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andrezito [222]
3 years ago
13

Use the product to simplify the expression

Mathematics
1 answer:
harkovskaia [24]3 years ago
7 0
Big y little nine/ y to the power of nine

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(-2/3, sqrt5/3) is a point on a unit circle. Find the cosine, cosecant, and sine of the angle.
Nana76 [90]

Look at the picture.

\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}

We have the right triangle x, y and r. From the Pythagorean theorem we have:

r^2=x^2+y^2\to r=\sqrt{x^2+y^2}

We have the point

\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)

Substitute:

r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1

\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}

8 0
3 years ago
The graph of F(x) shown below resembles the graph of G(x) = x ^ 2 but it has been changed somewhat . Which of the following coul
sukhopar [10]

Answer:

f(x) = 3x^{2} + 2

Step-by-step explanation:

Given G(x) = x^{2}

As we can see, the graph of f(x) is 2 units above the graphof g(x) in vertical (vertical shift)

=> f(x) = ax^{2} + 2

As you can see, the graph of f(x) is stretched vertically by a dilation factor of 3

and there is no reflection, so a= 3

=> the  equation of f(x) is:  f(x) = 3x^{2} + 2

5 0
3 years ago
Translate to an equation and solve the product of 2 and a number increased by 8 is -48
Marizza181 [45]
The equation would be 2x+8=-48 and x=-28
4 0
3 years ago
Find the value of x that will make a || B
belka [17]

Answer:

x = 30

Step-by-step explanation:

4x + 2x = 180

6x = 180  

x = 30

4 0
3 years ago
Kadin and Silas went to a movie that started at 1:55 p.m. and got out at 4:10 pm
elixir [45]

The movie should be 2 hours and 15 minutes long.

4 0
3 years ago
Read 2 more answers
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