MATHEMATICS HIGH SCHOOL

Which binomial expression are factors of 2x^3 + 5x^2 - x - 6

Answers

Answer 1

Answer:

Answer:

x - 1 and x + 2

Step-by-step explanation:

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Someone please help??

Answers

4 is the correct answer as 4th root of 1296 is 6

Find the vertex, focus, and directrix. y = 1/24(x+1)² - 3.

Answers

$y = (1)/(24)(x+1)^2 - 3\n\ny+3 =(1)/(24)(x+1)^2\ \ / *24\n\n (x+1)^2 = 24(y+3)$

This is an equation of a parabola that opens upwards.

$Its \ standard \ form: \n(x-h)^2=4p(y-k)\n (h,k)=(x,y) \ coordinates \ of \ the \ vertex\n\ (h,k)=(-1,-3) \n\naxis \ of \ symmetry: \ x= -1\n \n4p=24\ \ /:4\np=6$

$focus:(h,k+p)=(-1,-3+6)=(-1,3) \n \ndirectrix: \ y=k-p=-3-6=-9$

$the\ equation\ in\ the\ form\ (x-h)^2=4p(y-k)\ is \ a\ parabola\nwith\ a\ vertex\ at\ \ (h,\ k), \na\ focus\ at\ \ (h,k+p)\n\ and\ a\ directrix\ \ y = k - p \n\n y = 1/24(x+1)^2 - 3\ \ \ \ \Rightarrow\ \ \ y+3 = 1/24(x+1)^2\ /\cdot24\n\n 24\cdot(y+3)=(x+1)^2\n\n(x+1)^2=4p(y+3)\ \ \Rightarrow\ \ 4p=24\ \ \Rightarrow\ \ p=6\ \ \ and\ \ \ h=-1,\ k=-3\n\nthe\ vertex:\ \ \ (h;\ k)=(-1;\ -3)\n\nthe\ focus:\ \ \ (h;\ k+p)=(-1;\ -3+6)=(-1;\ 3)\n\nthe\ directrix:\ \ \ y=k-p\ \ \ \Rightarrow\ \ \ y=-3-6=-9$

The histogram shows the heights in meters of trees in a certain section of a park.How many trees are less than 16 meters tall?

A histogram titled Heights of Trees with Height in meters on horizontal x-axis and Frequency on vertical y-axis

5

9

16

12

Answers

Answer:

Step-by-step explanation:

Final answer:

In a histogram, the total number of trees that are less than 16 meters tall would be the sum of frequencies of all the bars representing heights less than 16 meters. To find this, locate the 16-meter mark on the x-axis and add up the frequencies of all intervals up to and including that point.

Explanation:

The total number of trees that are less than 16 meters tall would be the sum of frequencies of all the bars on the histogram representing heights less than 16 meters. Histograms provide a visual representation of data distribution. The x-axis lists the categories or numbers for the data, in this case tree heights, and the y-axis represents the frequency, or how often a particular height occurs. To find the total number of trees less than 16 meters tall, locate the 16-meter mark on the x-axis and add up the frequencies (height of the bars) of all intervals up to and including that point.

Learn more about Histogram Interpretation here:

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A coin is weighted so that the probability of getting heads is 0.70. If the coin is flipped twice, what is the probability of getting a tail followed by a head?