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
what's the answer???
Answers
Answer:
Step-by-step explanation:
y-4=-2(x-8)
Select the correct answer from each drop-down menu.
The slope of line p is___
and the slope of line q is ____
Answers
Slope is rise/run which is how I found the slopes.
Slope for line q is -3 and for line p it is 3.
Hope this helps !!
PLEASE HELP ITS MATH THANK YOUUUU
Answers
Answer:
44 millimeters
Step-by-step explanation:
The ratio is set up as millimeters : meters
On the map, 4 millimeters : 9 meters
The actual length ratio is represented as x millimeters : 99 meters
Since we know its proportional, we can set up the equation:
4/9 = x/99
Solve:
4/9 = x/99
4 * 99 = 9x
396 = 9x
x = 44 millimeters
Another Way
Since we already know it is proportional, 99 = 9 x 11
So we can multiply 4 x 11 to get 44 millimeters.
-Chetan K
Which of the following coordinate points have a y-value of 6? Select all that apply.
A) (3, 6)
B) (6, 5)
C) (8, 6)
D) (1, 6)
Answers
Answer
A, C, and D
Step-by-step explanation:
You are trying to find the y value in (x,y) form. Therefore, it has to be A, C, and D because they all have a 6 in the y value.
I have more question then this one
Answers
the force (F) needed to cause the acceleration (a) of an object of mass, m, is given by the equation, F = ma where m is the objects mass. if a 12-newton force causes the object to accelerate to 3 m/s2 , what is the object's mass? the unit for this mass is kg.
help me pls /ᐠ｡ꞈ｡ᐟ\
Answers
Answer: According to Newton s Second Law of Motion, also known as the Law of Force and Acceleration, a force upon an object causes it to accelerate according to the formula net force = mass x acceleration. So the acceleration of the object is directly proportional to the force and inversely proportional to the mass.
Step-by-step explanation:
If F = ma where m is the objects mass. if a 12-newton force causes the object to accelerate to 3 m/s2 , then the mass in kg of the objects is 4 kg
What is Force?When a body tends to modify or change the state by an external cause, it is called Force.
Given:
F=ma
Where,
F = Force (N)
m = mass (kg)
a = acceleration (m/s²)
If
F = 12-Newton
m = 3 m/s²
a = ?
F = ma
12 = m × 3
12 = 3m
divide both sides by 3
m = 12/3
m = 4 kg
Therefore, the mass in kg of the objects is 4 kg
To learn more on force click:
brainly.com/question/25250873
#SPJ2
Which equation does not belong? Explain your reasoning 2x + y = 4 y = -2x + 4 f(x) = -2x + 4 2x + 2y = 4
Answers
Answer:
2x + 2y = 4 does not belong
Step-by-step explanation:
2x + y = 4 → y = -2x + 4
y = -2x + 4 → y = -2x + 4
f(x) = -2x + 4 → y = -2x + 4
2x + 2y = 4 → y = -x + 2
Can anyone help me with the problem in the picture?
Answers
Since opposite exterior angles are congruent, you can set the 2 values equal to each other. When you solve for x, you should get 45.
PLEASE HELP WITH THIS ONE QUESTION
A 60 cm by 80 cm photo is to be surrounded with a matting of equal width. The photo and matting is to be covered by a 1 m^2 sheet of expensive glass. Find the width of the matting.
Answers
(60cm + x) (80cm + x) = 1m^2
And then convert the m^2 to cm^2 so it’s all the same units:
1m^2 = 1m x 1m = 100cm x 100cm = 10000cm^2
So we get:
(60cm + x) (80cm + x) = 10000cm^2
Then solve for x:
(60cm + x) (80cm + x) = 10000cm^2
4800 + 140x + x^2 = 10000
x^2 + 140x - 5200 = 0
Using the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
x = ( -140 +/- sqrt(140^2 - 4(1)(-5200)) )/ 2(1)
x = ( -140 +/- sqrt(19600 -(-20800)) )/ 2
x = ( -140 +/- sqrt(40400)) / 2
x = ( -140 + 200.9975 )/ 2
x = 30.49875
x = (140 - 200.9975)/2
x = -60.9975
So we get:
x = 30.49875 or -60.9975
The width of the matting is the part of the width underneath the photo (60cm) plus the spacing between the photo and the border, x (which would have to be 30.5 because it doesn’t make sense as a negative). So it’s:
60cm+30.50cm = 90.50 cm
The width of the matting is 90.50cm.
HELPPPPP I NEEED TO GET A GOOD GRADE OR I'M BUSTEDDDDDDDD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(MATH)
I WILL GIVE BRAINILEST! PIC DOWN BELOW!!
Answers
Answer:
D) -31
Step-by-step explanation:
use PEMDAS
3^2-(5 x 2^3)
3^2-(5 x 8)
3^2-40
9-40
-31
In 1995, the cost of tuition at a large Midwestern university was $146 per credit hour. In 2001, tuition had risen to $200 per credit hour.
Determine a linear equation to represent the cost, C, of tuition as a function of x, the number of years since 1990. (Assuming the cost increases by the same amount each year.)
Linear Equation:
In the year 2008, tuition will be ($ )per credit hour.
In the year( ) , tuition will be $317 per credit hour
Answers
Answer:
72 is the correct answer
Answer:
I believe 72 is the correct answer
Step-by-step explanation:
What is a pair of alternate interior angles?
Answers
Answer:
D. ∠2 and ∠8
Step-by-step explanation:
common sense lol
Negative 1/3 in decimal form
Answers
Answer:
-0.3333334
Step-by-step explanation:
common sense
Answer:
-0.33
Step-by-step explanation:
Question 1 (3 points)
CALCULATOR PERMITTED FOR SUBPART 3
At a bake sale, plates of cookies, p, are sold for $5 each. The amount of money
from the sale of cookies is expressed as dollars, d. Which equation represents the
earnings of the bake sale?
Plates of Cookies (p)
1
2
3
4
Earnings (d)
5
10
15
20
HN
o lol
O a
d = p + 5
Oь
d =P
=
5
Answers
done good job question giy
please answer the question above
Answers
If a polygon has 20 sides, then the sum of all of its interior angles is 3240°.
solve for w
6w+2=9w+14
Answers
Answer:
w = 4
Step-by-step explanation:
6w+2=9w+14
9w-6w=14-2
3w=12
w=12/3
w=4
Consider the equation 2b = a. Solve the equation for b.
Answers
Answer:
b = a/2
Step-by-step explanation:
Answer:
the coefficient of b is 1 so and 1*0 is 0
Whats the two answers? ( Branliest )
Answers
Answer:
B and CStep-by-step explanation:
Factors:
(A) x + y, no product(B) 5(x + y), two factors(C) (x - y)(x + y), two factors(D) xyz, three factors#A
x+yNo
#B
5(x+y)5x+5yYes
#C
(x-y)(x+y)Yes
#D
xyzNo
I WILL MARK BRAINLIST ASAP
Andre opened a bank account. He deposited $135 each month for 5 months. His bank charged him $5 each month to use the account.
How much money is in Andre's account after 5 months?
A.
$675

B.
$650

C.
$115

D.
$130
Answers
Answer:
B. $650
Step-by-step explanation:
Every month Andre is losing $5 each month and he adds on $135 each month. This can be expressed as:
($135 × 5) - ($5 × 5)
= $675 - $25
= $650
Note. $ 25 represents the total monthly charge for each month for 5 months (5x5=25)
Simplify (−4.5)(−6)(5.4).
i need the answer pls
Answers
Answer:
145.8
Step-by-step explanation:
−4.5 x −6 x 5.4
Answer:
the answer is 145.8
Step-by-step explanation:
sorry if I did it wrong
what is the slope of the line containing the points (3,-7) and (-3,7)
Answers
Answer:
-7/3
Step-by-step explanation:
To find the slope, we use the slope formula
m= ( y2-y1)/(x2-x1)
= ( 7 - -7)/(-3 -3)
= ( 7+7)/( -6)
= 14/-6
= 7/-3
= -7/3
Step-by-step explanation:
m = y2-y1 / x2-x1
= 7+7 / -3-3
= 14/-6
= -7/3
What is the result of the division?
2x^3-5x*4
—————-
x-3
Answers
Answer:
2x² + 6x + 13 remainder 43Step-by-step explanation:
Long division:
2x³ - 5x + 4 ÷ x - 3 = 2x² + 6x + 13 rem 43
2x³ - 6x²
6x² - 5x
6x² - 18x
13x + 4
13x - 39
43
The area of manang district is square kilometre is 2,246 find the prime factors of 2246
Answers
I have 47 questions I posted going to post the second if you answer all the I give you 100 points and brainlist
Answers
Answer:
1. 245
2. Rational Number
3.integers
4. false
5.square root
Step-by-step explanation:
solve the inequality. graph your solution
6(y+1)>6
Answers
Step-by-step explanation:
[tex]6(y + 1) > 6 \\ 6y + 6 > 6 \\ 6y > 0 \\ y > 0[/tex]
solve pls brainliest
Answers
Answer:
a) 52
B)6
Step-by-step explanation:
B) -5+11=6
It's not that hard, you shall know negative signs rules
-3-(-5)What is the answer to this equation
Answers
Answer:
2Step-by-step explanation:
[tex] - 3 - ( - 5) \\ - 3 + 5 \\ 2 \\ [/tex]
please help me with this sum
Answers
its upsidedown what are you doing
Sarina rounded a number to the nearest whole number and got 7.
which number could be the number Sarina rounded to the nearest whole number?
Answers
2/5 x 3/7
What is the answer please.
Answers
Answer:
6/35 pls brainliest
Step-by-step explanation: