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SIZIF [17.4K]
2 years ago
14

What is the value of the product (4 – 2i)(6 + 2i)? 20 – 4i 20 + 16i 28 + 16i 28 – 4i

Mathematics
2 answers:
Darya [45]2 years ago
8 0

(4 – 2i)(6 + 2i)

FOIL

First : 4*6 =24

Outer: 4*2i = 8i

Inner: -2i* 6 = -12i

Last: -2i*2i = -4i^2 =-4(-1) =4

Add together

24+8i-12i+4

28-4i

Answer: 28-4i

Ostrovityanka [42]2 years ago
5 0

Answer:

28-4i

Step-by-step explanation:

There for the answer is D

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Nicole is studying for her upcoming college entrance exams. She has already completed 20 practice problems and plans on completi
horsena [70]
Total number of problems Nicole will have completed: y
Number of nights she studies: x

She has already completed 20 practice problems:
When x=0, y=20

She plans on completing 6 more problems each night:
y=20+6x
y=6x+20

Please, see the attached graph.

Thanks.

8 0
1 year ago
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
Volgvan

Answer: We reject the null hypothesis, and we use Normal distribution for the test.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis : H_0:\mu\geq 50000

Alternate hypothesis : H_1:\mu

There  is 5% level of significance.

\bar{X}=46800\\\\\sigma=9800\\\\n=29

So, the test statistic would be

z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{46800-50000}{\dfrac{9800}{\sqrt{29}}}\\\\z=-1.75

Since alternate hypothesis is left tailed test.

So, p-value = P(z≤-2.31)=0.0401

And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.

So, we reject the null hypothesis, and we use Normal distribution for the test.

4 0
2 years ago
Which shows a recursive and an explicit formula for a sequence whose initial term is 14 and whose common difference is −4? A. A(
liberstina [14]

Answer: A. A(1) = 14; A(n) = (n − 1) −4; A(n) = 14 + (n − 1)(−4)

Step-by-step explanation:

Arithmetic sequence is a sequence that is identified by their common difference. Let a be the first term, n be the number of terms and d be the common difference.

For an arithmetic sequence, common difference 'd' is added to the preceding term to get its succeeding term. For example if a is the first term of a sequence, second term will be a+d, third term will give a+d+d and so on to generate sequence of the form,

a, a+d, a+3d, a+4d...

Notice that each new term keep increasing by a common difference 'd'

The nth term of the sequence Tn will therefore give Tn = a+(n-1)d

If the initial (first) term is 14 and common difference is -4, the nth of the sequence will be gotten by substituting a = 14 and d = -4 in the general formula to give;

Tn = 14+(n-1)-4 (which gives the required answer)

Tn = 14-4n+4

Tn = 18-4n

5 0
1 year ago
Read 2 more answers
Andre and Diego were each trying to solve 2x+6=3x−8. Describe the first step they each make to the equation. The result of Andre
Oksi-84 [34.3K]

Answer:

  • Andre subtracted 3x from both sides
  • Diego subtracted 2x from both sides

Step-by-step explanation:

<u>Andre</u>

Comparing the result of Andre's work with the original, we see that the "3x" term on the right is missing, and the x-term on the left is 3x less than it was. It is clear that Andre subtracted 3x from both sides of the equation.

__

<u>Diego</u>

Comparing the result of Diego's work with the original, we see that the "2x" term on the left is missing, and the x-term on the right is 2x less than it was. It is clear that Diego subtracted 2x from both sides of the equation.

_____

<em>Comment on their work</em>

IMO, Diego has the right idea, as his result leaves the x-term with a positive coefficient. He can add 8 and he's finished, having found that x=14.

Andre can subtract 6 to isolate the variable term, and that will give him -x=-14. This requires another step to get to x=14. Sometimes minus signs get lost, so this would not be my preferred sequence of steps.

As a rule, I like to add the opposite of the variable term with the least (most negative) coefficient. This results in the variable having a positive coefficient, making errors easier to avoid.

3 0
1 year ago
The volume of the sphere is StartFraction 500 Over 3 EndFractionπ cubic units. A sphere has a radius of x units. What is the val
Tpy6a [65]

Answer:

(b) Radius of the sphere = 5 units.

Step-by-step explanation:

Here, given:

The volume of the sphere  = (\frac{500}{3})\pi cubic units  ... (1)

Also, radius of the sphere  = x  units

Now, VOLUME OF SPHERE  = (\frac{4}{3}) \pi r^3

So, volume of a sphere with radius x  = (\frac{4}{3}) \pi (x)^3

But volume of sphere is given by (1).

\implies (\frac{500}{3})\pi = (\frac{4}{3}) \pi (x)^3\\\implies (\frac{500}{3}) = (\frac{4}{3}) (x)^3\\\implies x^3 = (\frac{500}{3})  \times (\frac{3}{4})  = 125\\\implies x^ 3 = 125 = (5)^3\\\implies x  = 5

Hence, radius of the sphere = 5 units.

4 0
2 years ago
Read 2 more answers
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