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3 years ago

4.(06.05 MC)

Mathematics

1 answer:

neonofarm [45]3 years ago

3 0

Answer:

where is the question can u atach a picture

Step-by-step explanation:

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Given a leading coefficient of 8, polynomial roots of 1 & 2, and the known point on the graph (4,5). Write an equation that

m_a_m_a [10]

Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

The graph passes through the point (4,5).

To find:

The 3rd root and the equation of the polynomial.

Solution:

The factor form of a polynomial is:

$y=a(x-c_1)(x-c_2)...(x-c_n)$

Where, a is a constant and $c_1,c_2,...,c_n$ are the roots of the polynomial.

Polynomial roots are 1 and 2. So, $(x-1)$ and $(x-2)$ are the factors of the polynomial.

Let the third root of the polynomial by c, then $(x-c)$ is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

$y=8(x-1)(x-2)(x-c)$

The graph passes through the point (4,5). Putting $x=4,y=5$ , we get

$5=8(4-1)(4-2)(4-c)$

$5=8(3)(2)(4-c)$

$5=48(4-c)$

Divide both sides by 48.

$\dfrac{5}{48}=4-c$

$c=4-\dfrac{5}{48}$

$c=\dfrac{192-5}{48}$

$c=\dfrac{187}{48}$

Therefore, the 3rd root on the polynomial is $\dfrac{187}{48}$ .

8 0

3 years ago

The speed limit is 25 miles per hour, but it seems that many of the cars are going faster. The city places 2 counter strips 360

klio [65]

You figure out how long it would take a car traveling at 25 mph
to cover 360 ft. Any driver who does it in less time is speeding.

   (25 mi/hr) · (5,280 ft/mile) · (1 hr / 3,600 sec)

   = (25 · 5280 / 3600) ft/sec = (36 and 2/3) feet per second.

To cover 360 ft at 25 mph, it would take

360 ft / (36 and 2/3 ft/sec) = 9.82 seconds .

Anybody who covers the 360 feet in less than 9.82 seconds
is moving faster than 25 mph.
_________________________________

If you're interested, here's how to do it in the other direction:

Let's say a car covers the 360 feet in ' S ' seconds.
What's the speed of the car ?

   (360 ft / S sec) · (1 mile / 5280 feet) · (3600 sec/hour)

   = (360 · 3600) / (S · 5280) mile/hour

   = 245.5 / S miles per hour .

The teacher timed one car crossing both strips in 7.0 seconds.
How fast was that car traveling ?

   245.5 / 7.0 = 35.1 miles per hour

Another teacher timed another car that took 9.82 seconds to cross
both strips. How fast was this car traveling ?

245.5 / 9.82 = 25 miles per hour

7 0

3 years ago

Van is studying the effects of an indoor pool

Artyom0805 [142]

Answer:

The answer is C

Step-by-step explanation:

hope this helps

7 0

3 years ago

The bryant family reuion and the jordan family reunion both include a visit to the zoo desert archers different amounts for chil

Anna35 [415]