle is vertical angles with the other unidentified angle
PLEASE HELP!!!!! A satellite telescope has a parabolic dish. Satellite signals are collected at the focal point (focus) of the
parabola. The distance from the vertex of the parabolic dish to the focus is 40 feet. The vertex of the dish is
located at a point 50 feet above the ground and 100 feet to the east of a computer that reads and records
data from the telescope. The diameter of the dish is 160 feet.
Answers
The dish illustrates operations on a parabola.
The depth of the parabolish dish is 160 feet.
The bowl is said to be a parabola.
So, we have:
[tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]
Where:
[tex]\mathbf{Focus: p = 40}[/tex]
[tex]\mathbf{Vertex:(h,k) = (0,0)}[/tex]
From the question, the diameter is 160 feet.
So, the radius (r) is:
[tex]\mathbf{r = \frac{160}{2} = 80}[/tex]
So, the coordinate of the depth of the parabola would be:
[tex]\mathbf{(x,y) = (60 + 100,y)}[/tex]
[tex]\mathbf{(x,y) = (160,y)}[/tex]
Substitute these values in [tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]
So, we have:
[tex]\mathbf{(160 - 0)^2 = 4 \times 40 \times (y -0)}[/tex]
[tex]\mathbf{160^2 = 160y}[/tex]
Divide both sides by 160
[tex]\mathbf{160 = y}[/tex]
Rewrite as:
[tex]\mathbf{y = 160 }[/tex]
Hence, the depth of the parabolish dish is 160 feet.
Read more about parabolas at:
https://brainly.com/question/4074088
Can someone please help me with this question
Answers
Answer:
40 degrees
Step-by-step explanation:
i'm use......
What do I do about this?
Answers
Answer:
you can get a VPN and it will let you view restricted content
Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 -4 2 -7 3 -10 4 -13
Answers
Answer:
y=-3x-1
Step-by-step explanation:
A worker gets paid overtime at the rate of normal time plus one third. One week he works 40 hours of normal time and 6 hours overtime. If his hourly rate is $15 how much did he earn for that week?
Answers
Answer:
$ 720
Step-by-step explanation:
Normal time $ 15
Overtime: 15 x 1/3 = $5 + $15 = $20
(40 x 15) + (6 x 20) = 600 + 120
A line passes through the point (2,8) and has a slope of 7
Answers
Answer:
y=7x-6
Step-by-step explanation:
Use point-slope equation.
y-y1=m(x-x1)
y-8=7(x-2)
y-8=7x-14
y=7x-6
The cost c, for manufacturing x flags is given by c=x? -24x +39. Find the number of flags manufactured if the cost is $120.
The number of flags are 0
(Simplify your answer.)
Answers
9514 1404 393
Answer:
27
Step-by-step explanation:
You want to find x when c = 120.
120 = x^2 -24x +39
x^2 -24x -81 = 0 . . . . . . subtract 120 to put in standard form
(x -27)(x +3) = 0 . . . . . .factor it
Solutions are ...
x = 27, x = -3 . . . . . values of x that make the factors zero
The number of flags manufactured for a cost of $120 is 27 flags.
Jenelle bought a home for $260,000, paying 10% as a down payment, and financing the rest at 5.4% interest for 30 years. Round your answers to the nearest cent. How much money did Jenelle pay as a down payment? $ What was the original amount financed? $ What is her monthly payment? $ If Jenelle makes these payments every month for thirty years, determine the total amount of money she will spend on this home. Include the down payment in your answer. $
Answers
Step-by-step explanation:
260000*0*54*30
$421200
(12c(5th power)) x 3c(4th power)
How do we simplify this equation?
Answers
Answer:
You can combine the powers and bases to get 36c^9
Step-by-step explanation:
12*3=36
Rule of exponents= n^m*m^n is (n*m)^m+n
Hope this helps.
Plz help I need help
Answers
I think it’s y=1.4x, but I don’t really know.
Solve pls brainliest
Answers
Answer:
In order: 7.5, 7.5061, 7.56, 9.213
Step-by-step explanation:
Find the Area of the figure below, composed of a parallelogram and one semicircle. Rounded to the nearest tenths place
Answers
Hi,
Recall that the area of a parallelogram is the product of the base b and the height or "altitude" h. So the formula is : b * h. b = 20 here, and h = 6, so we get : 20 * 6 = 120.
Now we have to compute the area of the semicircle, remember the formula for the area of a circle is : πr² where r is the radius of the circle. If we watch the figure, we already have the value of the diameter d = 8. So the radius is equal to half the diameter : r = 8 /2 = 4
Now applying the formula we get : πr² = π * 4² ≈ 50.3 rounded to the nearest tenth place.
But we don't wont the area of the circle, we want half the area of it, since it's a semicircle : πr² / 2 ≈ 25.1 rounded to the nearest tenth place.
Now to get the whole area of the figure, we need to sum the area of the parallelogram with the area of the semicircle : 120 + 25.1 ≈ 145.1 rounded to the nearest tenth place.
Good Luck
Help me please (I have to write something to send a question)
Answers
Answer:
1. This helps me to know if the answer of an opposite integer will be positive or negative by simply subtracting their absolute values then put the sign of the largest absolute value between the two.
2. By identifying first the largest absolute value of the two integers that are being add up. Without, calculations, i will know the sign of the sum.
3. the picture attached is the answer
Step-by-step explanation:
hope it will help you
Look at picure please
Answers
Answer:
[tex]2 {y}^{7} x - 5 {y}^{5} {x}^{2} - 4{y}^{8} {x}^{3}[/tex]
Choose the system of inequality's that matches the graph
Answers
DUE TOMORROW ANSWER USING STEPS: When Tyrese fell asleep one night, the temperature was
24°F. When Tyrese awoke the next morning, the
temperature was -16°F. Letting + denote a rise in
temperature and - denote a drop in temperature, what
was the change in temperature from the time Tyrese
fell asleep until the time he awoke?
Answers
Answer:
40°F
Step-by-step explanation:
When Tyrese fell asleep one night, the temperature was 24°F.
When Tyrese awoke the next morning, the
temperature was -16°F.
Letting + denote a rise in
temperature and - denote a drop in temperature, what was the change in temperature from the time Tyrese fell asleep until the time he awoke?
The temperature dropped from a high temperature to a low one : from 24° to -16°
This can be expressed mathematically as 24 - (-16), with - denoting a drop in the temperature
=24-(-16)
=24+16
=40°F
Please mark me brainliest
Answer:
a change of -40°F, i.e., a drop.
Step-by-step explanation:
use the formula
change = end - start
and find -16 - 24 = -40
