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Answer:
a) zeros: -2/3, 6
b) x < -2/3, signs: -, -; sign of product: +
-2/3 < x < 6, signs: +, -; sign of product: -
x > 6, signs: + +; sign of product: +
c) solution: x < -2/3 ∪ x > 6
Step-by-step explanation:
a) The zeros of the product are the values of x that make either factor zero. (A product is only zero if one of the factors is zero.)
3x +2 = 0 ⇒ x = -2/3
x -6 = 0 ⇒ x = 6
The zeros of the quadratic are x = -2/3 and x = 6.
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b) For values of x left of the left-most zero, both factors are negative. For values of x between the zeros, the left factor is positive and the right factor is negative. For values of x greater than the right-most zero, both factors are positive. That is, for large negative values of x, all factors are negative. Working left-to-right, each time a zero is crossed, one factor changes sign.
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c) The solution is where the signs of the factors match:
x < -2/3 or -6 < x
If the cost of mouth wash and frozen dinners are equal then he bought $1800 of mouth wash and $3600 worth of frozen dinners.
F(x) = 2/3x - 1......f(x) represents y
to find ur points, sub in any number for x and solve for f(x) or y
lets let x = 0
y = 2/3(0) - 1
y = -1
so when x = 0, y = -1......so (0,-1) is one point
let x = 3
y = 2/3x - 1
y = 2/3(3) - 1
y = 6/3 - 1
y = 2 - 1
y = 1.....so when x = 3, y = 1....(3,1) <== another point
let x = 6
y = 2/3(6) - 1
y = 12/3 - 1
y = 4 - 1
y = 3....so when x = 6, y = 3.....(6,3) <== another point
let x = 9
y = 2/3(9) - 1
y = 18/3 - 1
y = 6 - 1
y = 5.....so when x = 9, y = 5....(9,5) <== another point
let x = 12
y = 2/3(12) - 1
y = 24/3 - 1
y = 8 - 1
y = 7...so when x = 12, y = 7....(12,7) <== ur fifth point
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f(x) = 2/3x - 1
y = 2/3x - 1....in y = mx + b form, ur b represents the y int. So ur y intercept(where the line cross the y axis) is (0,-1)
to find the x intercept, sub in 0 for y and solve for x
y = 2/3x - 1
0 = 2/3x - 1
-2/3x = -1
x = -1 * -3/2
x = 3/2.....so ur x int (where ur line crosses the x axis) is (3/2,0)
now just plot all the points we just found, connect them, and they should make a straight line
Answer:
-9
Step-by-step explanation:
Replace x with -7 in the expression:
x^2 + 5 / x + 1
-7^2 + 5 / -7 + 1
49 + 5 / -6
54/-6
simplify the fraction
9/-1 = -9
Bizzare problem. What are the choices?
The triangle angles add to 180.
4x + 7 + 2x +3 + 6x - 10 = 180
12x = 180
x = 15
Dilation doesn't change the angles so we must have
4x + 7 = 5x - 8 and 2x + 3 = 3x - 12 and 6x - 10 = 7x - 25
Fortunately x=15 is the solution to all of these so it's consistent.