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3 years ago

What are the vertex and xintercepts of the graph of the function below? y=(x + 4)(x-2)

Mathematics

1 answer:

erik [133]3 years ago

3 0

Yo sup??

y=(x+4)(x-2)

to find the x intercept put y=0

0=(x+4)(x-2)

so either x=-4 or x=2

Therefore the graph intersects the x axis at -4 and 2

Lenght of x intercept=|-4-2|=6 units

y=(x+4)(x-2)

=x^2+2x-8

This is an upward opening parabola

To find the coordinates of the vertex we can apply the formula

(-b/2a,-D/4a)

b=2

a=1

D=b^2-4ac

=4-4*1*(-8)

=4+32=36

Vertex=(-2/2*1,-36/4*1)

=(-1,-9)

Hope this helps.

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With food prices becoming a great issue in the world; wheat yields are even more important. Some of the highest yielding dry lan

Rzqust [24]

Answer:

Option E) 61.6

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100 bushels per acre

Standard Deviation, σ = 30 bushels per acre

We assume that the distribution of yield is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(X>x) = 0.90

We have to find the value of x such that the probability is 0.90

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 100}{30})=0.90$

$= 1 -P( z \leq \displaystyle\frac{x - 100}{30})=0.90$

$=P( z \leq \displaystyle\frac{x - 100}{30})=0.10$

Calculation the value from standard normal table, we have,

$P(z$

$\displaystyle\frac{x - 100}{30} = -1.282\\x = 61.55 \approx 61.6$

Hence, the yield of 61.6 bushels per acre or more would save the seed.

7 0

3 years ago

The data sets show the years of the coins in two collections. Derek's collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910

KATRIN_1 [288]

Answer:

Derek's collection :

Mean= 1929

Median= 1930

Range= 54

IQR = 48

MAD= 23.75

Paul's collection:

Mean= 1929

Median= 1929.5

Range= 15

IQR = 6

MAD= 3.5

Step-by-step explanation:

1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910

Mean is given by:

(1950+1952+ 1908+1902+1955+1954+1901+1910)/8

=1929

absolute deviation from mean is:

|1950-1929|= 21

|1952-1929|= 23

|1908-1929|= 21

|1902-1929|= 27

|1955-1929|= 26

|1954-1929|= 25

|1901-1929|= 28

|1910-1929|= 19

from the mean of absolute deviation gives the MAD of the data i.e.

(21+23+21+27+26+25+28+`9)/8

23.75

:arrange the given data to get the range and median

1901 1902 1908 1910 1950 1952 1954 1955

The minimum value is: 1901

Maximum value is: 1955

Range is: Maximum value-minimum value

Range=1955-1901

Range= 54

median is (1910+1950)/2

1930

the lower set of data=

1901 1902 1908 1910

first quartile becomes

1902+1908)/2

Q1=1905

and upper set of data is:

1950 1952 1954 1955

we find the median of the upper quartile or third quartile is:

1952+1954)/2=1953

Q3-Q1=1953-1905=

IQR=48

Paul's collection:

1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920

Mean is given by:

1929+1935+ 1928+ 1930+ 1925+ 1932+1933+1920)/8

1929

absolute deviation from mean is:

|1929-1929|=0

|1935-1929|= 6

|1928-1929|= 1

|1930-1929|= 1

|1925-1929|= 4

|1932-1929|= 3

|1933-1929|= 4

|1920-1929|= 9

Hence, we get:

MAD=0+6+1+1+4+3+4+9/8

28/8

3.5

arrange the data in ascending order we get:

1920 1925 1928 1929 1930 1932 1933 1935

Minimum value= 1920

Maximum value= 1935

Range= 15 ( 1935-1920=15 )

The median is between 1929 and 1930

Hence, Median= 1929.5

Also, lower set of data is:

1920 1925 1928 1929

the first quartile or upper quartile is

1925+1928/2

1926.5

and the upper set of data is:

1930 1932 1933 1935

We have

1932+1933)/2

1932.5

IQR is calculated as:

Q3-Q1

7 0

3 years ago

Gary went to the farmer's market on Saturday. He has no more than

kkurt [141]

Answer:

7.00+2.50x>48.00

Step-by-step explanation:

He cant spend more than 48.00 so he'll have to spend less than or equal to 48.00

8 0

3 years ago

A travel agency made the table below to represent the profits it make on a certain vacation package.

Alex17521 [72]

Answer:

D. A quadratic function since the points are symmetric about the line $x=30$ .

Step-by-step explanation:

Please consider the complete question.

A travel agency made the table below to represent the profits it make on a certain vacation package.

x Profit per Person (in dollars), f(x)

10 500

20 800

30 900

40 800

50 500

Which of the following explains the best model for the data in the table?

A) An absolute value function since the values increase and then decrease

B) An exponential function since the ratio of the y-values are about the same.

C) A linear function since the function changes at a rate of 30 dollars per person

D) A quadratic function since the points are symmetric about the line x = 30.

First of all, we will graph all the given points on coordinate plane and then join the points to see the graph.

We can see that point (10,500) is symmetric to point (50,500). Point (20,800) is symmetric to point (40,800).

Upon looking at attached image, we can see that the data forms the shape of a downward opening parabola, which is symmetric to line $x=30$ .

Therefore, a quadratic function best represents the given data because the points are symmetric about the line $x=30$ .

7 0

3 years ago

Read 2 more answers

5 hundreds 5 tens ×10

labwork [276]

It would be 550x10 (5 tens = 50)

so you would solve for 550
<u> x10</u>
5500

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3 years ago