Answer:
![f(x)=x^4-9x^2-50x-150](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-9x%5E2-50x-150)
Step-by-step explanation:
Let f(x) be the polynomial function of minimum degree with real coefficients whose zeros are 5, -3, and -1 + 3i be f(x).
By the complex conjugate property of polynomials, -1-3i is also a root of this polynomial.
Therefore the polynomial in factored form is ![f(x)=(x-5)(x+3)(x-(-1+3i))(x-(-1+3i))](https://tex.z-dn.net/?f=f%28x%29%3D%28x-5%29%28x%2B3%29%28x-%28-1%2B3i%29%29%28x-%28-1%2B3i%29%29)
We expand to get:![f(x)=(x^2-2x-15)(x^2+2x+10)](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E2-2x-15%29%28x%5E2%2B2x%2B10%29)
We expand further to get:\
![f(x)=x^4-9x^2-50x-150](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-9x%5E2-50x-150)
The right answer is option 2.
Step-by-step explanation:
Let,
Slice of Cheese Pizza = x
Slice of Mushroom Pizza = y
According to given statement;
3x + 4y = 12.50 Eqn 1
3x + 2y = 8.50 Eqn 2
Subtract Eqn 2 from Eqn 1;
![(3x+4y)-(3x+2y)=12.50-8.50\\3x+4y-3x-2y=4.00\\2y=4.00\\y=\frac{4.00}{2} \\y=2.00](https://tex.z-dn.net/?f=%283x%2B4y%29-%283x%2B2y%29%3D12.50-8.50%5C%5C3x%2B4y-3x-2y%3D4.00%5C%5C2y%3D4.00%5C%5Cy%3D%5Cfrac%7B4.00%7D%7B2%7D%20%5C%5Cy%3D2.00)
As y is supposed as slice of mushroom, the price of one slice of mushroom pizza is $2.00
The right answer is option 2.
Keywords: Linear Equations, Subtraction.
Learn more about linear equations at:
#LearnwithBrainly
Answer: ![204\frac{2}{5}](https://tex.z-dn.net/?f=204%5Cfrac%7B2%7D%7B5%7D)
Step-by-step explanation:
Given the following expression:
![(\frac{7}{15}+\frac{125}{9})^2-16(\frac{0.25}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B7%7D%7B15%7D%2B%5Cfrac%7B125%7D%7B9%7D%29%5E2-16%28%5Cfrac%7B0.25%7D%7B2%7D%29)
You can follow these steps in order to solve the exercise:
1. You need to solve the operations inside the parentheses:
- Add the fractions. Since they have different denominators, you have to find the Least Comon Denominator (LCD):
![15=3*5\\9=3*3=3^2\\LCD=5*3^2=45](https://tex.z-dn.net/?f=15%3D3%2A5%5C%5C9%3D3%2A3%3D3%5E2%5C%5CLCD%3D5%2A3%5E2%3D45)
- Solve the division divididing the numerator 0.25 by the denominator 2.
Then, you get:
![(\frac{(3)(7)+(5)(125)}{45})^2-16(\frac{0.25}{2})\\\\(\frac{646}{45})^2-16(0.125)](https://tex.z-dn.net/?f=%28%5Cfrac%7B%283%29%287%29%2B%285%29%28125%29%7D%7B45%7D%29%5E2-16%28%5Cfrac%7B0.25%7D%7B2%7D%29%5C%5C%5C%5C%28%5Cfrac%7B646%7D%7B45%7D%29%5E2-16%280.125%29)
2. Solve the exponent:
![\(\frac{417,316}{2,025}-16(0.125)](https://tex.z-dn.net/?f=%5C%28%5Cfrac%7B417%2C316%7D%7B2%2C025%7D-16%280.125%29)
3. Solve the multiplication:
![\(\frac{417,316}{2,025}-2](https://tex.z-dn.net/?f=%5C%28%5Cfrac%7B417%2C316%7D%7B2%2C025%7D-2)
4. Solve the subtraction:
![\(\frac{417,316-(2,025)(2)}{2,025}=\frac{413,266}{2,025}\approx204.08](https://tex.z-dn.net/?f=%5C%28%5Cfrac%7B417%2C316-%282%2C025%29%282%29%7D%7B2%2C025%7D%3D%5Cfrac%7B413%2C266%7D%7B2%2C025%7D%5Capprox204.08)
5. Since :
![0.8=\frac{2}{5}](https://tex.z-dn.net/?f=0.8%3D%5Cfrac%7B2%7D%7B5%7D)
You can write the result as a mixed fraction:
![=204\frac{2}{5}](https://tex.z-dn.net/?f=%3D204%5Cfrac%7B2%7D%7B5%7D)
Answer:
B. y > 3x -7
Step-by-step explanation:
We can choose the correct inequality based on the y-intercept and the shading.
<h3>Y-intercept</h3>
The dashed line crosses the y-axis at approximately y=-7. This is the value of y when x=0. This observation eliminates choices D, E, F.
<h3>Shading</h3>
The shading on the graph is seen to be above and to the left of the line. This means the variables in relation to the inequality symbol must be ...
y > ( ) . . . . eliminates choice A
and
x < ( ) or ( ) > x . . . . eliminates choice C, confirms choice B
The inequality that matches the graph is y > 3x -7.
__
<em>Additional comment</em>
For looking at shading, we are interested in the relation of the inequality symbol to a variable term with a <em>positive coefficient</em>. If the coefficient is negative, you can do either of ...
- add the opposite of that variable term to both sides of the equation
- reverse the inequality symbol
That is, if you have -3x < ( ), when considering shading, you can consider the relation x > ( ) with the inequality reversed, or you can consider ( ) < x, which has x on the other side of the inequality. Both of these tell you shading is right of the line, where x-values are greater than those on the line.
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