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
Michelle divided her birthday cake into sixteen pieces and gave one piece to each of her nine friends. Express the total number of pieces of cake she gave to her friends as a fraction.
Answers
Answer:
give me 1 min ill answer it
Step-by-step explanation:
A vendor who sold bread at farmers' markets counted the number of leftover loaves at the
end of each day.
Day
Loaves of leftover bread
Leftover loaves
Tuesday
22
Wednesday 24
Thursday
20
Friday
22
Saturday
27
According to the table, what was the rate of change between Wednesday and Thursday?
Answers
Answer:
Step-by-step explanation:
4 loaves
Answer:
- 4
Step-by-step explanation:
Given:
Wednesday = day 3 = 24 loavesThursday = day 4 = 20 loavesRate of change:
Difference in the number of loaves / difference in the number of days(20 - 24)/(4 - 3) =- 4/1 = - 4Find the indicated values by using the graph.
1. h(2)=_____
2. h(4)=_____
3. h(1)=_____
4. h(5)=_____
5. h(____)=4
6. h(____)=1
7. What are the values for h(____)=2?
Answers
Answer:
1. 6
2. -1
3. 5
4. 2
5. -1
6. 5
7. 6
Help or don’t if so thank you
Answers
Answer: 12.60 per CD
Step-by-step explanation:
Tax 0.80 * 3 = 2.40
40.20 - 2.40 = 37.80
37.8 / 3 = 12.60
I’m don’t understand stand these that well, can someone please explain step by step to get marked.
Answers
Answer:
10
Step-by-step explanation:
press calculate
pls give brainliest
Answer: 10
Step-by-step explanation:
The sign √ means square root. Squaring is like multiplying a number by its own self again ( for example, x times x is equal to x squared). A square root is like dividing the square by its own self ( for example, √x^2 is equal to x ).
The square root of 100 is 10, since 10 squared is equal to 100.
if a system of equations have no solution, what does the graph look like?
Answers
Help me plz? What is the ANSWER?
Answers
Answer:
48
Step-by-step explanation:
To solve, multiply by 6:
2*6= 12
8*6= 48
Hope this helps!
Answer:
48
Step-by-step explanation:
answer is 48 i hope it helps you
Please solve this. I need help on it
Answers
Answer:
look at the photo............
9514 1404 393
Answer:
∠PTQ = 40°
∠PTR = 140°
Step-by-step explanation:
The two marked angles are "vertical" angles, so are congruent.
∠PTQ = ∠STR
(x +28)° = (2x +16)°
12 = x . . . . . . . . . . . . . . . divide by °, subtract x+16
Then the measure of angle PTQ is ...
∠PTQ = (x +28)° = (12 +28)° = 40°
That and angle PTR form a linear pair, so are supplementary.
∠PTR = 180° -∠PTQ = 180° -40° = 140°
write an equivalent expression for x^4 over 4
help
please
Answers
Answer:
1/4 · x⁴
Step-by-step explanation:
Simplify t^12/t^6
A. 2
B. 6
C. 6
D. 7-2
Answers
Answer:
t
12
/t
6
=t
12−6
=t
6
if this helps your welcome
The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per
year since.
Find the population at the beginning of 1994. Round to the nearest person.
Answers
Answer:
37356
Step-by-step explanation:
What would 4 divided 4/5 be and please explain step by step or show your work on a piece of paper to get marked =]
Answers
Answer:
5
Step-by-step explanation:
4/1 ÷ 4/5 = 4/1 x 5/4 = 20/4 = 5
Solve x2+12x=82 using completing the square. Answer the questions below.
Answers
Answer:
exact form : x = ± √ 118 − 6
Decimal form : x = 4.86278049 or − 16.86278049
Step-by-step explanation:
Use the formula ( b /2 ) ^2 in order to create a new term. Solve for x by using this term to complete the square.
36. The girls' gym teacher needs to purchase
15 softballs, 5 packages of tennis balls,
and 2 soccer balls. She plans to collect
$1 from each of her 15 students to help
pay for the balls. Write and evaluate an
expression to show how much more the
teacher will have to pay.
Help
Answers
Answer:Message me for full answer
Step-by-step explanation:
HELPPPPPPPPPPPPPPPppppppppppppp
Answers
The blue area on the graph are all the possible solutions. The chili beans need to be less than 3 and the corn husks need to be less than 7
Answers are: A, B, C and E
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
Step-by-step explanation:
The answer is B brace in this image it shows the words that it says plz trust me and tell me if this is wrong it should not be tho
HELP ME SOLVE THIS PLSS
Answers
no solution,
48x+43=47x+43
-43 -43
48x=47x
if x= 1
48 is not equal to 1
B
Answer:
B
Step-by-step explanation:
It's impossible to let these 2 equation have same answer!
How do you determine the number of electrons? (need the answer asap)
Question 1 options:
It is equal to the atomic mass
It is equal to the protons + the atomic number
It is the atomic mass + the atomic number
It is equal to the protons in a neutral atom
Answers
Answer:
It is equal to the protons in a neutral atom
more over
#proton =#electrons=atomic number
Answer:
It is equal to the protons in a neutral atom
Help I have a C in math. I don't understand this Alegbra. If you get it right then I will give you Brainlist! (Ignore the black dots because I am not sure if they are right)
Answers
Answer:
YOUR RIGHT FOR BOTHH
Step-by-step explanation:
Answer:
Step-by-step explanation:
Which statements are true about rational expression multiplication? Check all that apply.
The closure property states that the sum of two rational expressions is an irrational number.
Rational expressions are closed under multiplication.
The commutative property states that changing the order of two or more factors does not change the value of the product.
The associative property states that the way in which two or more factors are grouped in a product changes the value of the product.
The properties of rational expression multiplication are parallel to the properties of rational number multiplication.
Answers
9514 1404 393
Answer:
B, C, E
Step-by-step explanation:
(a) <does not refer to multiplication> FALSE
(b) Rational expressions are closed under multiplication.TRUE
(c) The commutative property states that changing the order of two or more factors does not change the value of the product. TRUE
(d) The associative property states that the way in which two or more factors are grouped in a product changes the value of the product. FALSE, the product will be unchanged.
(e) The properties of rational expression multiplication are parallel to the properties of rational number multiplication. TRUE
Answer:
The answer is B, C, E. aka, 2,3,5
Step-by-step explanation:
Here is proof! Hope you pass<33
spot the error and rewrite pllz I need now
Quotient ×Remainder+dividend=Divisor
Answers
Answer:
Divisor × Quotient + Remainder = Dividend
Step-by-step explanation:
Hope it is helpful.....
Answer:
Divisor×Quotient+Dividend=Remainder
Which ordered pair is a solution of the equation?
7x – 2y = -5
Answers
Answer:the answer should be (1,5)
Step-by-step explanation:
A tent in the shape of a triangular prism is set up at a camping site. Use the measurements to calculate the volume of the tent. Report the answer using the correct number of significant figures. Remember, the volume formula for a triangular prism is given by V=Bh
Please helpp !! Will mark brainlest
A. 132cm2
B. 130cm2
C. 100cm2
D. 140cm2
Answers
Answer:
100 cm2
Step-by-step explanation:
The volume of the triangular prism will be 132 cubic centimeters. The correct option is A.
What is the volume of the prism?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the cube or Cuboid. The volume of the rectangular prism is calculated by the product of the triangular base and the height of the prism.
Given that the dimensions of the base of the prism are height = 4cm and base = 6 cm and the length of the prism will be 11 cm.
The volume of the prism will be calculated as:-
V= ( 1/ 2 ) b x h x L
V = 0.5 x 4 x 6 x 11
V = 132 cubic centimeter
Therefore, the volume of the triangular prism will be 132 cubic centimeters. The correct option is A.
To know more about the volume of the prism follow
https://brainly.com/question/23963432
#SPJ5
Can I get help with 1C please?
Answers
Answer:
14
Step-by-step explanation:
IS
ΔABC » ΔQRS
Find the missing side length, x.
Answers
Answer:
x = 10
Step-by-step explanation:
x/8 = 15/12
x/8= 5/4
x= (8 x 5)/4
x = 10
Guys pls helpppp my project is due after 10 minuteesss
Answers
Answer: yo
Step-by-step explanation:
didnt i alr di this for you?
542+876-65+76×5444+556-77
Answers
Answer:
=415576
Step-by-step explanation:
=1418−65+(76)(5444)+556−77
=1353+(76)(5444)+556−77
=1353+413744+556−77
=415097+556−77
=415653−77
4/8 x 4/5 = ? Help me please
Answers
hope it helps...................
[tex] \frac{4}{8} \times \frac{4}{5} [/tex]
Simplify:
[tex] \frac{4}{2} \times \frac{1}{5} [/tex]
[tex] \frac{4}{10} = \frac{2}{5} [/tex]
solve pls brainliest
Answers
Answer:
Triangle A) acute
Triangle B) right
Triangle C) obtuse
Triangle D) obtuse
Step-by-step explanation:
Any triangle less than 90° is acute.
Triangles at exactly 90° are right triangles.
Any triangle more than 90° are called obtuse.
Zero or undefined algebraic fractions
Answers
Answer:
Step-by-step explanation:a fraction is said to be undefined or have no meaning when the denominator is 0 .solytion determine whwn the denominator equals 0 set the denominator is zero 0 and solve