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2 years ago

Two is a zero of the equation x3−x2−14x+24=0. Which factored form is equivalent to the equation?

Mathematics

1 answer:

ValentinkaMS [17]2 years ago

3 0

Answer:

The answer to your question is: letter A

Step-by-step explanation:

x³ - x² - 14x + 24 = 0

If two is a zero of the polynomial, then x = 2, divide the polynomial by 2.

Synthetic division

1 - 1 - 14 + 24 2

2 2 -24

1 1 -12 0

Result x² + x - 12 = 0

Factor the polynomial, find two numbers that multiply gives -12 and added gives + 1.

These numbers are + 4 and - 3

+4 - 3 = +1

(+4)(-3) = -12

(x + 4) (x - 3) = 0

Finally

(x +4)(x - 3)(x -2) = 0

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A basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modele

tresset_1 [31]

Answer:

Yes, between 0.84 seconds and 0.85 seconds after the shot is launched.

Step-by-step explanation:

$\text{The equation for ball height} : 6+30\cdot t-16\cdot t^{2}\\\text{The equation for shot blocker's height} : 9+25\cdot t-16\cdot t^{2}$

But, the shot is made before two tenths of a second or 0.2 seconds therefore modified equation for ball height is :

$6+30\cdot (t-0.2)-16\cdot (t-0.2)^{2}$

Now for the shot to be blocked,the height of shot blocker must be greater than the height of the ball which is shot before 0.2 seconds :

$\implies 9+25\cdot t-16\cdot t^{2}\geq 6+30\cdot (t-0.2)-16\cdot (t-0.2)^{2}\\\implies 9+25\cdot t-16\cdot t^{2}\geq 6+30\cdot t-6-16\cdot (t^{2}-0.4\cdot t+0.04)\\\implies9+25\cdot t-16\cdot t^{2}\geq 30\cdot t-16\cdot t^{2}+6.4\cdot t-0.64\\\implies 9+25\cdot t\geq 36.4\cdot t-0.64\\\implies 9.64\geq 11.4\cdot t\\\\\implies t\leq \frac{9.64}{11.4}\approx 0.846$

Hence, the shot was blocked between 0.84 and 0.85 seconds after the shot is launched.

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2 years ago

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Value of expression 6 3/4(-11.5)

Olenka [21]

Answer:

6 * 3/4 = 9 2 = 412 = 4.5

Step-by-ste

6 * 3/4 = 6/1 3*4 = 18/4 = 9/2

2 · 2 = 9/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 4) = 2. In the next intermediate step cancelling by a common factor of 2 gives 9

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2 years ago

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2 years ago

A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment i

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$x_{m}=\frac{x_{1}+x_{2}}{2}$

$y_{m}=\frac{y_{1}+y_{2}}{2}$

Isolating $x_{2}$ :

$2x_{m}=x_{1}+x_{2}$

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And $y_{2}$ :

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$y_{2}=2y_{m}-y_{1}$

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$y_{2}=(2*6)-19$

$y_{2}$ = -7

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