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2 years ago

What is the remainder in the synthetic division problem below?

Mathematics

2 answers:

omeli [17]2 years ago

8 0

Answer:

B.2

Step-by-step explanation:

apex

Naddik [55]2 years ago

6 0

Answer:

The remainder is 25 ⇒ answer (C)

Step-by-step explanation:

* The remainder will be the last number in the calculation

* From the picture the dividend is 3x³ + x² + 2x - 7 and x - 2 is the divisor

- In the synthetic calculation we use the coefficient of the dividend with the value of x when the divisor = 0

- From the picture the divisor is x - 2, when x - 2 = 0, then x = 2

∵ The coefficient of the dividend are 3 , 1 , 2 , -7

Step 1 : Write down the coefficients of the dividend , put x = 2 at the left

2 3 1 2 -7

_____________

Step 2 : Bring down the first coefficient to the bottom row.

2 3 1 2 -7

____________

Step 3 : Multiply it by 2, and carry the result into the next column.

2 3 1 2 -7

___6_________

Step 4 : Add down the column

2 3 1 2 -7

___6_________

3 7

Step 5 : Multiply it by 2, and carry the result into the next column

2 3 1 2 -7

___6_14_______

3 7

Step 6 : Add down the column

2 3 1 2 -7

___6_14_______

3 7 16

Step 7 : Multiply it by 2, and carry the result into the next column

2 3 1 2 -7

___6_14_32______

3 7 16

Step 8 : Add down the column

2 3 1 2 -7

___6_14_32______

3 7 16 25

∴ The quotient is (3x² + 7x + 16) and the remainder is 25

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Its not possible because if you try to multiply back and forth it wont work.

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1 year ago

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books

Marta_Voda [28]

Given:

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books.

To Find:

A system of linear equations represents the situation.

Answer:

$x+y=26\\\\x=y+12$

Step-by-step explanation:

We are given that x represents the number of fiction books and y is the number of non-fiction books.

We are also given that the total number of books Elliot has is 26 which includes both fiction and non-fiction. So, we may write

$x+y=26$

Next, we are given that there are 12 more fiction books than non-fiction books. This means, the fiction books are more in number and so, we may write

$x=y+12$

So, the total system of equations can be represented as

$x+y=26\\\\x=y+12$

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2 years ago

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The weight, w, in tons of a school bus is related linearly to its seating capacity, p. a 60-passenger bus weighs 10 tons, and an

lidiya [134]

The linear equation of relating two objects can be written in the form,
y = ax + b
Our x is the number of passenger and y is the weight (in tons). Using the first two conditions,
10 = 60(a) + b
13 = 84(a) + b
The values of a and b from the equations are 0.125 and 2.5.
For 50-passenger bus,
y = (50)(0.125) + 2.5
The value of y is 8.75.

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1 year ago

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Randy presses RAND on his calculator twice to obtain two random numbers between 0 and 1. Let $p$ be the probability that these t

anygoal [31]

Answer:

$\frac{\pi}{4}$

Step-by-step explanation:

Lets call x,y the numbers we obtain from the calculator. x and y are independent random variables of uniform[0,1] distribution.

Lets note that, since both x and y are between 0 and 1, then 1 is the biggest side of the triangle.

Lets first make a geometric interpretation. If the triangle were to be rectangle, then the side of lenght 1 should be its hypotenuse, and therefore x and y should satisfy this property:

x²+y² = 1

Remember that in this case we are supposing the triangle to be rectangle. But the exercise asks us to obtain an obtuse triangle. For that we will need to increase the angle obtained by the sides of lenght x and y. We can do that by 'expanding' the triangle, but if we do that preserving the values of x and y, then the side of lenght 1 should increase its lenght, which we dont want to. Thus, if we expand the triangle then we should also reduce the value of x and/or y so that the side of lenght 1 could preserve its lenght. With this intuition we could deduce that

x²+y² < 1

Now lets do a more mathematical approach. According to the Cosine theorem, a triangle of three sides of lenght a,b,c satisfies

a² = b²+c² - 2bc* cos(α), where α is the angle between the sides of lenght b and c.

Aplying this formula to our triangle, we have that

$1^2 = x^2 + y^2 - 2bc* cos(\alpha)$ , where $\alpha$ is the angle between the sides of lenght x and y.

Since the triangle is obtuse, then $\pi/2 < \alpha < \pi$ , and for those values $cos(\alpha)$ is negative , hence we also obtain

1 > x² + y²

Thus, we need to calculate P(x²+y² <1). This probability can be calculated throught integration. We need to use polar coordinates.

(x, y) = (r*cosФ,r*senФ)

Where r is between 0 and 1, and Ф is between 0 and $\pi /2$ (that way, the numbers are positive).

The jacobian matrix has determinant r, therefore,

${\int\int}\limits_{x^2+y^2 < 1} \, dxdy = \int\limits^1_0\int\limits^{\frac{\pi}{2}}_0 {r} \, d\phi dr = \frac{\pi}{2} * \int\limits^1_0 {r} \, dr = \frac{\pi}{2} * (\frac{r^2}{2} |^1_0) = \frac{\pi}{4}$

As a conclusion, the probability of obtaining an obtuse triangle is $\frac{\pi}{4}$ .

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1 year ago

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A. If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? Show your work a

bija089 [108]

A. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work and provide your answer in scientific notation. Jupiter = 778,500,000 km from sun. Venus = 108,200,000 km from sun.

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$10 {}^{8}$

B.Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer. Mercury = 57,909,000 km Venus = 108,200,000 km Earth = 149,600,000 km 57,909,000 + 108,200,000 + 149,600,000 = 315,709,000 Less because 315,709,000 km is less than 4,498,000,000 km

C.If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work. Earth = 149,600,000 km 149,600,000 x 10 = 1,496,000,000 Earth’s new distance = 1,496,000,000 Earth would be closest to Saturn. 1,496,000,000 – 1,429,000,000 = 67,000,000
They would be 67,000,000 km apart
Scientific notation: 6.7 x 10 with a 7 squared km (sorry I can't write this to show this figure but see below as you should write it exactly like how I typed it below followed by km)
$10 {}^{7}$

D. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work. Convert your answer into scientific notation if necessary. Earth = 149,600,000 km
Saturn = 1,429,000,000 km
1,429,000,000 - 149,600,000 = 1,279,400,000
1,279,400,000 km
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Scientific notation: 4.5693 x 10 with a 4 squared
(same with this one, it should be written as I have it shown below instead of how I first tried to explain it.)
$10 {}^{4}$

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2 years ago