There are a number of expressions that are equivalent to 10a+6.
To find them, you simply have to list the multiples of both 10 and 6.
10- 10 20 30 40 50 60 70 80 90 100
6- 6 12 18 24 30 36 42 48 54 60.
Then, when you multiply the fraction by anything, whether this is 2, 3 or 10, you just have to do this to both parts.
All of the following expressions are equivalent to 10a+6
20a+12, 30a+18, 40a+24, 50a+30, 60a+36, 70a+42, 80a+48, 90a+54, 100a+60

Or, if you're looking to simplfy, then you have to find a common multiple, which is 2. Therefore, 2 goes outside of the bracket, and you then have to divide 10 by 2 to find out what goes inside the brack. 10a/2= 5a. 6/2=3, therefore, in a bracket, it becomes 2(5a+3)

Hope this helps :)

8 0

3 years ago

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Which of the following is not equal to sin⁡(-230°)?

xenn [34]

From trigonometry we know that:

if $sin(\theta)=sin(\alpha)$

then, $\theta=n\pi+(-1)^n\alpha$ (where $n$ is an integer)

This can be rewritten in degrees as:

$\theta=n(180^{\circ})+(-1)^n\alpha$ .............(Equation 1)

Now, in our case, $\alpha=-230^{\circ}$

Therefore, (Equation 1) can be written as:

$\theta=n(180^{\circ})+(-1)^n(-230^{\circ})$ ..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of $\theta$ that match.

For n=2, (Equation 2) gives us: $\theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}$ .

Thus, $sin(230^{\circ})=sin(130^{\circ})$

Now, we know that: $-sin(-50^{\circ})=sin(50^{\circ})$

Let n=-1, then:

$\theta=(-1)\times 180^{\circ}+(-1)^{-1}(-230^{\circ})=-180^{\circ}+230^{\circ}=50^{\circ}$

Thus, $sin(-230^{\circ})=-sin(-50^{\circ})$

Likewise, $sin(-230^{\circ})=sin(50^{\circ})$

Only the last option $sin(-50^{\circ})$ will never match $sin(-230^{\circ})$ because no integral value of $n$ will ever give $\theta=-50^{\circ}$

Thus the last option is the correct option.

3 0

2 years ago

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A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored f

inysia [295]

Volume of the cube with side 4p = 4p x 4p x 4p = 64p³

Volume of the cube with side 2q² =  2q² x  2q² x  2q² = 8q⁶

Total Volume = 64p³ +  8q⁶

Total Volume = (4p)³ + (2q²)³

Total Volume = (4p + 2q²)( ( 4p)² - (4p)(2q²) + (2q²)²)

Total Volume = (4p + 2q²)( 16p² - 8pq² + 4q⁴)

Answer:  (4p + 2q²)( 16p² - 8pq² + 4q⁴)

7 0

3 years ago

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