Answer:
The common difference equals:
[tex]-3[/tex]
The sum of the sequence equals:
[tex]62[/tex]
The explicit formula of this sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
The recursive formula of this sequence is:
[tex]a_n=a_((n-1))-3[/tex]
The nth terms:
[tex]20,17,14,11,8,5,2...[/tex]
Step-by-step explanation:
An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference.
1. Find the common difference.Find the common difference by subtracting any term in the sequence from the term that comes after it.
[tex]a_2-a_1=17-20=-3\\a_3-a_2=14-17=-3\\a_4-a_3=11-14=-3[/tex]
The difference of the sequence is constant and equals the difference between two consecutive terms.
[tex]d=-3[/tex]
2. Find the sum.Calculate the sum of the sequence using the sum formula:
Formula
[tex]Sum=\frac{(n(a_1+a_n))}{2}[/tex]
Plug in terms
[tex]Sum=(4*(a_1+a_n))/2[/tex]
[tex]Sum=(4*(20+a_n))/2[/tex]
[tex]Sum=(4*(20+11))/2[/tex]
Simplify the expression
[tex]Sum=(4*(20+11))/2[/tex]
[tex]Sum=(4*31)/2[/tex]
[tex]Sum=124/2[/tex]
[tex]Sum=62[/tex]
The sum of this sequence is [tex]62[/tex].
This series corresponds to the following straight line [tex]y=-3x+20[/tex]
3. Find the explicit form.The formula for expressing arithmetic sequences in their explicit form is:
Formula: [tex]a_n=a_1+(n-1)*d[/tex]
Plug in the terms.
[tex]a_1=20[/tex] (this is the 1st term)
[tex]d=-3[/tex] (this is the common difference)
[tex]a_n[/tex] (this is the nth term)
[tex]n[/tex] (this is the term position)
The explicit form of this arithmetic sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
4. Find the recursive form.The formula for expressing arithmetic sequences in their recursive form is:
Formula: [tex]a_n=a_((1-n))+d[/tex]
Plug in the d term.
[tex]d=-3[/tex](this is the common difference)
The recursive form of this arithmetic sequence is:
[tex]a_n=a_((n-1))-3[/tex]
5. Find the nth element.[tex]a_1=a_1+(n-1)*d=20+(1-1)*-3=20[/tex]
[tex]a_2=a_1+(n-1)*d=20+(2-1)*-3=17[/tex]
[tex]a_3=a_1+(n-1)*d=20+(3-1)*-3=14[/tex]
[tex]a_4=a_1+(n-1)*d=20+(4-1)*-3=11[/tex]
[tex]a_5=a_1+(n-1)*d=20+(5-1)*-3=8[/tex]
[tex]a_6=a_1+(n-1)*d=20+(6-1)*-3=5[/tex][tex]a_7=a_1+(n-1)*d=20+(7-1)*-3=2[/tex]
Terms and topics:
Artithmetic Sequences
What is the image of (-4,-2) after a reflection over the line y = -x?
Answer:
(2, 4).
Step-by-step explanation:
For y = -x the transform is:
( x, y ) reflects to (-y, - x)
So (-4, -2) reflects to (2, 4)
What does 2k^4 * 10k^-7 equal?
Answer:
0.0000016k
Step-by-step explanation:
1. Solve
2k^4x10k^-7
16k*0.0000001k
0.0000016k
PLEASE HELP I NEED IT NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
what is the problem ? you teacher gave you even the conversion rates in the question.
so, when 1 gallon = 3.79 liters, then how much is 4 gallons ?
4 gallons is 4 times 1 gallon. so, of course, we need to apply the same factor to the other side too.
4 gallons = 4×3.79 = 15.16 ≈ 15 liters
and e do the same for all the other table elements :
8 liters = 8×0.26 = 2.08 ≈ 2 gallons
12.5 liters = 12.5×0.26 = 3.25 ≈ 3 gallons
6 gallons = 6×3.79 = 22.74 liters ≈ 23 liters
9. A man bought a calculator for Rs 1450 and sold at a loss of 12% Find the loss amount Hi. Find the selling price of the calculator.
Loss amount:-
12% of 14500.12(1450)₹174Hence
Selling price:-
Price-loss1450-174₹1276Answer:
1276 rupees
Step-by-step explanation:
Given
Price = 1450Loss % = 12%Solving
Selling price = 1450 x (100 - 12%) [as it a loss]1450 x 88%1450 x 0.881276 rupeesThe following graph shows the low temperatures for the past six nights. What was the low temperature for Saturday?
Answer:
31° F
Step-by-step explanation:
Although it is hard to see, Saturday's low temperature is approximately 31°. This is evident in its relative position to Friday's temperature, which measures 30° F -- Saturday is just one degree higher.
Hope this helps!
Answer:31
Step-by-step explanation:
help mean is 7.8 and standard deviation is 1 will give brainly
Answer:
a) Mean shoe size = 7.8
b) 8.8, 9.8 and 10.8
c) see attached
d) Shoe size
Step-by-step explanation:
[tex]\sf Mean \ \mu= 7.8[/tex]
[tex]\sf Standard \ deviation \ \sigma= 1[/tex]
Therefore,
[tex]\sf 1 \sigma=\mu+1 \sigma=7.8+1=8.8\\\sf 2 \sigma=\mu+2 \sigma=7.8+2 \cdot 1=9.8\\\sf 3 \sigma=\mu+3 \sigma=7.8+3 \cdot 1=10.8[/tex]
find the x !
please hurry! Thank you!
Step-by-step explanation:
2x+98=180° (angles in straight line )
2x=180-98
x=2/2
x=1
Answer:
x = 41
Step-by-step explanation:
the 2 angles are adjacent and sum to 180° , that is
2x + 98 = 180 ( subtract 98 from both sides )
2x = 82 ( divide both sides by 2 )
x = 41
I have a proof and I need help!
Answer:
Step-by-step explanation:
Find the slope of the line containing the points (-2, -3) and (-4, 1).
Answer:
- 2
Step-by-step explanation:
Slope, m = (y1-y2)/(x1-x2)
= ( -3 -1)/(-2- -4) =
-4 / ( 2) = - 2
Sloep:-
m=1-(-3)/-4-(-2)m=1+3/-4+2m=4/-2m=-2can someone help me with this?
Answer:
66°
Step-by-step explanation:
mJK = ( 6x - 45 )°
mJH = ( x + 20 )°
mJK = mJH
6x - 45 = x + 20
5x = 65
x = 13
mHK = ( x + 20 )° + ( 6x - 45 )°
mHK = 2 × 33° = 66 °
Help!!!!
The line segments in the circle to the right are both diameters with
length 2. Find the area of the white region. Leave your answer in
terms of pie
Answer:
pi/4
Step-by-step explanation:
diameter of the circle is 2
area of circle = pi * r^2
A = pi * 1^2
A = 1pi
1/4th of the area so
pi/4
Two numbers have a product of -36
They have a sum of -5
What are the two numbers?
Answer:
-9,4
Step-by-step explanation:
The following box plot shows the class scores on a particular math test:
10
20
30
70
80
90
100
40 50 60
Percent
Which of the following data sets is represented in the box plot?
{40, 50, 50, 77, 77, 100)
{0.50, 60, 75, 85, 100)
{50, 60, 60, 75, 75, 85, 85, 100)
[60, 65, 70, 75, 85, 85, 85)
Answer:
maybe the third one and i would also like to see the box plot
Step-by-step explanation:
DIRECTIONS: Type your answer in the space provided. The slope must be in fraction form.
What is the equation of the line parallel to the given line through the point (14,0)?
-4x - 7y = 14
help me with this question also
[tex]\text{Given that,}\\\\[/tex]
[tex]~~~~~~~\cos \theta = \dfrac 89\\\\\\\implies 2\cos^2 \left(\dfrac{\theta}2 \right) -1 = \dfrac 89~~~~~~;\left[1+ \cos 2\theta = 2\cos^2 \theta \right]\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)= \dfrac 89 +1\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)=\dfrac{17}9\\\\\\\implies \cos^2 \left(\dfrac{\theta}2 \right) = \dfrac{17}{18}\\\\\\\implies \cos \left(\dfrac{\theta}2 \right)=\sqrt{\dfrac{17}{18}}~~~~~~~~~~~;\left[\text{Positive value of} ~\cos \left(\dfrac{\theta}2\right) \right][/tex]
[tex]\implies \cos \left(\dfrac{\theta} 2 \right) =\dfrac{\sqrt{17}}{\sqrt{9 \times 2}}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17}}{3\sqrt 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17} \cdot \sqrt 2}{3\cdot 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{34}}{6 }[/tex]
25. The sales tax rates 7.25
Part A How much taxis added on an item that costs $56.007
Part B $36.25 in taxis added to the price of an item, what was the original price of the item? pie y pie
Answer:
A:60.14
B:3,379.95
Step-by-step explanation:
I assume that .007 is supposed to be .07
56.07*1.0725=60.14
B.
36.25 is 1.0725 of ...
3,379.95
36.25 * 0.010725
Jack hit a baseball on 13 out of 30 tries during practice. what is the experimental probability that he will hit the ball on his next trial write your answer as a fraction as a decimal and as a percent
Answer:
Fraction: 13/30
Decimal: 0.43
Percentage: 43%
The shortest leg of a 30-60-90 triangle is 5 inches. How long is the hypotenuse?
10 inches
10√2 inches
10√3 inches
5√2 inches
Answer:
the 2nd one
Step-by-step explanation:
i did the test and got correct
Find the perimeter of the composite figure
Answer:
104+16π
Step-by-step explanation:
Triangle Formula is bh1/2
Rectangle is lxw
Semicircle is 1/2 π r^2
find Y thanks don’t be guessing cuz girl
Answer:
3 inches
Step-by-step explanation:
It's like 2 inches, but a little bigger.
Hope this helps and is correct.
Btw it's my birthday.
& What value of x satisfies the system of equations below!
x+2y= 11
4x - y = 8
Answer:
[tex]\boxed{\sf{x=3 \quad y=4}}[/tex]Step-by-step explanation:
Isolate the term of x and y from one side of the equation.
x+2y=11 and 4x-y=8⇒ x+2y=11
⇒ x=11-2y
Substitute.
4(11-2y)-y=8
Solve.
Distributive property:
⇒ A(B+C)=AB+AC
4(11-2y)
4*11=44
4*2=8
Rewrite the problem down.
44-9y=8
Subtract by 44 from both sides.
44-9y-44=8-44
Solve.
-9y=-36
Divide by -9 from both sides.
-9y/-9=-36/-9
Solve.
-36/-9=4
y=4
Substitute of y=4.
⇒ x=11-2*4
Use order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract11-2*4
Multiply.
2*4=8
Rewrite the problem down.
11-8
Subtract.
11-8=3
x=3
Therefore, the correct answer is x=3 and y=4.I hope this helps you! Let me know if my answer is wrong or not.
The first rule is add 12, then divide by 2 starting from 4. The second rule is multiply by 2, then subtract 2 starting from 3. What are the first four ordered pairs using the two sequences? (4, 4), (8, 6), (10, 10), (11, 18) (0, 4), (3, 6), (4, 10), 5, 18) (4, 3), (8, 4), (10, 6), (11, 10) (0, 3), (3, 4), (4, 6), (5, 10). I WILL MARK BRAINLIST. MY BROTHER NEEDS HELP WITH MATH LOLOLOLOLOLOLOLOLOLOLOLOLOL
Answer:
(03,)(4,4(4,6),(5,10)
Step-by-step explanation:
I’m smart I have an A + so it’s correct
Use the formula for radian measure to calculate the measure of a central angle in a circle having a radius of 12 cm and intercepting an arc of 21 cm. theta = startfraction s over r endfraction the angle has a measure of radians.
The central angle has a measure of radians calculated by the formula for radian measure is 1.75 radians.
What is the formula for radian measure?The formula for radian measure to calculate the central angle is given as,
[tex]\theta=\dfrac{s}{r}[/tex]
Here, (r) is the radius of the circle and (θ) is the central angle.
In a circle having a radius of 12 cm and intercepting an arc of 21 cm. Put the value of radius and the length of the arc in the above formula as,
[tex]\theta=\dfrac{21}{12}\\\theta=1.75[/tex]
Thus, the central angle has a measure of radians calculated by the formula for radian measure is 1.75 radians.
Learn more about the radian measure formula here;
https://brainly.com/question/12939121
Answer:1.75 radians
Step-by-step explanation: edge
Locate root 9.8 on number line
Answer: See attached
Step-by-step explanation:
"Root 9.8" means the square root of 9.8, [tex]\sqrt{9.8}[/tex].
Since we are being asked to find it on the number line, I am guessing they want us to estimate. We know that the square root of 9, [tex]\sqrt{9}[/tex], is equal to 3. Since 9.8 is slightly bigger than 9, the square root of 9.8 will be a little bit over 3.
Want to confirm? Using a calculator for the square root of 9.8 gives us 3.13.
Help me please I don’t know what to do
Answer:
You didn't include the question, so people are unable to help you.
Solve for X. Its geometry, will mark branliest
Answer:
x=4
Step-by-step explanation:
right triangle calculator works well
A can of vegetables is 4.5 in. high and has a diameter of 3 in. Find the volume of the can to the nearest tenth of a unit. Use 3.14 for π.
Answer:
i dont know i tried really really hard i wish i could help
Step-by-step explanation:
Which expression is equivalent to 8 (a minus 6)?
8 a minus 48
2a
8 a minus 6
48a
Answer:
8 a minus 48
Step-by-step explanation:
you need to distribute!!
so you distribute the 8 to both the a and 6
8 times a equals 8 a
8 times 6 equals 48
and so that’s how you get 8 a minus 48 c:
Answer:
8 a minus 48
Step-by-step explanation:
What do a and b represent in the general term(tn)=an+b of sequence?
The sequence Tn = an + b is an arithmetic sequence.
b represents the first term, and a represents the common difference
How to interpret variables a and b?
The general term is given as:
Tn = an + b
The above term is an arithmetic sequence.
An arithmetic sequence is represented as:
Tn = T1 + (n - 1)d
Where T1 represents the first term, and d represents the common difference
By comparing Tn = an + b and Tn = T1 + (n - 1)d, we have:
b = T1
a = d
This means that b represents the first term, and a represents the common difference
Read more about sequence at:
https://brainly.com/question/7882626
Find the volume of the figure below.
Answer:
B. 86.625
Step-by-step explanation:
To find the volume of a shape the formula is this, length x width x height. 5.5 x 4.5 x 3.5 = 86.625.
