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nekit [7.7K]
3 years ago
8

identify the independent and dependent variables of A dance academy charges $20 to use the facility and $25 per hour of instruct

ion.
Mathematics
1 answer:
nikklg [1K]3 years ago
4 0

Answer: 45

20+25=45

that should be the answer bye enjoy! friend me foir more answers!

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If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?
Naddik [55]

Answer:

it must also have the root : - 6i

Step-by-step explanation:

If a polynomial is expressed with real coefficients (which must be the case if it is a function f(x) in the Real coordinate system), then if it has a complex root "a+bi", it must also have for root the conjugate of that complex root.

This is because in order to render a polynomial with Real coefficients, the binomial factor  (x - (a+bi)) originated using the complex root would be able to eliminate the imaginary unit, only when multiplied by the binomial factor generated by its conjugate: (x - (a-bi)). This is shown below:

(x-(a+bi))*(x-(a-bi))=\\(x-a-bi)*(x-a+bi)=\\([x-a]-bi)*([x-a]+bi)=\\(x-a)^2-(bi)^2=\\(x-a)^2-b^2(-1)=\\(x-a)^2+b^2

where the imaginary unit has disappeared, making the expression real.

So in our case, a+bi is -6i (real part a=0, and imaginary part b=-6)

Then, the conjugate of this root would be: +6i, giving us the other complex root that also may be present in the real polynomial we are dealing with.

5 0
3 years ago
What does this graph show<br> inverse <br>direct<br> neither​
grin007 [14]

Answer:

i think the given graph is inverse

3 0
2 years ago
Simplify (7 i) − (6 − 2i). a. −2 b. 1 − i c. 1 3i d. 4
Ksenya-84 [330]
(7 + i) - (6 - 2i) = 7 + i - 6 + 2i = 1 + 3i
5 0
3 years ago
Devon is 30 years older than his son, Milan. The sum of both their ages is 48. Using the variables d and m to represent the ages
statuscvo [17]

Answer+Step-by-step explanation:

m = man's age

s = son's age

m=s+36

(m+8)=3*(s+8)

Resolves to: s=10, m=46

So the man is 46 (=10+36).

In 8 years, son is 18 (=10+8), man is 54 (=3*18 and 46+8), thank you.

5 0
3 years ago
After 5 tests Dara's average score was 88 what score must she average on the next two tests to have a seven-test average of 90?
Tomtit [17]

After 5 tests, her average was 88. To have a seven-test average of 90, the total must be:

90 \times 7 = 630

Her average after 5 tests was 88. Her total score on the 5 tests is:

88 \times 5 = 440

Subtract:

630-440 = 190

Find the average by dividing by 2:

190 \div 2 = 95

Her average must be 95

3 0
3 years ago
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