Please help will mark as brainiest

At Silver Gym, membership is $25 per month, and personal training sessions are $30 each. At Fit Factor, membership is $65 per mo

ladessa [460]

Answer:

I belive B

25x+30=65x+20

4 0

3 years ago

Find the polynomial of minimum degree, with real coefficients, zeros at x=4±2⋅i and x=−8, and y-intercept at −480. Write your an

valkas [14]

Answer:

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

Step-by-step explanation:

According to the statement, we appreciate that polynomial pass through the following points:

(i) $(4 + 2\,i,0)$ , (ii) $(4 - 2\,i, 0)$ , (iii) $(-8, 0)$ , (iv) $(0, -480)$

From Algebra we know that any n-th grade polynomial can be constructed by knowing n+1 different points. Hence, the polynomial of minimum degree is a quartic function. The polynomial has the following form:

$p(x) = (x-4-2\,i)\cdot (x-4+2\,i)\cdot (x+8)\cdot (x-r_{1})$

We proceed to expand the expression until standard form is obtained:

$p(x) = (x^{2}-4\cdot x-2\,i\cdot x-4\cdot x +16+8\,i+2\,i\cdot x-8\,i+4)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{2}-8\cdot x+20)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{3}-8\cdot x^{2}+20\cdot x +8\cdot x^{2}-64\cdot x+160)\cdot (x-r_{1})$

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-r_{1})$

If we know that $p (0) = -480$ , then:

$-480=160\cdot (-r_{1})$

$-160\cdot r_{1} = -480$

$r_{1} = 3$

Then, the polynomial is:

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-3)$

$p(x) = x^{4}-44\cdot x^{2}+160\cdot x-3\cdot x^{3}+132\cdot x -480$

$p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

5 0

3 years ago

Suppose we wish to construct the perpendicular bisector of line segment EF. We can correctly begin by placing the compass point

julia-pushkina [17]

- to a point which is more than halfway to the point F. Then draw an arc around the point. Next place the compass point at F and, keeping the same distance between the points of the compass, draw another arc so as to intersect the first arc at 2 points above and below the line EF. Finally draw a line passing through these 2 points of intersection. This is the perpendicular bisector of EF.

3 0

3 years ago

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Joey Chestnut is trying to break his own world record for eating the most hot dogs and buns in 10 minutes. He needs to eat more

mr Goodwill [35]

73 (because you want more than 72 to break the record) - 10 = 63
63/9 ( the amount of minutes left) = 7

Joey would have to eat at least 7 hot dogs each minute to break his record.

x+10 > 72

hope this helps

3 0

3 years ago

Read 2 more answers

Is 0.62 a rational number?

dimaraw [331]

A rational number is any number that can be written <em>as a ratio of two integers</em>.

0.62 fits the bill, as it can be written as the ratio 62/100 (or simplified to the ratio 31/50)

7 0

4 years ago

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