Answer:
y = 3(x -2)² -5
Step-by-step explanation:
It looks like you want to write the standard-form quadratic ...
y = 3x² -12x +7
in vertex form.
The process is similar to that of "completing the square."
<h3>Steps</h3>
<u>Factor out the leading coefficient</u>
Do this for the variable terms only.
y = 3(x² -4x) +7
<u>Identify the x-term coefficient</u>
The x-term coefficient (inside parentheses) divided by 2 is the opposite of the x-coordinate of the vertex. It is the constant term in the squared binomial of the vertex form. Square this value.
x coefficient: -4
binomial constant: -4/2 = -2
square of this: (-2)² = 4
<u>Add this inside parentheses</u>
To keep the overall equation unchanged, you must also subtract an equal amount outside parentheses.
y = 3(x² -4x +4) +7 -3(4)
<u>Simplify to vertex form</u>
Write the trinomial in parentheses as a square, and simplify the y-coordinate of the vertex.
y = 3(x -2)² -5
Answer:
There is one solution.
You use substitution;
2(3x+2)=5x+4
6x+4=5x+4
x+4=4
x=0
y=2
To verify your answer, pug in x and y into both equations.
Step-by-step explanation:
Part A
(h + t)(x)
(5x - 2 + 4x + 6)(x) First plug in the numbers
(9x + 4)(x) Add h(x) and t(x)
(9x² + 4x) Then multiply it by x
x(9x + 4) Lastly, simplify x out (I'm including both answers because I don't know whether your questions will ask for either one)
Unsimplified Answer: 9x² + 4x Simplified Answer: x(9x + 4)
Part B
(h x t)(x)
(5x - 2)(4x + 6)(x) First step is to of cource, plug in the numbers
(20x² + 30x -8x -12)(x) Next we multiply h(x) and t(x)
(20x² + 22x -12)(x) Simplify it a little
(20x³ + 22x² - 12x) After that, multiply the whole thing by x
(2x)(10x² + 11x - 6) Simplify 2x out of the equation
(2x)(5x - 2)(2x + 3) Lastly, simplify the rest
Unsimplified Answer: (20x³ + 22x² -12x) Simplified Answer: (2x)(5x - 2)(2x + 3)
Part C
h[t(x)]
(5x - 2) [(4x + 6)(x)] Plug in the numbers
(5x - 2)(4x² + 6x) Multiply t(x) and x
(20x³ + 30x² - 8x² -12x) Multiply that by h(x)
(20x³ + 22x² -12x) Simplify a little... Wait! That looks like the answer to Part B! Perhaps we did something wrong, let's go back and alter the third step
(5x -2)(2x)(2x + 3) This time, simplify before multiplying oh wait, that's part B's simplified answer, isn't it.
Well, there's a good explanation for this: Part B and Part C are essentially the same equations, just in slightly different orders!
So, it will have the same answers and Part B! (At least, in theory, I'd recommend checking this for yourself too!)
Unsimplified Answer: (20x³ + 22x² - 12x) Simplified Answer: (2x)(5x-2)(2x+3)
Well, that's a wrap, Parts A, B, and, C with work and explanations; if you find that I made a mistake or did something wrong let me know. I hope this helped, and good luck!
The answer is 20, since it’s heads and tails you have a half and half chance, therefore you divide 40 in half and get 20
We know that
area of the square=b²-------> b=√area
where
b is the side length of the square
for the smaller square
area=256 m²
b=√256-------> b=16 m
for the larger square
area=625 m²
b=√625-----> b=25 m
<span>the ratio of their sides is 16/25</span>
