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dimulka [17.4K]

3 years ago

11

What is the simplified form of the expression? 5 c squared d minus 4 c + 3 minus 3 + 2 c squared d minus 3 c + d minus 7 3 c squ

ared d minus 7 c + 2 d minus 10 3 c squared d minus 7 c + 4 d minus 10 7 c squared d minus 7 c + 2 d minus 10 7 c squared d minus 7 c + 4 d minus 10

2 answers:

snow_lady [41]3 years ago

6 0

Answer:

7c²d-7c+4d-10

Step-by-step explanation:

Please thank or give 5 stars!

nikklg [1K]3 years ago

4 0

Answer:

7 c squared d minus 7 c + 4 d minus 10

Step-by-step explanation:

because thats the answer on edge 2020 I promise :)

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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:

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

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

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

or

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

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

The product of two rational numbers is (-28/81). If one of them is (-2/3), the find the other.

KatRina [158]

Answer:

The other rational number is $\dfrac{14}{27}$ .

Step-by-step explanation:

First rational number is $\dfrac{-2}{3}$

Let other rational number is $\dfrac{x}{y}$

The product of two rational numbers is $\dfrac{-28}{81}$

According to question,

$\dfrac{x}{y}\times \dfrac{-2}{3}=\dfrac{-28}{81}$

Multiplying both sides by (-3/2) such that,

$\dfrac{x}{y}\times \dfrac{-2}{3}\times \dfrac{-3}{2}=\dfrac{-28}{81}\times \dfrac{-3}{2}\\\\\dfrac{x}{y}=\dfrac{14}{27}$

So, the other rational number is $\dfrac{14}{27}$ .

6 0

3 years ago

Read 2 more answers

What is the slope and y-intercept of the graph? (write your answer in simplest form)

Basile [38]

Answer:

ok

Step-by-step explanation:

what do u mean by the simplest form?

8 0

2 years ago

Pl help it’s for a grade show work if you can

Savatey [412]

Answer:

m degree 2

Step-by-step explanation:

mujhe 1 hii pata hai sorry

8 0

3 years ago

Help please any One who can solve this equation? ☺

malfutka [58]

If y varies directly with x, that means they change at proportion rates. We can define their relationship using a constant k.

y = kx

Plug in what we know to find k.

-3 = 5k

k = -3/5

So:

y = -1 * (-3/5)

y = 3/5

6 0

3 years ago