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3 years ago

What is the quotient (3x4 – 4x2 + 8x – 1) ÷ (x – 2)?

1 answer:

8 0

To find the quotient of (3x^4 – 4x^2 + 8x – 1) ÷ (x – 2), First: divide 3x^4 by x to get 3x^3, then multiply 3x^3 to x - 2 to get 3x^4 - 6x^3 and subtract 3x^4 - 6x^3 from 3x^4 – 4x^2 + 8x – 1 to get 6x^3 - 4x^2 + 8x - 1 Next: divide 6x^3 by x to get 6x^2, then multiply 6x^2 to x - 2 to get 6x^3 - 12x^2 and subtract 6x^3 - 12x^2 from 6x^3 - 4x^2 + 8x - 1 to get 8x^2 + 8x - 1 Next: divide 8x^2 by x to get 8x, then multiply 8x to x - 2 to get 8x^2 - 16x and subtract 8x^2 - 16x from 8x^2 + 8x - 1 to get 24x - 1 Finally: divide 24x by x to get 24, then multiply 24 to x - 2 to get 24x - 48 and subtract 24x - 48 from 24x - 1 to get 47. Thus, (3x^4 – 4x^2 + 8x – 1) ÷ (x – 2) = 3x^3 + 6x^2 + 8x + 24 Remainder 47

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John needs 20 grams of 54% acid solution for his science project. His school's science lab has bottles of 30% solution and bottl

Paul [167]

Answer:

John should use:

4 grams of the 30% solution and 16 grams of the 60% solution

Step-by-step explanation:

Let the number of grams of the 30% solution = x

Let the number of grams of the 60% solution = y

John needs 20 grams of 54% acid solution for his science project.

Hence,

x + y = 20 grams..... Equation 1

x = 20 - y

His school's science lab has bottles of 30% solution and bottles of 60% solution.

30% × x + 60% × y = 54% × 20

0.3x + 0.6y = 10.8......Equation 2

We substitute 20 - y for x in Equation 2

0.3(20 - y) + 0.6y = 10.8

6 - 0.3y + 0.6y = 10.8

- 0.3y + 0.6y = 10.8 - 6

0.3y = 4.8

y = 4.8/3

y = 16 grams

x = 20 - y

x = 20 - 16

x = 4 grams

Therefore, John should use:

4 grams of the 30% solution and 16 grams of the 60% solution

7 0

3 years ago

Read 2 more answers

The height of a triangle is 8 centimeters greater than half its base. The area of the triangle is 48 square centimeters what is

emmainna [20.7K]

Answer:

base = 8 cm

height = 12 cm

Step-by-step explanation:

We will need the formula for area of a trianlge, which is

A = (1/2)bh where b is the base, and h is the height

We are given two formulas...

"The height of a triangle is 8 centimeters greater than half its base" becomes

h = (1/2)b + 8

"The area of the triangle is 48 square centimeters" becomes

48 = (1/2)bh

Plug the first formula into the second to solve for h

48 = (1/2)b[(1/2) + 8] (h becomes (1/2)b + 8)

Now solve for b

48 = (1/4)b² + 4b

**This is a quadratic euquation. Solve using factoring...

(1/4)b² + 4b - 48 = 0 (subtract 48 from both sides)

b² + 16b - 192 = 0 (multiply by 4 so b² is by itself, it's easier to factor this way)

Now factor...

(b + 24)(b - 8) = 0 (you need two numbers that add to 16 and multiply to -192)

Set each binomial equal to zero and solve for b

b + 24 = 0

b = -24

**this anwser is not valid because b is a length, and you can't have negative length

b - 8 = 0

b = 8

Since the other solution is invalid, the base is b

If the base is b, then the height is...

h = (1/2)b + 8

h = (1/2)(8) + 8

h = 4 + 8

h = 12

8 0

4 years ago

Plz help ill mark you......... PLZ i will do a give a away if you want?

Anuta_ua [19.1K]

Answer:

I believe the whole number will be 1 because 3+1 is 4 and 4/4 is one. then you just drop the 4/5. so the equation may be 1 - 4/5

8 0

3 years ago

Read 2 more answers

On a map, 4 inches represents 240 miles. What is the scale of the map?

Nookie1986 [14]

The answer would be 60 because to find the scale you would need to divide the miles by inches

7 0

3 years ago

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With a family bowling pass, families can bowl for $4 per game . The pass cost $10 per year. Use equation , a table and a graph t

Klio2033 [76]

Answer:

Part a) $a=4g+10$ (see the explanation)

Part b) see the explanation

Part c) The graph in the attached figure

Step-by-step explanation:

The complete question is

With a family bowling pass, families can bowl for $4 per game. The pass costs $10 per year. Use an equation, a table, and a graph to explain the relationship between the total amount of money spent on bowling in a year, a, and the number of games a family plays in a year, g. Part A Use words and an equation to represent this problem. Part B Create a table to show values for g and a. Part C Use the values from your table to draw a graph.

Part A) Use words and an equation to represent this problem

Let

a ----> the total amount of money spent on bowling in a year

g ---> the number of games a family plays in a year

we know that

The linear equation in slope intercept form is equal to

$a=mg+b$