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3 years ago

How many terms are in the expansion (a + b)15.

1 answer:

7 0

First you must distribute
Multiple 15 by a and 15 by b
You should get
15a + 15b
There are two terms in the expanded form

Your two terms are 15a and 15b

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Raina must choose a number between 55 and 101 that is a multiple of 2, 8 and 10. Write all the numbers that she could choose. If

Aleonysh [2.5K]

Answer:

The only possible number is $80$ .

Step-by-step explanation:

The number in question needs to be a multiple of all three of $2$ , $8$ , and $10$ . As a result, it must also be a multiple of the least common multiplier (lcm) of the three number.

Start by finding the least common multiplier of the three numbers.

Factor each number into its prime components:

$2$ is a prime number itself.
$8 = 2^3$ .
$10 = 2 \times 5$ .

The only prime factors are $2$ and $5$ .

The greatest power of $2$ among the three numbers is $3$ .
The greatest power of $5$ among the three numbers is $1$ .

Therefore, the least common multiplier of the three number should be the product of $2^3$ and $5$ . That's equal to $2^3 \times 5 = 8 \times 5 = 40$ .

In other words, the number (or numbers) in question could be written in the form $40\, k$ , where $k$ is an integer.

The question requires that this number be between $55$ and $101$ . In other words,

$55 \le 40\, k \le 101$ .

The goal is to find the possible values of $k$ . Note that from integer division by $40$ ,

$55 = 1 \times 40 + 15$ , and
$101 = 2 \times 40 + 21$ .

The inequality becomes:

$1 \times 40 + 15 \le 40\, k \le 2 \times 40 + 21$ .

However,

$1 \times 40 < 55 = 1 \times 40 + 15$ , and
$2 \times 40 + 21 = 101 < 3 \times 40$ .

Hence,

$1 \times 40 < 1\times 40 + 15 \le 40\, k \le 2 \times 40 + 21 < 3 \times 40$ .

$1 \times 40 < 40\, k < 3 \times 40$ .

Divide by the positive number $40$ to obtain:

$1 < k < 3$ .

Since $k$ is an integers, $k = 2$ .

Indeed, $40 \, k = 80$ is between $55$ and $101$ .

Therefore, $80$ is the number in question.

5 0

3 years ago

Read 2 more answers

Please answer ASAP!! Consistently wash your hands for 1 minute.

diamong [38]

Each peach costs $0.56 and the equations used to solve that is $4x= 2.24$ where x is the cost of 1 peach.

Step-by-step explanation:

Step 1:

It is given that all the peaches weigh the same and that 4 peaches weigh 1 pound.

Assume that each peach costs x.

So the cost for 4 peaches is given by $4x.$

Step 2:

The cost of 1 pound of peaches is given as $2.24.

1 pound of peaches $=4x.$

So $4x= 2.24, x = \frac{2.24}{4}.$

$x = 0.56.$

So each peach costs $0.56.

5 0

3 years ago

Could Someone help me, thank you so much!

maxonik [38]

Answer: Answer choice A

Step-by-step explanation:

Because 2 has 20 copies 4 has 40 so we can only assume that 6 will follow the pattern and be 60.

Hope it helps!

5 0

3 years ago

Read 2 more answers

Paul was making some brownies and cupcakes for his school fundraiser. If the brownies needed 4.8 cups of sugar and the cupcakes

ArbitrLikvidat [17]

Answer:

10 cups in total.

Step-by-step explanation:

4.8+5.2= 10.00

add the .2 to the 4.8 you get get 5 then add 5.0+5.0

8 0

3 years ago

the width of a rectangle is 15 units less than the length. if the area is 76 square units, then find the dimensions of the recta

Lelu [443]

W = L - 15
WL = 76

(L-15)L = 76

L^2 - 15L - 76 = 0
(L-19)(L+4) = 0

L = 19 or -4
Since a length cannot be negative, the length must be 19 units.
The width is 19-15=4 units.

6 0

4 years ago