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3 years ago

Let f(x)=16x^5-48x^4-8x^3 and g(x)= 8x^2. find f(x)/g(x)

Mathematics

2 answers:

Gekata [30.6K]3 years ago

3 0

Answer:

2x³ - 6x² - x

Step-by-step explanation:

Divide each term in f(x) by g(x), that is

$\frac{16x^5}{8x^2}$ - $\frac{48x^4}{8x^2}$ - $\frac{8x^3}{8x^2}$

= 2 $x^{(5-2)}$ - 6 $x^{(4-2)}$ - $x^{(3-2)}$

= 2x³ - 6x² - x

Natalija [7]3 years ago

3 0

Answer:

f(x) / g(x) = 2x³-6x²-x

Step-by-step explanation:

We have given two functions.

f(x) = 16x⁵-48x⁴-8x³

g(x) = 8x²

We have to find the quotient of given functions.

f(x) / g(x) ?

Firstly , simplify f(x).

f(x) = 8.2x².x³-8.6x².x²-8x².x

Taking 8x² as common , we have

f(x) = 8x²(2x³-6x²-x)

Now,

f(x) / g(x) = 8x²(2x³-6x²-x) / 8x²

f(x) / g(x) = 2x³-6x²-x which is the answer.

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A shelf has different sizes of bottles of laundry detergent. This line plot shows the number of cups of laundry detergent in eac

salantis [7]

Answer:

2 / 3 loads

Step-by-step explanation:

From. The plot, we can conclude that, the detergent that has the most bottles is that with 5 ; the number of cups in the detergent with 5 bottles is 12 cups

Number of cups used for each load of laundry = 18 cups

The loads of laundry Eric can do is thus :

Number of cups of detergent / number of cups used for each load of laundry

= 12 / 18

= 2 / 3 loads

8 0

2 years ago

What is the y- intercept of the function described in the table x: 1,2,3,4 y: 8,6,4,2

weeeeeb [17]

Answer:

The y-intercept of the function is: b=10

Step-by-step explanation:

Given the table

x y

1 8

2 6

3 4

4 2

Taking any two points to find the slope

(1, 8)

(2, 6)

The slope between (1, 8) and (2, 6) is:

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(2,\:6\right)$

$m=\frac{6-8}{2-1}$

$m=-2$

We know that the slope-intercept form of the line equation is

$y=mx+b$

where m is the slope and b is the y-intercept.

Substituting m=-2 and any point i.e. (1, 8) in the slope-intercept form of the line equation to find the y-intercept (b).

$y=mx+b$

8 = -2(1) + b

8 = -2 + b

b = 8+2

b = 10

Thus, the y-intercept of the function is: b=10

6 0

3 years ago

Read 2 more answers

A volleyball uniform costs $13 for the shirt, $11 for pants, and $8 for socks. Write two

alexdok [17]

13^12 + 11^12 + 8^12 = 384 It will cost 384 dollars for all 12 uniforms

5 0

3 years ago

Read 2 more answers

Use synthetic division to determine if x+2 is a factor of f(x)=5x2+13x+6

Karolina [17]

Answer:

x+2 is a factor of $f(x) = 5x^2 + 13x + 6$

Step-by-step explanation:

To check: If (x+2) is a a factor of the polynomial $f(x) = 5x^2 + 13x + 6$

We need to check if x = -2 is the FACTOR of the given polynomial.

⇒ To show: f (-2) = 0

Now

$f(-2) = 5(-2)^2 + 13(-2) + 6\\=5(4) -26 + 6\\= 20 + 6 - 26\\= 26 - 26 = 0\\\implies f(-2) = 0$

Since, f(-2) = 0

⇒ -2 is the ROOT of the Polynomial f(x).

⇒(x +2) is the factor of the given polynomial.

Hence, x+2 is a factor of $f(x) = 5x^2 + 13x + 6$

4 0

3 years ago

A bag contains 20 slips of paper Individually numbered. If a slip of paper and a letter in the word PENNSYLVANIA is chosen at ra

Soloha48 [4]

Answer:

$P(M4\ n\ V) = 2.083\%$

Step-by-step explanation:

Given

Paper = 20 slips

Word: PENNSYLVANIA

Required

Determine P(Multiple of 4 and V)

The sample size of the 20 slips is:

$n(S) = 20$

The outcomes of multiples of 4 is:

$M4= \{4,8,12,16,20\}$

$n(M4) = 5$

So, the probability of multiples of 4 is:

$Pr(M4) = \frac{5}{20}$

$Pr(M4) = \frac{1}{4}$

The sample size of PENNSYLVANIA is:

$n(S) = 12$

The outcome of V is:

$n(V) = 1$

So, the probability of V is:

$P(V) = \frac{1}{12}$

So, the required probability is: P(Multiple of 4 and V)

$P(M4\ n\ V) = P(M4) * P(V)$

$P(M4\ n\ V) = \frac{1}{4} * \frac{1}{12}$

$P(M4\ n\ V) = \frac{1}{48}$

$P(M4\ n\ V) = 0.02083$

Express as percentage

$P(M4\ n\ V) = 0.02083 * 100\%$

$P(M4\ n\ V) = 2.083\%$

4 0

3 years ago