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3 years ago

What is the length of the altitude of the equilateral triangle below? Thank you! <3

Mathematics

2 answers:

creativ13 [48]3 years ago

8 0

Answer:

The correct answer option is C. $4\sqrt{3}$ .

Step-by-step explanation:

We are given an equilateral triangle which is divided into two equal halves and that makes two right angled triangles with known measures of angles.

We are to find the length of the altitude of the triangle. For that we can use the trigonometric ratios.

$sin 60 = \frac{a}{8}$

$\frac{\sqrt{3} }{2} =\frac{a}{8}$

$a= \frac{\sqrt{3} }{2} \times 8$

$a = 4\sqrt{3}$

Therefore, the correct answer option is C. $4\sqrt{3}$ .

irga5000 [103]3 years ago

5 0

Answer:

The correct answer option is C. . \

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Can someone help me with this question please. I'll give the brainliest answer to whoever helps me.

Doss [256]

Answer: $\sqrt[5]{y}$

I realize its probably not the largest readable font. If you are having trouble reading it, it is the square root of y; however, there is a tiny little 5 in the upper left corner to indicate a fifth root. So you would read it out as "the fifth root of y"

The rule I'm using is

$x^{1/n} = \sqrt[n]{x}$

and the more general rule we could use is

$x^{m/n} = \sqrt[n]{x^m}$

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3 years ago

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1 year ago

Given that x-1 and x+2 are factors of f(x)=x³+px+q where p and q are integers, find p and q. Hence, find the remainder when x³+p

alexandr1967 [171]

Answer:

p = -3
q = 2
remainder = 4

Step-by-step explanation:

We want to find the constants 'a', 'p', and 'q' such that ...

(x -a)(x -1)(x +2) ≡ x³ +px +q

(x -a)(x² +x -2) ≡ x³ +px +q

x³ +x² -2x -ax² -ax +2a ≡ x³ +px +q

This gives rise to three equations:

1 -a = 0 . . . . coefficient of x²

-2 -a = p . . . coefficient of x

2a = q . . . . . constant

The first of these tells us a=1. Then, p=-3 and q=2.

The values of p and q are -3 and 2, respectively.

The remainder from division by (x+1) is the value of the cubic for x=-1. That value is ...

(-1)³ -3(-1) +2 = -1 +3 +2 = 4

The remainder from division by (x+1) is 4.

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