The function f(x) = x2 – 9 is shifted 2 units up and 3 units to the left. Select the new function. A) g(x) = 2x2 – 6 B) g(x) = (x – 3)2 + 7 C) g(x) = 3x2 – 7 D) g(x) = (x + 3)2 – 7

Answers

Answer 1

Answer: We have the following function:
f (x) = x ^ 2 - 9
Applying the transformations we have:
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
h (x) = x ^ 2 - 9 + 2
h (x) = x ^ 2 - 7
Horizontal translations
Suppose that h> 0
To graph y = f (x + h), move the graph of h units to the left.
g (x) = (x + 3) ^ 2 - 7
Answer:
D) g (x) = (x + 3) ^ 2 - 7

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Use an inequality symbol (<, >, =, ≤) to compare −3 + 7 _____ −10 − 2 A. > B. < C. = D. ≤

Answers

By using the concept of inequality, the solution for the correct inequality used between the given numbers is,

$(- 3 + 7 ) > (- 10 - 2)$

Used the concept of inequality, which states that,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that,

Compare the numbers (- 3 + 7) and ( - 10 - 2).

Now, to compare the numbers we can solve each side,

(- 3 + 7) = - 3 + 7

= 7 - 3

= 4

(- 10 - 2) = - 10 - 2

= - 12

So, by the definition of positive and negative numbers, we get,

4 > - 12

As positive numbers are always greater than negative numbers.

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A would be the best choice because -3 + 7 is 4 and -10 - 2 is -12.

Find the value of x. Your answer must be exact.
X
12.
600
X=

Answers

Answer:

x = 6√3

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use sine

sin ∅ = opposite / hypotenuse

From the question

The hypotenuse is 12

The opposite is x

Substitute the values into the above formula and solve for x

That's

$\sin(60) = (x)/(12)$

$\sin(60) = ( √(3) )/(2)$

$x = ( √(3) )/(2) * 12$

We have the final answer as

x = 6√3

Hope this helps you

Graph f(x)=3/2x+2. Use the line tool and select two points to graph the line.

Answers

The points are (-1.333, 0) and (0, 2).

What is equation of line?

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation.

An equation of a line is an algebraic expression that represents the several points that together make up a line in the coordinate axis as a set of variables, x, and y.

The given term is,

f(x) = 3/2x+2,

Substitute f(x) = y

y=3/2x+2 (1)

Since, the standard form of equation of line is y=mx+c

compare equation (1) which standard equation of line,

m=3/2, and c=2

On the graph of the line the points are, (-1.333, 0) and (0, 2).

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if k is a constant, determine and state the value of kids such that the polynomial k^2x^3-6kx+9 divisible by x-1

Answers

By the polynomial remainder theorem, $k^2x^3-6kx+9$ will be divisible by $x-1$ if the value of the polynomial at $x=1$ is 0.

$k^2(1)^3-6k(1)+9=k^2-6k+9=(k-3)^2=0$

which occurs for $k=3$ .