Triangle ABC is congruent to triangle DFE. Find x 6 12 8 4

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

Math question down below

allochka39001 [22]

24000 is your answer

4 0

3 years ago

2.4z+1.2z-6.5=0.7 I don't get it

almond37 [142]

Basically that answer is incorrect. If you'd learn about combining, multiplying, dividing or subtracting like terms, this will be a simple problem. To be specific, like term is a number with a letter with it.

For example, 2.4z is a like term.

so you can only add like term, not any other normal number. When two terms have the same "letter", you will have to do what the sign said so in the problem....

2.4z + 1.2z - 6.5 = 0.7
3.6z - 6.5 = 0.7 (Add but leave the z alone because you are not multiplying)

The final answer is 3.6z - 6.5 because you cannot do anything else to that problem.

3.6z-6.5=0.7 is not true.

3 0

3 years ago

NO LINKS,!!! NO ASSESSMENTS OR TEST. NOT MULTIPLE CHOICE.

Paladinen [302]

Answers:

a) cost is going down by 1 cent for every 1000 units produced
b) f(x) = -0.00001x + 0.97
c) $0.78 or 78 cents

==============================================

Explanation:

Part (a)

The two points (12000, 0.85) and (38000,0.59) of interest here. Use the slope formula on them

m = (y2-y1)/(x2-x1)

m = (0.59-0.85)/(38000-12000)

m = -0.26/26000

m = -0.00001

The rate is -0.00001 dollars per unit

In other words, the cost is going down by 0.00001 each time 1 unit is made.

This amount is incredibly small when focusing on one unit, but we can multiply by 10^3 (aka 1000) to get to -0.00001*10^3 = -0.01 which is more manageable.

What does this mean? It means that the cost is going down by 1 cent for every 1000 units produced, which to me seems like a more realistic phrase that is easier to grasp.

Of course, all of this applies only when 120000 < x < 38000.

---------------------------------

Part (b)

In the previous part, we found the slope was m = -0.00001

Plug in (x,y) = (12000, 0.85) and solve for b

y = mx+b

0.85 = (-0.00001)*(12000)+b

0.85 = -0.12+b

0.85+0.12 = b

b = 0.97

The y intercept is 0.97

The function for that diagonal line is f(x) = -0.00001x + 0.97

However, that function is restricted to the domain [12000, 38000] as the graph shows.

---------------------------------

Part (c)

Plug x = 19000 into the function we just found

Note how x = 19000 is in the domain [12000, 38000]

f(x) = -0.00001x + 0.97

f(19000) = -0.00001*19000 + 0.97

f(19000) = -0.19 + 0.97

f(19000) = 0.78

When you produce 19000 units, the cost per unit is $0.78 or 78 cents.

---------------------------------

As for the tax question, I'm not entirely sure. But it appears that the city council may have given the company tax relief as long as the company has made more than 12000 units (since this is where the cost curve starts to decrease). Perhaps this is the council's way of encouraging more economic activity and job growth.

Keep in mind that average cost curves tend to dip downhill when the amount produced goes up. After a certain point however, the average cost will start to increase. The company cannot expand forever and keep costs at a minimum. All of this is independent of taxes so it's not entirely clear if taxes played a role in that decreasing curve or not.

5 0

3 years ago

Aisha has $300 in her account. On average, she deposits $14 into her account, every day, for k days. Enter an expression to to c

MaRussiya [10]

Answer:

342

Step-by-step explanation

14+14+14 = 42

42 + 300 = 342

4 0

3 years ago