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2 years ago

What is the slope of the given graph?

Mathematics

1 answer:

Reptile [31]2 years ago

7 0

Answer:

Looks like it's 1.

Step-by-step explanation:

Since it is a positive slope and it goes up 1 unit, the slope is 1.

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What is the slope of the line determined by the equation -1/2x+3/4y=0

kvasek [131]

Answer:

The slope is 2/3

Step-by-step explanation:

-1/2x+3/4y=0

To find the slope, we need to get the equation in the form y= mx+b

Add 1/2x to each side

-1/2x+ 1/2 x+3/4y=0+1/2x

3/4 y = 1/2x

Multiply by 4/3 to isolate y

4/3 * 3/4 y = 4/3 * 1/2 x

y = 2/3 x

The slope is 2/3 and the y intercept is 0

7 0

3 years ago

4 divide by8/9 - 1/2

Sever21 [200]

I think 4 divided by 8/9 - 1/2 = 4

6 0

3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

2 years ago

What is 1/4 of a 100 yard by 60 yard field

Tema [17]

Ok, im not going to answer it, but I'm gonna tell you what you need to do to get the answer, first, multiply 100 with 60, then take a quarter out, this is a very simple way to do it, and most people just overthink things.

8 0

3 years ago

What is the slope of the parallel line to 6x + 3y=-6

Artyom0805 [142]

Answer:

-2

Step-by-step explanation:

6x+3y=-6

-6-6x=3y

divided by 3

-2-2x=y

6 0

3 years ago