What polynomial identity should be used to prove that 61 = 125 − 64?

a
Difference of Cubes

b
Difference of Squares

c
Square of a Binomial

d
Sum of Cubes

Let's begin by listing out the information given to us:

Cost (c) = $1500, interest (r) = 8% /annum

The equation for this is given by:

11. The exponential function is given by: y = c * 1.08^z

12. The artwork is worth $3238.39

Answer:

the answer to the question is 1/8

From the equations we get 'x' as '-2' and 'y' as '-7'

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. An equation consists of two expressions joined by an equals sign ("="). The expressions on each side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side." The right-hand side of an equation is frequently considered to be zero.

4x - 2y = 6....................equation (1)

-2x + 4y = -24...............equation (2)

Multiply equation (1) by 2 and add with equation (2)

8x - 4y =   12

-2x + 4y = -24

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

6x         = -12

or, x = -12/6 = -2

from equation (1),

     4x - 2y = 6

or, 4(-2) - 2y = 6

or, -2y = 6 + 8

or, y = 14/-2 = -7

Hence, from the equations we get 'x' as '-2' and 'y' as '-7'

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The Recurrence interval for tornadoes in tuscaloosa county is 0.909

What is recurrence interval ?

The time period in which a new occurrence of something that happened or appeared before : a repeated occurrence or The time frame in which a previously occurring event or appearance first occurs: a recurring occurrence

Given that,

Total number of tornadoes is 77

Total time for Recurrence is 70 years

Using these data,

Recurrence = Total time for recurrence / Total number of tornadoes

Substituting we get,

Recurrence interval = 70/77

= (70/77)

= (0.909)

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Since the diagonal is less than the circle's diameter, the Pythagorean theorem reveals that the square may fit within the circle without touching its edge.

Since squares are made up of two right triangles of equal length, the Pythagorean theorem is used to calculate the length of the hypotenuse of right triangles, which corresponds to the diagonals in squares.

The diagonal (L) of the square must be less than the diameter of the circle if it can fit within the circle without touching the edge (d). Therefore, we continue to establish this connection:

[tex]L=\sqrt{2}.5cm[/tex]

L ≈ 7.071 cm

Because the diagonal is less than the circle's diameter, the Pythagorean theorem reveals that the square may fit within the circle without touching its edge.

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Answer:

Month:

1             = 32$

2            =  64$

3            = 96$

4            = 128$

Step-by-step explanation:

The option that describes the sample you would ask is A. twenty students from one elementary class in your town.

It should be noted that a simple random sampling simply means a form of sampling whereby everybody has an equal chance of being selected.

In this case, it should be noted that the person wanted to take a simple random sample for a study on screen time in elementary school students in the town. Therefore, twenty students can be chosen to illustrate this.

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The equation obtained for Kim will be t = x/2

Equation obtained for Jake will be t = (x - 6)/1.5

As for the problem, Kim and Jake are competing in the big race. And the values of their speed are given below.

Kim moves at a 2-meter-per-second running pace.

Jake moves at a 1.5 meter per second running pace (3 meters per 2 seconds)

Jake gets 6 meters ahead of Kim.

To get equations for the same case to both persons we should get it as,

Let x be the complete race distance and t be either Kim's or Jake's total race time.

Time = Speed/Distance

Kim's time equation is t = x/ 2.

The time equation that Jake uses is t = (x - 6)/1.5.

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Answer:

+ 9

Step-by-step explanation:

x² + 6x

to complete the square

add ( half the coefficient of the x- term )² to x² + 6x

x² + 2(3)x + 3²

= x² + 2(3)x + 9

= (x + 3)² ← a perfect square

1. The θ lies in the 2nd quadrant of the graph.

2. The θ lies in the 1st quadrant of the graph.

3. The θ lies in the 3rd quadrant of the graph.

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198, 714

a. What digit is in the ten thousands place? - 9

b. Which place is used to decide which way to round the ten thousands place? - thousands place

c. What is the digit in this place? - 8

d. Should you round the number in the ten thousands place up or down? - UP

e. What happens when you round up a 9? - It becomes 10.

f. What do you do when the value of a place is 10 or more? - The number becomes 0 and we add 1 to the next place to the right.

g. What is the value of the ten thousands place when the number is rounded to the nearest ten thousand? 100,000

h. What is 198,714 rounded to the nearest ten thousand? - 200,000

i. What is 302,895 rounded to the nearest thousand? - 303, 000

j. What is 7,142 rounded to the nearest ten? - 7, 140

k. Round 24,793 to the nearest hundred? - 24, 800



Answer:

see below

Step-by-step explanation:

km   *   miles/km  

     see how the 'km' then 'cancels out' and you are left with 'miles'         the underlined shows the units of the conversion factor

central angle Θ  of the circle is equal to =  3.6633333 radian

While a radian is another unit of measurement that is used to measure angles, a degree is a unit of measurement that is used to measure circles, spheres, and angles. The radian, or one pi radian, is only half the diameter of a circle, which has 360 degrees, or its entire area.

central angle of the circle is equal to = (14 * 3.14 )/12

                                                              = 3.6633333 radian
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The solution to the system is 6 and 11.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation.

Given equation:

y=2x-1 .....(1)

y=x+5....(2)

Now solving equation 1 and 2, we get

2x -1 = x + 5

2x - x= 5 +1

x = 6

and, y= 2x-1

y= 2(6)-1

y= 12 -1

y= 11

Hence, the value of x is 6 and y is 11.

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Answer:

x=15

Step-by-step explanation:

You can set up the equation like this

60 =3x+15

Get x by itself

45=3x

Divide both sides by 3

x=15

By completing squares we will rewrite the equation as:

(x + 2)^2 - 2

Here we have the quadratic equation:

x^2 + 4x + 2

And we want to complete squares, remember that the square trinomial is:

(a + b)^2 = a^2 + 2ab + b^2

We can rewrite the quadratic as:

x^2 + 2*2*x + 2

Now, adding and subtracting 2 we get:

x^2 + 2*2*x + 2 + 2 - 2

x^2 + 2*2*x + 4 - 2

(x^2 + 2*2*x + 2^2) - 2

(x + 2)^2 - 2

So the first option is the correct one.

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Answer:

-49 and then -63

Step-by-step explanation:

it is going by -14s

3/7 + 2/ 7 = (3+2)/7 = 5/7

Then Jaclyn is WRONG

Because 5/7 is the inverse of 7/5

Answer:

answer is 2 since k =1 and 4n will be 2 ×2 so 8 will be equivalent to 4 which will be 2

Answer:

E. 4x - 1

Explanation:

An equation that represents the table satisfies that when we replace each value of x in the table, we get its respective value of y in the table.

So, the answer is:

y = 4x - 1

Because:

For x = -2, we get:

y = 4(-2) - 1

y = -8 - 1

y = -9

For x = -1, we get:

y = 4(-1) - 1

y = -4 - 1

y = -5

For x = 1:

y = 4(1) - 1

y = 4 - 1

y = 3

For x = 2:

y = 4(2) - 1

y = 8 - 1

y = 7

At the end of the sixth second, the coin will have fallen 176 feet in Arithmetic Progression.

What is Arithmetic Progression (AP)?

16, 48, 80, ?

Use  The sum up to nth terms of an AP is given as :-

S(n) = (n/2)[2a + (n - 1)d]

In this arithmetic sequence, each term is 32 more than the one immediately before it.

So,

16, 48, 80, 112, 144,  176

At the end of the sixth second, the coin will have fallen 176 feet.

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The probability a randomly selected worker primarily drives a car or takes public transportation to work is 0.915

Here's the complete question:

According to the U.S. census bureau, the probability a randomly selected worker primarily drives a car to work is 0.76. the probability a randomly selected worker primarily takes public transportation to work is 0.05. what is the probability a randomly selected worker primarily drives a car or takes public transportation to work?

Given that according to the U.S. Census Bureau:

The probability that a randomly selected worker primarily drives a car to work  is 0.867

The probability that a randomly selected worker primarily takes public transportation to work is 0.048

The probability that a randomly selected worker primarily drives a car or takes public transportation to work is

= 0.867 +0.048 = 0.915

(since these two are disjoint sets)

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For each additional slice of pizza that is purchased, the amount by which the total cost of lunch increase is: C. $2.50.

A graph refers a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.

Next, we would calculate the difference between the total cost when an additional slice of pizza is purchased:

Difference = 10 - 7.5 = 12.5 - 10 = 15 - 12.5 = $2.50

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Answer:

y=-2x+5

Step-by-step explanation:

This is my last one for today hahaha. Good luck on the rest.

Henry can write 13 pages in 8 hours, at this rate.

This is a problem from the unitary method. We can solve this question following a few steps.

Here if Henry can write 5 pages of his novel in 3 hours. We have to find the number of pages that Henry can write within 1 hour.

The number of pages Henry can write within 1 hour is 5/3 pages.

[Number of pages within a unit hour = number of total pages/ total hour]

Therefore, Henry writes in 8 hours is, ( 5/3 × 8 ) = 40/3 = 13.33 ≈ 13 pages

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Answer: The slope is 0.

Step-by-step explanation:

      We will use the slope formula to find the slope of the line going through these two points.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\displaystyle \frac{3-3}{2--4}=\frac{0}{2+4} =0[/tex]

      The slope of this line is 0.

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The common denominators and the equivalent fractions are discussed below.

A fraction represents a part of the whole or group of objects.

Given are the pair of fractions.

1 -  1/8 and 1/2

The common denominator will be - 16

(1 x 2)/(8 x 2) = 2/16

(1 x 8)/(2 x 8) = 8/16

2 -  1/8 and 9/5

The common denominator will be - 40

(1 x 5)/(8 x 5) = 5/40

(9 x 8)/(5 x 8) = 72/40

3 - 1/8 and 11/6

The common denominator will be - 48

(1 x 6)/(8 x 6) = 6/48

(11 x 8)/(6 x 8) = 88/48

Therefore, the common denominators and the equivalent fractions are discussed above.

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Answer:

A (3; 4)

B (5; 2)

C (4; 0)

D (-6; -2)

E (-2; -5)

I hope this helps!

The function is f(x) = 1/3(27)ˣ, the key aspects are domain: -oo < x < oo and range: y ≥ 1/3

From the question, the equation of the function is given as

f (x) = one-third (81) Superscript StartFraction 3 x Over 4 EndFraction

Rewrite the equation properly

So, we have

f(x) = 1/3(81)³/⁴ˣ

Express 81 as 3 exponent 4

So, we have the following equation

f(x) = 1/3(3⁴)³/⁴ˣ

Evaluate the exponents

f(x) = 1/3(3)³ˣ

Further, evaluate the exponents

f(x) = 1/3(27)ˣ

Next, we calculate the key aspects i.e. the domain and the range

The above function is an exponential function.

The domain of an exponent is the set of all real values

Set the radicand to 1, to calculate the range

So, we have

y = 1/3 * 1

Evaluate

y = 1/3

Since the coefficient, this value is a minimum

So, the range is

y ≥ 1/3

Hence, the simplified function is f(x) = 1/3(27)ˣ

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Answer:

1/3

27

all real numbers

y > 0

or B. C. D. B.

Step-by-step explanation:

hope I could help

Answer: it would be either: 1 or 0 or 62

Step-by-step explanation:

ok