All categories

3 years ago

The graph below shows a quadratic function f(x) and an absolute value function g(x)

Mathematics

1 answer:

Sophie [7]3 years ago

6 0

Answer:

The x-values that are approximate solution of the equation $f(x) = g(x)$ are $x_{1} \approx -3.5$ and $x_{2}\approx 5$ , respectively.

Step-by-step explanation:

From graph we infer that the x-values that represents a solution to the system of equations corresponds to those values of x in which both functions coincide. As we see, there are two x-values for $f(x) = g(x)$ , which are described below:

$x_{1} \approx -3.5$ and $x_{2}\approx 5$

The x-values that are approximate solution of the equation $f(x) = g(x)$ are $x_{1} \approx -3.5$ and $x_{2}\approx 5$ , respectively.

You might be interested in

The average score on a biology test was 72.1 (1 repeats). write the average score using a fraction.

Yuri [45]

72 $\frac{1}{9}$ 1÷9 = 111.... 2÷9 = 222.... and so on.

The proof is a little more difficult.

Think of all those repeating ones as a variable - let's call it n

so n= .111111......... repeating

How can we get a single one of those ones to jump across the decimal and be on the left side. We can multiply all of those ones by 10.

10n (ten times the original number) = 1.1111111 (ones still go on forever)

Now here is the interesting part. Let's take all the repeating ones in the first number we made away from the second number.

10n = 1. 1111111......
- n = . 1111111....
9n = 1 (all of the repeaters are gone and only the one we moved to the left
of the decimal is left)

Now let's divide by 9 to get n by itself
9n = 1
9 9

And voila! n = 1/9

So to repeat 72.111... written as a fraction is 72 $\frac{1}{9}$

6 0

3 years ago

The standard form of a quadratic equation is given as y=ax^2+bx+c and vertex form is given as y=a(x−h)^2+k. Write a formula that

Tju [1.3M]

Answers:

$h = -\frac{b}{2a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

where 'a' cannot be zero.

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

Explanation:

The vertex is (h,k)

The x coordinate of the vertex is h which is found through this formula

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

For example, if we had the quadratic $y = 3x^2-6x+5$ , then we'll plug in a = 3 and b = -6 to get: $h = -\frac{b}{2a} = -\frac{-6}{2*3} = 1$

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

To find the value of k, we plug that h value into the original standard form of the quadratic and simplify.

$y = ax^2+bx+c\\\\k = ah^2+bh+c\\\\k = a\left(\frac{-b}{2a}\right)^2+b\left(\frac{-b}{2a}\right)+c\\\\k = a*\frac{b^2}{4a^2}+\frac{-b^2}{2a}+c\\\\k = \frac{b^2}{4a}+\frac{-b^2}{2a}+c\\\\$

$k = \frac{b^2}{4a}+\frac{-b^2}{2a}*\frac{2}{2}+c*\frac{4a}{4a}\\\\k = \frac{b^2}{4a}+\frac{-2b^2}{4a}+\frac{4ac}{4a}\\\\k = \frac{b^2-2b^2+4ac}{4a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

It's interesting how we end up with the numerator of $-b^2+4ac$ which is similar to $b^2-4ac$ found under the square root in the quadratic formula. There are other ways to express that formula above. We need $a \ne 0$ to avoid dividing by zero. The values of b and c are allowed to be zero.

7 0

3 years ago

Are me and April are breeding a rug. Jeremy makes 4 braids every 11 minutes. April makes 7 braids every 17 minutes. Who is braid

bulgar [2K]

You have to divide the number of braids by the number of minutes it took them to make those braids, jeremy- 4/11= .363636 braids per minute and april- 7/17=.4118 braids per minute so april is braiding at a faster rate

5 0

3 years ago

What is the solution |x-2|>-3

forsale [732]

Answer:

this might help

Step-by-step explanation:

Step 1 : Trying to factor as a Difference of Squares : 1.1 Factoring: x2-3. Check : 3 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares. ...

Step 2 : Solving a Single Variable Equation : 2.1 Solve : x2-3 = 0. Add 3 to both sides of the equation : x2 = 3.

8 0

3 years ago

Solve.

Anna [14]

Answer:

The first angle is 68.

Step-by-step explanation:

$x_{1}+x_{2}+x_{3}=180\\x_{1} = 4*x_{2}\\x_{3}=x_{2}+ 78\\4*x_{2} + x_{2} + x_{2}+ 78 = 180\\6*x_{2}=102\\x_{2} = 17\\$