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2 years ago

Solve for x in the diagram below

Mathematics

1 answer:

mario62 [17]2 years ago

7 0

Answer: x° = 20

Steps:
100 + x + 3x = 180
x + 3x = 80
4x = 80
x = 80/4
x = 20

Check:
100 + x + 3x = 180
100 + 20 + 3(20) = 180
100 + 20 + 60 = 180
180 = 180 ✅

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3 years ago

Let f be the function given by f(x)= (x-1)(x^2-4)/x^2-a. For what positive values of a is f continuous for all real numbers x?

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Answer:

a =1 and a=4.

Step-by-step explanation:

The function is

$f(x)=\frac{(x-1)(x^2-4)}{x^2-a}$

If we want f(x) to be continuous the denominator needs to be different to 0, otherwise f(x) will be indeterminate.

Now, for a a positive real we have that $x=\sqrt{a}$ will annulate the denominator, i.e

$(\sqrt{a})^2-a = a-a = 0$ . But, if a = 1 we have:

$f(x)=\frac{(x-1)(x^2-4)}{x^2-1} = \frac{(x-1)(x^2-4)}{(x-1)(x+1)}=\frac{(x^2-4)}{x+1}$

so, the value $x=\sqrt{a} = \sqrt{1} = 1$ won't annulate the denominator.

Now, for a = 4 we have:

$f(x)=\frac{(x-1)(x^2-4)}{x^2-4} = x-1$

so, the value $x=\sqrt{a} = \sqrt{4} = 2$ won't annulate the denominator.

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3 years ago

WILL GIVE BRAINLIEST

stira [4]

The air force plane travelled for a total of 6.9 hours.

<u>SOLUTION: </u>

Given, An Air Force plane left Nairobi and flew west at an average speed of 159 mph. A cargo plane left sometime later flying in the same direction at an average speed of 207 mph. After flying for 5.3 hours the cargo plane caught up with the Air Force plane.

We have to find the number of hours the Air Force plane flew before the cargo plane caught up.

Now, we know that, $\text { distance travelled }=\text { speed } \times \text { time }$

For air force plane $\rightarrow \text { distance travelled }=159 \mathrm{x} \text { time taken by air force plane }$

$\text { For cargo plane } \rightarrow \text { distance travelled }=207 \times 5.3 \text { hours }$

Now, when cargo plane caught the air force plane the distance travelled by the planes will be equal.

So, $159 \times \text { time taken by air force plane }=207 \times 5.3$

$\Rightarrow =\frac{207 \times 5.3}{159}$

$\Rightarrow =\frac{1097.1}{159}$

Time taken by air force plane = 6.9 hrs

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3 years ago