Answer:
see explanation
Step-by-step explanation:
note when x = - 3
(- 3)³ + 2(- 3)² + 4(- 3) + 21 = - 27 + 18 - 12 + 21 = 0
hence x = - 3 is a zero and (x + 3) is a factor and dividing gives
= (x + 3)(x² - x + 7)
For zeros equate to zero
(x + 3)(x² - x + 7) = 0
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x² - x + 7 = 0 ← solve using quadratic formula
x = (1 ± 
) / 2 = (1 ± 3i
) / 2
x = 
± 
zeros are x = - 3, x = ±
Answer:
The equation is y= 0,65 x
If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately pays (y) is the original price (x) minus a 35% of this price: y= x -0.35 x . By association: y= (1-0.35) x and then y= 0.65 x.
The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).
Step-by-step explanation:
- The price without discount (or without the coupon) is x.
- The price with discount (or with coupon) is y.
- y and x are both related: y is a percentage of x, specifically, y is 35% smaller than x. This means that y =0.65 x.
The point slope form is y - 8 = 4(x + 6) and the slope intercept form would be y = 4x + 32.
In order to find this, we'll start with the base form of point-slope form.
y - y1 = m(x - x1) ----> Plug in the numbers
y - 8 = 4(x - -6) ----> Simplify
y - 8 = 4(x + 6)
Now to find slope intercept form, solve for y.
y - 8 = 4(x + 6) ----> distribute the 4
y - 8 = 4x + 24 -----> add 8 to both sides
y = 4x + 32
The answer is choice D
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Explanation:
We can rule out choice B and choice C which are y = 2.4^x and y = 3.5^x respectively. Why can we eliminate these? Because they are growth functions (the bases are larger than 1). The graph shown is a decay function. It goes downhill as you read it from left to right.
The answer is either choice A or choice D
If we plug in x = -2 into the equations for A and D, we get
y = 0.65^x = 0.65^(-2) = 2.36686
y = 0.32^x = 0.32^(-2) = 9.765625
The result for choice D is much closer to what the graph is showing. The graph appears to have the point (-2,11) on the curve. So that's why choice D is the best answer.
Note: the graph is a bit small and its not entirely clear which points are on this graph other than (0,1). So this is a bit of educated guesswork.
Here's a tip Subtracting a fraction is the same as multiplying it's reciprocal so for 3/4 - 3/8 you can do 3/4 x 8/3. Multiplying its reciprocal mean turn the 2nd fraction around
