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2 years ago

According to the synthetic division below, which of the following statements are true?

Mathematics

2 answers:

makkiz [27]2 years ago

4 0

Answer:

Correct options are A and D

Step-by-step explanation:

According to the synthetic division in the diagram you can write down the result of division:

$2x^2+9x-7=(x-(-6))(2x-3)+11,\\ \\2x^2+9x-7=(x+6)(2x-3)+11.$

Therefore,

when $2x^2+9x-7$ is divided by $x+6,$ the remainder is 11 (option D is correct). To find the remainder after division by $x-6,$ you have to use another synthetic division. Actually, $2x^+9x-7=(x-6)(2x+21)+119,$ then the remainder is 119 (option C is false).
when $x=-6,$ the expression $x+6$ is $-6+6=0$ and $2x^2+9x-7=0\cdot (2x-3)+11=11$ (option A is correct). You cannot state the same when $x=6$ (option B is false).
neither $x-6$ nor $x+6$ is a factor of $2x^2+9x-7,$ because the remainders in both cases are not equal to 0 (options E and F are false).

Ugo [173]2 years ago

3 0

When $x= - 6,2{x^2} + 9x -7= 11$ and when $2{x^2} + 9x -7$ is divided by $\left( {x + 6} \right)$ , the remainder is 11.Option (A) is correct and option (D) is correct.

Further Explanation:

Given:

Explanation:

The synthetic division can be expressed as follows,

$\begin{aligned}- 6\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,9\,\,\,\,\,\,\,\,\,\,\, - 7} \,}} \right. \hfill\\\,\,\,\,\,\,\underline {\,\,\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,\,\,\,18} \hfill\\\,\,\,\,\,\,\,\,2\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,11 \hfill \\\end{aligned}$

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is 11. Therefore, the remainder of the synthetic division is 11.

When $x= - 6, 2{x^2} + 9x -7= 11$ and when $2{x^2} + 9x -7$ is divided by $\left( {x + 6} \right)$ , the remainder is 11. Option (A) is correct and option (D) is correct.

Learn more:

Learn more about inverse of the functionhttps://brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, factor (x+5), remainder 12, statements, true, apply, divided, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.

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A snowboarder leaves an 8-foot-tall ramp with an upward velocity of 28 feet per second. The function h   16t 2  28t 8 gives

mr_godi [17]

The complete question is;

A snowboarder leaves an 8-foot-tall ramp with an upward velocity of 28 feet per second. The function h = -16t² + 28t + 8 gives the height h (in feet) of the snowboarder after t seconds. The snowboarder earns 1 point per foot of the maximum height reached, 5 points per second in the air, and 25 points for a perfect landing. With a perfect landing, how many total points does the snowboarder receive?

Answer:

Total points earned with a perfect landing = 111 points

Step-by-step explanation:

First of all, let's find the maximum height of the given parabolic function h = -16t² + 28t + 8

h_max = c - (b²/4a)

where: a = -16, b = 28, c = 8

h_max = 8² - 28²/(4*(-16))

h_max = 64 + 784/64

h max = 76.25 ft ≈ 76 ft

The question says that the snowboarder earns 1 point per foot of the maximum height reached.

Thus, the points from the maximum height reached are 76 points

Now, let's find the maximum time in air by solving the equation for h = 0 Thus;

-16t² + 28t +8 = 0

Using quadratic formula,

t = [-28 ± √(28² - (4*-16*8))]/(2*-16)

t = 2 or -0.25

We'll use 2 as we are looking for maximum time.

The question says at maximum time, it's 5 points for each second in the air,

thus, points for seconds in air = 5 × 2 = 10 points

We are told 25 points for perfect landing.

Thus,

Total points earned with a perfect landing = 76 + 10 + 25 = 111 points

7 0

2 years ago

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horsena [70]

Answer:

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Step-by-step explanation:

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