The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes therefore, option (a) is correct.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
As per the given polynomial,
61 = 125 - 64
It is known that a³ = a × a × a
Therefore, 5³ = 5 × 5 × 5 = 125
And, 4³ = 4 × 4 × 4 = 64
Therefore, 61 = 5³ - 4³
Hence "The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes".
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Choose all that apply.
You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the firstsecond, 48 feet the next second, 80 feet the third second, 112 feet the fourth second, and so on. Determine if this represents an arithmetic or geometric sequence and explain why you made your choice.
A arithmetic
B geometric
The sequence is adding each time.
D The sequence is multiplying each time.
At the end of the sixth second, the coin will have fallen 176 feet in Arithmetic Progression.
What is Arithmetic Progression (AP)?
The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount.For instance, the sequence 2, 6, 10, 14,... is an arithmetic progression (AP) because it adheres to the rule that each number is obtained by adding 4 to the term before it. The nth term in this series equals 4n-2. You can determine the terms of the series by changing the nth term to n=1,2,3,...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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I really need help with the problem in the photo
The common denominators and the equivalent fractions are discussed below.
What is a fraction?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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Simplify the function f (x) = one-third (81) Superscript StartFraction 3 x Over 4 EndFraction. Then determine the key aspects of the function.
The function is f(x) = 1/3(27)ˣ, the key aspects are domain: -oo < x < oo and range: y ≥ 1/3
How to simplify the equation of the function?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
Find the value of x.
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
Please help me !! due tonight
Answer:
y=-2x+5
Step-by-step explanation:
This is my last one for today hahaha. Good luck on the rest.
Complete the square to transform the expression x2 + 4x + 2 into the form a(x − h)2 + k. (1 point) (x + 2)2 − 2 (x + 2)2 + 2 (x + 4)2 − 2 (x + 4)2 + 2
By completing squares we will rewrite the equation as:
(x + 2)^2 - 2
How to complete squares?
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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Please help me on this question:
A circle has diameter 9 cm
A square has side length 5 cm
Use Pythagoras' theorem to show that
the square will fit inside the circle without
touching the edge of the circle.
9 cm
5 cm
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.
How to use the Pythagorean theorem to determine if a square fits within a circle or notSince 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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please help asap
this is an assignment due today please help real quick
Answer:
A (3; 4)
B (5; 2)
C (4; 0)
D (-6; -2)
E (-2; -5)
I hope this helps!
Solve the system of equations by elimination
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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find the next two number 7,-7,-21,-35
Answer:
-49 and then -63
Step-by-step explanation:
it is going by -14s
Jaclyn says 7 5 has the same answer as 3/7 + 2/7 is she correct explain why or why not
3/7 + 2/ 7 = (3+2)/7 = 5/7
Then Jaclyn is WRONG
Because 5/7 is the inverse of 7/5
What is the measure (in radians) of central angle in the circle below?
central angle Θ of the circle is equal to = 3.6633333 radian
What is difference between radians and degrees ?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.
Calculationcentral angle of the circle is equal to = (14 * 3.14 )/12
= 3.6633333 radian
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X _-2, -1, 1, 2Y_ -9, -5, 3,7find the equation that represents the table
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
Caroline’s cell phone plan costs $32 per month. Create a table that shows the sum of the amounts that Caroline will pay for her cell phone plan over the next 4 months. Can y'all please help me
Answer:
Month:
1 = 32$
2 = 64$
3 = 96$
4 = 128$
Step-by-step explanation:
Use the number line to add the fraction.
Drag and drop the answer into the box to match the sum
Answer:
the answer to the question is 1/8
on a piece of paper, graph the system of equations. Find the solution to the system. y=2x-1 y=x+5
The solution to the system is 6 and 11.
What is equation?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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If you wanted to take a simple random sample for a study on screen time in elementary school students in your town, which describes the sample you would ask?
twenty students from one elementary class in your town
twenty students from each elementary school in your town
twenty students that are friends from an elementary school in your town
twenty students that are friends from each elementary school in your town
The option that describes the sample you would ask is A. twenty students from one elementary class in your town.
What is a simple random sampling?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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√31+√31. I’ve been trying to figure this out for the last hour and no luck hoping someone could help me.
Answer: it would be either: 1 or 0 or 62
Step-by-step explanation:
ok
he graph below shows the total cost for lunch, c, when Will and his friends buy a large salad to share and several slices of pizza, p.
A graph titled Lunch Cost. The x-axis shows the number of slices purchased, numbered 1 to 8, and the y-axis shows the cost in dollars, numbered 5 to 40. Blue diamonds appear at points (0, 7.5), (1, 10), (2, 12.5), (3, 15), (4, 17.5), (5, 20), (6, 22.5), (7, 25), (8, 27.5).
For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?
$1.50
$2.00
$2.50
$3.00
For each additional slice of pizza that is purchased, the amount by which the total cost of lunch increase is: C. $2.50.
What is a graph?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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When you round up to a place that has a 9, you create a 10. Then you need to round up the next place to the left of the place you are rounding to.There are 198,714 people living in Belleville. What is the number of people rounded to the nearest ten thousand?a. What digit is in the ten thousands place?b. Which place is used to decide which way to round the ten thousands place?c. What is the digit in this place?d. Should you round the number in the ten thousands place up or down?e. What happens when you round up a 9?f. What do you do when the value of a place is 10 or more?g. What is the value of the ten thousands place when the number is rounded to the nearest tenthousand?h. What is 198,714 rounded to the nearest ten thousand?i. What is 302,895 rounded to the nearest thousand?j. What is 7,142 rounded to the nearest ten?k. Round 24,793 to the nearest hundred.?
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
A total of 77 tornadoes have been documented in tuscaloosa county in the period beginning on january 1, 1950 and ending on december 31, 2020. What is the recurrence interval for tornadoes in tuscaloosa county?.
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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Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (-4, 3), (2,3)
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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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 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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PLEASE HELP!!!
Assignment name: Trigonometry, Evaluation of Functions
Hi, can someone help find the GRAPHS that belong to these problems, please! I only need a picture of a graph for each problem that I've attached below :)
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.
In the first question, Secθ = -13/5 and Tanθ is negative.Secθ is negative in the 2nd and 3rd quadrants.Tanθ is negative in the 2nd and 4th quadrants.Thus, θ lies in the 2nd quadrant of the graph.In the second question, Sinθ = 7/10 and Cotθ is positive.Sinθ is positive in the 1st and 2nd quadrants.Cotθ is positive in the 1st and 3rd quadrants.Thus, θ lies in the 1st quadrant of the graph.In the third question, Tanθ = 3/4 and Sinθ is negative.Tanθ is positive in the 1st and 3rd quadrants.Sinθ is negative in the 3rd and 4th quadrants.Thus, θ lies in the 3rd quadrant of the graph.To learn more about quadrants, visit :
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A piece of artwork, purchased for $1500, increases in value by 8% each year,11) (3pt) Write an exponential function to represent the value of the artworkafter z number of years.12) (2pt) What will the artwork be worth in 10 years?
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:
[tex]\begin{gathered} y=c\cdot(1+r)^z\Rightarrow y=c(1+0.08)^z \\ c=\text{ \$1500, }r=0.08 \\ y=c(1.08^z)^{}=1500\cdot1.08^z \\ \\ z=10 \\ y=1500\cdot1.08^{10} \\ y=\text{ \$}3238.39 \end{gathered}[/tex]11. The exponential function is given by: y = c * 1.08^z
12. The artwork is worth $3238.39
enry can write 5 pages of his novel in 3 hours. At this rate, how many pages can Henry write in 8 hours?
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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Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 6x + ___?
1
3
6
9
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
Kim and jake are competing in the big race. jake starts at the starting line and rides at 2 meters per second. kim gets a 6 meter head start and rides at 3 meters every 2 seconds. write an equation for kim and jake
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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What is the answer to
k + 4n+ 8=
Answer:
answer is 2 since k =1 and 4n will be 2 ×2 so 8 will be equivalent to 4 which will be 2
Suppose you want to convert kilometers to miles. Which unit should be in the
numerator of the conversion factor? Which unit should be in the denominator?
Explain your reasoning.
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