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3 years ago

What is the length of AC?

Mathematics

2 answers:

MatroZZZ [7]3 years ago

8 0

The sin <ABC means that AC/AB. So we know AB=34. AC/AB=8/17. So the length of AC is 16. cos<ABC means BC/AB. tan<ABC means AC/BC.

algol [13]3 years ago

5 0

We have that
$AB=34$
sin ∠ABC= $\frac{8}{17}$

we know that
in the right triangle ABC
sin ∠ABC is equal to $\frac{AC}{AB}$
AC is the opposite side angle B
AB is the Hypotenuse

sin ∠ABC= $\frac{8}{17}$ equation 1

sin ∠ABC= $\frac{AC}{34}$ equation 2

equate equation 1 and equation 2

$\frac{8}{17} = \frac{AC}{34} \\ \\ AC=34* \frac{8}{17} \\ \\ AC=16$

the answer is
$AC=16$

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Determine if the following relations represent y as a function of x.

lana [24]

<h3>Answers:</h3>

A) No, it is not a function
B) Yes it's a function
C) Not a function
D) Yes it's a function
E) Yes it's a function

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Explanation:

If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.

Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.

The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.

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4 years ago

Find the measure of the missing angle.

diamong [38]

Answer:

Step-by-step explanation:

7 0

3 years ago

Which linear inequality represents the graph below?

Y_Kistochka [10]

Given:

The graph of an inequality.

To find:

The inequality.

Solution:

In the given graph, the boundary line passes through the points (-3,3) and (0,1).

So, the equation of the boundary line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-3=\dfrac{1-3}{0-(-3)}(x-(-3))$

$y-3=\dfrac{-2}{3}(x+3)$

$y-3=-\dfrac{2}{3}(x)-\dfrac{2}{3}(3)$

Adding 3 on both sides, we get

$y=-\dfrac{2}{3}(x)-2+3$

$y=-\dfrac{2}{3}(x)+1$

The boundary line is a solid line and the shaded region is above the boundary line. So, the sign of inequality must be $\geq$ and the required inequality is:

$y\geq -\dfrac{2}{3}(x)+1$

Therefore, the correct option is B.

8 0

3 years ago

Determine if x = 1 is the solution to this linear equation. 3x - 6(5x + 5) = 9x + 6 Is x = 1 the solution? No. When 1 is substit

FromTheMoon [43]

Answer: No. When 1 is substituted for the variable, the result is a false statement

Step-by-step explanation:

3x - 6(5x + 5) = 9x + 6

3x - 30x - 30 = 9x + 6

-27x -30 = 9x +6

-27x - 9x = 30 +6

-36x = 36

x = -1.

Substitute with x = -1 :

-3 - 6(-5 + 5) = -9 +6

-3 -30 + 30 = -3

-3 = -3

Therefore, the correct option is:

No. When 1 is substituted for the variable, the result is a false statement

7 0

4 years ago

Triangle ABC is a right triangle. if AC =7 and BC= 8 find AB. Leave your answer in simplest radical form.

RSB [31]

Use the Pythagorean Theorem: $a^2+b^2=c^2$ where a and b are the legs of the right triangle, and c is the hypotenuse (longest side!).

There is no picture provided with the problem, so it might be possible for the right angle to be at C and the hypotenuse is AB. But that won't work with the answer choices given, because then $(AB)^2=7^2+8^2 \\ (AB)^2=49+64=113 \\ AB = \sqrt{113}$

Now you know that the 7 must be a leg and 8 the hypotenuse. Then $7^2+(AB)^2=8^2 \\ 49+(AB)^2=64 \\(AB)^2=64-49 \\ AB=\sqrt{15}$ .

By the way, it cannot be that 7 is the hypotenuse because it's the longest side and 8 is longer.

5 0

3 years ago