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pickupchik [31]
3 years ago
11

Determine the intercepts of the line that passes through the following points

Mathematics
1 answer:
sladkih [1.3K]3 years ago
6 0

Answer:

(2,0) - x -intercept

(0, 1.5) - y-intercept

Step-by-step explanation:

The slope of the points can be found by writing a ratio of vertical change to horizontal change. It can be found in the table by subtracting y values from each other and subtracting x values from each other. The y values decrease by 3 each time or -6 - -3 = -6 + 3 = -3.

The x values increase by 4.

So the rate of change is -3/4.

This means if you go backwards on the table the previous point would be (2, 0). This is the x-intercept.

To find the y-intercept, you must go further back. Going back 2 more units would make the table appear as:

x                      y

-2                    3

0                      ???

2                      0

6                     -3

10                    -6

14                    -9

Since the y values decrease by 3 each time and we went back half the usual amount, then the value would be 1.5.

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If B is the midpoint of AC, AB = 8x + 5, and BC = 5x2 - 16, then find x and AC
Murljashka [212]

Answer:

Step-by-step explanation:

AB = 8x + 5

BC = 5x² - 16

5x² -  16 = 8x + 5

5x² - 8x - 21 = 0

Quadratic formula

x = [8 ± √(8² – 4·5(-21))] / [2·5]

 = [8 ± √484] / 10

 = [8 ± 22] /10

 = -1.4, 3

-1.4 is an extraneous solution.

x = 3

AB = 8x+5 = 29

AC = 58

5 0
3 years ago
13 x-2(8+5 x)=12-11 x
77julia77 [94]

Expand

13x - 16 - 10x = 12 - 11x

Simplify 13x - 16 - 10x to 3x - 16

3x - 16 = 12 - 11x

Add 16 to both sides

3x = 12 - 11x + 16

Simplify 12 - 11x + 16 to -11x + 28

3x = -11x + 28

Add 11x to both sides

3x + 11x = 28

Simplify 3x + 11x to 14x

14x = 28

Divide both sides by 14

x = 28/14

Simplify 28/14 to 2

x = 2

4 0
3 years ago
Hey guys! Can u help me with these three questions?
Margaret [11]
Hey guys it equals 12 alight
5 0
2 years ago
Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Da
alexgriva [62]

Answer:

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>Recorded here are the germination times (in days) for ten randomly  chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.</em>

<em />

We start calculating the sample mean M and standard deviation s:

M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\

s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=15.8.

The sample size is N=10.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075

The degrees of freedom for this sample size are:

df=n-1=10-1=9

The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_M=3.25 \cdot 1.075=3.49

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3

The 99% confidence interval for the mean germination time is (12.3, 19.3).

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A softball has a volume of 1256π cubic inches. Find the radius of the softball.
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3 years ago
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