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2 years ago

Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.

Mathematics

1 answer:

Reil [10]2 years ago

7 0

Answer:

(1 , 1)

Step-by-step explanation:

Given in the question two equations

Equation 1

y = x² – x + 1

Equation 2

y = x

Equate both equations

x² – x + 1 = x

0 = x² – x + 1 - x

x² – 2x + 1 = 0

x² - x - x + 1 = 0

x(x - 1) -1(x - 1) = 0

(x - 1)(x - 1) = 0

(x-1)² = 0

x - 1 = 0

x = 1

Plug x = 1 in first equation

y = 1² – 1 + 1

y = 1

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A random sample of 28 statistics tutorials was selected from the past 5 years and the percentage of students absent from each on

Zielflug [23.3K]

Answer:

The 90% confidence interval using Student's t-distribution is (9.22, 11.61).

Step-by-step explanation:

Since we know the sample is not big enough to use a z-distribution, we use student's t-distribution instead.

The formula to calculate the confidence interval is given by:

$\bar{x}\pm t_{n-1} \times s/\sqrt{n}$

Where:

$\bar{x}$ is the sample's mean,

$t_{n-1}$ is t-score with n-1 degrees of freedom,

$s$ is the standard error,

$n$ is the sample's size.

This part of the equation is called margin of error:

$s/\sqrt{n}$

We know that:

$n=28$

$\bar{x}=10.41$

degrees of freedom $= 27$

$1-\alpha = 0.90 \Rightarrow \alpha = 0.10$

$t_{n-1} = 1.703$

$s = 3.71$

Replacing in the formula with the corresponding values we obtain the confidence interval:

$\bar{x}\pm t_{n-1} \times s/\sqrt{n} = 10.41 \pm 1.70 \times 3.71/\sqrt{28} = (9.22, 11.61)$

Download xlsx

8 0

2 years ago

Read 2 more answers

Draw the graphs of the functions y=1.2x+.9 and y=−1.3x+4.4. Using the graph, locate the points of intersection of the two graphs

jasenka [17]

To draw a graph of any linear function you need two points only. We usually use x and y intercepts because these are easiest to work with.
To find x-intercept we set y to be 0. This is also called zero of a function. Let us find x-intercepts for those two functions:
$y=1.2x+0.9$
$y=-1.3x+4.4$
Now we simply set y=0 and solve for x:
$0=1.2x+0.9$
$0=-1.3x+4.4$

$1.2x=-0.9$
$1.3x=4.4$

$x=-0.75$
$x=3.4$
Now we need to find y-intercepts. To do this we simply set x to be zero.
$y=1.2x+0.9$
$y=-1.3x+4.4$

$y=0.9$
$y=4.4$
Graphs of our functions are not defined by these two points.
$y=1.2x+0.9; (0,-0.75),(0.9,0)$
$y=-1.3x+4.4; (0,3.4),(4.4,0)$
To draw a graph you simply draw a line through these two points.
To find intersection we can use a fact that at the point of intersection both functions have the same value. We can write that down mathematically this way:
-1.3x+4.4=1.2x+0.9
Now we need to solve for x. This will give us an x coordinate of the intersection point.
$2.5x=3.5$
$x=1.4$
Now we simply plug in these value of x in any function to obtain y coordinate of the interception point.
$y=1.2x+0.9$
$y=1.2(1.4)+0.9$
$y=2.6$
Our intersection point the following coordinates (1.4,2.6).
I have attached the graph with all the points that we calculated highlighted.

7 0

2 years ago

The solid graph is a translation of RootIndex 3 StartRoot x EndRoot. On a coordinate plane, 2 cube root functions are shown. The

serious [3.7K]

Answer: 2 units up.

Step-by-step explanation:

If you take a look at the graph, it shows that it is 2 units up from where it initially started, therefore it is moved 2 units up. It says the SOLID graph is the translation, therefore it would be moving 2 units up.

6 0

2 years ago

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Professor Perez used a spreadsheet to compile the data shown. Which value best approximates the

marishachu [46]

Answer:

The answer is "The value to this question is positive".

Step-by-step explanation:

In this question, the value of the correlation coefficient is lies between -1 to 1.

The value of n is given that is 7, and in this question one value is extra given, that is "64".

To calculate $x^2 = x*x , \ \ \ y^2= y*y\\$ .

please find the attachment.

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2 years ago

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A bee flew 840 \text{ cm}840 cm840, start text, space, c, m, end text and landed on a flower to collect some pollen. Then the be

Volgvan

Answer:

The bee traveled 11.7 meters.

Step-by-step explanation:

Solution,

The bee firstlt flew 840 cm to land.

And second distance bee traveled = 330 cm

For finding the total distance traveled by bee, we have to just add first distance and second distance.

So, Total distance traveled = first distance + second distance

Total distance traveled = $840\ cm+330\ cm=1170\ cm$

Now We all know that, 1 meter is equal to 100 cm. So, for converting 'cm' into 'meter' , we need to divide the value of total distance traveled by 100.

∴Total distance traveled = $\frac{1170}{100}=11.7\ meters$

Thus the bee traveled 11.7 meters to go back to her hive.

3 0

2 years ago