Algebra

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I have a few questions I need help with. They are to help review for our exam.

4) Without graphing, is each system independent, dependent, or inconsistent?
-x-3y=0
x-y=4
(i believe dependent)
dependent
independent
inconsistent

6) Which matrix represents the system of equations below?
-2x-7y=3
7x-6y=12
(not sure)
-2 -7 3
7 -6 12

-2 -7 -3
7 -6 12

7 -6 12
-2 -7 3

-2 -7 -3
7 -6 12

7) Which steps translate the graph of y=x^2 to y=-(x-3)^3+2
(my choice translate 3 unite to right translate up 2 units)

translate 3 units to the right, translate up 2 units

reflect across the x-axis, translate 3 units to the left, translate down 2 units

translate 3 units to the left, translate down 2 units

reflect across the x-axis, translate 3 units to the right, translate up 2 units

15) The half-life of a certain radioactive material is 68 hours. An initial amount of the material has a mass of 641kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 4 hours. Round your answer to the nearest thousandth.

y=641(1/2)^68x;0kg

y=1/2(1/641)^1/68x;0.342kg

y=641(1/2)^1/68x;615.390kg

y=2(1/641)^1/68x;1.367kg

18) Name the property of real numbers illustrated by the equation

5*(sqrt 9*4)=(5*sqrt9)*4
(my choice commutative property of multiplication)

commutative property of multiplication
associative property of multiplication
distributive property
associative property of addition

20) The table shows the median home prices in Florida. What is the equation of a trend line that models a relationship between time and home prices? Use the equation to predict the median home price in 2020.

year 1940 1950 1960 1970 1980 2000
median price($) 20,600 38,300 54,000 60,500 85,300 100,300 111,100
(my choice y=1508.33x+20,600;$141,300)

y=45.25x+20,600;111,100
y=1508.33x+20,600;141,300
y=1508.33+20,600;111,100
y=45.25x+20,600;141,300

I know this may seem like alot but it is review, so if someone might beable to help me out so I can be ready to take exam. Thank you in advance

  • Algebra -

    4) already did this:
    independent
    dependent if the lines are parallel

    6)
    look at the coefficients!
    1st set matches

    7)
    already did this:
    reflect across the x-axis, translate 3 units to the right, translate up 2 units

    15)
    think about it: every 68 hours it divides in half. So, the exponential will be (1/2)^(x/68)

    y=641(1/2)^1/68x;615.390kg

    18)
    associative
    You have a*(b*c) = (a*b)*c

    commutative would be a*(b*c) = a*(c*b) or (b*c)*a

    20)
    If x represents the years since 1940, then I agree.

  • Algebra -

    Thank you Steve this helps alot studying for exam

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