All categories

3 years ago

Look at the attached file. please show your work on how you got the answer

Mathematics

1 answer:

statuscvo [17]3 years ago

8 0

Answer:

Step-by-step explanation:

$\frac{f(x)}{g(x)}$

= $\frac{2x+4}{2x^2+4x}$

Factor out 2 on the numerator and 2x on the denominator.

= $\frac{2(x+2)}{2x(x+2)}$

Cancel the factor (x + 2) on the numerator/ denominator

= $\frac{2}{2x}$ ← cancel the 2 on numerator/ denominator

= $\frac{1}{x}$ : x ≠ 0

You might be interested in

Write the equation for the following table: X. Y. 0 3 1 7 2 11 3 15

Vanyuwa [196]

Answer:

$y = 4x + 3$

Step-by-step explanation:

The equation of the table of values given can be written as $y = 4x + 3$ .

When x = 0,

$y = 4(0) + 3$

$y = 0 + 3 = 3$ this corresponds with what we have in the table above.

Let's try another.

When x = 2,

$y = 4(2) + 3$

$y = 8 + 3$

$y = 11$

This also corresponds with what we have in the table.

Therefore, the equation of the table given is $y = 4x + 3$ .

4 0

3 years ago

Read 2 more answers

I have these factoring questions I need help with.

snow_lady [41]

$f(x)=4x^2+4x-3$

1. Determine y-intercept.

The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.

2. Determine the zeros.

Factor the polynomials first. $(2x-1)(2x+3)$ This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2

3. Determine the Axis of Symmetry

We can solve this by using the formula of $x=-\frac{b}{2a}$ However, I'll be solving the Axis of Symmetry with Calculus instead.

$f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4$

Then let f'(x) = 0 to find the Axis of Symmetry.

$8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}$

Therefore, the Axis of Symmetry is -1/2

4. Determine the vertex.

Substitute the value of Axis of Symmetry in f(x).

$f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4$

Therefore the vertex is at (-1/2, -4)

5. Does the vertex representing max-pont or min-point?

The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE.

7. Graph f(x)

Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).

--------------------------- End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

$y=ax^2+bx+c$

The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is.

For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.

3. Write in Factored Form

$y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)$

These are factored forms with different types of operators.

The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)

4. Write in Vertex Form.

$y=a(x-h)^2+k$

The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.

The vertex is at (h,k) and the axis of symmetry is at x = h.

For example, $y=(x-2)^2+3$

The vertex would be at (2,3) and the axis of symmetry is x = 2.

3 0

3 years ago

NEED HELP ASAP PLEASE Y+1=3/4(x+3) What is this equation in standard form?

kvasek [131]

Answer:

y=0.75x + 1.25

Step-by-step explanation:

You just need to isolate y by transferring all the numbers to the other side of the equation (& the numbers with x)

Glad to help

4 0

4 years ago

I would like to borrow $1,200 for 3 years. Your interest rate is 8%. How much interest will I pay over the course of the loan?

kkurt [141]

Answer:

answer is a or $228

Step-by-step explanation:

1200x3x0.08= 228

3 0

3 years ago

Read 2 more answers

Does the table show a direct proportional relationship? If so, what is the constant of proportionality?

lesantik [10]

Answer:

C. Yes, 3.5.

Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality ( $k$ ) is described by the following expression:

$k = \frac{y}{x}$ (1)

Where:

$x$ - Input.

$y$ - Output.

If we know that $(x_{1}, y_{1}) = (13, 45.5)$ , $(x_{2}, y_{2}) = (14, 49)$ and $(x_{3}, y_{3}) = (15, 52.5)$ , then the constants of proportionalities of each ordered pair are, respectively: