Answer:
Step-by-step explanation:
Reasoning A store sells packages of comic books with a poster. A poster and 5 comics cost $13.99. A poster and 12 comics cost $20.99. Write a linear function rule that models the cost y of a package containing any number x of comic books. Suppose another store sells a similar package, modeled by a linear function rule with initial value $. Use pencil and paper. Explain which store has the better deal. The linear function rule is y nothing.
- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant
With our equation, plug in the values:
![x=\frac{4\pm \sqrt{(-4)^2-4*1*13}}{2*1}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B%28-4%29%5E2-4%2A1%2A13%7D%7D%7B2%2A1%7D)
Next, solve the exponent and multiplications:
![x=\frac{4\pm \sqrt{16-52}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B16-52%7D%7D%7B2%7D)
Next, solve the subtraction:
![x=\frac{4\pm \sqrt{-36}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B-36%7D%7D%7B2%7D)
Next, factor out i (i = √-1):
![x=\frac{4\pm \sqrt{36}i}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B36%7Di%7D%7B2%7D)
Next, solve the square root:
![x=\frac{4\pm 6i}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%206i%7D%7B2%7D)
Lastly, divide and <u>your answer is:</u>
![x=2\pm 3i](https://tex.z-dn.net/?f=x%3D2%5Cpm%203i)
Answer: -3/2
Step-by-step explanation:
The axis of symmetry, and thus the x-coordinate of the vertex, is given by ![x=-\frac{b}{2a}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7Bb%7D%7B2a%7D)
So, the answer is ![x=-\frac{9}{2(3)}=\boxed{-\frac{3}{2}}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B9%7D%7B2%283%29%7D%3D%5Cboxed%7B-%5Cfrac%7B3%7D%7B2%7D%7D)
Answer:
L = 25
Step-by-step explanation:
Let's call the Length x and width x - 15 since the width is 15 less than length
Eric needs 70 of fencing in total, the perimeter of a rectangle is calculated by adding all sides
x + x + (x - 15) + (x - 15) = 70 add like terms
4x - 30 = 70 add 30 to both sides
4x = 100 divide both sides by 4
x = 25
Answer:
Katie will collect more than 100 seashells in 5 and a half days.
Step-by-step explanation:
Katie already has 34 seashells in her collection.
Each day, she finds 12 more seashells on the beach.
Let x be the number of days Katie is collecting seashells.
In x days, she will collect 12x seashells.
In total, she will collect
seashells.
Katie wants to collect over 100 seashells, so
![34+12x> 100](https://tex.z-dn.net/?f=34%2B12x%3E%20100)
Solve this inequality. Subtract 34:
![34+12x-34>100-34\\ \\12x>66\\ \\2x>11\\ \\x>5 \dfrac{1}{2}](https://tex.z-dn.net/?f=34%2B12x-34%3E100-34%5C%5C%20%5C%5C12x%3E66%5C%5C%20%5C%5C2x%3E11%5C%5C%20%5C%5Cx%3E5%20%5Cdfrac%7B1%7D%7B2%7D)
Katie will collect more than 100 seashells in 5 and a half days.