Rationalize the denominator
-x5
√12x - 9

Check the picture below.

Answer:

g

Step-by-step explanation:

A quotient is an answer in the division. The divisor (denominator) and the quotient are the factors. The dividend (numerator) is the amount being divided — it doesn’t matter whether the dividend is larger or smaller than the divisor.

In elementary school, we refer to this process only in terms of fractions, so many people don’t realize that fractions are just division. If your fraction is proper, you will get a decimal number or simplified equivalent fraction. If the numerator (multiple) is the larger number, then the quotient will represent the other factor after dividing.

For example, in the equation x + 5 = 10, x is the unknown variable, and you want to find some number, which when added to 5 would result in 10.

Quotients are answers to a division problem.

For example, the quotient of 8÷2 would be 4.

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The zeroes of the function f(x) = x⁴ - 3x³ - 4x² are x = -1 , 0 , 4.

The zeroes of a function are the x - intercepts (the points where the graph cuts the x - axis) of the graph of the function f(x).

Given is a function f(x) as → f(x) = x⁴ - 3x³ - 4x²

In order to find the zeroes of the function → f(x) = x⁴ - 3x³ - 4x², we will plot the graph of the function. The graph is attached at the last. We can see that the graph cuts the x - axis at three coordinates → (- 1, 0) , (0, 0) , (4, 0). The x - intercepts will be → -1, 0, 4.

Therefore, the zeroes of the function f(x) = x⁴ - 3x³ - 4x² are x = -1 , 0 , 4.

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The range of the data provided in the boxplot given the minimum number and the maximum number is 2.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines known as the whiskers and a box. The left whisker represents the lowest number in the dataset. The right whisker represents the highest number in the dataset. The difference between these numbers is the range.

The box can be used to determine the first quartile, median and the third quartile. These values can be determined using the lines on the box.

The range of a data set is the difference between the highest number and the lowest number. Range is used to measure the variance of a dataset.

Range = highest number - lowest number

7.5 - 5.5 = 2

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Answer:

48x^2 - 48x + 38

Step-by-step explanation:

To get the composite function first understand the process of which a function inside another operates.

First solve one step at a time by trying to evaluate the inside before evaluating the outside using substitution.

For instance, h(g(f(x))) is the h function of g function of f.

Since f(x) is the inner component of the composite function, replace the x of g with the value of f(x).

Such that g(x) = 3x^2 + 5 → 3(f(x))^2 + 5 →

3(2x - 1)^2 + 5 → 3(2x - 1)(2x - 1) + 5 [foil] → 3(4x^2 - 4x + 1) + 5 → 12x^2 - 12x + 3 + 5 →

12x^2 - 12x + 8

Thus g(f(x)) = 3(f(x))^2 + 5 = 12x^2 - 12x + 8.

Finally to compute h(g(f(x))), using the process from the first composite function, same can be applied here:

Since h(x) = 4x + 6 →

h(g(f(x))) =

h(12x^2 - 12x + 8) =

4(12x^2 - 12x + 8) + 6 [distribute] →

48x^2 - 48x + 32 + 6 [combine like terms] →

48x^2 - 48x + 38

[tex]\stackrel{3x}{R\rule[0.35em]{10em}{0.25pt}} A\stackrel{5x-12}{\rule[0.35em]{10em}{0.25pt}T} \\\\\\ 3x~~ = ~~5x-12\implies 3x+12=5x\implies 12=2x\implies \cfrac{12}{2}=x\implies \boxed{6=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE RT}}{3(6)~~ + ~~5(6)-12\implies 18+18\implies \text{\LARGE 36}}[/tex]

The chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.

There are two types of proportions.

1) Direct Proportion - shows the direct relationship between two quantities. It can be represented by the equation y = kx. As one quantity increases, the other quantity also increase.

2) Inverse Proportion - describes the indirect relationship between two quantities.  It can be represented by the equation y = k/x. As one quantity increases, the other quantity decreases.

According to the problem, a body’s weight varies inversely with the square of its distance from the center of the earth.

y = k/x

let y = a body's weight

x = square of its distance from the center of the earth

Solving for the proportionality constant, k.

y = k/x

12 = k / (5000^2)

k = 12 x 25, 000, 000

k = 300, 000, 000

The equation for the relationship in the problem can now be represented by:

y = 300,000,000/x

where

y = a body's weight

x = square of its distance from the center of the earth

Evaluating the new equation where x = square of 10,000:

y = 300,000,000/x

y = 300,000,00/(100,000,000)

y = 3

Hence, the chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.

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Answer:

0.10x + 0.13y = 10780

x + y = 100000

x = 74000 --------------10%

y = 26000 --------------13% (more risky)

Answer:

46 miles

Step-by-step explanation:

First, set up an equation:

(48 + 58 + 68 + 50 + x) ÷ 5 = 54

Add the miles in the parentheses:

(48 + 58 + 68 + 50 + x) ÷ 5 = 54

48 + 58 + 68 + 50 = 224

(224 + x) ÷ 5 = 54

Multiply by 5 on each side:

[(224 + x) ÷ 5] × 5 = (54) × 5

(224 + x) = 270

Subtract 224 on each side to isolate x:

(224 + x) - 224 = (270) - 224

x = 46 miles

Hope this helps! I'd appreciate brainliest but if not that's fine!

Given the total spent on buying favors = 2.03 $

Let the number of favors she bought = x

let the amount of each favor = y

She bought favors for less than 10 be

x < 10

The amount she spent can be written as  

x * y = 2.03

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Answer:

Fruit Juice = 24 litres

Lemonade = 16 litres

Step-by-step explanation:

So, the ratio: [tex]3:2[/tex] really just means: "for every every 3 litres of fruit punch, there is 2 litres of lemonade.

Or in other words, every 3 litres of fruit punch, the entire mixture of both fruit punch and lemonade will be 5 litres, since there is 3 litres and 2 litres.

So dividing the 40 litres, by this 5 litres, we get 8. So we know there will be "8" of 3 litres of fruit punch, and "8" of 2 litres of lemonade.

Thus there will be 24 litres of fruit punch, and 16 litres of lemonade.

Answer:

Step-by-step explanation:

A common monomial factor is a single-term polynomial that divides into each term of a given polynomial evenly.

the range of possible profits, in dollars, is given by the inequality:

-13 < y < 86

We know that the linear equation:

y = 11*x - 200

Shows the profit for selling x pokemon cards.

We know that he sells more than 17 and less than 26, then:

17 < x < 26

Then the minimum profit is:

y = 11*17 - 200 = -13

The maximum profit is:

y = 11*26 - 200 = 86

We conclude that the range of possible profits, in dollars, is:

-13 < y < 86

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The recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2. (Correct choice: A)

A recursive formula is a formula to find the value of an element in terms of previous elements of the same series. According to the statement, a sequence is defined by f(n) = - 4 + 2 · n. To derive the recursive definition, we must use algebra properties on the following difference:

Δf = - 4 + 2 · (n + 1) - (- 4 + 2 · n)

Δf = 2

n = 1

f(1) = - 4 + 2 · 1

f(1) = - 2

Then, the recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2.

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Hi there!

From the given conditions:

[tex]1→1 ⟹1 \times 1 = 1[/tex]

[tex]5→7⟹ 5 \times 7 = 35[/tex]

[tex]8→11 ⟹8 \times 11 = 88[/tex]

[tex]9→4 ⟹9 \times 4 = 36[/tex]

[tex]10 →2 ⟹10 \times 2 = 20[/tex]

Sum = 180, no. of customers = 25

[tex]average = \frac{sum}{no.ofcustomers} [/tex]

[tex] ⟹ \frac{180}{25} = 7.2[/tex]

Therefore, on average, the satisfaction rating of the landscape company was 7.2

(a) The equation to find x is :  (6x)°  + (x-8)°  = 90°

(b) The degree measure of the  complementary angles, m∠1 = 84° and m∠2 = 6°

Complementary angles are two angles whose sum is 90 degree.

Given are two complementary angles ∠1 and ∠2 whose measures are given m∠1 = (6x)° and m∠2 =(x-8)°

From the given figure we can see that sum of  ∠1 and ∠2 is 90°, which means they are complementary.

m∠1 + m∠2 = 90°

And  (6x)°  + (x-8)°  = 90°

Or      6x +x-8 = 90

7x = 90+8

7x= 98

x= 98/7 =14

Then m∠1 = (6x)° = (6*14)° = 84° and m∠2 = (x-8)° = (14-8)° = 6°

Therefore, The equation to find x is (6x)°  + (x-8)°  = 90° and measure of the  complementary angles, m∠1 = 84° and m∠2 = 6°

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The measure of angle FLH is 31x  + 4

See attachment for the image that completes the question

The given parameters are

m∠FLG = 14x + 5°

m∠HLG = 17x − 1 °

The measure of FLH is calculated as

FLH = m∠FLG +  m∠HLG

This gives

FLH = 14x + 5 + 17x - 1

Collect the like terms

FLH = 14x + 17x  + 5 - 1

Evaluate the like terms

FLH = 31x  + 4

Hence, the measure of FLH is 31x  + 4

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The expression is [tex](x - \sqrt{6} )^{n}[/tex] , n = 1, 2, 3....

Polynomial expression:

A polynomial expression is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

It is given that

x = √6

x - √6 = 0

[tex](x - \sqrt{6} )^{n}[/tex] where n = 1,2,3.....

Therefore the expression of the polynomial given roots is [tex](x - \sqrt{6} )^{n}[/tex] .

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Answer: 3.5

Step-by-step explanation:

If your trying to solve for X the answer would be 3.5 because you calculate 2 to the power of 1 and get 2 which then by now your equation should look along the lines of 3×2X+1−4^1 X=8

Calculate 4 to the power of 1 and get 4 then you Subtract 1 from both sides.

and then Subtract 1 from 8 to get 7. Combine all terms containing X which would make the equation come down to a standard form which then means you would have to divide both sides by 2, by dividing by 2 undoes the multiplication by 2. You should get 7/2 which then = 3 and 1/2 converted into 3.5

The yard is 6 meters wide by use of Pythagoras crossing the diagonal to create a rectangular triangle.

The formula for the Pythagoras theorem is written as c2 = a2 + b2, where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, to generate a Pythagoras triangle, the Pythagoras equation can be used to any triangle with one angle that is precisely 90 degrees.

d² = l² + w²

d = 10

l = 8

Solving for w, the width is

w² = d² - l²

So, we can replace the values with d = 10 and l = 8, to get

w² = 10² - 8²

w² = 100 - 64

w² = 36

w = 6

Hence the width of the yard is 6.

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Answer:

68 acres per day

Step-by-step explanation:

34 acres per day × 2 days = x

34 × 2 = x

x = 68 acres per day

Hope this helps!

Answer:

68 acres

Step-by-step explanation:

34 acres= 1 day

x=2 days

x=68 acres

they can plant 68 in 2 days

The mean time that a certain model of light bulb will last is ​hours is 900 hours and the required percentage of bulbs is 2.5%

Here,

x is the time that a certain bulb will last.

(in houses.

μ=900 hours;

σ=1200 hours.

The standardized value for a light bulbs lasts 1100 hours, is,

z=x-μ/σ

z=1100-900/100=2

We know, for a bell-shaped distance, Approximately,

68% of the data falls within M-uσ;

By rule (ii), here,

95% of the data falls within (μ-2σ,u+2σ)

(900-2x100,900+2x100)

(700,1100)

So (100-95=5%) falls outside of (700,1100)

Since, the distance is symmetric (i.e. bell-shaped); we find the percentage of bulbs that is expected lo lase longer than 1100 hours, is

5/2% =2.5%

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Answer:

(x,y,z) = (1,1,4)

Step-by-step explanation:

[tex]A: -2x + 3y - z = -2\\B: 3x+y=4\\C: -2y+2z=4\\[/tex]

[tex]Solve\ B\ for\ y: y = 4-3x\\Solve\ C\ for\ z: 2z=4+2y\ \ z=2+y\\Substitute\ B_y\ into\ C_z: z = 2+4-3x\ \ z=6-3x\\Substitute\ B_{y\ in\ terms\ of\ x}\ and C_{z\ in\ terms\ of\ x} into A: \\-2x + 3(4-3x) - (6-3x) = -2\\Distribute: -2x + 12-9x-6+3x=-2\\Combine\ Like\ Terms\ on\ either\ side: -2x-9x+3x=-2-12+6\\Factor\ out\ x\ and\ perform\ arithmetic\ on\ right: x(-2-9+3) = -8\\Perform\ Arithmetic: x(-8)=-8\\Divide:x=1[/tex]

[tex]Plug\ x\ into\ B_y: y=4-3(1)\\Perform\ Arithmetic: y=1\\Plug\ y\ into\ C_z: z=2+2(1)\\Perform\ Arithmetic: z=4[/tex]

Answer:

n=-2/3

Step-by-step explanation:

2/3n + 3/2n = -13/4

Make 2/3n and 3/2n into 4/6n and 9/6n so you can add them together.

13/6n = -13/4

Divide both sides by 13/6

n=-2/3

^ i hope thats what you were asking for :)

Using a linear function, it is found that Tamara will need to order a new bag after 46 days.

A linear function is modeled according to the following rule:

y = mx + b

In which:

The slope and the intercept in the context of this problem are given as follows:

Hence the weight of the bag after d days is given by:

W(d) = 20 - 0.4d.

He needs to order a new bag when W(d) = 1.6, hence:

1.6 = 20 - 0.4d.

0.4d = 18.4

d = 18.4/0.4

d = 46 days.

Hence she needs to order the new bag in 46 days.

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The Height of the frame having area of 560cm² is 50cm.

By splitting a rectangle into two equal-sized right triangles, the formula for calculating the area of a rectangle may be obtained. For instance, a diagonal is drawn from vertex A to vertex C in the rectangle ABCD that is supplied.

The rectangle is split into two identical right-angled triangles by the diagonal AC.

(ABCD) Area = b × h

Given,

The area of the frame = 560cm²

Width of the frame = 11 1/5

Length = ?

Area of the rectangle = Length × Breadth

560 = 11 1/5 × L

⇒ L = 560 × 5/56

⇒ L = 50cm

The frame is 50cm tall.

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Correct question -

Claire is making a frame to display a drawing she made. The frame is 11 1/5 cm wide. The frame has a rectangular shape and an area of 560cm². How tall is the frame?

Answer: -32+5√6

Step-by-step explanation:

(3√3 - 5√2) (2√3 + 5√2)=

(3√3 * 2√3) + (3√3 * 5√2) - (5√2 * 2√3) - (5√2 * 5√2) =

(3*2*√3*√3) + (3*5*√3*√2) - (5*2*√2*√3) - (5*5*√2*√2)=

6*3 + 15*√(3*2) - 10*√(2*3) - 25*2=

18+15√6-10√6-50=

18-50+(15-10)*√6=-32+5√6

The product should have a 1 significant digit.

When multiplying Scientific notations, the significant figure of the final result must be approximated to the scientific notation that has the least decimal place.

From the question given, if we 4.5160 x 10^3, 2.09 x 107, and 5.8 x 10^3 are multiplied, the product should have 1 significant digits since the least decimal value that occur in question is 1dp

Hence the product should have a 1 significant digit.

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