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Serjik [45]
3 years ago
13

(Please help) The expression (x^16)(x^-24) is equivalent to x^n. What is the value of n?

Mathematics
1 answer:
victus00 [196]3 years ago
6 0

Answer:

8

Step-by-step explanation:

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What are the key features of a graph of a quadratic equation with only complex solutions
dybincka [34]

Answer:

If  D< 0, the roots of the quadratic equation will b complex.

Step-by-step explanation:

Let ax^{2}  + bx + c =0 is the given quadratic equation.

So, if the Discriminant (D) = b^{2}  - 4ac  < 0, the the equation will have only complex solutions.

Complex roots are represented in the form of (x \pm iy)

1.  <u> x represents the X axis (real) co ordinate,</u>

    <u>y represents the Y axis (imaginary) coordinate</u>

<u />

<u />

2. Also, the graph of the with equation  D < 0  NEVER CROSSES the X - axis, as there are no real roots of the equation, only complex roots.

3. Here. roots are always identical but are opposite in signs. Such pair or roots with opposite sign are called CONJUGATE PAIRS.

4 0
3 years ago
Grandma baked 969696 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received ccc fewer cookies tha
Angelina_Jolie [31]

The total number of cookies baked by grandma = 96

Number of grandchildren = 8

As given, all cookies were evenly divided among 8 children, let us assume that everyone except Cindy got equal share. So on being divided equally, it becomes, \frac{96}{8}=12 cookies per children.

But, as mentioned that Cindy received 'c' cookies less, so let us suppose Cindy received 'x' cookies.

Expression becomes: x=12-c

Hence, Cindy received 12-c cookies.

6 0
3 years ago
Prime factorization of 1050
Shkiper50 [21]
The Prime Factorization of 1050: 2*3*5^2*7<span />
7 0
3 years ago
2y+3x² +5+y+2x+x²+2 what are the coefficients?
saw5 [17]

Answer: 200

The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Any quadratic function can be rewritten in standard form by completing the square. (See the section on solving equations algebraically to review completing the square.) The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation.

Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.

Example 3.

Write the function f(x) = x2 - 6x + 7 in standard form. Sketch the graph of f and find its zeros and vertex.

f(x) = x2 - 6x + 7.

= (x2 - 6x )+ 7.        Group the x2 and x terms and then complete the square on these terms.

= (x2 - 6x + 9 - 9) + 7.

We need to add 9 because it is the square of one half the coefficient of x, (-6/2)2 = 9. When we were solving an equation we simply added 9 to both sides of the equation. In this setting we add and subtract 9 so that we do not change the function.

= (x2 - 6x + 9) - 9 + 7. We see that x2 - 6x + 9 is a perfect square, namely (x - 3)2.

f(x) = (x - 3)2 - 2. This is standard form.

From this result, one easily finds the vertex of the graph of f is (3, -2).

To find the zeros of f, we set f equal to 0 and solve for x.

(x - 3)2 - 2 = 0.

(x - 3)2 = 2.

(x - 3) = ± sqrt(2).

x = 3 ± sqrt(2).

To sketch the graph of f we shift the graph of y = x2 three units to the right and two units down.

If the coefficient of x2 is not 1, then we must factor this coefficient from the x2 and x terms before proceeding.

Example 4.

Write f(x) = -2x2 + 2x + 3 in standard form and find the vertex of the graph of f.

f(x) = -2x2 + 2x + 3.

= (-2x2 + 2x) + 3.

= -2(x2 - x) + 3.

= -2(x2 - x + 1/4 - 1/4) + 3.

We add and subtract 1/4, because (-1/2)2 = 1/4, and -1 is the coefficient of x.

= -2(x2 - x + 1/4) -2(-1/4) + 3.

Note that everything in the parentheses is multiplied by -2, so when we remove -1/4 from the parentheses, we must multiply it by -2.

= -2(x - 1/2)2 + 1/2 + 3.

= -2(x - 1/2)2 + 7/2.

The vertex is the point (1/2, 7/2). Since the graph opens downward (-2 < 0), the vertex is the highest point on the graph.

Exercise 2:

Write f(x) = 3x2 + 12x + 8 in standard form. Sketch the graph of f ,find its vertex, and find the zeros of f. Answer

Alternate method of finding the vertex

In some cases completing the square is not the easiest way to find the vertex of a parabola. If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.

The x-intercepts of the graph above are at -5 and 3. The line of symmetry goes through -1, which is the average of -5 and 3. (-5 + 3)/2 = -2/2 = -1. Once we know that the line of symmetry is x = -1, then we know the first coordinate of the vertex is -1. The second coordinate of the vertex can be found by evaluating the function at x = -1.

Example 5.

Find the vertex of the graph of f(x) = (x + 9)(x - 5).

Since the formula for f is factored, it is easy to find the zeros: -9 and 5.

The average of the zeros is (-9 + 5)/2 = -4/2 = -2. So, the line of symmetry is x = -2 and the first coordinate of the vertex is -2.

The second coordinate of the vertex is f(-2) = (-2 + 9)(-2 - 5) = 7*(-7) = -49.

Therefore, the vertex of the graph of f is (-2, -49).

8 0
2 years ago
You want to place a towel bar that is 10 1⁄4 inches long in the center of a door that is 26 1⁄3 inches wide. How far should you
Alenkinab [10]

Center of the door

26 1/3 divided by 2

change to an improper fraction

(3*26+1)/3 =79/3

79/3 divided by 2

copy dot flip

79/3 * 1/2

79/6

change to a mixed number

13 1/6

10 1/4 divided by 2

change to an improper fraction (4*10+1)/2 = 41/4

41/4 divided  by 2

copy dot flip

41/4 * 1/2 =41/8

change to a mixed number

5 1/8

the left of the bar should be 5 1/8 from the center

to find how far from the left side to place the bar

13 1/6 - 5 1/8 =

get a common denominator

13 4/24 - 5 3/24= 8 1/24 inches


Answer:  place the bar 8 1/24 inches  from each  edge



4 0
3 years ago
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