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Nookie1986 [14]
1 year ago
12

Is (x-3) a factor of f(x) = x^2 - 32?

Mathematics
1 answer:
Leokris [45]1 year ago
3 0

Answer:

No

Explanation:

Here, we want to use the factor theorem to check if the given linear expression is a factor of the binomial

Now, according to the factor theorem, a factor of a polynomial would leave no remainder when divided by it

Mathematically, it means when we substitute the factor value into the polynomial, it is expected that the remainder is zero is the substituted is a factor of the polynomial

We set x-2 to zero:

\begin{gathered} \text{ x-2 = 0} \\ x\text{ = 2} \end{gathered}

Now, we substitute 2 into the polynomial as follows:

f(2)\text{ = }2^2-32\text{ = 4-32 = -28}

There is a remainder of -28 and thus, the linear factor is not a factor of the binomial

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A 1400 kg car moving +13.7 m/s makes an elastic collision with a 3200 kg truck, initially at rest. What is the velocity of the c
Kamila [148]

Answer:

The velocity of the car after the collision is -5.36 m/s

Step-by-step explanation:

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.

let the following:

m₁ = mass of the car = 1400 kg

m₂ = mass of the truck = 3200 kg

u₁ = velocity of the car before collision = 13.7 m/s

u₂ = velocity of the truck before collision = 0 m/s

v₁ = velocity of the car after collision

v₂ = velocity of the truck after collision

v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)

   =  [ 13.7 * (1400 - 3200) + 0 * 2 * 3200 ]/ (1400 + 3200)

   = - 5.36 m/s

So, <u>the velocity of the car after the collision is -5.36 m/s</u>

7 0
3 years ago
-19/2 divided by 38/5
slavikrds [6]

Answer:

-1.25

Step-by-step explanation:

The result can be shown in multiple forms. Exact Form: 385 38 5. Decimal Form: 7.6 7.6. Mixed Number Form: 735 7 3 5. 385 3 8 5 .

8 0
3 years ago
Lets see who is smart lol
Simora [160]

9514 1404 393

Answer:

  \square\quad{y=\dfrac{1}{2}x+4}\\\\\square\quad{\dfrac{y-5}{x-2}=\dfrac{1}{2}}

Step-by-step explanation:

The slope of a line is the same everywhere, so an equation can be written making use of that fact.

  \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}\\\\\dfrac{y-5}{x-2}=\dfrac{7-5}{6-2}=\dfrac{2}{4}\\\\\boxed{\dfrac{y-5}{x-2}=\dfrac{1}{2}}

Cross-multiplying gives ...

  2(y -5) = x -2

  2y -10 = x -2  . . . eliminate parentheses

  2y = x +8 . . . . . . . add 10; next, divide by 2

  \boxed{y=\dfrac{1}{2}x+4}

__

These equations match choices B and D.

6 0
3 years ago
Matt have 2 cookies, while christine have 2 more than matt how many cookies will they have if the add them altogethe?.
mojhsa [17]

Answer:

6 cookies

____________________

Christine has 2 MORE than Matt.

2 + 2 = 4(Christine)

4 + 2 = 6(total)

5 0
2 years ago
Read 2 more answers
A satellite flies 55584 miles in <br> 7.72 hours. How many miles has it flown in 23.19 hours?
dedylja [7]

Answer:

Miles flown in 23.19 hours = 166968 miles

Step-by-step explanation:

Given that:

A satellite flies 55584 miles in 7.72 hours

We will find the unit rate first,

Unit rate = \frac{55584}{7.72}

Unit rate = 7200 miles per hour

Miles flown in 23.19 hours,

Miles flown = 7200 * 23.19

Miles flown = 166968 miles

Hence,

Miles flown in 23.19 hours = 166968 miles

5 0
3 years ago
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