complette the square to get vertex form or y=a(x-h)^2+k
(h,k) is vertex
1. group x terms, so for y=ax^2+bx+c, do y=(ax^2+bx)+c
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2, factor out the leading coefinet (constant in front of the x^2 term), basicallly factor out a
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3. take 1/2 of the linear coefient (number in
front of the x), and square it ,then add negative and positive of it
inside parnthases
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4. complete the squre and expand
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so
y=-1/4x^2+4x-19
group
y=(-1/4x^2+4x)-19
undistribute -1/4
y=-1/4(x^2-16x)-19
take 1/2 of -16 and squer it to get 64 then add neg and pos inside
y=-1/4(x^2-16x+64-64)-19
factorperfect square
y=-1/4((x-8)^2-64)-19
expand
y=-1/4(x-8)^2+16-19
y=-1/4(x-8)^2-3
vertex is (8,-3)
Answer:
(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12)
Step-by-step explanation:
Given:
Polynomial 27a^3 b^9+8c^18
Factoring the given polynomial
27a^3b^9 can be written as
=3^3.a^3.b^3^3
=(3ab^3)^3
Also 8c^18 can be written as
=2^3.c^6^3
=(2c^6)^3
Hence Polynomial 27a^3 b^9+8c^18 can be written as
=(3ab^3)^3+(2c^6)^3
Applying sum of cubes formula i.e. a^3 + b^3=(a+b)(a^2 – ab + b^2)
=(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12) !
Answer:
the answer is a. 89 miles
Step-by-step explanation:
first you do 59.40 x 3 = 178.47
then you do 222.08 - 178.47 = 43.61
finally you do 43.61 divided by 0.49 = 89
Answer:
We need to multiply the percentage as a decimal (0.30) with the amount of chocolate (50 g):
0.30*50 = 15 g
There are 15 grams of cocoa in the chocolate bar.
Step-by-step explanation:
Answer:
(a) Because the expression is not an equation
(b) Because the expression is an equation
Step-by-step explanation:
Solving (a): a + 2
The above expression can assume any value for a because it is not an equation.
Take for instance:
a = 2;
<em>The reason for this is because the expression is not an equation</em>
Solving (b): 
The above expression can assume only value for b, and the value is:
This means that only will make the equation true.
<em>The reason for this is because the expression is an equation</em>
