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4 years ago

2sec^2x - secx - 1 = 0

1 answer:

8 0

What are you trying to do here?
Solve the graph, or make it appear as something else?

First, we're going to take one sec (x) out so that we get:
sec (x) (2sec (x) -1 -1) = 0

sec (x) (2sec (x) -2) = 0

Then we're going to separate the two to find the zeros of each because anything time 0 is zero.

sec(x) = 0

2sec (x) - 2 = 0

Now, let's simplify the second one as the first one is already.

Add 2 to both sides:

2sec (x) = 2

Divide by 3 on both sides:

sec (x) = 1

I forgot my unit circle, so you'd have to do that by yourself. Hopefully, I helped a bit though!

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Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

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Answer:

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3 years ago

Use distributive property to rewrite 5 (x+4)

Serggg [28]

The answer is 5x + 20.

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3 years ago

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A culinary club earns $1350 from a dinner service. They sold 35 adult meals and 58 student meals. An adult meal costs $12 more t

liq [111]

The adult meal is $38.57 and the student meal is $26.27. You can try it out on a calculator, all you have to do is divide $1350 by 35 and then subtract your answer by 12!

7 0

4 years ago

Explain how you can tell whether a parabola opens upward, downward, to the left, or to the right

netineya [11]

Answer:

Step-by-step explanation:

If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.

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3 years ago

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