how would the expression x^3-64 be written using difference of cubes

Answer:

101.5 cm

Step-by-step explanation:

You find the area of the rectangle and then the area of the triangle. Then, you subtract the area of the rectangle and the area of triangle.

If the area of the rectangle is 40 square centimeters and length is 7 cm less than 3 times the breadth then the length will be 8 cm and breadth will be 5 cm.

Given area of the rectangle is 40 square centimeters and length is 7 centimeters less than 3 times the breadth.

let the breadth of rectangle be x.

According to question

Length=3x-7

Breadth=x

Area of  rectangle=length* breadth

=[tex](3x-7)x[/tex]

=[tex]3x^{2} -7x[/tex]

Area is given as 40 square centimeters.

40=[tex]3x^{2} -7x[/tex]

[tex]3x^{2} -7x-40=0[/tex]

By factorization

[tex]3x^{2} -15x+8x-40=0[/tex]

3x(x-5)+8(x-5)=0

(3x+8)(x-5)=0

3x+8=0

x=-8/3

x-5=0

x=5

We should neglect x=-8/3 because side cannot be negative. So we have taken x=5.

Put x=5 in 3x-7 to get length

length=3(5)-7

=15-7

=8

Hence the length will be 8 cm and breadth will be 5 cm.

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The answer is B.

the graph of x²+2 (quadratic) has domain values less than 1 because the circle in the graph is an open circle

The graph of -x+2 (linear) has domain values greater than or equal to 1 because the circle in the graph is a closed circle

Hope it helps!

Answer:

Sprinter #1

Step-by-step explanation:

Sprinter #1 is running at 96/12 feet per second: 8 feet per second

Sprinter  #2 is running at 475/60 feet per second: approximately 7.9 feet per second

Sprinter #1 covers more distance per second.

Answer:

200 miles

Step-by-step explanation:

Set up a cost equation for each plan using x for miles.

Set the equations equal.

Solve for x, the miles.

For a 1 day rental.

Plan A:

C = 0.18x + 30

Plan B:

C = 66

0.18x + 30 = 66

0.18x = 36

x = 36/0.18

x = 200

Answer: 200 miles

The cost to paint the walls and the ceiling is $855

First, we need to find the area that will be painted.

The area of two of the walls is:

A = 20ft*12ft = 240ft²

The area of the other two walls:

A' = 30ft*12ft = 360ft²

The area of the ceiling is:

A'' = 20ft*30ft = 600ft²

We also need to subtract the areas of the two doors and the 4 windows.

Each door is 7ft by 3ft, so the area of each door is:

a = 7ft*3ft = 21ft²

Each window is 4ft by 3ft:

a' = 4ft*3ft = 12ft²

Then the total area that will be painted is:

area = 2A + 2A' + A - 2a - 4a'

area = 2*( 240ft²) + 2*(360ft²) + 600ft² - 2*(21ft²) - 4*(12ft²)

area = 1,710 ft²

We know that we need two coats of paint to cover that area, and the cost per square foot of paint is $0.25, then the total cost is:

C = $0.25*2*(1,710) = $855

The cost to paint the walls and the ceiling is $855

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Answer:

Hello, look at the picture

Answer:

c.) [tex]x^{3} -16x^{2} +75x-108[/tex]

Step-by-step explanation:

Check the attachment.

Answer:

it is 3 i think

Step-by-step explanatplease mark brainlest

Answer:

[tex](5d^4-8)^2[/tex]

Step-by-step explanation:

[tex]\textsf{Let }\:u=d^4[/tex]

[tex]\implies 25d^8-80d^4+64=25u^2-80u+64[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex] :

[tex]\implies ac=25 \cdot 64=1600[/tex]

[tex]\implies b=-80[/tex]

Two numbers that multiply to 1600 and sum to -80 are:

-40 and -40

Rewrite b as the sum of these two numbers:

[tex]\implies 25u^2-40u-40u+64[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 5u(5u-8)-8(5u-8)[/tex]

Factor out the common term (5u - 8):

[tex]\implies (5u-8)(5u-8)[/tex]

Simplify:

[tex]\implies (5u-8)^2[/tex]

Substitute back [tex]u=d^4[/tex]

[tex]\implies (5d^4-8)^2[/tex]

Therefore:

[tex]25d^8-80d^4+64=(5d^4-8)^2[/tex]

Let's see

Used formula

Answer:

a.) 3(x^2 + 7x + 4) – 14x - 8

Step-by-step explanation:

a.) 3(x^2 + 7x + 4) – 14x - 8

3x^2 + 21x + 12 - 14x - 8

3x^2 + 7x + 4

b.) 3x^2 + 7x + 4 – 14x

3x^2 -7x + 4

c.) 3x^2 + 7x + 4 – 8

3x^2 + 7x - 4

d.) 3x^2 + 7x

Already simplified

9/20 is the probability that Bob's password consists of an odd single-digit number followed by a letter and a positive single-digit number

It is given that bob's password consists of a non-negative single-digit number followed by a letter and another non-negative single-digit number (which could be the same as the first one).

P (odd single digit number )  =  ( 5 odd single digits / 10 non-negative single digits)  = (5/10)  = 1/2

P (positive single digit number ) =  (9 positive single digits / 10 non-negative single digits)  = 9/10

The total probability is   (1/2) (9/10)  =  9/20

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Answer:

9 units and 12 units to nearest hundredth.

Step-by-step explanation:

Let one leg be x units long  then the other = x+3 units.

By Pythagoras:

x^2 + (x+3)^2 = 15^2 = 225

2x^2 + 6x + 9 = 225

2x^2 + 6x - 216 =0

x^2 + 3x - 108 = 0

(x - 9)(x + 12) = 0

x = 9

So the other 2 legs are 9 and 12.

The property that best matches the equation is the associative property.

It should be noted that the associative property simply implies that the way the factors are grouped in a multiplication problem doesn't change the product.

In this case, since it's illustrated that (5 × 3) × 2 = (2 × 3) × 5. They both will give a value of 40.

In this case, the associative property is illustrated.

The complete question is:

Write the property that best matches the following: (5 × 3) × 2 = (2 × 3) × 5.

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Question 5

1) Given

2) Definition of congruent segments

3) Reflexive property of equality

4) Addition property of equality

5) Substitution

6) Commutative property of addition

7) Segment addition postulate

8) Substitution

9) Segments with equal measure are congruent

Question 6

1) Given

3) Segment addition postulate

4) Substitution

5) Subtraction property of equality

7) SSS

The equation, in point-slope form is (y - 45) = 5(x - 9) option first is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

A manager measured the number of goods, y, that his company produced in x hours.

The slope:

m = 5

From the problem:

The point (9, 45) will satisfy the line.

(y - 45) = 5(x - 9)

Thus, the equation, in point-slope form is (y - 45) = 5(x - 9) option first is correct.

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Answer:

Step-by-step explanation:

Answer:

26.9 ft

Step-by-step explanation:

So this answer is going to require one of the trigonometric functions, which is the ratio of sides of a triangle. So I attached a diagram to my answer, which is depicting the given information and hopefully this should be able to help a bit.

Anyways, we know the hypotenuse, an angle, and the opposite side of the angle. There is a trigonometric function which is defined as: [tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]. We can use the sine function to solve for the opposite side. So let's plug in known values into this equation:

Known Values: theta=85 degrees, hypotenuse = 27 ft

[tex]sin(85)=\frac{opposite}{27 ft}[/tex]

Multiply both sides by 27 ft]

[tex]sin(85)*27ft=opposite[/tex]

Now you can approximate the value of sin(85) using your calculator, and make sure it's in degree mode not radian mode.

[tex]0.996194698*27ft\approx opposite[/tex]

Simplify

[tex]26.8973 ft\approx opposite[/tex]

Rounding this to one decimal place makes it

[tex]26.9 ft\approx opposite[/tex]

The number of books on each shelf is 11 remainder 11

The toffees left over is 22 r 4

The oranges that would remain is 11 r30

The pages left to read is 22 r 16

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Number of books on each shelf = 3542 / 321 = 11 remainder 11

The toffees left over = 246 / 11 = 22 r 4

The oranges that would remain: 1702 / 152 = 11 r30

The pages left to read = 676 / 30 = 22 r 16

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In order to get 97% confidence level, with confidence interval of

+/- 1%, and standard deviation of 0.5 our sample size should be 11,772 samples

A confidence interval for a population mean, when the population standard deviation is known based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.

Accordingly, the Necessary Sample Size is calculated as follows:

Necessary Sample Size = [tex](Z-score)^{2} . StdDev*(1-StdDev) / (Margin Of Error)^{2}[/tex]

Given:-

Substituting in the given formula we get

Necessary Sample Size =

= ((2.17)² x 0.5(0.5)) / (0.01)²

= (4.7089x 0.25) / .0001

= 1.177225 / 0.0001

= 11,772.25

Hence in order to get 97% confidence level, with confidence interval of

+/- 1%,  and standard deviation of 0.5 our sample size should be 11,772

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When Shanti had crossed the finish line, she was a distance of 250 m ahead of Belle

We are given;

Length of Race = 1000 m

When nina crossed the finish line, she was 200 m ahead of Shanti and 400 m ahead of Belle.

Thus;

Shanti had run 4/5 of the race when Nina finished.

So, if Nina's time was x, then by variation, we can say that;

Time it took Shanti to finish the race = 5/4x

So, Belle had run 5/4 * 600 = 750 meters when Shanti finished.

Thus, means Shanti was; 1000 - 750 = 250m ahead of Belle.

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Answer:

-3/2

Step-by-step explanation:

gradient= y2-y1 over x2-x1

2-5 over 6-4

which equals to -3 over 2

Answer:

 -3/2.

Step-by-step explanation:

Slope of a line joining the points (x1, y1) and (x2, y2) is:

(y2 - y1) / (x2 - x1)  so here we have

Slope = (2 - 5)/(6 - 4)

          =  -3/2

Answer:

10

Step-by-step explanation:

median is the middle number of the list of numbers.

thereby counting through, the middle number which is the fifth number is 10

Answer:

7

Step-by-step explanation:

Answer:

first brand: 42 gallons

second brand: 28 gallons

Step-by-step explanation:

So you know that the first brand is 20% antifreeze, this means that if you have x gallons then 0.20x is pure antifreeze. The same thing can be applied for the second brand except the coefficient is 0.45 and I'll just say the variable is y. If you haven't noticed, the coefficients are simply the percentages of antifreeze, but in decimal form. Anyways, since it's asking for a mixture that's 30% antifreeze and is 70 gallons that means 0.30(70) gallons is pure antifreeze. This simplifies to 21 gallons. So if we take the pure antifreeze of both mixtures we get the following equation:

[tex]21 = 0.2x + 0.45y[/tex]

the x represents how many gallons of the first brand, and the y represents how many gallons of the second brand. Since that's what it represents we also get the equation:

[tex]70=x+y[/tex]

In this equation there aren't any coefficients, since x and y represent the whole amount. the 0.2x and 0.45 simply represent how much is pure antifreeze.

So to solve this systems of equation we can solve for y or x, either works, and then substitute it into the other equation. So in this example I'll solve for y

Original equation:

[tex]70=x+y[/tex]

Subtract x from both sides

[tex]70-x=y[/tex]

So now we can substitute this into the pure antifreeze question

[tex]21 = 0.2x + 0.45y \implies21=0.2x+0.45(70-x)[/tex]

So now we can solve for x since it's the only variable in this equation

[tex]21=0.2x+31.5-0.45x[/tex]

Simplify

[tex]21=-0.25x+31.5[/tex]

Subtract 31.5 from both sides

[tex]-10.5=-0.25x[/tex]

Now divide both sides by -0.25

[tex]42=x[/tex]

So this means we have to use 42 gallons of the first brand, now we can substitute this into either equation to solve for y, but it's much easier to use the total gallon equation:

[tex]x+y=70\implies 42+y=70[/tex]

Subtract 42 from both sides

[tex]y=28[/tex]

So this means we need to use 42 gallons of the first brand and 28 gallons of the second brand

The total purchase price is $41,625.00

Capital gain was recorded

The capital gain is $41,625.00

What is total initial initial investment?

Was a capital gain or loss made?

What is the dollar value of gain or loss recorded?

Cost per share=$83.25(note 1/4=0.25)

Total purchase price=purchase price per share*number of shares

Total purchase price=$83.25*500

Total purchase price=$41,625.00

The fact that the price at which Sherry sold the stocks a year later is more than the initial purchase price of $83.25, means that a capital gain was recorded, in other words, she bought low and sold high.

The capital gain can be computed as the total selling price(selling price per stock multiplied by the number of shares sold) minus the total purchase price.

total selling price=$95.50(i.e. 1/2=0.500

total selling price=$95.50*500

total selling price=$47,750.00

capital gain=$47,750.00-$41,625.00

capital gain=$6,125.00

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Answer:

8.  Domain: (-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

9.  Domain: [7/13, ∞)

    Range: [1, ∞)

Step-by-step explanation:

Question 8

Given rational function:

[tex]f(x)=\dfrac{x}{x^2+20x+75}[/tex]

Factor the denominator of the given rational function:

[tex]\implies x^2+20x+75[/tex]

[tex]\implies x^2+5x+15x+75[/tex]

[tex]\implies x(x+5)+15(x+5)[/tex]

[tex]\implies (x+15)(x+5)[/tex]

Therefore:

[tex]f(x)=\dfrac{x}{(x+15)(x+5)}[/tex]

Asymptote: a line that the curve gets infinitely close to, but never touches.

The function is undefined when the denominator equals zero:

[tex]x+15=0 \implies x=-15[/tex]

[tex]x+5=0 \implies x=-5[/tex]

Therefore, there are vertical asymptotes at x = -15 and x = -5.

Domain: set of all possible input values (x-values)

Therefore, the domain of the given rational function is:

(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

---------------------------------------------------------------------------------

Question 9

Given function:

[tex]f(x)=\sqrt{13x-7}+1[/tex]

Domain: set of all possible input values (x-values)

As the square root of a negative number is undefined:

[tex]\implies 13x-7\geq 0[/tex]

[tex]\implies 13x\geq 7[/tex]

[tex]\implies x\geq \dfrac{7}{13}[/tex]

Therefore, the domain of the given function is:

[tex]\left[\dfrac{7}{13},\infty\right)[/tex]

Range: set of all possible output values (y-values)

[tex]\textsf{As }\:\sqrt{13x-7}\geq 0[/tex]

[tex]\implies \sqrt{13x-7}+1\geq 1[/tex]

Therefore, the range of the given function is:

[1, ∞)

The probability that the manufacturing unit has carbon emissions beyond the permissible emission level is 0.2975

Given that the probability that carbon emissions from the company’s factory exceed the permissible level is 35% and the accuracy of the test is 85%.

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.

Event A: The given Carbon emission beyond to the given permissible emission level.

Event B: Test predicts this.

To get the probability of this problem, first we need to divide by 100 the given values.

A=35/100

A=0.35

The probability of event A is P(A)=0.35

And the probability is P(B|A)=85/100=0.85

Now, we will use the conditional probability formula, we get

P(B|A)=P(A∩B)/P(A)

0.85=P(A∩B)/0.35

P(A∩B)=0.85×0.35

P(A∩B)=0.2975

Hence, the probability that the manufacturing unit has carbon emissions beyond the permissible emission level and the test predicts is0.2975.

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Answer:

Step-by-step explanation:

To answer this, you also need to click the transversal pic above.

Answer:

1.   Cost per customer:  10 + x

     Average number of customers:  16 - 2x

[tex]\textsf{2.} \quad -2x^2-4x+160\geq 130[/tex]

3.    $10, $11, $12 and $13

Step-by-step explanation:

Given information:

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer:  10 + x

Average number of customers:  16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130.  Therefore, we can use the expressions found in part 1 to write the inequality:

[tex](10 + x)(16 - 2x)\geq 130[/tex]

[tex]\implies 160-20x+16x-2x^2\geq 130[/tex]

[tex]\implies -2x^2-4x+160\geq 130[/tex]

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

[tex]\implies -2x^2-4x+160\geq 130[/tex]

[tex]\implies -2x^2-4x+30\geq 0[/tex]

[tex]\implies -2(x^2+2x-15)\geq 0[/tex]

[tex]\implies x^2+2x-15\leq 0[/tex]

[tex]\implies (x-3)(x+5)\leq 0[/tex]

Find the roots by equating to zero:

[tex]\implies (x-3)(x+5)=0[/tex]

[tex]x-3=0 \implies x=3[/tex]

[tex]x+5=0 \implies x=-5[/tex]

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

[tex]\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144[/tex]

As 144 ≥ 130, the solution to the inequality is between the roots:  

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.  

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost.  It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:  

[tex]x =0 \implies 10 + 0=\$10[/tex]

[tex]x=3 \implies 10+3=\$13[/tex]

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.