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3 years ago

Factor the expression X^2 + 6x + 8

Mathematics

1 answer:

zubka84 [21]3 years ago

3 0

Answer: (x + 4)(x + 2)

Step-by-step explanation: In this problem, we're given a trinomial with an x² term, an x term, and a constant term so we can factor it as the product of two binomials.

The first term in each binomial will be a factor of x² and since x² factors as x time x, we use x as the first term in each binomial.

To fill the second position in each binomial, we use the factors of the last term that add together to equal the coefficient of the middle term.

So we're looking for factors of +8 that add to +6.

+8 factors as 8 x 1 or 4 x 2. Since 4 and 2 add together to equal +6, we put a +4 in our first binomial and a +2 in our second binomial and we have our answer (x + 4)(x + 2) which is a factored version of x² + 6x + 8.

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3 years ago

PLEASE HELP! WILL MARK BRAINLIEST!

makkiz [27]

Answer:

The maximum height a rider will experience is 55 feet.

Step-by-step explanation:

Let's start writing the function that defines the path of a seat on the new Ferris wheel. This function will depend of the variable ''t'' which is time.

$X(t)=(x,y)$

In which $X(t)$ are the coordinates of the seat (the x - coordinate and the y - coordinate) that depend from time.

$''x''$ and $''y''$ are functions that depend from the variable ''t''.

For this exercise :

$X(t)=[-25sin(\frac{\pi}{30}t);-25cos(\frac{\pi}{30}t)+30]$

In order to find the maximum height a rider will experience we will study the behaviour of the y - component from the function $X(t)$ .

The function to study is $y(t)=-25cos(\frac{\pi}{30}t)+30$

To find its maximum, we will derivate this function and equalize it to 0. Doing this, we will find the ''critical points'' from the function.

⇒ $y(t)=-25cos(\frac{\pi}{30}t)+30$ ⇒

$y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)$

Now we equalize $y'(t)$ to 0 ⇒

$y'(t)=0$ ⇒ $\frac{5}{6}\pi sin(\frac{\pi}{30}t)=0$

In this case it is easier to look for the values of ''t'' that verify :

$sin(\frac{\pi}{30}t)=0$

Now we need to find the values of ''t''. We know that :

$sin(0)=0\\\\sin(\pi)=0\\sin(-\pi)=0$

Therefore we can write the following equivalent equations :

$\frac{\pi}{30}t=0$ (I)

$\frac{\pi}{30}t=\pi$ (II)

$\frac{\pi}{30}t=-\pi$ (III)

From (I) we obtain $t_{1}=0$

From (II) we obtain $t_{2}=30$

And finally from (III) we obtain $t_{3}=-30$

We found the three critical points of $y(t)$ . To see if they are either maximum or minimum we will use the second derivative test. Let's calculate the second derivate of $y(t)$ :

$y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)$ ⇒

$y''(t)=\frac{\pi ^{2}}{36}cos(\frac{\pi }{30}t)$

Now given that we have an arbitrary critical point '' $t_{n}$ '' ⇒

If $y''(t_{n})>0$ then we will have a minimun at $t_{n}$

If $y''(t_{n})$ then we will have a maximum at $t_{n}$

Using the second derivative test with $t_{1},t_{2}$ and $t_{3}$ ⇒

$y''(t_{1})=y''(0)=\frac{\pi ^{2}}{36} >0$ ⇒ We have a minimum for $t_{1}=0$

$y''(t_{2})=y''(30)=\frac{-\pi^{2}}{36}$ ⇒ We have a maximum for $t_{2}=30$

$y''(t_{3})=y''(-30)=\frac{-\pi^{2}}{36}$ ⇒ We have a maximum for $t_{3}=-30$

The last step for this exercise will be to find the values of the maximums.

We can do this by replacing in the equation of $y(t)$ the critical points $t_{2}$ and $t_{3}$ ⇒

$y(t_{2})=y(30)=55$

$y(t_{3})=y(-30)=55$

We found out that the maximum height a rider will experience is 55 feet.

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3 years ago

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Step-by-step explanation:

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3 years ago

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of

Andru [333]

Let the side length of the original square be x, then
1/4 x^2 = (x - 3)^2
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x - 6 = 0 or x - 2 = 0
x = 6 or x = 2
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3 years ago

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7. What is the value of the expression 3(2 - 7)

zimovet [89]

Answer:

-15

Step-by-step explanation:

3(2 - 7)

PEMDAS says parentheses first

Subtract

3 (-5)

Multiply

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3 years ago

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