<h3>
Answer:</h3>
<h3>
Step-by-step explanation:</h3>
The rules of exponents tell you ...
... (a^b)(a^c) = a^(b+c) . . . . . . applies inside parentheses
... (a^b)^c = a^(b·c) . . . . . . . . applies to the overall expression
The Order of Operations tells you to evaluate inside parentheses first. Doing that, you have ...
... x^(4/3)·x^(2/3) = x^((4+2)/3) = x^2
Now, you have ...
... (x^2)^(1/3)
and the rule of exponents tells you to multiply the exponents.
... = x^(2·1/3) = x^(2/3)
therefore there exist two real solutions.
In total, there are 3 real roots. But, real roots are also complex roots (doesn't work the other way round!), so there are 3 complex roots.
Answer: 10
Explanation:
formula for hypotenuse : a^2+b^2=c^2
8^2+6^2=c^2
64+36=c^2
100=c^2
so we find the square root of 100 and its is:
c=10
<span>The solution for a system of equations is the value or values that are true for all equations in the system. The graphs of equations within a system can tell you how many solutions exist for that system. Look at the images below. Each shows two lines that make up a system of equations.</span>
<span><span>One SolutionNo SolutionsInfinite Solutions</span><span /><span><span>If the graphs of the equations intersect, then there is one solution that is true for both equations. </span>If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.</span></span>
When the lines intersect, the point of intersection is the only point that the two graphs have in common. So the coordinates of that point are the solution for the two variables used in the equations. When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.
Some special terms are sometimes used to describe these kinds of systems.
<span>The following terms refer to how many solutions the system has.</span>
Solving Systems of Equations
#1 y = 3x - 7 and y = -x + 1 (2, -1)
#2 8x + 2y = -2 and y = -5x + 1 (2, -9)
#3 4x + y = 8 and -3x - y = 0 (8, -24)
#4 2x + 5y = 20 and 3x - 10y = 37 (11, -0.4)
#5 3x + 2y = -10 and 2x - 5y = 7 (-1.5, -2)
Simplifying Exponents
#1 c^3v^9c^-1c^0 (pg. 467 #3) c^2v^9
#2 2y^-9h^2(2y^0h^-4)^-6 (pg. 467 #4) h^26/32y^9
#3 (a^3/5m)^-4 (pg. 467 #2) 625m^4/a^12
#4 (-3q^-1)^3q^2 (pg. 467 #6) -27/q
#5 (12a^-1b^6c^-3)/(4a^5b^-1c^5) (pg. 443 #23) 3b^7/a^6c^8
Scientific Notation
#1 Write in standard form: 4.25 * 10^-6 .00000425
#2 Write in scientific notation: 375,000,000,000,000 3.75 * 10^14
#3 Write in scientific notation: .000000000107 1.07 * 10^-10
#4 Simplify and write in scientific notation: (6*10^4)(4.8*10^9) 2.88*10^14
#5 Simplify and write in scientific notation: (1.5*10^7)/(5*10^-2) 3.0*10^8
Exponential Growth and Decay
#1 Identify whether the function represents growth or decay. Identify the growth or decay factor. y = 5.2 * 3^x exponential growth; 3
#2 Identify whether the function represents growth or decay. Identify the growth or decay factor. y = 0.15(3/2)^x exponential growth; 3/2
#3 Identify whether the function represents growth or decay. Identify the growth or decay factor. y = 7*0.32^x exponential decay; 0.32
#4 A customer deposits $2000 in a savings account that pays 5.2% interest compounded quarterly. How much money will the customer have in the account after 2 years? $2,217.71
#5 A band performs a free concert in a local park. There are 200 people in the crowd at the start of the concert. The number of people in the crowd grows 15% every half hour. How many people are in the crowd after 3 hours? 463 people
Permutations, Combinations, Probability, and Odds
#1 9P3 504
#2 8C2 28
#3 You have 6 shirts, 7 pairs of pants, and 3 pairs of shoes. How many different outfits can you wear? 126 outfits
#4 You randomly pick two marbles from a bag containing 3 yellow marbles and 4 red marbles. You pick a second marble without replacing the first marble. P(red then red)? 2/7
#5 You randomly pick two marbles from a bag containing 3 yellow marbles and 4 red marbles. What are the odds that you pick a yellow marble? 3/4
Final Question
Write an equation for the line that is parallel to y = 5x + 4 and passes through the point (0, 9). y = 5x + 9
