Need help with these--
6. Chase scored 14 points on Monday, and he doubled his score each day thereafter. How many points did he score on Thursday?
8. Find a solution to the following system of equations using elimination:
-5x + y = -5
-4x + 2y = 2
21. Factor completely: 6x^4 - 9x^3 - 36x^2 + 54x
a. 3x(x^2 - 6)(2x - 3)
b. 3x(x^2 + 6)(2x + 3)
c. 6x(x^2 - 6)(2x - 3)
d. 6x(x^2 + 6)(2x + 3)
30. Suppose the area of a square is x^2 - 6x + 9. What is the perimeter of the square?
Thanks
-MC
6)112 8)x=-4/3,y=35/3 30)p=12
Attempt problem 21 if you want help..what do they all have in common? That can be taken out. Post as new if you want it checked.
Sure, I can help you with your questions! Let's go through each of them one by one.
6. Chase scored 14 points on Monday, and he doubled his score each day thereafter. To find out how many points he scored on Thursday, we can start by figuring out how many times his score doubled. Since there are 4 days between Monday and Thursday, his score would have doubled 3 times.
Starting with his score on Monday, which is 14, we can multiply it by 2 three times to calculate his score on Thursday:
14 * 2 * 2 * 2 = 14 * 8 = 112.
So, Chase scored 112 points on Thursday.
8. To solve the given system of equations using elimination, we want to eliminate one variable by adding or subtracting the equations. Let's start by eliminating the x term.
Multiply the first equation by 4, and the second equation by 5 to make the coefficients of x the same:
-20x + 4y = -20
-20x + 10y = 10
Now, subtract the first equation from the second equation:
(-20x + 10y) - (-20x + 4y) = 10 - (-20)
Simplifying, we get:
6y = 30
To isolate y, divide both sides of the equation by 6:
y = 5
Now substitute the value of y back into one of the original equations (for example, the first equation):
-5x + 5 = -5
Adding 5 to both sides of the equation, we get:
-5x = 0
Dividing both sides by -5, we find:
x = 0
Therefore, the solution to the system of equations is x = 0 and y = 5.
21. To factor the expression completely: 6x^4 - 9x^3 - 36x^2 + 54x, we can start by finding the greatest common factor (GCF). In this case, the GCF is 3x.
Factoring out the GCF, we get:
3x(2x^3 - 3x^2 - 12x + 18)
Now we can factor the expression inside the parentheses further. Group the terms:
3x((2x^3 - 3x^2) + (-12x + 18))
Factor out the GCF from each group:
3x(x^2(2x - 3) - 6(2x - 3))
We can see that both terms have a common factor of (2x - 3). Factor it out:
3x(2x - 3)(x^2 - 6)
So the completely factored form of the expression is 3x(2x - 3)(x^2 - 6).
The correct option is a. 3x(x^2 - 6)(2x - 3).
30. The area of a square is given as x^2 - 6x + 9. The area of a square is equal to side length squared. So, if A represents the area and s represents the side length, we have the equation A = s^2.
We can equate this to the given expression:
x^2 - 6x + 9 = s^2
To find the perimeter of the square, we need to find the length of one side first. We can solve the equation for s by taking the square root of both sides:
√(x^2 - 6x + 9) = √s^2
Simplifying:
x - 3 = s
Now that we know the length of one side of the square is x - 3, we can find the perimeter. The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length.
Substituting the length of one side into the formula, we get:
P = 4(x - 3)
Simplifying:
P = 4x - 12
Therefore, the perimeter of the square is 4x - 12.
I hope this helps! Let me know if you have any further questions.