A number is divisible by another number if the quotient is a counting number and the remainder is 0.
NO LINKS!!!
Please help me with parts b and c.
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.
need an answer, please need an answer, please.
Answer:
Step-by-step explanation:
1) c
x² = 1
x² - 1 = 0
Degree of quadratic equation should be 2.
2) 'a'- coefficient of x² cannot be 0
option a
3) option c
Standard form: ax² + bx +c = 0
4) c = 5
3x² + 8x = -5
3x² + 8x + 5 = 0
option c
5) b= 0
option a
I need help please !!! Help noww
Answer:
Sorry link only if you have enough rupees
Step-by-step explanation:
78x
87x
09x
cc
bb
dom=cb
makes sense now c.r.y because this answer is too smart f/.or y.o.u not helping you? just pray and god will give you your answer or talk morshu he'll give you help BUT only if you have enough rupees.
Using the graph of y = f(x) to the right, and given that the zero of the function is x=20, find the following.
Answer:
3.5
Step-by-step explanation:
"andrea sells cell phones in sydney, but never on sunday. she is paid 3500 a month plus 20% of her monthly sales. she needs to earn atleast 4800 a month to pay for her rent, food, fun, and other life essentials. to afford her lifestyle, what amount of sales will andrea need to achieve?"
Answer: Answer. $6500.
Step-by-step explanation:
The equation to solve it is
3500 + 0.2*x = 4800,
Simplify and solve it:
0.2x = 4800 - 3500,
0.2x = 1300,
x = 1300%2F0.2 = 6500.
Solve: (-5) + (-18)
A -23
B- 13
C 13
D 23
Does anyone know 1/4 x ? = -2?
Please scalping on a piece of paper or explain in the comment, that would be really helpful =]
Answer:
-8
Step-by-step explanation:
1/4 x = -2
You want the value of x. x is being multiplied by 1/4. To get x alone on the left side, you need to divide both sides by 1/4. Dividing by 1/4 is the same as multiplying by 4.
Multiply both sides of the equation by 4.
4 * 1/4 x = -2 * 4
4 * 1/4 = 1, so on the left side you get 1x which is just x.
x = 8
Answer: -8
the answer is 8
Step-by-step explanation:
1/4×8=-2
Bvtcctctctc CJ bububuv
Answer:
A) [tex]y+7=-3(x-4)[/tex]
Step-by-step explanation:
Hi there!
The given equations are written in point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope of the line and [tex](x_1,y_1)[/tex] is a point that falls on the line
Notice how the line is travelling infinitely down as x increases. This means that the slope is negative.
Therefore, the equation of the line is either A or B.
Now, let's look at A:
[tex]y+7=-3(x-4)[/tex]
This equation suggests that the point (4,-7) falls on the line, which it does.
Therefore, the equation of the graph is [tex]y+7=-3(x-4)[/tex].
I hope this helps!
Answer: A.) y + 7 = - 3 ( x - 4 )
Step-by-step explanation:
i didnt know i was a graph lolz im just playin have a nice day kind person and sorry for answering late!!!!!!
Peter owns a store that sells men's clothing. His most significant monthly expenses to run the store are the cost of retail items and the power bill. This month, he purchased 50 suits for his store. He also
needed to buy 35 pairs of shoes, which cost $25 dollars more than each suit. The expression shows Peter's total expenses for this month:
50 (x) + 35 (x + 25) + 450
What does (x + 25) represent?
А-the cost of 25 suits
B-the cost of each pair of shoes
C-the total cost of the pairs of shoes
D-the price of one suit and one pair of shoes
Answer:
B-the cost of each pair of shoes
Step-by-step explanation:
This is because each pair of shoes cost $25 dollars more than each suit (which is represented by x)
x + 25, represents the cost of each pair of shoes. Option B is correct.
Given that,
This month Peter purchased 50 suits for his store. He also needed to buy 35 pairs of shoes, which cost $25 dollars more than each suit. The expression shows Peter's total expenses for this month
50 (x) + 35 (x + 25) + 450, What x + 25 represents the equation is to e determined.
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Here,
Let x be the rate of each suit,
and the cost of the shoe is $25 dollars more than each suit. So,
50 (x) + 35 (x + 25) + 450
In the equation, x + 25 represent the cost of each pair of shoe.
Thus, x + 25, represents the cost of each pair of shoes. Option B is correct.
Learn more about polynomial function here:
https://brainly.com/question/12976257
#SPJ2
Write each equation in slope intercept form Underline the slope and circle the y intercept in each equation 5x + 3y = 30
The slope - intercept form is ___
The slope is ___
The y - intercept is (_, _)
Answer:
y=-5/3x+10
-5/3
(0,10)
Step-by-step explanation:
5x+3y=30
-5x. -5x
3y=-5x+30
÷3. ÷3
y=-5/3x+10
the number by the x is the slope and the constant
is the y intercept. in a y intercept the x=0 and they y=the constant which is 10 in this case making it (0,10)
what does this mean??
Answer:
"do you mock people's mental states?"
Fred borrows $2710 at 3.8% simple interest per month. When Fred pays the loan back 3 months later, what is the total amount that Fred ends up repaying?
Answer:
3,018.94
Step-by-step explanation:
If x=8, find the value of y in the equation 4x-2y=28
Answer:
The answer is 2
Step-by-step explanation:
[tex]4x - 2y = 28 \\ 4 \times 8 - 2y = 28 \\ 32 - 2y = 28 \\ 32 - 28 = 2y \\ 4 = 2y \\ devided \: by \: 2 \\ then \\ y = 2[/tex]
5−1/4x=15−14/x helppppppppppppppppppppppppppppppppppppppppppp
Answer:
x=-41.354157 or x=1.354157
Answer:
x = -2(10 + √114) , x = 2(-10 + √114)
Step-by-step explanation:
5 − 1/4x = 15 − 14/x
-5 -5
----------------------------
-1/4x = 10 - 14/x
*4x *4x
-----------------------------
-x^2 = -56 + 40x
-----------------------------
x = -2(10 + √114) , x = 2(-10 + √114)
A penguin walks 10 feet in 6 seconds. At this speed how far does he walk in 45 seconds?
Explain or show your reasoning.
Answer:
75 feet
Step-by-step explanation:
45/6 equals 7.5
7.5*10=75
1. Preeta watches an ant and a beetle crawl in a hole in the ground. The beetle is inch below ground level. The beetle climbs the distance the ant is below ground level. The beetle is now inches below ground level.
(a) Let x = the position of the ant relative to ground level. What equation can be written to solve for x?
(b) Solve the equation from Part (a). Show your work.
(c) What is the distance between where the ant is and where the beetle is? Answer the question in a complete sentence. Show your work.
Answer:
1a: [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
1b: See below
1c: [tex]2\frac{3}{4}[/tex] inches between the beetle and ant
Step-by-step explanation:
1a. To build the equation, we need to see that the beetle started at 3/4th inches below ground level, then "climbed" (which is poor English, it should be descended) a certain distance, and then it ended up at 2 1/2 inches below ground. The distance "climbed" can be represented as 1/3X, where "X" is the ant's current distance. We would do 1/3rd times "X" to figure out how much the beetle climbed down.
So that means, if we added together the starting position of 3/4, plus the distance the beetle descended (1/3X), that would get us TO 2 1/2 inches below ground (the beetle's new current position). So therefore our equation is:
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
1b. Solve the equation written above from 1a.
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
-3/4 -3/4 [subtract 3/4 to start the process of getting x by itself]
[tex]\frac{1}{3}x[/tex] = 1[tex]\frac{3}{4}[/tex]
*3/1 *3/1 [Multiply Reciprocal to get X by itself]
x= [tex]5\frac{1}{4}[/tex]
1c. So we take the position of the ant figured out on 1b (5 1/4 inches), and the new current position of the beetle (2 1/2 inches), and subtract them
5 1/4 - 2 1/2 = [tex]2\frac{3}{4}[/tex]
These answers were found by using this info:
the beetle is 3/4 inch below the ground level. The beetle climbs 1/3 the distance. The beetle is now 2 1/2 inches below ground.
1. A new drill is used to dig a hole in the ground. At noon, the hole is 13.2 feet deep when the new drill is turned on for the first time that day. At 2 p.m., the drill has dug the hole to be feet deep. The new drill dug 1.5 times as much of the hole as the old drill would have in the same length of time.
(a) What expression represents the number of feet the new drill dug?
(b) How many feet would the old drill have dug in the same length of time? Show your work. Answer the question in a complete sentence.
Using the subtraction and division operation, the depth dug by the new drill, and the depth that would have been dug by the old drill are 29.05 feets and 19.37 feets respectively.
The expression for the number of feets dug by the new drill can be calculated thus :
Final depth - Initial depthDepth dug = 42.25 feets - 13.2 feets
Depth dug = 29.05 feets
The new drill dug 1.5 times the depth that woukd have been dug by the old drill :
Depth dug by old drill = 29.05 / 1.5
Depth dug by old drill = 19.37 feets
Therefore, the depth dug by old drill will be 19.37 feets
Learn more : https://brainly.com/question/12474772
Brisa is 2 years older than Aja. Damaris is 1 year younger than half of Brisa's age. The sum of all their ages is 27.
brisa is 12.5 aja is 10.5 and damaris is 4
Which of the following is the correct interpretation of 2?
In a statistics class, a teacher had the students
complete an activity in which they grabbed as many
bite-sized pretzels as they could with their dominant
hand, without crushing them. The teacher then
measured their handspan in centimeters. A regression
analysis was completed and the value for was
52.1%
* About 52.1 percent of the variation in handspan is
accounted for by the linear relationship formed with
the number of bite-sized pretzels grabbed with the
dominant hand.
About 52.1 percent of the variation in number of
bite-sized pretzels grabbed with the dominant hand
is accounted for by the linear relationship formed
with handspan
About 47.9 percent of the variation in handspan is
accounted for by the linear relationship formed with
the number of bite-sized pretzels grabbed with the
dominant hand
About 72.1 percent of the variation in number of
bite-sized pretzels grabbed with the dominant hand
is accounted for by the linear relationship formed
with handspan
Answer:
B
Step-by-step explanation:
EDGEN
Answer:
B. About 52.1 percent of the variation in number of bite-sized pretzels grabbed with the dominant hand is accounted for by the linear relationship formed with handspan.
Step-by-step explanation:
If F(x)=4x-1 and G(x)=2x-4 what is (FoG) (x)?
solve pls brainliest
Answer:
1(5/8)
step-by-step:
divide the numerator (top number) by the denominator (bottom number)
write whole number off to the left and put the remainder over the denominator to the right
solve pls branliest!
Answer:
(a) -7+3
(b)-7+(-3)
solve pls brainliest
Answer:
(1,6)
Step-by-step explanation:
all u gotta do is look at the graph, the school is at x=1 and y=6 so therefore (1,6)
Answer:
(1,6)
Step-by-step explanation:
Whatia the slops of the lime through (-2,16) and (2,2)
: $800 invested at a 9% interest rate for 8 years.
Answer:
576$
Step-by-step explanation:
$800×9/100×8=576$
Culver has 1 quarter, 3 dimes and 1 penny. How much money does he have
Answer:
56 cents
Step-by-step explanation:
1 quarter = 25 cents
3 dimes = 30 cents
1 penny = 1 cent -_-
25 + 30 + 1 = 56
I need the answer and a step by step
Answer:
hii
Step-by-step explanation:
plzz see attachment
hope it helps u
plz mark as brainliest
Mike jogged a total distance of 5 and 1 over 3 miles during the months of October and November. If Mike only jogged 1 over 6 mile every day, which expression shows the number of days in which he went jogging?
5 and 1 over 3 multiplied by 1 over 6
5 and 1 over 3 plus 1 over 6
5 and 1 over 3 minus 1 over 6
5 and 1 over 3 divided by 1 over 6
HELP MEH PLZ !!! IT'S (15 POINTS) T^T
Answer:
Step-by-step explanation:
5 1/3 x 1/6 = 8/9
5 1/3 + 1/6 = 5 2/6
5 1/3 - 1/6 = 31/6
5 1/3 / 1/6 = 32
Answer:
the correct answer for this problem is D: 5 and 1/3 divided by 1/6
Step-by-step explanation:
What is a multiplication table
Answer:
a table of products of two factors especially the integers 1 to 12 have a nice day
Step-by-step explanation:
:)
10 more than a number divided by -8
Answer:
6X8=48 10 more is 58
Step-by-step explanation: