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3 years ago

5

Consider the graph above. Write about a situation that could be modeled using this graph. In your response, use the prompts belo

w to guide your thinking:

1 answer:

Vikentia [17]3 years ago

5 0

Answer:

See Explanation

Step-by-step explanation:

Given

See attachment for graph

Required

A situation that can be modeled by the graph.

The prompt and the response are as follows:

<u>The type of function:</u>

It is a linear function

<u>The variables modeled in the function</u>

The variables are x and y

<u>The domain and the range</u>

From the graph, we can see that x and y values are not limited to any constraints.

So, the domain and the range are:

$Domain: \{-\infty \le x \le \infty \}$

$Range: \{-\infty \le y \le \infty \}$

<u>Question that could be </u> $answered$ <u></u>

The graph could be used to predict y value, given the x value.

Take for instance, find y when x = 10

The answer can be handpicked directly from the graph. However, the best way is to calculate the graph equation, first.

So, we have:

Pick any two points on the line of the graph

$(x_1,y_1) = (-2,0)$

$(x_2,y_2) = (0,4)$

Calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4 - 0}{0 - -2}$

$m = \frac{4}{2}$

$m =2$

The equation of the graph is:

$y = m(x - x_1) + y_1\\$

So, we have:

$y = 2(x - -2) + 0$

$y = 2(x +2)$

Expand

$y = 2x +4$

To solve for y when x = 10;

$y = 2 * 10 +4$

$y = 20 +4$

$y = 24$

You might be interested in

To overcome an infection an anti-biotic is injected into David’s bloodstream. After the injection the anti-biotic in his body de

meriva

Answer:

4.45 ccs will remain after 5 hours.

Step-by-step explanation:

The anti-biotic in his body decreases at a rate proportional to the amount, Q(t), present at time t.

(dQ/dt) = - kQ ((Minus sign because it's a rate of reduction)

(dQ/dt) = -kQ

(dQ/Q) = -kdt

∫ (dQ/Q) = -k ∫ dt

Solving the two sides as definite integrals by integrating the left hand side from Q₀ to Q and the Right hand side from 0 to t.

We obtain

In (Q/Q₀) = -kt

(Q/Q₀) = e⁻ᵏᵗ

Q(t) = Q₀ e⁻ᵏᵗ

the initial injection was 8 ccs and 5 ccs remain after 4 hours

Q₀ = 8 ccs,

At t = 4 hours, Q = 5 ccs

5 = 8 e⁻ᵏᵗ

e⁻ᵏᵗ = 0.625

-kt = In (0.625) = -0.47

-4k = 0.47

k = 0.1175 /hour

Q(t) = Q₀ e⁻⁰•¹¹⁷⁵ᵗ

At t = 5 hours, Q = ?

Q = 8 e⁻⁰•¹¹⁷⁵ᵗ

0.1175 × 5 = 0.5875

Q = 8 e(^-0.5875)

Q = 4.45 ccs

Hope this Helps!!!

8 0

3 years ago

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options.

Nady [450]

Answer:

Domain is all real numbers.

The range is $\{y|y\le 6\}$

The function is increasing over $(-\infty,-2)$ .

The function is decreasing over $(-2,\infty)$

The function has a positive y-intercept.

-----------------This is a guess if I had interpreted your choices correctly:

Second option: The range is $\{y|y\le 6\}$

Third option: The function is increasing over $(-\infty,-2)$ .

Last option: The function has a positive y-intercept.

I can't really read some of your choices. So you can read my above and determine which is false. If you have a question about any of what I said above please let me know.

Note: I guess those 0's are suppose to be infinities? I hopefully your function is $f(x)=-x^2-4x+2$ .

Step-by-step explanation:

$f(x)=-x^2-4x+2$ is a polynomial function which mean it has domain of all real numbers. All this sentence is really saying is that there exists a number for any value you input into $-x^2-4x+2$ .

Now since the is a quadratic then it is a parabola. We know it is a quadratic because it is comparable to $ax^2+bx+c$ , $a \neq 0$ .

This means the graph sort of looks like a U or an upside down U.

It is U, when $a>0$ .

It is upside down U, when $a$ .

So here we have $a=-1$ so $a$ which means the parabola is an upside down U.

Let's look at the range. We know the vertex is either the highest point (if $a$ ) or the lowest point (if $a>0$ ).

The vertex here will be the highest point, again since $a$ .

The vertex's x-coordinate can be found by evaluating $\frac{-b}{2a}$ :

$\frac{-(-4)}{2(-1)}=\frac{4}{-2}=-2$ .

So the y-coordinate can be found by evaluate $-x^2-4x+2$ for $x=-2$ :

$-(-2)^2-4(-2)+2$

$-(4)+8+2$

$4+2$

$6$

So the highest y-coordinate is 6. The range is therefore $(-\infty,6]$ .

If you picture the upside down U in your mind and you know the graph is symmetrical about x=-2.

Then you know the parabola is increasing on $(-\infty,-2)$ and decreasing on $(-2,\infty)$ .

So let's look at the intevals they have:

So on $(-\infty,-2)$ the function is increasing.

Looking on $(-4,\infty)$ the function is increasing on (-4,-2) but decreasing on the rest of that given interval.

The function's y-intercept can be found by putting 0 in for $x$ :

$-(0)^2-4(0)+2$

$-0-0+2$

$0+2$

$2$

The y-intercept is positive since 2>0.

8 0

4 years ago

Anastasy [175]

i. Let t be the line tangent at point J. We know that a tangent line at a point on a circle, is perpendicular to the diameter comprising that certain point.

So t is perpendicular to JL

let l be the tangent line through L. Then l is perpendicular to JL

ii. So t and l are 2 different lines, both perpendicular to line JL.

2 lines perpendicular to a third line, are parallel to each other, so the tangents t and l are parallel to each other.

Remark. Draw a picture to check the steps

4 0

3 years ago

Read 2 more answers

Solve the equation for y. 4x - 5y = 9

babymother [125]

Answer:

y = (4x - 9) / 5 or y = 4/5x - 9/5

Step-by-step explanation:

Solving for y

4x - 5y = 9

-5y = -4x + 9

5y = 4x - 9

y = (4x - 9) / 5 or y = 4/5x - 9/5

3 0

3 years ago

Which linear inequality is represented by the graph?<br> O y>2/3x-2

DIA [1.3K]

Answer: x<6/2

Step-by-step explanation:

0y>2/3 x-2

You want to flip it

2/3 x-2<0

You want to add 2 to both sides

2/3 x-2+2<0+2

2/3x<2

You want to divide both sides by 2/3

2/3x < 2

-—— —

2/3 < 2/3

X<6/2

8 0

2 years ago