6x+3>3x+30
The thing about solving inequalities, you just need to treat the symbol, which is the less than symbol in this case, as an equal sign.
So our problem becomes: 6x+3=3x+30
Now we solve this like a normal algebra problem.
First, get all the variables on one side. Since 3x is smaller than 6x, we'll get rid of that by subtracting it from each side.
3x+3=30 is what we end up with.
Now to get the variable alone and get rid of that constant. To do that, we are going to subtract 3 from each side.
We end up with 3x=27
Now, to get the 'x' alone, we need to divide each side by 3.
x=9 is what we end up.
BUT WE FORGOT TO DO SOMETHING
We started this as an inequality problem, so we need to end it as an inequality solution.
Since there wasn't any negatives we need to worry about (Which is something else entirely) we just need to transfer the symbol we started with down.
x>9
Any Questions?
Answer:
4.5
Step-by-step explanation:
Answer:
a = 8
b = 4√5
Step-by-step explanation:
Corresponding sides of similar triangles are proportional.
short side/long side = a/16 = 4/a
a² = 64 . . . . . . multiply by 16a
a = 8 . . . . . . take the square root
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hypotenuse/short side = b/4 = 20/b
b² = 80 . . . . . . . multiply by 4b
b = 4√5 . . . . . take the square root
_____
<em>Additional comment</em>
These relations for the right triangle can be summarized by the rule "the length of a segment that touches the hypotenuse is the geometric mean of the two hypotenuse segments it touches." In the case of b, that means ...
b = √((4)(4+16)) = 4√5
The same sort of relation applies to the unmarked vertical segment on the left:
c = √((16)(16+4)) = 8√5
And, we saw ...
a = √((4)(16)) = 8
Of course, if this rule is to make sense, you need to know that the geometric mean of two numbers is the square root of their product. (In general, the geometric mean of n numbers is the n-th root of their product.)
The graph you chose has a y intercept of 5. In other words, the point (0,5) is on that graph. However, if we plugged x = 0 into the function f(x), we get
f(x) = 3*5^x
f(0) = 3*5^0
f(0) = 3*1
f(0) = 3
So the point (0,3) is actually on the graph. The graph is increasing. So the answer is the upper left corner (instead of the upper right corner)
