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2 years ago

A right triangle has one angle that measures 65°. What is the measure of the other acute angle?

1 answer:

8 0

The other angle is 25 degrees.

This is because the sum of all angles must add up to 180. To find the last angle, you must subtract the other angles you know from 180. We know the angle measurements are 65 and 90 (a right angle is 90)
180 - (65+90) = 25

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*Asymptotes*<br> g(x) =2x+1/x-3 <br><br> Give the domain and x and y intercepts

Nataly [62]

Answer: Assuming the function is $g(x)=\frac{2x+1}{x-3}$ :

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The horizontal asymptote is $y=2$ .

The vertical asymptote is $x=3$ .

Step-by-step explanation:

I'm going to assume the function is: $g(x)=\frac{2x+1}{x-3}$ and not $g(x)=2x+\frac{1}{x}-3$ .

So we are looking at $g(x)=\frac{2x+1}{x-3}$ .

The x-intercept is when y is 0 (when g(x) is 0).

Replace g(x) with 0.

$0=\frac{2x+1}{x-3}$

A fraction is only 0 when it's numerator is 0. You are really just solving:

$0=2x+1$

Subtract 1 on both sides:

$-1=2x$

Divide both sides by 2:

$\frac{-1}{2}=x$

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is when x is 0.

Replace x with 0.

$g(0)=\frac{2(0)+1}{0-3}$

$y=\frac{2(0)+1}{0-3}$

$y=\frac{0+1}{-3}$

$y=\frac{1}{-3}$

$y=-\frac{1}{3}$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The vertical asymptote is when the denominator is 0 without making the top 0 also.

So the deliminator is 0 when x-3=0.

Solve x-3=0.

Add 3 on both sides:

x=3

Plugging 3 into the top gives 2(3)+1=6+1=7.

So we have a vertical asymptote at x=3.

Now let's look at the horizontal asymptote.

I could tell you if the degrees match that the horizontal asymptote is just the leading coefficient of the top over the leading coefficient of the bottom which means are horizontal asymptote is $y=\frac{2}{1}$ . After simplifying you could just say the horizontal asymptote is $y=2$ .

Or!

I could do some division to make it more clear. The way I'm going to do this certain division is rewriting the top in terms of (x-3).

$y=\frac{2x+1}{x-3}=\frac{2(x-3)+7}{x-3}=\frac{2(x-3)}{x-3}+\frac{7}{x-3}$

$y=2+\frac{7}{x-3}$

So you can think it like this what value will y never be here.

7/(x-3) will never be 0 because 7 will never be 0.

So y will never be 2+0=2.

The horizontal asymptote is y=2.

(Disclaimer: There are some functions that will cross over their horizontal asymptote early on.)

6 0

3 years ago

A shop sells chocolate, vanilla and strawberry ice creams. 45% of the ice creams sold are vanilla, and 1/4 are strawberry. What

OverLord2011 [107]

Answer:

30%

Step-by-step explanation:

Well since we know that 45% is vanilla that means we have part of our answer

Also we know we sold 1/4 strawberry which in percent that would be 25%

If we add 45% with 25% 45+25=70 then since something can only be 100%

100%-70%=30%

you sold 30% chocolate

<3 <;

6 0

2 years ago

A spinner has 12 equal sections:5 red 4 green and the rest are black. In 921 spins how many times can you expect to spin black?

Komok [63]

Answer:

230

Step-by-step explanation:

12 sections total

5 red, 4 green, the rest black

12-5-4 = 3 sections are black

3/12 = 1/4 of the sections are black

1/4 represents the probability of landing on black for one spin

(1/4)*921 = 230.25 which rounds to 230

We expect to land on a black section about 230 times out of 921 times total.

8 0

3 years ago

on the grid, which point is located in the quadrant where the x-coordinate is a negative number and the y- coordinate is a posit

lina2011 [118]

Answer:

Step-by-step explanation:

because if you look at it the x-coordinate is -6 and the y-coordinate is positive 4

8 0

3 years ago

If two objects have the same weight dors the gravitational feild strength effect the mass

ycow [4]

It is important to remember that weight is not the same as mass - the weight of an object and its mass are directly proportional . This means that for a given gravitational field strength, the greater the mass of the object, the greater its weight.

4 0

2 years ago