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3 years ago

According to the function shown in the graph above are there two x intercepts? If so are they both meaningful?

Mathematics

1 answer:

NemiM [27]3 years ago

3 0

Answer:

Graph has one x-intercept only

Step-by-step explanation:

Given: Graph of the function

To check: If there are two x-intercepts

Solution:

x-intercepts are the x-coordinate of the point where the graph intersects the x-axis.

The graph of the function intersects x-axis at one point only. So, the graph has one x-intercept only. From the graph, the graph can not be extended further on the left as the distance can not be negative.

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The table below shows the heights of 6 pairs of brothers and sisters, labeled A through F .

scoray [572]

Answer:

The difference is 2 inches

Step-by-step explanation:

Firstly, we identify the equation as given in the question;

y = 1.42105x - 32.2632

We need to know which of the two is the dependent variable i.e y-value and which is the independent variable x-value between the brothers' heights and the sisters' heights. To do this, we have to start with an assumption and check which of the two is for the brothers' or for the sisters,

Let's say the brothers' heights is x, we select any of the data points; (68,64)

we input this into the line of best fit equation; 64 =1.42105(68) - 32.2632 = 96.6314-32.2632= 64.3682

We can see the value on the left hand side of the equation correlates with that on the right hand side. This confirms our assumption that the brothers' heights refer to the independent variable x.

Now, let's plug the values for the 71 inches heights

y = 1.42105(71) - 32.2632 = 68.63 approximately 64

In the table, we can see that the predict sister height at that particular data point is 71 inches. The difference between the predicted height and the actual height is thus 71-69 = 2 inches

4 0

3 years ago

Susan saw a recipe for a fruit salad she thought was fantastic for her upcoming get together of 20 people. It called for 1/2c of

natta225 [31]

Answer:

i would take 2c/ four servings of pineapples to serve all six people

Step-by-step explanation:

7 0

3 years ago

Factor each expression

Helen [10]

Answer:

7 ( 7 g + 9 y )

Step-by-step explanation:

thats the answer

5 0

3 years ago

Read 2 more answers

Calculate the sum of 12.7, 24.8, 4.1

adell [148]

41.6 is the answer I got

4 0

4 years ago

A biologist is studying the growth of a particular species of algae. She writes the fall inclusion to show the radius of the alg

horrorfan [7]

Answer:

Part A)

A reasonable domain to plot the growth function is:

$0\leq d \leq 12$

Part B)

The y-intercept represents that when the biologist started her study, the radius of the algae was five millimeters.

Part C)

The average rate of change from d = 4 to d = 11 was about 0.11. This means that from the 4th day to the 11th, the radius of the algae grew, on average, at a rate of 0.11 mm per day.

Step-by-step explanation:

The radius of the algae f(d) in millimeters after d days is given by the function:

$f(d)=5(1.02)^d$

Part A)

We know that the radius of the algae was approximately 6.34 mm when the biologist concluded her study. To find the reasonable domain, we can substitute 6.34 for f(d) and solve for d. Therefore:

$6.34=5(1.02)^d$

Divide both sides by five:

$(1.02)^d=1.268$

Take the log of both sides with base 1.02:

$\displaystyle d=\log_{1.02}1.268$

Using the Change of Base Property, evaluate for d:

$\displaystyle d=\frac{\log 1.268}{\log 1.02}=11.9903...\approx 12$

So, the biologist concluded her study after 12 days.

Therefore, a reasonable domain to plot the growth function is:

$0\leq d\leq 12$

Part 2)

The y-intercept of the function is when d = 0. Find the y-intercept:

$f(0)=5(1.02)^{(0)}=5(1)=5$

Since d represent the amount of days after the study had begun, the y-intercept represents the radius of the algae on the initial day.

So, when the biologist started her study, the radius of the algae was five millimeters.

Part 3)

To find the average rate of change for a nonlinear function, we find the slope between the two endpoints on the interval.

We want to find the average rate of change of f(d) from d = 4 to d = 11.

Find the endpoints:

$f(4)=5.4121...\text{ and } f(11)=6.2168...$

And find the slope between them:

$\displaystyle m=\frac{f(11)-f(4)}{11-4}=0.1149...\approx 0.11$

Since f(d) measures millimeters and d measures days, this tells us that, on average, the radius of the algae grew by about 0.11 mm per day from the 4th day to the 11th day.

5 0

3 years ago