Answer:
See picture.
Sorry about the scrawly handwriting!
Step-by-step explanation:
You can split the figure into 2 trapezoids as shown.
Graph the image of the given segment under a di6with scale factor -1/3 and center of dilatation (0,0). Line on graph is A (-6,9)
B (-3,3) please explain to me how I solve this.
1 answer:
Answer:
A ' = (2, -3)
B ' = (1, -1)
See attached image below for the diagram
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Explanation:
Point A is originally at (-6, 9). It moves to A ' (2,-3) after applying the scale factor. This is because we basically multiply the scale factor (-1/3) by each coordinate of point A
-6 * (-1/3) = 2
9 * (-1/3) = -3
The negative scale factor is like a mirror in a way. Points in negative regions move to positive regions, and vice versa. Since |-1/3| = 1/3 is less than 1, this means the new point (2,-3) is closer to (0,0) compared to its original counterpart.
Point B follows the same idea
B(-3,3) moves to B ' (1, -1) after multiplying each coordinate by -1/3
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Side note: The segment A'B' is 1/3 as long compared to segment AB.
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I found width=13.72 ft and length=43.72 ft.
Call one dimension of the rectangle x, the other will be x+30
You want an area A=600 ft^2 but A=length x width=x*(x+30)=600
Rearranging you get:
solving this quadratic equation you get a negative solution and a positive one that gives your result.
Call one dimension of the rectangle x, the other will be x+30
You want an area A=600 ft^2 but A=length x width=x*(x+30)=600
Rearranging you get:
solving this quadratic equation you get a negative solution and a positive one that gives your result.
Answer:
a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)
b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.
c, d) See attached
Step-by-step explanation:
Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.
Synthetic division is essentially polynomial long division with some modifications:
- the variables are omitted ("place value" is used instead)
- the constant in the divisor is <em>negated</em> so its product with the partial quotient can be <em>added</em> to obtain the new dividend
- the divisor binomial is assumed to have a leading coefficient of 1.
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<h3>a) </h3>The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.
When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.
Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.
The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.
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<h3>b)</h3>The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.
Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.
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<h3>c)</h3>The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)
Maybe this is the table you want:
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<h3>d)</h3>The second attachment shows synthetic division by the factor (x+4).
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<em>Additional comment</em>
The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.
The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.
