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3 years ago

Divide f(x) by d(x), and write a summary statement in the form indicated.

Mathematics

2 answers:

aleksandrvk [35]3 years ago

8 0

Answer:

$x^{2} +5x-3$

Step-by-step explanation:

If we divide these two polynomials, we would have:

$\frac{x^{4}+5x^{3}-2x^{2}+5x-3}{x^{2}+1}=x^{2} +5x-3$

To do a long division form, we have to divide term by term, like its shown in the image.

Using the image is better that writing it down here, because this doesn't have a format to divide polynomials.

Therefore, the answer is:

$x^{2} +5x-3$

Mice21 [21]3 years ago

3 0

F ( x ) : d ( x ) =
( x^4 + 5 x³ - 2 x² + 5 x - 3 ) : ( x² + 1 ) = x² + 5 x - 3
- x^4 - x²
-----------------------
5 x³ - 3 x²
- 5 x² - 5 x
----------------------------
- 3 x² - 3
+ 3 x² + 3
---------------------
R ( x ) = 0
Answer: x² + 5 x - 3

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Use each picture or description of a triangle, write and solve an equation in order to find the number of degrees in each angle

TiliK225 [7]

4x + 7x - 2 + 5x - 10 = 180

16x - 12 = 180

16x = 192

x = 12

m<A= 4x = 4(12) = 48

m<B = 7x - 2 = 7(12) - 2 = 84 - 2 = 82

m<C = 5x - 10 = 5(12) - 10 = 60 - 10 = 50

7 0

3 years ago

A Food Marketing Institute found that 39% of households spend more than $125 a week on groceries. Assume the population proporti

Anuta_ua [19.1K]

Answer:

0.6210

Step-by-step explanation:

Given that a Food Marketing Institute found that 39% of households spend more than $125 a week on groceries

Sample size n =87

Sample proportion will follow a normal distribution with p =0.39

and standard error = $\sqrt{\frac{0.39(1-0.39)}{87} } \\=0.0523$

the probability that the sample proportion of households spending more than $125 a week is between 0.29 and 0.41

= $P(0.29$

There is 0.6210 probability that the sample proportion of households spending more than $125 a week is between 0.29 and 0.41

7 0

3 years ago

Sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0

andreev551 [17]

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0

sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2

sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ

… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π

… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5

sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ

… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π

… … … … … ==> x = nπ or x = (2n + 1)π/2

cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ

… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ

… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ

(where n is any integer)

5 0

2 years ago

9. The equation y = x2 - 1 is

SashulF [63]

It depends on whether or not you have written the question correctly. If the 2 is an exponent, it needs to be preceded by a ^. Otherwise, it is considered a multiplier.
x^2 = x²
x2 = x⋅2

y = x²-1 is nonlinear and nonproportional.

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3 years ago

Nolan wrote 1.63 as a fraction in simplest

Naya [18.7K]

Answer:

Step-by-step explanation:

First, I wrote the fraction as 1 63/100. I believe this is simplest form so the numerator is 63.

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2 years ago