Answers
The recursive formula of the arithmetic sequence is
[tex]a_n=a_{n-1}+d[/tex]Where d is the common difference between each 2 consecutive terms
The explicit form of the arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
Since the given explicit form of the sequence is
[tex]a_n=13+(n-1)6[/tex]Then
a = 13
d = 6
The recursive form of the sequence should be
[tex]a_n=a_{n-1}+6[/tex]The missing number is 6
The answer is D
Related Questions
Find the value of a.
Answers
The value of a is √10/2 if |x| = 2√2 and a|x| = 2√5 in the given Functions respectively.
What is function?Functions are the foundation of calculus in mathematics. The functions are the various types of relationships. In mathematics, a function is represented as a rule that produces a unique output for each input x.
In mathematics, mapping or transformation is used to denote a function. These functions are usually represented by letters like f, g, and h. The domain is defined as the set of all possible values for which the function can be defined.
We have given that f(x) = |x|
Where x is hypotenuse the triangle made by the line
The formula for hypotenuse = c² = a² + b²
Here each side = 2 units
so hypotenuse is
c² = 4² + 4²
c² = 16 + 16
c² = 32
c = 4√2
Thus, f(x) = 2√2
In f(x) = a|x|
The blue lines with the base and side also makes a right angles triangle and the blue line is the hypotenuse
c² = 4² + 2²
c² = 16 + 4
c² = 20
c = 2√5
Thus, f(x) = 2√5
Now, if |x| = 2√2 and a|x| = 2√5
Taking |x| in common we get the equation
2√2 = (2√5)/a
a = (2√5)/(2√2)
a = √5/√2
a = √10/2
Thus, the value of a is √10/2 if |x| = 2√2 and a|x| = 2√5 in the given Functions respectively.
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The circle below is centered at (10,4) and has a radius of 4. What is itsequation?101010O A. (x - 10)2 + (y - 4)2 = 16O B. (x-4)2 + (-10)2 = 4O C. (x-4)2 + (-10)2 = 16OD. (x-10)2 + (x-4)2 = 4
Answers
The general equation of a circle with centre (h,k) and radius r is given as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where,} \\ (h,k)=(10,4) \\ r=4 \end{gathered}[/tex]By substitution, we will have,
[tex]\begin{gathered} (x-10)^2+(y-4)^2=4^2 \\ =(x-10)^2+(y-4)^2=16 \end{gathered}[/tex]Hence,
The correct answer is OPTION A
Find the intersection points when the line y = 12-4x meets the curve y =12-x^3. Hence, sketch in the same diagram, the line y = 12 - 4x and the curve y=12-x^3 Calculate the area of the region bounded by the curve and the line
Answers
The equations of the line and the curve are
[tex]\begin{gathered} y=12-4x \\ y=12-x^3 \end{gathered}[/tex]We will equate their right sides to find the values of x
[tex]12-4x=12-x^3[/tex]Subtract 12 from both sides
[tex]\begin{gathered} 12-12-4x=12-12-x^3 \\ -4x=-x^3 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-4x}{-1}=\frac{-x^3}{-1} \\ 4x=x^3 \end{gathered}[/tex]Subtract 4x from both sides
[tex]\begin{gathered} 4x-4x=x^3-4x \\ 0=x^3-4x \end{gathered}[/tex]Switch the two sides
[tex]x^3-4x=0[/tex]Take x as a common factor
[tex]\begin{gathered} x(\frac{x^3}{x}-\frac{4x}{x})=0 \\ x(x^2-4)=0 \end{gathered}[/tex]Factor the bracket using the rule of the difference between two squares
[tex](a^2-b^2)=(a+b)(a-b)[/tex][tex]\begin{gathered} (x^2-4)=(x+2)(x-2) \\ x(x+2)(x-2)=0 \end{gathered}[/tex]Now, equate each factor by 0
[tex]\begin{gathered} x=0 \\ x+2=0,x-2=0 \\ x=-2,x=2 \end{gathered}[/tex]Substitute the values of x in the equation of the line to find their corresponding values of y
[tex]\begin{gathered} y=12-4(0)=12 \\ y=12-4(-2)=12+8=20 \\ y=12-4(2)=12-8=4 \end{gathered}[/tex]The points of intersection between the line and the curve are
(0, 12), (-2, 20), (2, 4)
Let us draw the graph
The red line represents the equation of the line
The blue curve represents the equation of the curve
To find the area bounded between the line and the curve we will use the integration
Since the line is above the curve at the point (-2, 20), then
We will subtract the curve from the line and use the values of x -2 and 2 as the limits of integration
[tex]A=\int_{-2}^2[(12-4x)-(12-x^3)]dx[/tex]Simplify the terms inside the brackets first.
[tex]\begin{gathered} A=\int_{-2}^2[12-4x+12+x^3]dx \\ A=\int_{-2}^2[-4x+x^3]dx \end{gathered}[/tex]In integration, we will add the power by 1 and divide the term by the new power
[tex]A=[\frac{-4x^{1+1}}{1+1}+\frac{x^{3+1}}{3+1}]_{-2}^2[/tex]Simplify it
[tex]\begin{gathered} A=[\frac{-4x^2}{2}+\frac{x^4}{4}]_{-2}^2 \\ A=[-2x^2+\frac{x^4}{4}]_{-2}^2 \end{gathered}[/tex]Substitute x by 2 and -2, then subtract the answer
[tex]A=[-2(2)^2+\frac{2^4}{4}]-[-2(-2)^2+\frac{(-2)^4}{4}][/tex]Solve each bracket
[tex]A=8[/tex]The area of the region bounded between the line and the curve is 8 square unit
In parallelogram FGHJ if m^GHJ=55° find m ^ FGH. I
Answers
Given:
[tex]m\angle GHJ=55^o\text{ and m}\angle FGH=x^o[/tex]Recall that the adjacent angles of the parallelogram are supplementary.
[tex]\begin{gathered} m\angle GHJ\text{ and m}\angle FGH\text{ are adjacent angles of the given parallelogram and these are supplementary.} \\ \end{gathered}[/tex]We know that the sum of the supplementary angles is 180 degrees.
[tex]m\angle GHJ+\text{m}\angle FGH=180^o[/tex][tex]55^o+x^o=180^o[/tex][tex]x^o=180^o-55^o[/tex][tex]x^o=125^o[/tex]Hence the answer is
[tex]\text{ m}\angle FGH=125^o[/tex]A car can travel 20 4/5 miles on 4/5 gallons of gas. What is the unit rate for miles per gallon
Answers
Answer:
26 miles per gallon
Step-by-step explanation:
[tex] \frac{20.8}{.8} = \frac{208}{8} = 26[/tex]
(x-8)(2x+5)=0 solve the equation
Answers
Solution:
Given the equation:
[tex](x-8)(2x+5)=0[/tex]To solve the equation, we use the zero factor principle.
From the zero factor principle, we have
[tex]\begin{gathered} When\text{ } \\ ab=0 \\ \Rightarrow a=0\text{ or b=0} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} x-8=0\text{ or 2x+5 =0} \\ when \\ x-8=0 \\ add\text{ 8 to both sides of the equation} \\ x-8+8=0+8 \\ \Rightarrow x=8 \\ when \\ 2x+5=0 \\ add\text{ -5 to both sides of the equation,} \\ 2x+5-5=0-5 \\ \Rightarrow2x=-5 \\ divide\text{ both sides by the coeffient of x, which is 2} \\ \frac{2x}{2}=\frac{-5}{2} \\ \Rightarrow x=-\frac{5}{2} \end{gathered}[/tex]Hence, the solution to the equation is
[tex]x=8,\text{ x=-}\frac{5}{2}[/tex]A home has a triangular backyard. The second angel of the triangle is 3 more than the first angel. The third angel is 9 more than four times the first angel.
Answers
The measure of three angles of triangular backyard are 28°, 31° and 121°.
Given that, a home has a triangular backyard.
What is the angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Let the measure of first angle be x.
The second angel of the triangle is 3 more than the first angel = x+3
The third angel is 9 more than four times the first angel = 4x+9
Using angle sum property of a triangle
x+x+3+4x+9 = 180°
⇒ 6x + 12 = 180
⇒ 6x = 168
⇒ x = 28°
So, x+3 = 31° and 4x+9 = 121°
Therefore, the measure of three angles of triangular backyard are 28°, 31° and 121°.
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Im stuck on question 5-91 in cpm geometry the question asks me to find the area of a triangle... I figured out the 30 60 90's are but i still have triangle left over ill send a photo of the triangle
Answers
Answer
Area of the triangle = 72 square units
Explanation
For a triangle whose two sides (a and b) are given, and an angle that exists between them is also given, the area of that triangle is given as
Area of the triangle = ½ ab Sin θ
For this question,
a = 12 units
b = 24 units
θ = 30°
Area of the triangle = ½ ab Sin θ
Area of the triangle = ½ (12) (24) (Sin 30°)
Sin 30° = 0.5
Area of the triangle = ½ (12) (24) (Sin 30°)
Area of the triangle = ½ (12) (24) (0.5) = 72 square units
Hope this Helps!!!
You are reducing a map of dimensions 24 in. by 36 in. to fit onto a piece of paper 8 in. by 10 in. What are the dimensions of the largest possible map that can fit on the page?
Answers
We have
scale factor
[tex]\frac{24}{36}=\frac{2}{3}[/tex]The largest side 10 in
Then we need to obtain the shortest side
[tex]\frac{2}{3}=\frac{x}{10}[/tex][tex]x=\frac{2\cdot10}{3}=\frac{20}{3}=6\frac{2}{3}[/tex]Therefore the dimensions of the largest possible map are
6 2/3 in by 10 in
Complete the description of how to find the sums −4 + 1 and −4 + (−1) on a number line.
To find −4 + 1, start at −4 and move 1 unit to the _____ to _____.
To find the sum −4 + (−1), start at −4 and move 1 unit to the ______ to ______
Answers
Integer Sums on a Number Line,
Start in the location that the first number denotes. Move the equivalent amount of units to the left if the second number is negative. Move that many units if it's affirmative.
How can I calculate the total on a number line?
Result for an image Fill in the blanks to describe how to locate the sums 4 + 1 and 4 + (1) on a number line. Start at 4, then move one unit to the ____ to ____ to find 4 + 1. Start at 4, then move 1 unit to the _____ to _____ to find the sum 4 + (1).
Utilizing a number line, combine two integers:
Make a number line first.
Next, locate the first integer's position on the number line.
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Due to temporary tax cuts in 2010, a person with typical deductions earning $50,000 per year would have saved 2% of their income plus $850 in federal taxes. How much money did a typical person save?
Answers
If the person earns $50,000, we must find how much is 2% of that and then add it to $850. Then we would have how much a typical person saves.
First let's find 2% of $50,000
[tex]\begin{gathered} 2\%\text{ of }50000=\frac{2}{100}\cdot500000=\frac{2\cdot50000}{100}=\frac{100000}{100}=1000 \\ \\ \\ \end{gathered}[/tex]Therefore 2% of $50,000 is $1000. Now we add it to $850 and we get
[tex]1000+850=1850[/tex]The final result is $1850
A medical survey was conducted in order to establish the proportion of the population which was infected with cancer. The results indicated that 40% of the population was suffering from the disease. A sample of 6 people was later taken and examined for the disease. Find the probability that the following outcomes were observed:
Only one person had the disease (4 mks)
Exactly two people had the disease (4 mks)
At most two people had the disease (4 mks)
At least two people had the disease (4 mks)
Three or four people had the disease (4 mks)
Answers
The probability that Only one person had the disease is 0.1866, Exactly two people had the disease is 0.311, At most two people had the disease is 0.0467, At least two people had the disease is 0.9533, Three or four people had the disease is 0.41472 for the given distribution.
What is Probability?
The probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.Given that,
n=6
P=40%=0.4
q=0.6
(i) P(X=1)=6C1(0.4)^1(0.6)^(6-1)
= 6X0.4X(0.6)^5
=0.1866
(ii) P(X=2)=6C2(0.4)^2(0.6)^(6-2)
=15X(0.4)^2X(0.6)^4
=0.311
(iii) P(X≥2)=1-P(X<2)
=1-[P(X=0)+P(X=1)+P(X=2]
P(X=0)=6C0(0.4)^0(0.6)^6-0
=0.0467
(iv) P(X≤2)= 1- P(X≥2)
=1-0.0467
=0.9533
(v)P(X=3)+P(X=4)=6C3(0.4)^3(0.6)^(6-3)+6C4(0.4)^4(0.6)^(6-4)
=6C3(0.4)^3(0.6)^(6-3)+6C4(0.4)^4(0.6)^(6-4)
=20X0.013824+15X0.009216
=0.41472
The probability that Only one person had the disease is 0.1866, Exactly two people had the disease is 0.311, At most two people had the disease is 0.0467, At least two people had the disease is 0.9533, Three or four people had the disease is 0.41472 for the given distribution.
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One of your classmates was absent on the day that you learned how to write and solve an equation from a contextual situation. Your teacher has asked you to explain the four steps and their application to the problem that follows.
Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, how many did Elena steal?
Using the four steps from this lesson, write and solve an equation to find the number of bases Elena stole.
Answers
e = number of bases stolen by Elena
So, n = 2e -3
So, if n=15, 15 = 2e-3 >>
e=9 bases stolen by Elena
The number of bases Elena stole is 9 if Natasha stole three fewer bases than twice the number Elena stole.
What is a linear equation?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.
It is given that:
Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases,
Let n be the number of bases stolen by Natasha
Let e be the number of bases stolen by Elena.
From the data given in the question:
The linear equation in two variables can be framed:
n = 2e -3
Plug n = 15
15 = 2e - 3
After solving:
e = 9
e = 9 bases stolen by Elena
Thus, the number of bases Elena stole is 9 if Natasha stole three fewer bases than twice the number Elena stole.
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If e-X = 6. write x in terms of the natural logarithm. O In 6 In -6 O -In 6 06
Answers
to cancel the exponential we apply natural log on both sides
[tex]\begin{gathered} \ln (e^{-x})=\ln 6 \\ -x=\ln 6 \end{gathered}[/tex]multiply -1 on each side
[tex]x=-\ln 6[/tex]The ceiling of Judy's living room is a square that is 15 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Judy can buy rolls that each contain 20 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.
Answers
Given the following question:
Judy's room is a square 15 feet long on each side
One roll of crepe paper equals 20 feet
[tex]\begin{gathered} \text{perimeter =} \\ 4\times s \end{gathered}[/tex][tex]\begin{gathered} 4\times15=60 \\ p=60ft \end{gathered}[/tex]The line she plans to hang the crepe paper from one corner to it's oppsite corner. So think about a X in the middle of the square. Since it's a square it will be particually smaller than the actual length of each side of the square.
[tex]60\div10=6[/tex]Let 10 represent the length of one side of the X
Let 60 represent the perimeter
Judy will need a minimum of 6 rolls of crepe paper for this party.
Which statements are true for the function y= \xi - 2? Select all that apply. The value of the function is never negative. Its graph has a V-shape There is only one input for which the output is 0. There are two inputs for which the output is 5 The vertex. of ts graph 13 81 (0.-2).
Answers
Explanation:
We need to check out each of the options to determine which of the statements are true:
The given function: y = |x| - 2
a) The symbol '| |' means absolute. So any number you put in it either positive or negative number,becomes positive after it is removed.
For example: if x = -2, y = |-2| - 2 = 2 -2 = 0
if x = -1, y = |-1| -2 = 1 -2 = -1
Hence from the example above, the value of the function can be negative.
Statement is wrong
b) Yes, the graph has a V shape: (statement is correct)
c) For the output to be 0, it means y = 0
Let's find out the value of x when y= 0
y = |x| -2
0 = |x| -2
0 + 2 = |x|
|x| = 2
|x| = x or -x
From the above we have only one x value (the input) which is 2
Statement is correct
d) For the output to be 5, y = 5
5 = |x| -2
|x| = -2 -5
|x| = -7
|x| = x or -x
x = -7 or -x = -7
x = -7 or x = 7
Mumbai is approximately
845
845845 kilometers
(
km
)
(km)left parenthesis, start text, k, m, end text, right parenthesis away from Bangalore, and Mumbai is approximately
1160
km
1160km1160, start text, k, m, end text away from Delhi. The distances, measured in centimeters
(
cm
)
(cm)left parenthesis, start text, c, m, end text, right parenthesis, between the cities on Allyson's map are proportional to the real distances
Answers
Answer:
A the answer is a
Step-by-step explanation:
btc u lied jj
Answer:
B, D, and E
Step-by-step explanation:
to whoever said btc u lied-
is also wrong : )
Solve the inequality.
-1/4 y > -6
Answers
Answer:
y < 24
Step-by-step explanation:
The inequality of -1/4 y > -6 is y< 24
Let's solve your inequality step-by-step.
[tex]\frac{-1}{4} > -6[/tex]
Step 1: Multiply both sides by [tex](\frac{4}{-1} )[/tex]
[tex]=(\frac{-1}{4}) (\frac{4}{-1} ), -6 (\frac{4}{-1} )\\= y < 24\\[/tex]
Answer y< 24
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What is the answer to 4.18 + 86.53=
Answers
Answer:
90.71
Step-by-step explanation:
Just columnar addition
On a coordinate plane, each point on ST is defined by coordinates (x,y). The segmentis rotated 90° counterclockwise to create S'T'. Which of the following defines a pointon S'T' that corresponds to a point on ST.
Answers
The coordinates of S'T' are (-y,x)
Here, we want to get the result of rotating a point 90 degrees counterclockwisely
What we have here is that we will have a change in the coordinates of the point as follows;
[tex](x,y)\Rightarrow\text{ (-y,x)}[/tex]eleven is fifteen more than four times a number.
translate to an equation. let x be the unknown number . solve for x
Answers
The equation is 15+4x= 11 and the value for x= -1
what are equations?An equation is a mathematical statement between two expressions that have equal values. For example, 15+4x= 11. The symbol = shows that 11 and 15+4x are the same
Word problems can be translated into equation with variables.
Representing the unknown with x,
4×x= 4x
the word problem is therefore translated to
11= 15+4x
collecting like terms
4x= 11-15
4x= -4
divide both side by 4
x=-1
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the blank of a fraction is the part that tells how many units the fraction contains
Answers
Answer:
The Denominator of a fraction is the part that tells how many units the fraction contains.
(Got it from another Expert-Verified answer)
Answer:
Step-by-step explanation:
numerator
What is 1/4 x 3
Give it's answer in its simplest form
Answers
================================================
Explanation:
Think of 3 as 3/1. Then multiply the numerators together separate from the denominators being multiplied together
(1/4)*(3/1) = (1*3)/(4*1) = 3/4
------------------
An alternative route
1/4 x 3 means we have 3 copies of 1/4 being added
1/4 + 1/4 + 1/4 = (1+1+1)/4 = 3/4
------------------
If you are a visual learner, draw a circle and split it into 4 equal pizza slices. Shade 1 out of the 4 to represent 1/4.
Imagine that you did this 3 times. That would mean you have 3 shaded slices. Each slice represents 1/4, so you would have 3/4 of the total pizza.
Put another way: you have 3 friends who get 1/4 of a pizza each. That shades 3 out of the 4 total slices to get 3/4.
If f(x) = 5x+27, find the instantaneous rate of change of f(x) at x=9
Answers
The instantaneous rate of change refers to the derivative of f(x), so let's find that first, following the power rule, we have.
[tex]f^{\prime}(x)=1\cdot5x^{1-1}=5x^0=5\cdot1=5[/tex]As you can observe, the instantaneous rate of change is a constant, which means we don't have to evaluate it at x=9.
Therefore, the instantaneous rate of change is f'(x) = 5.the measure of an interior angle of a regular polygon is given. find the number of sides in a polygon. show work. Number 8.
Answers
Given the following interior angle of a regular polygon:
[tex]120\degree[/tex]You need to remember that, by definition, a regular polygon is a polygon whose sides have all equal lengths.
Therefore, you can apply the following formula:
Where "n" is the number of sides of the polygon and β is the measure of one interior angle of the polygon.
Knowing that, in this case:
[tex]\beta=120\degree[/tex]Therefore, you can substitute this value into the formula and solve for "n":
[tex]\begin{gathered} 120=\frac{(n-2)\cdot180}{n} \\ \\ 120n=180n-360 \end{gathered}[/tex][tex]\begin{gathered} 120n-180n=-360 \\ \\ -60n=-360 \\ \\ \\ n=\frac{-360}{-60} \end{gathered}[/tex][tex]n=6[/tex]Hence, the answer is:
[tex]n=6[/tex]
Select the statement that correctly compares two numbers. (2 points)
Group of answer choices
4.09 = 4.90
2.03 < 2.021
1.470 > 1.70
0.36 > 0.187
Answers
Answer:
the last one
Step-by-step explanation:
you have to look at which number is bigger than the other
it usually depends which number is first
ex:
3>1
0.3>0.1
0.3>0.12
What is the slope of BC in the simplest form?
Answers
Explanation:
The slope of BC can be calculated
Slope = rise/run
In this case, the rise is the height of the blue triangle and the run is the base of the blue triangle, so
Slope = 2/6 = -2/6
To simplify the slope, we need to divide by 2, so
[tex]\text{Slope}=-\frac{2\div2}{6\div2}=-\frac{1}{3}[/tex]Find all Polar coordinates of point P where P= (5,-π/6)
Answers
Given :
[tex]P\text{ = (5, }\frac{-\pi}{6})[/tex]Required: All polar coordinates of the given point
We can have the following points:
[tex]\begin{gathered} (5\text{ , }\frac{-\pi}{6}\text{ + 2n}\pi)\text{ or (-5 ,( }\pi-\frac{-\pi}{6}+\text{ 2n}\pi)\text{ )} \\ \text{This simplifies to } \\ (5\text{ , }\frac{-\pi}{6}\text{ + 2n}\pi)\text{ or (-5, (}\frac{-\pi}{6}\text{ + (2n + 1)}\pi) \end{gathered}[/tex]The correct option is the third option
Why is unit rate the only attribute we use to compare proportional relationships? Consider the graph of a
proportional relationship and the attribute(s) that all proportional relationships share to help you answer this
question.
Answers
Answer:
Step-by-step explanation:
Because its an internationally accepted method.
a right triangle ABC is shown below the area of the triangle above will equal 1/2 of the rectangle that is 5 units long and underscore units wide
Answers
for the ahe area of triangle
Height of the triangle = 2 units, base= 5 unit
Area of triangle =1/2 Breadth x height
Susbtitute the value and simplify:
[tex]\begin{gathered} \text{ area of triangle=}\frac{1}{2}\times2\times5 \\ \text{ area of triangle= }5\text{ units} \end{gathered}[/tex]Answer =5 units
