Answers
Answer:
see the attachment
i hope it helps u ✌️✌️✌️☠️
a) The highest common factor and the least common multiple are 12 and 48, respectively.
b) The highest common factor and the least common multiple are 12 and 72, respectively.
c) The highest common factor and the least common multiple are 8 and 160, respectively.
d) The highest common factor and the least common multiple are 12 and 48, respectively.
e) The highest common factor and the least common multiple are 14 and 840, respectively.
Procedure - Determination of the Highest Common Factor and the Least Common Multiple of two integersIn this question we must determine the highest common factor and the least common multiple of two integers.
The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.
Now, we proceed to determine the numbers for each case:
a) 12 and 48First, we factorize each integer:
[tex]12 = 2^{2}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex]
Then the highest common factor and the least common multiple are, respectively:
[tex]LCM = 2^{4}\times 3 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]
The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]
b) 24 and 36First, we factorize each integer:
[tex]24 = 2^{3}\times 3[/tex], [tex]36 = 2^{2}\times 3^{2}[/tex]
Then, the highest common factor and the least common multiple are, respectively:
[tex]LCM = 2^{3}\times 3^{2} = 72[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]
The highest common factor and the least common multiple are 12 and 72, respectively. [tex]\blacksquare[/tex]
c) 32 and 40First, we factorize each integer:
[tex]32 = 2^{5}[/tex], [tex]40 = 2^{3}\times 5[/tex]
Then, the highest common factor and the least common multiple are, respectively:
[tex]LCM = 2^{5}\times 5 = 160[/tex], [tex]HCF = 2^{3} = 8[/tex]
The highest common factor and the least common multiple are 8 and 160, respectively. [tex]\blacksquare[/tex]
d) 24, 48 and 60First, we factorize each integer:
[tex]24 = 2^{3}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex], [tex]60 = 2^{2}\times 3 \times 5[/tex]
Then, the highest common factor and the least common multiple are, respectively:
[tex]LCM = 2^{4}\times 3 \times 5 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]
The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]
e) 42, 56 and 70First, we factorize each integer:
[tex]42 = 2\times 3 \times 7[/tex], [tex]56 = 2^{3}\times 7[/tex], [tex]70 = 2\times 5\times 7[/tex]
Then, the highest common factor and the least common multiple are, respectively:
[tex]LCM = 2^{3} \times 3 \times 5 \times 7 = 840[/tex], [tex]HCF = 2\times 7 = 14[/tex]
The highest common factor and the least common multiple are 14 and 840, respectively. [tex]\blacksquare[/tex]
To learn more on prime numbers, we kindly invite to check this verified question: https://brainly.com/question/4184435
Related Questions
Jose and Gavin are reading the same book. At the beginning of the month, Jose was
on page 10 and Gavin was on page 37. Jose will read 17 pages per day and Gavin will
read 14 pages per day. Let J represent the page of the book that Jose is on at the end
oft days into the month, and let G represent the page of the book that Gavin is on at
the end oft days into the month. Write an equation for each situation, in terms of t,
and determine what page Jose and Gavin will be on on the day they are both on the
same page.
Answers
Using linear functions, it is found that:
Jose's equation is: [tex]J = 17x + 10[/tex].Gavin's equation is: [tex]G = 14x + 37[/tex].They will be on the same page on the 9th day.Linear function:A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.Jose:
Initially, he was on page 10, hence [tex]b = 10[/tex].He reads 17 pages per day, hence [tex]m = 17[/tex].Hence, Jose's equation is: [tex]J = 17x + 10[/tex].Gavin:
Initially, he was on page 37, hence [tex]b = 37[/tex].He reads 14 pages per day, hence [tex]m = 14[/tex].Hence, Gavin's equation is: [tex]G = 14x + 37[/tex].The day they will both be on the same page is x for which:
[tex]J = G[/tex]
Hence:
[tex]17x + 10 = 14x + 37[/tex]
[tex]3x = 27[/tex]
[tex]x = \frac{27}{3}[/tex]
[tex]x = 9[/tex]
They will be on the same page on the 9th day.
To learn more about linear functions, you can take a look at https://brainly.com/question/16302622
Two polygons have a similarity ratio of 4:5. If the perimeter of the first one is 10 inches, then what is the perimeter of the second?
Group of answer choices
11 inches
8 inches
12.5 inches
15 inches
Answers
The length of a slide on a swing set is 10 ft. The
distance from the base of the ladder to the base of the slide
is 2 ft more than the height of the ladder. Find the height of
the ladder.
Answers
Answer:
6cm
Step-by-step explanation:
let height of ladder be x
so if height of ladder is x then the distance from the base of the ladder to the base of the slide is x+2
Assuming this is a right angle triangle, the slide is the longest lenght (c)
so
x²+(x+2)²=10²
x²+x²+4x+4=100
2x²+4x+4=100
2x²+4x+4-100=0
2x²+4x-96=0
2(x²+2x-48)=0
x²+2x-48=0 -- Factor
(x+8)(x-6)=0
x=-8 and x=6
since height cannot be a negative number
height of ladder is 6 cm
The base length is 8 feet. Then the height of the triangle will be 6 feet.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The length of a slide on a swing set is 10 ft.
The distance from the base of the ladder to the base of the slide is 2 ft more than the height of the ladder.
Let x be the length of the height of the triangle. Then the base of the triangle will be (x + 2).
10² = (x + 2)² + x²
100 = x² + 4x + 4 + x²
96 = 2x² + 4x
48 = x² + 2x
0 = x² + 2x - 48
0 = (x - 6)(x + 8)
x = 6, -8
Then the base length is 6 ft. Then the height of the triangle will be
B = x + 2
B = 6 + 2
B = 8 ft
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ2
What is 8 hours and 37 minutes converted into minutes?
Answers
Answer:
517 minutes
Step-by-step explanation:
Hope this helps:))
Answer:
517 mins
Step-by-step explanation:
1hour=60min
8hour=480min
37min is the same because it is already in minutes
480+37=517mins
For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the equation. Be sure to include at least two terms from the word bank. 4+ x = 7
Answers
Answer:
x=33
Step-by-step explanation:
you move the 4 to the other side
x=7-4
so
x=3
Answer:
x=3
Step-by-step explanation:
This should be easy.
4+x=7
-4 -4
x=7-4
x=3
Word explanation:
Here, we're solving for the variable x, first, we need to isolate x and therefore subtract 4 on both sides, 7 minus 4 is 3, so x is equal to 3.
(y-5)+0=(y-5)
Identify the property
Answers
Answer:
Identity property of addition
Step-by-step explanation:
If you spend 3/5 of your $40 gift card, how much money will be left on it?
Answers
Answer:
$16
Step-by-step explanation:
1-⅗=⅖
40×⅖=16
Here's the answer
Please help me solve this math problem
Answers
Answer:
(b)
Step-by-step explanation:
A suitable calculator or spreadsheet can find the matrix product for you. Here, the answer choices differ in their upper left term, so we can determine the correct choice by finding the value of that term. It is the dot product of the first row of B and the first column of A.
(5)(3) +(7)(3) +(3)(2) = 15 +21 +6 = 42
This matches choice B.
i need help fast plz
Answers
Answer:
27/16
Step-by-step explanation:
[tex]12 \div \left(2 + \dfrac 23 \right)^2\\\\\\=12 \div \left(\dfrac 83 \right)^2\\\\\\=12 \div \dfrac{64}9\\\\\\=12 \times \dfrac{9}{64}\\\\\\= \dfrac{3 \times 9}{16}\\\\\\=\dfrac{27}{16}\\\\\\=1\dfrac{11}{16}[/tex]
One-half of one-seventh of T equals one-third of one-fifth of 90. What is the value of T
Answers
Answer:
Step-by-step explanation:
This is the equation. Read it carefully.
1/2 * 1/7 T = 1/3 * 1/5 * 90 Reduce
(1/14) * T = 1/15 * 90
1/15 * 90 = 6
(1/14)*T = 6 Multiply both sides by 14
T = 14 * 6
T = 84
x+3x+3y+3z=21
Find the value of X.
Answers
Answer:
[tex] x = \frac{21 - 3y - 3z}{4} [/tex]Step-by-step explanation:
Question:-To find value of xEquation:-x + 3x + 3y + 3z = 21Solution:-=> x + 3x + 3y + 3z = 21
[On adding like terms x and 3x]=> 4x + 3y + 3z = 21
[On subtracting both sides with 3y]=> 4x + 3y + 3z - 3y = 21 - 3y
[On Simplification]=> 4x + 3z = 21 - 3y
[On subtracting both sides with 3z]=> 4x + 3z - 3z = 21 - 3y - 3z
[On Simplification]=> 4x = 21 - 3y - 3z
[On dividing both sides with 4][tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]
[On Simplification][tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]
Given :
x + 3x + 3y + 3z = 21To Find :
The value of xSolution :
[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]
Adding the like terms :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]
Transposing 3y to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]
Now, Transposing 3z to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]
Dividing both sides by 4 :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
Therefore, the value of x = 21 – 3y – 3z/4
Evaluate.
(jk−1)÷j when j=−4 and k=−0.7
Enter your answer as a decimal in the box.
Answers
Answer:
(jk - 1) / j
jk = (-4 x -0.7) = 2.8
(2.8 - 1) / - 4
1.8 / -4 = -0.45
Answer is -0.45 when j = -4 and k = -0.7
Quantity is proportional of 40/8
Answers
40/8=5
2 FOR 2.20 UNIT RATE
Answers
Answer: (if your asking for the unit rate of that)
the unit rate is 1.10
Answer:
1.10
Step-by-step explanation:
2 /2 = 1
20/ 2 = 10
1.10 is the unit rate
PLEASE HELP ME THIS IS THE 5TH TIME I HAVE HAD TO POST THIS AND GIVING BRAINLIST TO FIRST ANSWER
B.
C.
D.
Answers
Answer:
C.
Step-by-step explanation:
OMG HELP RN I GIVE BRAINLIST
Which of the following correctly describes the solutions to the inequality?
A.
There are 5 solutions. The solutions are the numbers between 4 and 8.
B.
There are an infinite number of solutions. The solutions are all numbers less than 3.
C.
There are 6 solutions. The solutions are the numbers between -2 and 3.
D.
There are an infinite number of solutions. The solutions are all numbers greater than 3.
Answers
The number 3 isn't included because the point isn't included.
The arrow points to the left, representing any number less than 3 to be a solution.
Inequality: x < 3
Mrs. Baca uses a phone card to call a relative in Colombia, It cost her 45 cents to talk for 15 minutes. Choose True or False for each statement.
A. For 45 cents, Mrs. Baca can talk for 3 minutes. True or False.
B. The call rate is 3 cents per minute. True or False.
C. The call rate can represent by the ratio 445:15. True or False.
D. Divide 75 by 15 to find the number of minutes Mrs. Baca can talk. True or False.
Answers
Answer:
A: False
B: True
C: False
D: False
Hope This Helps!!!
Helppppppppppppp helppppppppppppp
Answers
Answer:
Should be the first answer, x=5
Step-by-step explanation:
This would flip the graph and the square would land on top of where it currently is.
What is the answer to the equation?
Answers
the slope is negative because the line is going down from left to right
the y-intercept is 5 because that’s where the line crosses the y-axis
What are the coordinates of the point (-4, 2) after a translation 2 units left and 2 units up?
A (-2, 0)
B (-6,0)
C (-2, 4)
D (-6, 4)
Answers
Answer:
the answer you're looking for is D. when you move to the left the -4 becomes -6 and when you move up 2 becomes 4.
A linear function and an exponential function are shown below.
Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?
Answers
Answer:
x >2
Step-by-step explanation:
*The exponential function gets steeper when x is greater than 2
Answer:
D. x>2 is the answer got it right
Which of the equations will be a true statement if p = 10 3 ? Select the two choices that apply.
A. 3.4 ÷ p = 0.034
B. 437 ÷ p = 0.437
C. 53.45 ÷ p = 53.45
D. 6,340 ÷ p = 6.34
E. 2,458.2 ÷ p = 24.582
Answers
Answer:A
Step-by-step explanation: make me brainlist if correct
factorise
18p+6
please im so bad
Answers
At a video arcade, the action video games this week cost $25, which is 125% of last week's price. What was its price last week?
A. $20
B. $15
C. $40
D. $25
Answers
Answer:
A
Step-by-step explanation:
125% of 25 is the same as 5/4 of 25.
Divide by 5 and you get 5. 1/4 is 5, so 100% or 4/4 is 20
Answer:
it's a
Step-by-step explanation:
trust
Lena bought 40 tickets to use at a carnival. She used some of the tickets to ride the bumper cars and play some games. Now she has 24 tickets left. What is the percent of decrease in the number of tickets that he has?
a. 66.6
b. 40
c. 60
d. 80
Answers
Answer:
40
Step-by-step explanation:
that's how it is done hope it will help
solve for x. 2/x-3=x/12-4x
Answers
Answer:
x= 47 18+2 201 i ≈0.382978723+0.603295612i x= 47 −2 201 i+18 ≈0.382978723−0.603295612i Hopefully this makes just the same amount of sense as this question
TRUE OR FALSE
There are whole numbers that are not integers.
All rational numbers are whole numbers.
All integers are whole numbers.
All integers are rational numbers.
Answers
Hope you could get an idea from here.
Doubt clarification - use comment section.
help me plsss! need help
Answers
Determine whether a triangle with the given side lengths is a right triangle.
Answers
Answer:
yes yes no no
Step-by-step explanation:
use the Pythagorean theorem. sub a^2+b^2=c^2.
c is the largest number, and you can plug the 2 other values into a and b.
fnd the highest common factor of -8xy and 20y
Answers
Answer:
[tex]\huge\boxed{\boxed{2}\cdot\boxed{2}\cdot\boxed{y}=4y}[/tex]
Step-by-step explanation:
[tex]-8y=-2\cdot\boxed{2}\cdot\boxed{2}\cdot \boxed{y}\\\\20y=\boxed{2}\cdot\boxed{2}\cdot5\cdot\boxed{y}[/tex]