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1 answer:

5 0

X - the percent of increase

$210+210x=260 \\
210x=260-210 \\
210x=50 \\
x=\frac{50}{210} \\
x \approx 0.238 \\
x \approx 23.8\%$

The percent of increase is approximately 23.8%.

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Read the caption! Thanks, if you can helps thank you

Kamila [148]

Step-by-step explanation:

For a triangle, any 2 side lengths of the triangle must be greatee than the 3rd side.

Given a triangle with side lengths 11, 23 and x,

we have:

11 + 23 > x,
11 + x > 23, and
23 + x > 11.

Therefore 34 > x and x > 12. => 12 < x < 34.

8 0

3 years ago

Read 2 more answers

The line with equation −a+3b=0 coincides with the terminal side of an angle θ in standard position and sinθ<0 .

Anna11 [10]

If $a$ is the variable of the horizontal axis, then you can solve for $b$ to get the equation of the line in slope-intercept form in the $a,b$ plane:

$-a+3b=0\implies b=\dfrac a3$

i.e. a line with slope $\dfrac13$ through the origin, which means it is contained in the first and third quadrants. Since the terminal side of $\theta$ has a negative sine, the angle must lie in the third quadrant.

Because the slope of the line is $\dfrac13$ , you can choose any length along the line to make up the hypotenuse of a right triangle with reference angle $\theta$ . Any such right triangle will have $\tan\theta=\dfrac13$ , regardless of whether the angle is the first or third quadrant. But since $\theta$ is known to lie in the third quadrant, and so $\sin\theta$ and $\cos\theta$ are both negative, you have

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac13\implies \dfrac{\sin\theta}{\cos\theta}=\dfrac{-1}{-3}\implies \cos\theta=-3$