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marin [14]
3 years ago
7

Find the measure of x in each figure

Mathematics
1 answer:
uysha [10]3 years ago
7 0

Answer:

x = 20

Step-by-step explanation:

The two angle are a linear pair. Their measures has a sum of 180 deg.

2x + 140 = 180

2x = 40

x = 20

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Which equation represents the standard form of the equation y= (x + 3)² - 4?
lilavasa [31]

Answer:

The answer is B. y = x^2 + 6x + 5

Step-by-step explanation:

Because y = (x + 3)^2 - 4 = x^2 + 6x + 9 - 4 = x^2 + 6x + 5

So the answer in this question is B.

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2 years ago
For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?
lina2011 [118]

Answer:

The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

Step-by-step explanation:

To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.

First, we will determine y''.

From y = sin(kt)

y' = \frac{d}{dt}(y)

y' = \frac{d}{dt}(sin(kt))\\

y' = kcos(kt)

Now for y''

y'' = \frac{d}{dt}(y')

y'' = \frac{d}{dt}(kcos(kt))

y'' = -k^{2}sin(kt)

Hence, the equation y'' + 144y = becomes

-k^{2}sin(kt) + 144(sin(kt)) = 0

(144 - k^{2})(sin(kt)) = 0

(144 - k^{2})= 0

∴ k^{2} = 144\\

k = ±\sqrt{144}\\

k = ± 12

∴ k = +12 or -12

Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

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3.24 as a mixed number
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