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malfutka [58]
3 years ago
12

True or false every whole number is a multiple of 1?

Mathematics
1 answer:
jenyasd209 [6]3 years ago
3 0
Every whole number is not a factor of 1. However, 1 is a factor of every whole number
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What is a prime number.?
Naddika [18.5K]

Answer:

prime numbers are the natural numbers greater than one that are not products of two smaller natural numbers

Step-by-step explanation:

7 0
3 years ago
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For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
Elina [12.6K]

Answer:

<em>C.</em> (5-\frac{1}{2})^6

Step-by-step explanation:

Given

15(5)^2(-\frac{1}{2})^4

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

Sum = 2 + 4

Sum = 6

Each term of a binomial expansion are always of the form:

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

Where n = the sum above

n = 6

Compare 15(5)^2(-\frac{1}{2})^4 to the above general form of binomial expansion

(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......

Substitute 6 for n

(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

By direct comparison of

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

and

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

We have;

^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4

Further comparison gives

^nC_r = 15

a^{n-r} =(5)^{6-4}

b^r= (-\frac{1}{2})^4

[Solving for a]

By direct comparison of a^{n-r} =(5)^{6-4}

a = 5

n = 6

r = 4

[Solving for b]

By direct comparison of b^r= (-\frac{1}{2})^4

r = 4

b = \frac{-1}{2}

Substitute values for a, b, n and r in

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

Solve for ^6C_4

(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em>(5-\frac{1}{2})^6<em />

3 0
3 years ago
2. Jill swam 200 meters in 2 minutes 42 seconds. If each lap is 50 meters long,
Morgarella [4.7K]

Answer:

40.5

Step-by-step explanation:

there are 4 laps in 200 metres.

(200m÷50m)

2min 42 sec=120 sec+42sec (162sec)

so,

162÷4=40.5

3 0
3 years ago
The circumference of a circle is about 50 centimeters (cm). Which is closest to the length of its radius? You may use 3.14 for
Romashka-Z-Leto [24]

Answer:

8 cm

Step-by-step explanation:

The formula of circumference is c= πd------(1)

where C = circumference, π = 3.14 and d = diameter

as we know that diameter is equal to d= 2r

put the diameter formula in eq(1)

we get c= π2r-------(2)

from eq (2) separate r means radius

hence, r= c/(π2)------(3)

put the values in eq(3)

and radius is equal to 8 cm.

5 0
3 years ago
Please help ASAP ty!
Butoxors [25]

Answer:

C. 70

Step-by-step explanation:

  • 5(x+9)
  • 5(5+9)
  • 25+45
  • 70

<h2>stay safe healthy and happy..</h2>
4 0
3 years ago
Read 2 more answers
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