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Olenka [21]
3 years ago
15

In segment AC, the midpoint is B. If segments AC = 5x-9 and AB = 2x, what is the measure of segment AC.

Mathematics
1 answer:
IgorLugansk [536]3 years ago
8 0

Answer:

The measure of segment AC is 36 units

Step-by-step explanation:

- The mid-point divides the segment into two equal parts in length

- B is the mid point of segment AC

- That means B divides segment AC into two equal parts in length

∴ AB = BC

∵ AC = 5x - 9

∵ AB = 2x

- The two parts AB and BC are equal in length

∴ BC = 2x

∵ AC = AB + BC

- Substitute the values of AB and BC in the expression of AC

∴ AC = 2x + 2x

∴ AC = 4x

∵ AC = 5x - 9

- Equate the two values of AC

∴ 5x - 9 = 4x

- Add 9 to both sides

∴ 5x = 4x + 9

- Subtract 4x from both sides

∴ x = 9

- Substitute the value of x in any expression of AC

∵ AC = 4x

∵ x = 9

∴ AC = 4(9) = 36

* The measure of segment AC is 36 units

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<h2>0</h2>

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7 0
3 years ago
A researcher wants to test whether a certain sound will make rats do worse on learning tasks. It is known that an ordinary rat c
AveGali [126]

Answer:

So we reject the null hypothesis and accept the alternate hypothesis that rats learn slower with sound.

Step-by-step explanation:

In this data we have

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Standard deviation = s= 6

1) We formulate the null and alternate hypothesis as

H0:  u = 18  against           Ha : u > 18  One tailed test .

2) The significance level alpha = ∝= 0.05 and  Z alpha has a value ± 1.645 for one tailed test.

3)The test statistics used is

Z= X- u / s

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Then we find the value of z for the given significance value given and the test about to be checked.

Then the test statistic is determined and calculated.

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The figure shows that the calulated z value lies outside the given z values

4 0
3 years ago
Find the derivative of f(x) = 9x + 5 at x = 7.
Sergeeva-Olga [200]
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                                   d(x^n) = (n)(x^n-1)
So, from the given
                                 d(9x + 5) = (1)(9x^1-0)  + 5(0)
                                                = 9
The given value of x is irrelevant to this item because the derivative does not contain any variable x. 
8 0
4 years ago
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