Please answer fast needed as soon as possible

Mathematics

1 answer:

irakobra [83]2 years ago

3 0

Answer:

Option B

Step-by-step explanation:

Equation of the graph,

f(x) = x²

If the graph is translated 5 units to the right,

g(x) = f(x - 5)

Therefore, g(x) = (x - 5)²

If the function 'g' is translated 3 units up,

h(x) = g(x) + 3

Therefore, h(x) = (x - 5)² + 3

If the function 'h' is vertically compressed by a factor of $\frac{2}{3}$ ,

Then the new function will be,

k(x) = $\frac{2}{3}(x-5)^2+3$

Option B will the correct option.

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The given question is a quadratic equation and we can use several methods to get the solutions to this question. The solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

<h3>Quadratic Equation</h3>

Quadratic equation are polynomials with a second degree as it's highest power.

An example of a quadratic equation is

$y = ax^2 + bx + c$

The given quadratic equation is $24x^2 + 2x = 15$

Let's rearrange the equation

$24x^2 + 2x = 15\\24x^2 + 2x - 15 = 0$

This implies that

a = 24
b = 2
c = -15

The equation or formula of quadratic formula is given as

$y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}$

We can substitute the values into the equation and solve

$y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\y = \frac{-2 +- \sqrt{2^2 -4 * 24 * (-15)} }{2*24} \\y = \frac{-2+-\sqrt{4+1440} }{48} \\y = \frac{-2+-\sqrt{1444} }{48} \\y = \frac{-2+- 38}{48} \\y = \frac{-2+38}{48} \\y = \frac{3}{4}\\ \\or\\y = \frac{-2-38}{48} \\y = \frac{-40}{48} \\y = -\frac{5}{6}$