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Kisachek [45]
3 years ago
8

1.

Mathematics
1 answer:
Margarita [4]3 years ago
5 0

Answer:

The ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.

Step-by-step explanation:

The quadratic function h(t) = -4.9t^2 + 22t + 5.5 represents the height of the ball above the ground, h(t), in meters, with respect to time, t, in seconds.

To find h(3), substitute t = 3 into the function expression:

h(3)=-4.9\cdot 3^2+22\cdot 3+5.5\\ \\=-4.9\cdot 9+66+5.5\\ \\=-44.1+71.5\\ \\=27.4

Meaning: the ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.

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Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0)A(2,0)A
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Answer:

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Step-by-step explanation:

The rectangle is 7-0 = 7 units high and 6-2 = 4 units wide. Its area is the product of these dimensions:

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3 years ago
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7 0
3 years ago
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lutik1710 [3]
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3 years ago
Write the polynomial in factored form as a product of linear factors f(r)=r^3-9r^2+17r-9
adelina 88 [10]

Answer:

  f(r) = (x -1)(x -4+√7)(x -4-√7)

Step-by-step explanation:

The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.

The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.

Using polynomial long division, synthetic division (2nd attachment), or other means, you can find the remaining quadratic factor to be r^2 -8r +9. The roots of this can be found by various means, including completing the square:

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This is zero when ...

  (r -4)^2 = 7

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Now, we know the zeros are {1, 4+√7, 4-√7), so we can write the linear factorization as ...

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_____

<em>Comment on the graph</em>

I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)

7 0
3 years ago
24xy-10y-18x from 13xy+12y+14x with explanation
Sav [38]

Answer:

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Step-by-step explanation:

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24xy−10y−234x​2fromy+12y+14x

24xy+(−10y+12y)−234x​2fromy+14x

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