<h2>
Greetings!</h2>
Answer:
y = 
and x = 
Step-by-step explanation:
To solve simultaneous equations, you need to have the number in front of both x's or y's the same. (signs doesn't matter)
To get -x to -10x we simply need to multiply the first equation by 10:
-x * 10 = -10x
-9y * 10 = -90y
16 * 10 = 160
-10x - 90y = 160
Now we can add the two equations:
-10x + 10x = 0
-90y + 20y = -70y
160 + 20 = 180
-70y = 180
70y = -180
7y = -18
y =
Now plug into the second equation:
10x + 20() = 20
10x - 
= 20
Move the over to the other side, making it a positive:
10x = 20 +
10x = 
Divide both sides by 10:
x =
So y = and x =
<h2>Hope this helps!</h2>
There are 8 possible outcomes for a marble being drawn and numbered.
{1,2,3,4,5,6,7,8}
There are 4 possible outcomes for a card being selected from a standard deck.
{ <span>hearts, diamonds, clubs, spades}
So the number of outcomes in the sample space would be 8 x 4 = 32.
In the event "an even number is drawn", there are only 4 possible outcomes for a marble being drawn, {2,4,6,8}, whereas there are still 4 possible outcomes for a suit. So the number of outcomes in the event is 4 x 4 = 16.
</span><span>In the event "a number more than 2 is drawn and a red card is drawn", there are 6 possible outcomes for the marble being drawn, {3,4,5,6,7,8}, whereas there are only two possible suits for a card being selected as red, {heart, diamond}. So the number of outcomes in this event is 6 x 2 = 12.
In the event </span><span>"a number less than 3 is drawn or a club is not drawn", the number drawn could be 1 or 2 whereas a spade/heart/diamond could be selected. So the number of outcomes is 2 x 3 = 6.</span><span>
</span>
Answer:
y = 1/4x - 6
Step-by-step explanation:
Slope intercept form is y = mx+b
The y-intercept is b
The slope is mx
So just plug in
y = 1/4x - 6
The reason is it minus is because -6 is negative so it'll rule out the plus either way.
Recall that the derivative of a function f(x) at a point x = c is given by
By substituting h = x - c, we have the equivalent expression
since if x approaches c, then h = x - c approaches c - c = 0.
The two given limits strongly resemble what we have here, so it's just a matter of identifying the f(x) and c.
For the first limit,
recall that sin(π/3) = √3/2. Then c = π/3 and f(x) = sin(x), and the limit is equal to the derivative of sin(x) at x = π/3. We have
and cos(π/3) = 1/2.
For the second limit,
we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have
and 2e⁰ = 2.
