Answer:
2 solutions
Step-by-step explanation:
I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...
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To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:
3x(x -4) +5 -x -(2x -7) = 0
3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses
3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms
3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor
The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.
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<em>Alternate method</em>
Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...
d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c
d = (-15)^2 -4(3)(12) = 225 -144 = 81
This positive value means the equation has 2 real solutions.
For the answer to the two questions above,
3x + 2y = 36.50 (I)
2x + 5y = 50 (II)
Eliminating x from the two equations by subtraction:
first we multiply equation I by 2 and equation II by 3
6x + 4y = 73
6x + 15y = 150
Subtracting the two,
-11y = -77
y = 7
He earns $7 at the coffee cart
Substituting y into equation I,
3x + 14 = 36.5
x = $7.50
So we can conclude that, he earns a greater wage of $7.50 at the library,
For this case we have the following function:
f (x) = (1/6) ^ x
We must evaluate the function for x = 3
We have then:
f (3) = (1/6) ^ 3
Rewriting:
f (3) = (1/216)
Answer:
The function evaluated at x = 3 is:
f (3) = (1/216)
option C
11.5 * 2.3 = large door size
large door size / 12 = large door size in feet
large door size in feet / 10 = how many large doors can be cut from the board. (you have to round it down if there's a decimal- no 1/2 doors.)
Answer:
904.32 cm^3
Step-by-step explanation:
The formula for the volume of a sphere is V=4/3πr³. Since r is given, we can plug that in for r. I'm assuming that we are using 3.14 for pi, so when we plug in all the values in the equation we get V = 4/3*3.14*6³, which solves out to 904.32.
