The explicit and recursive forms of the arithmetic sequence are f(n) = 2 - 6 · (n - 1) and f(n) = f(n - 1) - 6, f(1) = 2, respectively.
How to derive equations for the elements of an arithmetic sequence
In this problem we need to find the explicit and recursive equations for an arithmetic sequence, whose definitions are described below:
Explicit form
f(n) = a + r · (n - 1)
Recursive form
f(n) = f(n - 1) + r, f(1) = a
Where:
a - First element of the sequence.r - Common difference.n - Index of the n-th element of the sequence.If we know that a = 2, r = - 6, then the explicit and recursive forms of the sequence are:
Explicit form
f(n) = 2 - 6 · (n - 1)
Recursive form
f(n) = f(n - 1) - 6, f(1) = 2
The first four elements of the sequence generated by the formulas are 2, - 4, - 10, - 16.
To learn more on arithmetic sequences: https://brainly.com/question/10396151
#SPJ1
give the coordinates of the image of each point under a reflection across to given line.(0,8); y=x
Answer:
(8, 0)
Explanation:
Whenever a point (x,y) is reflected across the line y=x, the transformation rule is given below:
[tex](x,y)\to(y,x)[/tex]That is, the x-coordinate and y-coordinate change places.
Therefore, the image of the point (0,8) when reflected across the line y=x is:
[tex](8,0)[/tex]The correct answer is (8,0).
A triangle has angle measurements of 15°, 90°, and 75°. What kind of triangle is it?
The triangle has one angle of 90 degrees, so it is a rigth triangle.
As the other two angles are different between them, the triangle is also scalene (all sides are different)
.
2. (5 points) A very special island is inhabited only by knights and knaves. Knights always tell
the truth, and knaves always lie. You meet two inhabitants: Sue and Marge. Sue says that
Marge is a knave. Marge claims. "Sue and I are not the same." Determine who is a knight and
who is a knave.
Answer:
Sue is knave and Marge be knightStep-by-step explanation:
Let Sue be knight and Marge be knave.
Sue says: "Marge is a knave". Since Sue is knight, she is right and Marge should lie.
Marge says: "Sue and I are not the same." - this is right answer too, so this is not a correct response and our assumption is wrong.
Now, let Sue be knave and Marge be knight. Then Marge's response is right and Sue's is wrong. This is a match and this assumption is correct.
The given diagram shows the steps for constructing a parallel line to line AB and passing through point P, but an error has occurred in the construction
Given:
Constructing a parallel line to line AB and passing through point P.
To find:
The error occurred in the construction.
Explanation:
The procedure is,
The first arc must be drawn centred at C.
The second must be drawn centred at P.
Finally, the third arc must be drawn centred at F.
But here, the third arc is drawn centred at D. This is wrong.
Therefore, the correct step is that the third arc must be centred at F.
Final answer:
The third arc should be drawn centred at F.
Not sure on how to do this. Would really like some help.
Given:
[tex]\cos60^{\circ}[/tex]To find:
The value
Explanation:
We know that,
[tex]\cos\theta=\sin(90-\theta)[/tex]So, we write,
[tex]\begin{gathered} \cos60^{\circ}=\sin(90-60) \\ =\sin30^{\circ} \\ =\frac{1}{2} \end{gathered}[/tex]Final answer:
[tex]\cos60^{\circ}=\frac{1}{2}[/tex]how many km/h equals 880ft/min? Explain how you solved this problem
The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour
How does km/h relate to ft/ min?Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.
In other words, 1 km / h is equal to 54.6807 feet per minute.
If there are 880 ft / minute therefore, the number of kilometers per hour is:
= Speed in feet per minute / feet per minute per kilometer per hour
= 880 / 54.6807
= 16.09 kilometers per hour
Find out more on kilometers per hour at https://brainly.com/question/17263672
#SPJ1
I’m doing conversions and need to convert from years to months
Answer:
There are 126 months in 10 years and 6 months.
Explanation:
In a year there are 12 months.
[tex]1\text{ }year=12\text{ }months[/tex]Then, to know how many months are in 10 years, we multiply by 10:
[tex]10\cdot1\text{ }year=10\cdot12\text{ }months[/tex][tex]10\text{ }year=120\text{ }months[/tex]Now we add the additional 6 months:
[tex]120+6=126\text{ }months.[/tex]The answer is 126.
3.50 divide by 24.50
Answer:
1/7 or 0.143
Step-by-step explanation:
i hope this helps
What’s the correct answer asap for brainlist
Answer:
Step-by-step explanation:its a 69420 dum as
Which comparison is NOT correct?2 > -3-7 < -5-9 < 10 < -4
0 > -4 is incorrect
as -4 is a negative number and it comes on the left of 0 on a number line
and we know number increase from left to right
so option D is the answer.
Answer this question and show me how to check it
We write numbers that are very small or very large in standard form. Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form
Given that the length and thickness as
[tex]\begin{gathered} l=8\times10^4 \\ t=5\times10^{-6} \end{gathered}[/tex]The ordinary form of the wire is
[tex]\begin{gathered} l=8\times10^4m=8\times10000m=80000m \\ t=5\times10^{-6}m=5\times\frac{1}{1000000}m=0.000005m \end{gathered}[/tex]From the defination of standard form, taking the length, 8 is a number between 1.0 and 10.0 and 10⁴m is a power of 10.
Also, the width, 5 is a number between 1.0 and 10.0 and 10 ⁻⁶ is a power of 10.
Hence, the standard form of the length and thickness of the wire is
length = 8.0 x 10⁴m
thickness = 5.0 x 10 ⁻⁶m
A country with 16 states and a population of 615529 contains 128 seats in a House of Representatives.What is the average number of seats assigned per state?
Since there are 128 seats available and these 128 seats will be filled in by people from 16 states, we will divide 128 by 16 to get the average number of seats assigned per state.
[tex]128\div16=8[/tex]Therefore, the average number of seats assigned per state is 8.
how do you simplify this complex fraction in the lowest terms
[tex]\frac{77x^9/15y^5}{7x^7/10y^4}[/tex]
Answer:
[tex]\frac{22x^{2}}{3y}[/tex]
Step-by-step explanation:
[tex]\frac{(77x^{9})(10y^{4}) }{(7x^{7})(15y^{5}) }[/tex]
[tex]\frac{(11x^{2})(2)}{3y}[/tex]
a diver takes a dive in the red sea. He initially descends 100 feet. Then rises 28 before descending another 33. What is his final position
Descending: subtraction
Rises: Addition
The diver descends 100ft: Position -100 (the 0 is the sea level)
Then rises 28: Add 28 to the previous position: Position -72
[tex]-100+28=-72[/tex]...before descending another 33: Subtract 33 to the previous position:
[tex]-72-33=-105[/tex]Then, the final position is -105ft (105 ft under the sea level)
In triangle XYZ, | XZ | = | YZ | ∆YXZ = 40⁰ and ∆XZY = (13x - 20)⁰. Find the value of x.
Given the triangle XYZ with the following parameters
[tex]\begin{gathered} |XZ|=|YZ| \\ \measuredangle YXZ=40^0 \\ \measuredangle XZY=(13x-20)^0 \\ \text{Therefore} \\ \measuredangle ZYX=40^0 \end{gathered}[/tex]The diagram of the triangle is shown below
To find the value of x, we will apply sum of interior angle of triangle theorem
[tex]\begin{gathered} 40^0+40^0+(13x-20)^0=180^0(\text{ sum of angles in a triangle)} \\ 80^0+13x-20^0=180^0 \\ 13x+60^0=180^0 \\ 13x=180^0-60^0 \\ 13x=120^0 \\ x=\frac{120^0}{13} \\ x=9.2308^0 \end{gathered}[/tex]Hence, the value of x is 9.2308°
A tub of theater popcorn has 247.5 grams of popcorn, which is 275% larger than a regular bag of popcorn. How many grams of popcorn would be in a regular sized bag.
Let's begin by listing out the information given to us:
A tub has this: 247.5 grams of popcorn = 275%
regular-sized bag: x grams = 100%
We will solve using simple proportion
[tex]\begin{gathered} 247.5g=275 \\ xg=100 \\ \text{Cross Multiply, we have:} \\ 247.5\cdot100\cdot g=275\cdot x\cdot g \\ \text{Make x the subject of formula (divide by 275g)} \\ \frac{247.5\cdot100\cdot g}{275\cdot g}=\frac{275\cdot x\cdot g}{275\cdot g} \\ 0.9\cdot100=x\Rightarrow x=900 \\ x=900g \end{gathered}[/tex]Describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. Look at image for example. Let’s do problem number 11
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given functions.
[tex]\begin{gathered} f(x)=-(x+5)^2-6 \\ h(x)=\frac{1}{3}f(x) \end{gathered}[/tex]STEP 2: Explain the transformation that occurs
What are Vertical Stretches and Shrinks?
While translations move the x and y intercepts of a base graph, stretches and shrinks effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without altering its shape. When a graph is stretched or shrunk vertically, the x -intercepts act as anchors and do not change under the transformation.
This can be explained further as:
For the base function f (x) and a constant k > 0, the function given by:
[tex]\begin{gathered} h(x)=k\cdot f(x) \\ A\text{ vertical shrinking of f\lparen x\rparen by k factor where }0Calculate the equation that represents h in terms of x[tex]\begin{gathered} f(x)=-(x+5)^2-6 \\ h(x)=\frac{1}{3}\cdot f(x)=\frac{1}{3}\cdot-(x+5)^2-6 \end{gathered}[/tex]Hence, the transformation from the graph is a vertical shrinking by 1/3 factor and the equation that represents h in terms of x is given as:
[tex]\frac{1}{3}\times(-(x+5)^2-6)[/tex]Triangle BCA is similar to Triangle STR . What is the value of x?
Sin the triangles are similar the ratio 4 to 6 should hold for any side, this means that:
[tex]\frac{4}{6}=\frac{x}{9}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{9} \\ x=9(\frac{4}{6}) \\ x=\frac{36}{6} \\ x=6 \end{gathered}[/tex]Therefore. x=6.
In the diagram below of AGJK, H is a point onGJ, HJ = JK, m2 = 28, and mZGJK = 76.What is mZGKH?2870H
Problem
Solution
For the triangle GKJ we can find the angle K on this way:
28 +70 + Now we know that HJ= JK so then the triangle HJK is an isosceles triangle so then < JHK = < HKJ and we can do this:
70+ 2x = 180
2x= 110
x= 55
And then we can find the angle < GKH with the following equation:
28+70 + (55+y) = 180
y= 180-55 -28-70= 27
A spinner can land on either red or blue You spin seven times and then roll a six sided die. Find the number of possible outcomes in the sample space?
If we spin the spinner once, we can get two possible outcomes (red or blue).
If we spin it twice, the outcomes can be (blue, blue), (blue, red), (red, blue), (red, red); this is, 4 different results.
Then, if we spin the spinner 7 times, there are 2^7=128 possible outcomes.
Finally, we can get any of the 128 possible outcomes from the spinner and rolling a 1; similarly, for rolling a 2, 3,..., 6.
Therefore, the number of possible outcomes of spinning the spinner seven times and rolling a die is
[tex]2^7\cdot6=128\cdot6=768[/tex]There are 768 possible outcomes in the sample space.
WITHOUT using a graphing device, find the x- and y-intercepts of the graph:y = 3x^3 - 9x^2
Given:
The function is,
[tex]y=3x^3-9x^2[/tex]To find the x intercept set y=0,
[tex]\begin{gathered} y=3x^3-9x^2 \\ 3x^3-9x^2=0 \\ x^2(3x-9)=0 \\ \Rightarrow x^2=0,3x-9=0 \\ x=0,3x=9 \\ x=0,x=\frac{9}{3} \\ x=0,x=3 \end{gathered}[/tex]So, x-intercepts are ( 0 , 0 ), ( 3, 0 ).
Now to find y-intercepts set x=0.
[tex]\begin{gathered} y=3x^3-9x^2 \\ y=3(0)-9(0) \\ y=0 \end{gathered}[/tex]y- intercept is ( 0 ,0 )
Answer: option e)
Each face of a pyramid is an isosceles triangle with a 70 degree vertex angle. What are the measures of the base angles?
We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:
Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:
[tex]70+x+x=180[/tex]Adding like terms, we get:
[tex]70+2x=180[/tex]Now we solve for "x", first by subtracting 70 on both sides:
[tex]\begin{gathered} 70-70+2x=180-70 \\ 2x=110 \end{gathered}[/tex]Now we divide both sides by 2
[tex]x=\frac{110}{2}=55[/tex]Therefore, the base angles of the pyramid are 55 degrees.
Describe the correlation in the scatter plot below.----------------The scatter plot shows (positive linear, positive linear with one outlier, negative linear, negative linear with one outlier, nonlinear, or no) correlation because as the plotted values of x increase, the values of y generally (decrease, increase, show no pattern or follow a nonlinear pattern).
A scatter plot shows a positive correlation when the values of y tend to increase as the values of x increases.
From this scatter plot, we can see that as the values of x increase, the values of y also increase. Therefore, this scatter plot shows a positive linear correlation.
An outlier is the the dot which doesn't fit with other dots or is far away from the rest of the dots. Here, we have one outlier.
Therefore, we can say the scatter plot shows positive linear with one outlier correlation because as the plotted values of x increase, the values of y generally increase.
ANSWER:
The scatter plot shows positive linear with one outlier correlation because as the plotted values of x increase, the values of y generally increase.
If the m< P is 65 degrees, then what is the measure of Arc XY
Answer:
[tex]\text{ArcXY}=115\text{ degrees}[/tex]Step by step explanation:
We can solve this situation by the theorem of the angle formed outside of a circle by intersection:
*For two tangents:
[tex]mThen, if m
[tex]\begin{gathered} 65=\frac{1}{2}((360-mXY)-mXY) \\ 65=\frac{1}{2}(360-\text{mXY-mXY)} \\ 65=\frac{1}{2}(360-2\text{mXY)} \\ 65=180-\text{mXY} \\ \text{mXY}=180-65 \\ \text{mXY}=115 \end{gathered}[/tex]
Number 5 need help I really forgot how to solve this problem
Line Segments and Rays
A line segment has two endpoints. It contains these endpoints and all the points of the line between them,
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
The figure shows a line that starts in B and goes infinitely to the left side, passing through A, thus the correct choice is B. Ray BA
write the slope intercept form:through: (2, 5), perp. to y= -5
If the original line is y = -5, then the perpendicular line would be x = a, where a is the x value of the point where it passes through, then the line is x = 2
Answer:
x = 2
How to write slope intercept form
Answer:
See below
Step-by-step explanation:
If you are given slope (m) and intercept (b) , then write the line equation like this:
y = mx + b
A scale drawing of a game room is shown below:A rectangle is shown. The length of the rectangle is labeled 2 inches. The width of the rectangle is labeled 4.5 inches. The scale is 1 to 30.What is the area of the actual game room in square feet? Round your answer to the nearest whole number.9 ft223 ft256 ft2270 ft
The scale factor from the drawing to the room is 1 to 30. Then, multiply the dimensions of the drawing by 30 to obtain the real dimensions of the room. Then, use the real values to find the area of the room.
Since the length is labeled 2 inches, the real length of the room is:
[tex]2in\times30=60in[/tex]Since the width is labeled 4.5 inches, the real with of the room is:
[tex]4.5in\times30=135in[/tex]1 foot is equal to 12 inches. Then, divide the dimensions by 12 to find the measurements in feet:
[tex]\begin{gathered} 60in=60in\times\frac{1ft}{12in}=5ft \\ \\ 135in=135in\times\frac{1ft}{12in}=11.25ft \end{gathered}[/tex]Multiply the width and the length to find the area of the room:
[tex]A=(5ft)(11.25ft)=56.25ft^2\approx56ft^2[/tex]Therefore, to the nearest whole number, the area of the game room is 56ft^2.
a. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 48 and 51 months?b. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 64?
In this case
[tex]\begin{gathered} 48=45+3 \\ 51=45+2(3) \end{gathered}[/tex]Therefore, the percentage that lies between 45 and 48 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]And, the percentage that lies between 45 and 51 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]Real numbersA stock lost 8 and 3/8 on Monday, 1 and 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stocks for these three days?
Answer: The net gain was 3 stocks for these three days.
Explanation
Given
• Monday: lost 8 and 3/8.
,• Tuesday: lost 1 and 5/8 points.
,• Wednesday: gained 13 points.
Procedure
To calculate the net gain, we have to add all the values we are giving, considering that the stock lost will have a negative sign:
[tex]\text{Net gain}=Gains-losses[/tex]0. Calculating the losses
We have to mixed numbers, for which we can add the whole numbers and the fractions separately.
• Whole numbers
[tex]-8-1=-9[/tex]• Fractions
[tex]-\frac{3}{8}-\frac{5}{8}=-\frac{8}{8}=-1[/tex]At last, we add both results and we get the losses:
[tex]losses=-9-1=-10[/tex]2. Calculating the gains
As we only have one quantity, there is no need for calculations:
[tex]Gains=13[/tex]3. Calculating net gain
Finally, we put both quantities in the formula:
[tex]\text{Net gain}=13-10=3[/tex]