Answer:
The answer should be 420.
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Step-by-step explanation:
Answer: a is equal to b
Step-by-step explanation:
Answer:
(-3, 3√3)
Step-by-step explanation:
Evaluate each of the coordinates. Keep or drop the "i" as your convention requires.
6(cos(120°), i·sin(120°)) = (6·cos(120°), i·6·sin(120°)) = (6(-0.5), i·6·√3/2)
= (-3, 3√3 i)
You may want the (x, y) coordinates written as (-3, 3√3).
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In the complex plane, this is -3+i·3√3.
<span>In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = <span>bx</span>, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.</span>
<span>An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.</span>
<span>Before you start, f(0) = 2<span>0 </span>= 1</span>
<span>After 1 hour f(1) = 21 = 2</span>
<span>In 2 hours f(2) = 22 = 4</span>
<span>In 3 hours f(3) = 23 = 8</span>
and so on.
<span>With the definition f(x) = <span>bx</span> and the restrictions that b > 0 and that b ≠ 1, the domain of an exponential function is the set of all real numbers. The range is the set of all positive real numbers. The following graph shows f(x) = 2x.</span>
<span> </span>
Answer x = 12 and y = 9
Step by step
First identify the equations
The sum of two numbers is 21
x + y = 21
Change to y intercept for ease of math
y = 21 - x ( call this equation a)
Three times the larger is equal to four times the smaller
3x = 4y (call this equation b)
Now substitute the value of y = 21 -x into equation b
3x = 4(21-x)
Distribute
3x = 84 - 4x
Now we want to isolate x by adding 4x to each side
3x + 4x = 84 -4x + 4x
Combine like terms
7x = 84
Now solve for x by dividing both sides by 7
x = 12
Now to find y
Using equation a from above
y = 21 - x
Substitute our x value of 12 into equation
y = 21 - 12
solve for y
y = 9
Now check your work
x = 12 and y = 9
The sum of two numbers is 21
12 + 9 = 21
Three times the larger (x) is equal to four times the smaller (y)
3x12 = 4x9
36 = 36
Problem solved!!
