The cost of each Piano Lesson = $30
If there are x lessons, the total cost of lessons can be expressed as 30x.
Since the number of lessons cannot be negative, the value of x can be 0 or greater than 0, where x=0 shows no lesson.
For 1 lesson, x = 1
So the cost will be = 30(1) = $30
In ordered pair we can write it as (1, 30)
If we consider there is an option to attend half portion of a lecture, then for 1 and half lectures, x = 1.5
So, the cost for 1.5 lectures will be = 30(1.5) = $45
In ordered pair we can write it as (1.5, 45)
For 3 lesson, x = 3
The cost of 3 lessons will be = $90
In ordered pair we can write this as (3, 90)
So, from the given options, only following 2 ordered pairs satisfy the given conditions:
1) (1,30)
2) (3, 90)
Volume of the 1st package : 8.5x11x2 =187 in³
Volume of the 2nd package = 17.5x12x10 = 2,100 in³
Number of packages that fit = V₂/V₁ = 2100/187 = 11.23 Packages
Answer:
water + vinegar = 24 oz
W + V = 24
Also, we know V = 2 W add 2 parts of vinegar to 1 part water
2W + W = 24 oz
W = 8 oz
V = 16 oz amounts to add
A factorization of 
is 
.
<h3>What are the properties of roots of a polynomial?</h3>
- The maximum number of roots of a polynomial of degree
is . - 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
is a root, then 
is also a root.
If the roots of the polynomial 
are 
, then it can be factorized as 
.
Here, we are to find a factorization of 
. Also, given that 
and 
are roots of the polynomial.
Since is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.
Hence, 
and 
are also roots of the given polynomial.
Thus, all the four roots of the polynomial , are: 
.
So, the polynomial 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)](https://tex.z-dn.net/?f=%5C%7Bx-%28-2%2Bi%5Csqrt%7B7%7D%29%5C%7D%5C%7Bx-%28-2-i%5Csqrt%7B7%7D%29%5C%7D%5C%7Bx-%281-i%5Csqrt%7B3%7D%29%5C%7D%5C%7Bx-%281%2Bi%5Csqrt%7B3%7D%29%5C%7D%5C%5C%3D%28x%2B2-i%5Csqrt%7B7%7D%29%28x%2B2%2Bi%5Csqrt%7B7%7D%29%28x-1%2Bi%5Csqrt%7B3%7D%29%28x-1-i%5Csqrt%7B3%7D%29%5C%5C%3D%5C%7B%28x%2B2%29%5E2%2B7%5C%7D%5C%7B%28x-1%29%5E2%2B3%5C%7D%5Chspace%7B1cm%7D%20%5B%5Cbecause%20%28a%2Bb%29%28a-b%29%3Da%5E2-b%5E2%5D%5C%5C%3D%28x%5E2%2B4x%2B4%2B7%29%28x%5E2-2x%2B1%2B3%29%5C%5C%3D%28x%5E2%2B4x%2B11%29%28x%5E2-2x%2B4%29)
Therefore, a factorization of is .
To know more about factorization, refer: brainly.com/question/25829061
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