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3 years ago

Determine the common factors and HCF for each of the following terms.

Mathematics

1 answer:

Ahat [919]3 years ago

3 0

Answer: Please see explanation column for answers

Step-by-step explanation:

When a number divides into another number without a remainder, it s called a factor of that number. Lets say we want to find the common factors of two numbers, we get the factors of each one and compare them. The common factor is the one that is found in both lists

While The Highest common factor, is the highest factor number found in both lists.

b) 2b , 3b

Factors of 2b= 1, 2 and b

Factors of 3b=1, 3 and b

Common factors =1 and b

HCF=1b

e) 5bc, 2c2, 3cd

Factors of 5bc= 1, 5, b, c

Factors of 2c2= 1, 2, c, c2

Factors of 3cd= 1, 3, c, d

Common factors = 1 and c

HCF= 1c

f) 4a2b, 8b2c, 6bcd

Factors of 4a2b= 1, 2, 4, a, a2, b

Factors of 8b2c= 1, 2, 4, 8, b, b2, c

Factors of 6bcd= 1, 2,3,6, b, c,d

Common factors = 1, 2 , b

HCF= 2b

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One urn contains one blue ball (labeled b1) and three red balls (labeled r1, r2, and r3). a second urn contains two red balls (r

Flura [38]

Answer:

12 possibilities

Step-by-step explanation:

In the first urn, we have 4 balls, and all of them are different, as they have different labels, so the group of two red balls r1 and r2 is different from the group of red balls r2 and r3.

The same thing occurs in the second urn, as all balls have different labels.

The problem is a combination problem (the group r1 and r2 is the same group r2 and r1).

For the first urn, we have a combination of 4 choose 2:

C(4,2) = 4!/2!*2! = 4*3*2/2*2 = 2*3 = 6 possibilities

For the second urn, we also have a combination of 4 choose 2, so 6 possibilities.

In total we have 6 + 6 = 12 possibilities.

3 0

3 years ago

Read 2 more answers

Find k. ..................

Nonamiya [84]

Answer:

k = -10

Explanation:

f(x) = 4x³ - 3kx² + 44x - 30

The divisor is:

(x - 2)

Set divisor to zero:

(x - 2) = 0

x = 2

Insert this into equation.

⇒ 4(2)³ - 3k(2)² + 44(2) - 30 = 210

⇒ 32 - 12k + 88 - 30 = 210

⇒ -12k + 90 = 210

⇒ -12k = 210 - 90

⇒ -12k = 120

⇒ k = 120/-12

⇒ k = -10

6 0

2 years ago

Read 2 more answers

Please help. Write the equation of the graph. (Do not use spaces. Use ^ to represent exponents. Example 2^3 is 23.)

lana66690 [7]

This graph has a horizontal asymptote so it is an exponential graph. It also passes through two points (0,-2) and (1,3). The horizontal asymptote is at y=-3.
The unchanged exponential equation is y=a(b)^x +k
For exponential equations, k is always equal to the horizontal asymptote, so k=-3.
You can check this with the ordered pair (0,-2). After that plug in the other ordered pair, (1,3).
This gives you 3=a(b)^1 or 3=ab. If you know the base the answer is simple as you just solve for a.
If you don't know the base at this point you have to sort of guess. For example, let's say both a and b are whole numbers. In that case b would have to be 3, as it can't be 1 since then the answer never changes, and a is 1. Then choose an x-value and not exact corresponding y-value. In this case x=-1 and y= a bit less than -2.75. Plug in the values to your "final" equation of y=(3)^x -3.
So -2.75=(3^-1)-3.
3^-1 is 1/3, 1/3-3 is -8/3 or -2.6667 which is pretty close to -2.75. So we can say the final equation is y=3^x -3.
Hope this helps! It's a lot easier to solve problems like these given either more points which you can use system of equations with, or with a given base or slope.

7 0

3 years ago

Write the unit rate if you travel 100 miles in 4 h

Ymorist [56]

100 miles/4 hours = 25 miles per hour

3 0

3 years ago

Find all of the factors of 72. 1, 2, 3, 4, 6, 8, 9 1, 2, 3, 4, 8, 12, 16, 24, 36, 72 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36 1, 2,

Andrew [12]

Answer:

Find all of the factors of 72

1,2,3,4,6,8,9,12,18,24,36,72

Step-by-step explanation:

3 0

4 years ago