Answer:
49
Step-by-step explanation:
I think I have read this right!
You let me know if you did not mean to write the following:
[tex]\sum_{k=1}^{7}(1+(k-1)(2)[/tex]
Alright so the lower limit is 1 and the upper limit is 7.
All this means is we are going to use the expression 1+(k-1)(2) and evaluate it for each natural number between k=1 and k=7 and at both k=1 and k=7.
The sigma thing means we add those results.
So let's start.
Evaluating the expression at k=1: 1+(1-1)(2)=1+(0)(2)=1+0=1.
Evaluating the expression at k=2: 1+(2-1)(2)=1+(1)(2)=1+2=3.
Evaluating the expression at k=3: 1+(3-1)(2)=1+(2)(2)=1+4=5.
Evaluating the expression at k=4: 1+(4-1)(2)=1+(3)(2)=1+6=7.
Evaluating the expression at k=5: 1+(5-1)(2)=1+(4)(2)=1+8=9.
Evaluating the expression at k=6: 1+(6-1)(2)=1+(5)(2)=1+10=11.
Evaluating the expression at k=7: 1+(7-1)(2)=1+(6)(2)=1+12=13.
Now for the adding!
1+3+5+7+9+11+13
4+ 12+ 20+13
16+ 33
49
In a city study about recycling, researchers found that of the 148,227
residents participating in the program, 72% responded that they would prefer
that newspaper and plastic be picked up on the same day. This is an example
of
B im pretty sure its B
Answer:
D. descriptive statistics.Step-by-step explanation:
Notice that the paragraph is describing some results they got of a recent survey. That is, they are giving specific statistical data about what people prefer.
So, this is an example of descriptive statistics. Remember that descriptive statistics is about using means, medians, standard deviation, percentages or any other stats that help to describe a phenomenom.
Therefore, the right answer is D.
HELP!!Use the figure to decide the type of angle pair that describe <6 and<4.
Angle 6, an acute angle, measures below 90 degrees, reflecting a sharp inclination. Angle 4, a right angle at precisely 90 degrees.
In the geometric configuration, Angle 6 is characterized as an acute angle, signifying that its measure falls between 0 and 90 degrees. Acute angles are typically associated with sharp inclinations, emphasizing a compact angular span. On the other hand, Angle 4 is identified as a right angle, precisely measuring 90 degrees.
Right angles are distinctive for their perpendicular alignment, forming the cornerstone of rectangular shapes and providing structural stability. The significance of Angle 4 lies in its pivotal role in defining perpendicularity within geometric constructs.
This geometric interplay showcases the diversity of angles, with acute angles like Angle 6 emphasizing sharpness and right angles like Angle 4 embodying orthogonality, contributing to the intricacies and precision inherent in geometric relationships.
Dion is performing a hypothesis test in which the population mean is 92 and the standard deviation is 2. His sample size is 7 with a mean of 93.5. Which of the following correctly depicts the z-statistic for this data?
a. 0.28. b.0.36. c.1.98. d.2.63
Answer:
Step-by-step explanation:
Answer:
Answer is 1.98
You're welcome.
Find the slope of DE and FG
slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]
slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]
To find the slope of line segments DE and FG from a trapezoid on a coordinate plane, we can follow these steps:
1. Identify the Coordinates of Endpoints:
- For DE, identify coordinates D and E.
- For FG, identify coordinates F and G.
2. Use the Slope Formula:
- The slope m of a line passing through two points [tex]\( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \).[/tex]
3. Calculate the Slope for DE:
- Plug the coordinates of D and E into the slope formula.
4. Calculate the Slope for FG:
- Plug the coordinates of F and G into the slope formula.
Given the coordinates in the image, let's calculate the slopes for DE and FG:
For DE:
- Let's say D has coordinates (-a, b) and E has coordinates (0, 2c)
- The slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]
For FG:
- Let's say F has coordinates[tex]\( (a+b, c) \)[/tex] and G has coordinates (0, 0) .
- The slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]
what is the average rate of change from x=-4 to x=1
Answer:
- 1
Step-by-step explanation:
The average rate of change of f(x) in the close interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ - 4, 1 ]
From the graph
f(b) = f(1) = - 1
f(a) = f(- 4) = 4
average rate of change = [tex]\frac{-1-4}{1-(-4)}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1
Why do you think the acceleration due to gravity is represented by a negative number?
Answer:
Step-by-step explanation:
Acceleration due to gravity is the rate at which an object changes its velocity due to the force of gravity.On Earth, the average acceleration due to gravity is -9.81 m/s².The acceleration due to gravity is ALWAYS negative. Any object affected only by gravity (a projectile or an object in free fall) has an acceleration of -9.81 m/s², regardless of the direction.
The acceleration is negative when going up because the speed is decreasing. The acceleration is negative when going down because it is moving in the negative direction, down. Even at the top of the path where the instantaneous speed is 0 m/s, the acceleration is still -9.81 m/s². ...
What is the exact distance from (−1, 4) to (6, −2)?
Answer:
The exact distance is √(29) or 29^(1/2)
Step-by-step explanation:
Find the answer using the distance formula (aka the Pythagorean theorem)
d=√(x1+x2)^2+(y1+y2)^2)
d=√(-1+6)^2+(4+-2)^2), Solve for d:
d= √((25)+(4))
d=√(29)
Answer:
[tex]\sqrt{35}[/tex]
Step-by-step explanation:
To calculate the distance (d) use the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)
d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]
= [tex]\sqrt{7^2+(-6)^2}[/tex]
= [tex]\sqrt{49+36}[/tex] = [tex]\sqrt{85}[/tex] ← exact value
Solve 2^(x-1) =11 change of base
Answer:
[tex]x=4.459[/tex]
Step-by-step explanation:
We have the following equation
[tex]2^{(x-1)} =11[/tex]
To solve the function, apply the equation [tex]log_2[/tex] on both sides of the equation
[tex]log_2(2^{(x-1)}) =log_2(11)[/tex]
Remember that
[tex]log_b(b)^x =x[/tex]
So
[tex](x-1) =log_2(11)[/tex]
[tex]x =log_2(11) + 1[/tex]
Finally
[tex]x=4.459[/tex]
Answer:
x = 4.46
Step-by-step explanation:
We are to solve the following expression:
[tex]2^{(x-1)}=11[/tex]
Taking the natural logarithm of both sides of the equation to remove the variable from the exponent. to get:
[tex] ln ( 2 ^ { x - 1 } ) = l n ( 1 1 ) [/tex]
[tex] ( x - 1 ) l n ( 2 ) = l n ( 1 1 ) [/tex]
Applying the distributive property:
[tex]xln(2)-1ln(2)=ln(11)[/tex]
Solving for x to get:
[tex]x=\frac{ln(11)}{ln(2)} +1[/tex]
x = 4.46
Two kilograms of ground cinnamon is packaged into bags containing 38 g each . There will also be some cinnamon left over . How many bags will there be
Answer:
52
Step-by-step explanation:
2 kg is the same as 2000 g.
2000 g / 38 g = 52.6
There will be 52 bags (with some cinnamon left over).
Which fraction is equivalent to 20%?
1/20
2/20
4/20
5/20
Answer:
4/20
Step-by-step explanation:
20 %
Percent means out of 100
20/100
Divide top and bottom by 10
2/10
We want the denominator to be 20 so multiply the top and bottom by 2
4/20
For this case we must find a fraction equivalent to 20%
We have to:
[tex]\frac {1} {20} =[/tex] 0.05 * 100% = 5%
[tex]\frac {2} {20} =[/tex] 0.1 * 100% = 10%
[tex]\frac {4} {20} =[/tex] 0.2 * 100% = 20%
[tex]\frac {5} {20} =[/tex] 0.25 * 100% = 25%
Thus, the correct option is option C, [tex]\frac {4} {20}[/tex]Answer:
[tex]\frac {4} {20}[/tex]
Option C
what is 1 1/4÷ by 3 4/5
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}[/tex]
Answer:
1/3
Step-by-step explanation:
covert the mixed number to an improper fraction
1x4+1 / 4
any expression multiplied by 1 remains the same
4+1 / 4
Add the numbers
5 / 4
Dividing is equivalent to multiplying with the reciprocal value
5 / 4 x 1 / 3 x 4 / 5
reduce the numbers with greatest common divisor 5
1 / 4 x 1 / 3 x 4
reduce the numbers with greatest common divisor 4
1 /3
X-y +2=-1
X+y +32=-3
2x-y +22=0
A class consists of 55% boys and 45% girls. It is observed that 25% of the class are boys and scored an A on the test, and 35% of the class are girls and scored an A on the test. If a student is chosen at random and is found to be a girl, the probability that the student scored an A is .
Answer:
The probability that the student scored an A is : 0.778
Step-by-step explanation:
There are 55% boys and 45% girls
So, No of boys is: 55/100
No of girls is: 45/100
So, total no of girls are: 45
Since 35% of the girls scored A on test
No of girls who scored A on test = 35
The probability that the student scored an A is: 35/45
The probability that the student scored an A is : 0.778
Answer:
[tex]P(A | B)=\frac{7}{9}=0.778[/tex]
Step-by-step explanation:
Let's call B the event that consists of the selected student being a girl
Call A to the event in which the selected student obtained an A.
Then we look for the probability that A will occur given that B. That is, we look for P(A | B)
This is a conditional probability and is calculated using the following formula
[tex]P(A | B)=\frac{P(A\ and\ B)}{P(B)}[/tex]
In this case
[tex]P(B)=0.45\\P(A\ and\ B)=0.35[/tex]
So
[tex]P(A | B)=\frac{0.35}{0.45}[/tex]
[tex]P(A | B)=\frac{7}{9}=0.778[/tex]
The lengths in centimeters of four line segments are shown below 3.1,3.5,3 1/5, 4.2 which list shows the lengths in order from least to greatest
ok i think your answer will be from least to greatest it would be this 3 1/5, 3.1, 3.5, 4.2
Hope i helped let me know if i got it right if not i am very sorry.
The order of four line segments from least to greatest is 3.1, 3.2, 3.5, 4.2 or 3.1. 3 1/5, 3.5, 4.2.
What is number?A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56, 2.6, 34 etc. are the numbers.
We have:
The lengths in centimetres of four line segments are:
3.1, 3.5, 3 1/5, 4.2
We can write 3 whole 1/5 as 16/5 or 3.2
3 1/5 = 3.2
3.1, 3.5, 3.2, 4.2
Order from least to greatest:
3.1, 3.2, 3.5, 4.2 or
3.1. 3 1/5, 3.5, 4.2
Thus, the order of four line segments from least to greatest is 3.1, 3.2, 3.5, 4.2 or 3.1. 3 1/5, 3.5, 4.2.
Learn more about the number here:
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Please help with 1 and 2
Answer:
1. B. a=14, b=2
2. D. a=1, b=1.4
Step-by-step explanation:
The exponential growth function can be represented as
[tex]y=a\cdot b^x,[/tex]
where b is the growth factor.
1. When the function has equation
[tex]g(x)=14\cdot 2^x,[/tex]
then
[tex]a=14,\\ \\b=2[/tex]
The initial amount is the value of the function at x=0:
[tex]g(0)=14\cdot 2^0=14\cdot 1=14[/tex]
The growth factor is b=2
2. When the function has equation
[tex]f(t)=1.4^t,[/tex]
then
[tex]a=1,\\ \\b=1.4[/tex]
The initial amount is the value of the function at t=0:
[tex]f(0)=1.4^0=1[/tex]
The growth factor is b=1.4
Help, what is the measure of arc QS
Answer:
168°
Step-by-step explanation:
∠QRS is an angle formed by 2 chords of the circle and is half the measure of its intercepted arc QS, that is
m QS = 2 × 84° = 168°
Applying the inscribed angle theorem, the measure of arc QS is: 168°.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, the measure of an inscribed angle in a circle equals half of the measure of the intercepted arc.
Based on the inscribed angle theorem,
arc QS = 2(m∠QRS)
arc QS = 2(84)
arc QS = 168°
Therefore, applying the inscribed angle theorem, the measure of arc QS is: 168°.
Learn more about the inscribed angle theorem on:
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A couple finds that they are experiencing debt problems and decide to find a credit counseling agency. What are three (3) things that the couple should find out about an agency before they allow the agency to represent them?
Answer:
This is an odd question...
The couple should find out the following:
1.) is the agency legitimate?
2.) Will they be doing a hard inquiry on our credit history? if so, this could affect our current credit score
3.) Will they charge me to review my current credit reports?
Three things that should be considered about a credit agency are : Credibility and Reliability, Financial Efficiency, Accreditation and Acclamation
Given - The couple are facing debt issues. They need a credit counselling agency.
While choosing an agency, they should be careful about the following aspects of respective agency.
Credibility & Reliability - ie how trustworthy they are Financial Efficiency - denotes their competence in handling with funds Accreditation and Acclamation - represents the recognition and public image held by the agency.To learn more, refer https://brainly.com/question/1430582?referrer=searchResults
Which choice is equivalent to the product below? For any nonnegative real number √2•√10•√5
A. 4√25
B. 5√2
C. 2√50
D. 10
Answer: The answer is D. 10! its correct I checked.
Step-by-step explanation:
ASAP PLS.
#22-6: A particular substance is worth $1.46 per cubic centimeter. Assume the figure is composed of this substance. What would it's value be?
Answer:
[tex]\$19,710[/tex]
Step-by-step explanation:
step 1
Find the volume of the composite figure
The volume of the composite figure is equal to the volume of the cube plus the volume of the square prism
so
[tex]V=15^{3}+15^{2}(45)[/tex]
[tex]V=13,500\ cm ^{3}[/tex]
step 2
Find the value of the figure
Multiply the volume by $1.46 per cubic centimeter
[tex]13,500(1.46)=\$19,710[/tex]
What is -0.8+1.4n=2+0.7n
Answer:
n=4
Step-by-step explanation:
To solve combine your like terms.
You can start by adding 0.8 to both sides and subtracting 0.7n from both sides.
[tex]-0.8+1.4n=2+0.7n\\1.4n=2.8+0.7n\\0.7n=2.8[/tex]
Next, divide both sides by 0.7 to isolate for n.
[tex]0.7n=2.8\\n=4[/tex]
What must be a factor of the polynomial function f(x) graft on the coordinate plane below
Answer:
The correct answer option is B. (x - 1).
Step-by-step explanation:
We are to determine the factor of the polynomial function [tex]f(x)[/tex] which is graphed on the given coordinate plane.
We know that if the zeros (or intercepts) of an equation are [tex] r _ 1 [/tex] and [tex] r _ 2 [/tex] then the factors for this equation will be [tex] ( x - r _ 1 ) [/tex] and [tex]( x - r _ 2 ) [/tex].
From the graph, we can see that it intercepts the x axis at [tex]1[/tex] and [tex]6[/tex]. So the roots will be [tex](x-1)[/tex] and [tex](x-6)[/tex].
Therefore, the correct answer option is B. (x - 1).
Answer: SECOND OPTION.
Step-by-step explanation:
We can verify each option by making eac equal to zero and solving for "x":
First option
[tex]x-3=0\\x=0+3\\x=3[/tex]
The first option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=3[/tex].
Second option
[tex]x-1=0\\x=0+1\\x=1[/tex]
The second option is a factor of the polynomial function, because the parabola intersects the x-axis at [tex]x=1[/tex].
Third option
[tex]x+1=0\\x=0-1\\x=-1[/tex]
The third option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-1[/tex].
Fourth option
[tex]x+3=0\\x=0-3\\x=-3[/tex]
The fourth option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-3[/tex].
Which of the following is the equation of a line that passes through (-2,1) and (-4,-3)?
Answer:
The equation is y= 2x+5
Step-by-step explanation:
Lets find the slope of the line through the points (-2,1) and (-4,-3).
where x1 = -2, y1= 1, x2= -4, y2 = -3.
Now apply slope formula:
m= y2-y1/ x2-x1
m= -3-1/-4-(-2)
m = -4/-4+2
m= -4/-2
Divide the term by 2:
m = 2
Now we will apply point slope formula:
y-y1 = m (x-x1)
Now substitute the values in the formula:
y-1=2(x-(-2))
y-1 =2(x+2)
y-1=2x+4
Now combine the constants:
y= 2x+4+1
y=2x+5
So the equation is y= 2x+5 ....
The expression on the left side of an equation is shown below. 3x+9= []
If the equation has no solution, which expression can be written in the box on the other side of the equation?
A. –9
B. –3
C. 3x
D. 3x + 9
Answer:
C. 3x
Step-by-step explanation:
The first two choices give 1 solution each.
The last choice gives an infinite number of solutions.
Choice C. gives no solution.
3x + 9 = 3x
Subtract 3x from both sides.
9 = 0
Since 9 = 0 is false, equation 3x + 9 = 3x has no solution.
The expression can be written in the box on the other side of the equation as C. 3x.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given expression is
3x + 9 = _
Subtract 3x from both sides;
9 = 0
Since 9 = 0 is false,
The equation 3x + 9 = 3x has no solution.
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What is the simplified form of the quantity y squared plus 7y plus 12 over the quantity y squared minus 3y minus 18?
y minus 4 over y minus 6
y minus 4 over y plus 6
y plus 4 over y minus 6
y plus 4 over y plus 6
Answer:
The correct option is C
Step-by-step explanation:
The given expression is:
=y²+7y+12/y²-3y-18
Break the middle term of both the numerator and denominator:
=y²+4y+3y+12/y²-6y+3y-18
Take the common from the expressions:
=y(y+4)+3(y+4)/y(y-6)+3(y-6)
=(y+3)(y+4)/(y+3)(y-6)
The same terms will be cancelled: Then we have,
=(y+4)/(y-6)
Therefore the correct option is C....
Answer:
A iS the answer i got it right on my test
Step-by-step explanation:
Y-4/Y-5
1.) Which system of equations below give the solution (-1,-2)?
(1)
(3)
y = x - 3
y = -x - 1
y = -x - 3
y = x - 1
(2)
y = x - 3
(4)
y = -x - 3
y=-x-1
y = x - 1
Answer:
y = -x - 3
Step-by-step explanation:
Plug in -1 for x and your result will come out to 1 because of that double negative [-(-1) = 1]. Next, deduct 3 from 1 to get -2.
I am joyous to assist you anytime.
Solve the equation by completing the square. Round to the nearest hundredth if necessary. 4x2 + 8x – 32 = 0
[tex]4x^2 + 8x - 32 = 0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4[/tex]
For this case we must solve the following expression by completing squares:
[tex]4x ^ 2 + 8x-32 = 0[/tex]
We divide between 4 on both sides of the equation:
[tex]x ^ 2 + 2x-8 = 0[/tex]
We add 8 to both sides of the equation:
[tex]x ^ 2 + 2x = 8[/tex]
We divide the middle term between 2 and square, this we add to both sides of the equation:
[tex]x ^ 2 + 2x + (\frac {2} {2}) ^ 2 = 8 + (\frac {2} {2}) ^ 2\\x ^ 2 + 2x + 1 ^ 2 = 8 + 1\\x ^ 2 + 2x + 1 ^ 2 = 9\\(x + 1) ^ 2 = 9[/tex]
We apply root to both sides:
[tex]x + 1 =\pm \sqrt {9}[/tex]
We have two roots:
[tex]x_ {1} = \sqrt {9} -1 = 3-1 = 2\\x_ {2} = - \sqrt {9} -1 = -3-1 = -4[/tex]
Answer:
[tex]x_ {1} = 2\\x_ {2} = - 4[/tex]
Answer this problem. 3⁄14 ÷ 2⁄7 = ?
Answer:
3/4
Step-by-step explanation:
3/14 ÷ 2⁄7
Copy dot flip
3/14 * 7/2
We rewrite
3/2 * 7/14
Canceling a 7 from 7 and 14
3/2 * 1/2
Multiplying straight across
3*1 =3
2*2=4
3/4
For this case we must solve the following expression:
[tex]\frac {\frac {3} {14}} {\frac {2} {7}} =[/tex]
Applying double C we have:
[tex]\frac {3 * 7} {14 * 2} =\\\frac {21} {28} =[/tex]
for simplify we divide the numerator and denominator by 7, then we have:
[tex]\frac {\frac {21} {7}} {\frac {28} {7}} =\\\frac {3} {4}[/tex]
In decimal form we have to:
[tex]\frac {3} {4} = 0.75[/tex]
Answer:
[tex]\frac {3} {4} = 0.75[/tex]
the scale of a map is 1:500000 the actual distance between two town is 172 km calculate the distance, in centimeters, between two towns on the map.
Answer:
34.4 cm
Step-by-step explanation:
The scale of the map is 1:500000
This means 1 cm in the map is equivalent to 500000 cm in actual.
So, first we need to convert the distance between the 2 towns in centimeters.
The distance between two towns is 172 km
172 km = 172 x 1000 meters = 172,000 meters
172,000 meters = 172,000 x 100 cm = 17,200,000 cm
500,000 cm in actual on the map = 1 cm
1 cm in actual on the map = [tex]\frac{1}{500000}[/tex] cm
17,200,000 cm in actual on the map will be = [tex]\frac{1}{500000} \times 17200000 = 34.4[/tex] cm
Thus, 172 km actual distance would be represented by 34.4 cm on the map
The distance between two towns on a map, with a scale of 1:500000 is 34.4 cm.
The question asks us to calculate the distance, in centimeters, between two towns on a map given the scale of the map is 1:500000, and the actual distance between the two towns is 172 km. First, we convert the actual distance from kilometers to centimeters by multiplying 172 km by 100,000 (since 1 km = 100,000 cm). This gives us 17,200,000 cm. Then, we use the map's scale to find the map distance. The scale 1:500000 means that 1 cm on the map equals 500000 cm in the real world. Therefore, we divide the real-world distance in centimeters by the scale factor (17,200,000 cm / 500000 = 34.4 cm). Thus, the distance between the two towns on the map is 34.4 cm.
Find the answer to each word problem.
29. Diane bought 48 bottles of water. Ewan
bought 60 bottles. The water came in
packs of the same number of bottles.
What is the greatest number of bottles
that could be in a pack?
Answer:
Step-by-step explanation:
This is a way of asking you what the highest common factor is. So factor into primes and find the highest that is between them.
48: 2 * 2 * 2 * 2 * 3
60: 2 * 2 * 3 * 5
The answer is Bolded and underlined.
HCF: 2 * 2 * 3
HCF: 12
The greatest number that could be in a pack is 12
Factored form of x^12 y^16+1
Answer:
B
Step-by-step explanation:
let's recall that
1² = 1
1⁴ = 1
1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1
[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{12}y^{18}+1\implies x^{4\cdot 3}y^{6\cdot 3}+1^3\implies (x^4)^3(y^6)^3+1^3\implies (x^4y^6)^3+1^3 \\[2em] [x^4y^6+1][(x^4y^6)^2-(x^4y^6)(1)+1^2]\implies (x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]