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Setler [38]
2 years ago
15

Profit:p=r-c;solve for c

Mathematics
2 answers:
eduard2 years ago
5 0
If you would like to solve p = r - c for c, you can do this using the following steps:

p = r - c         /+c
p + c = r - c + c
p + c = r       /-p
p + c - p = r - p
c = r - p

The correct result would be c = r - p.
LuckyWell [14K]2 years ago
5 0
P=r-c
Subtract by r on both sides.
p-r=-c
Divide by negative one on both sides.
(p-r)/(-1)=c
(-1)(p-r)=c
<span>c=-p+r
c=r-p

</span>{\boxed{\sf c=-p+r}
{\boxed{\sf c=r-p}
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Find a factorization of x² + 2x³ + 7x² - 6x + 44, given that<br> −2+i√√7 and 1 - i√/3 are roots.
Levart [38]

A factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

<h3>What are the properties of roots of a polynomial?</h3>
  • The maximum number of roots of a polynomial of degree n is n.
  • For a polynomial with real coefficients, the roots can be real or complex.
  • The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if a+ib is a root, then a-ib is also a root.

If the roots of the polynomial p(x)=ax^4+bx^3+cx^2+dx+e are r_1,r_2,r_3,r_4, then it can be factorized as p(x)=(x-r_1)(x-r_2)(x-r_3)(x-r_4).

Here, we are to find a factorization of p(x)=x^4+2x^3+7x^2-6x+44. Also, given that -2+i\sqrt{7} and 1-i\sqrt{3} are roots of the polynomial.

Since p(x)=x^4+2x^3+7x^2-6x+44 is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.

Hence, -2-i\sqrt{7} and 1+i\sqrt{3} are also roots of the given polynomial.

Thus, all the four roots of the polynomial p(x)=x^4+2x^3+7x^2-6x+44, are: r_1=-2+i\sqrt{7}, r_2=-2-i\sqrt{7}, r_3=1-i\sqrt{3}, r_4=1+i\sqrt{3}.

So, the polynomial p(x)=x^4+2x^3+7x^2-6x+44 can be factorized as follows:

\{x-(-2+i\sqrt{7})\}\{x-(-2-i\sqrt{7})\}\{x-(1-i\sqrt{3})\}\{x-(1+i\sqrt{3})\}\\=(x+2-i\sqrt{7})(x+2+i\sqrt{7})(x-1+i\sqrt{3})(x-1-i\sqrt{3})\\=\{(x+2)^2+7\}\{(x-1)^2+3\}\hspace{1cm} [\because (a+b)(a-b)=a^2-b^2]\\=(x^2+4x+4+7)(x^2-2x+1+3)\\=(x^2+4x+11)(x^2-2x+4)

Therefore, a factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

To know more about factorization, refer: brainly.com/question/25829061

#SPJ9

3 0
1 year ago
Read 2 more answers
52,908 round to the nearest hundred.
IrinaVladis [17]

The hundredth is the 3rd number after the decimal place (so the 9). Look at the number before it and if it is 5 or above then round it to the next hundredth. In this case it is only a zero so we don't change the 9 just substitute it 0's. Therefore the answer is 52,900.

If you need further help let me know, hope this helped you.

6 0
3 years ago
(9 x 10) + (4 x 0.1)<br> how is this temperature in degrees fahrenheit written as a numeral?
mash [69]

Answer:

360°F

Step-by-step explanation:

When you multiply the numerals in the brackets . The first set of brackets is 90 then the second is 4.0 then multiply them and you will get 360.0°F

3 0
2 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=f%28x%29%3D16t%5E2%2B32t" id="TexFormula1" title="f(x)=16t^2+32t" alt="f(x)=16t^2+32t" align="
Nataly_w [17]

Answer:

- time = 1second

- maximum height = 16m

Step-by-step explanation:

Given the height of a pumpkin t seconds after it is launched from a catapult modelled by the equation

f(t)=-16t²+32t... (1)

The pumpkin reaches its maximum height when the velocity is zero.

Velocity = {d(f(x)}/dt = -32t+32

Since v = 0m/s (at maximum height)

-32t+32 = 0

-32t = -32

t = -32/-32

t = 1sec

The pumpkin reaches its maximum height after 1second.

Maximum height of the pumpkin is gotten by substituting t = 1sec into equation (1)

f(1) = -16(1)²+32(1)

f(1) = -16+32

f(1) = 16m

The maximum height of the pumpkin is 16m

6 0
3 years ago
Look at this expression.
g100num [7]
Multiply x<span> and </span>3

<span>Multiply x and 1</span>

<span>The x just gets copied along.</span>

<span>The answer is x</span>

x

<span>3*x evaluates to 3x</span>

Because of the minus sign

<span>3x becomes - 3x</span>

<span>The answer is -3x</span>

<span>Multiply y and 2</span>

<span>Multiply y and 1</span>

<span>The y just gets copied along.</span>

<span>The answer is y</span>

y

<span>2*y evaluates to 2y</span>

<span>-3*x-2*y evaluates to -3x-2y</span>

<span>The answer is -3x-2y-2</span>

<span>-3*x-2*y-2 evaluates to <span>-3x-2y-2</span></span>

<span><span>so the first one is right</span></span>

<span><span>
</span></span>

4 0
3 years ago
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