Answers
Step-by-step explanation:
Equation to find the sum of the first n terms :
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] x (2[tex]a_{1}[/tex] + (n - 1)d)
- where n is the first n terms
- where [tex]a_{1}[/tex] is the first term in the sequence
- where d is the difference (To find the difference: [tex]a_{1}[/tex] - [tex]a_{2}[/tex])
How to find n for the given sum :
1. Using the previous equation, plug in all the numbers that you know
2. PEMDAS then combine all like terms
3. Distribute what's on the outside to the inside of the parenthesis
4. Move [tex]S_{n}[/tex] to the other side to make a quadratic equation
5. Solve the quadratic, then use the positive number and round that number (term of numbers that isn't whole isn't possible ig??)
Question 1:
Sum of first 10 terms : [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] ( 2 x 2 + (10 - 1)6)
[tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] (4 + (9)6) = (4 + 54) = 58
[tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] x 58
Answer : 290
Find n for the given sum : 1704 = [tex]\frac{n}{2}[/tex] x (2 x 2 + (n - 1)6)
distribute 6 into (n-1)
1704 = [tex]\frac{n}{2}[/tex] x ( 4 + 6n - 6)
combine like terms
1704 = [tex]\frac{n}{2}[/tex] x ( -2 + 6n )
Distribute [tex]\frac{n}{2}[/tex] to ( -2 + 6n )
1704 = [tex]\frac{-2n}{2}[/tex] - [tex]\frac{6n^{2} }{2}[/tex]
Simplify fractions and move 1704 to the other side
-3[tex]n^{2}[/tex] - n + 1704 = 0
Use a quadratic calculator to find the answer and use the answer with the whole number
Answer : -24
Question 2:
(i'm just gonna show you the answers for the rest of them-)
Sum of the first 14 terms: 490
Find n for the given sum: 33.65 (I'm gonna round it to 34)
Question 3:
Sum of the first 21 terms: 483
Find n for the given sum: 11.48 (rounded: 11)
Question 4:
Sum of the first 32 terms: -1328
Find n for the given sum: -9.34 (rounded -9)
really hope this helps in any way :D
Related Questions
23 lbs of onions cost $46. How many lbs of onions can you get with $30 ?
Answers
Answer:
15 lbs of onions.
Step-by-step explanation:
23 lbs divided by $46 = 0.5 lbs per $1
0.5 lbs times $30
15 lbs
=============================================================
Work Shown:
(23 pounds)/(46 dollars) = (x pounds)/(30 dollars)
23/46 = x/30
1/2 = x/30
1*30 = 2*x
30 = 2x
2x = 30
x = 30/2
x = 15
---------------
Another approach:
Divide the cost over the number of pounds to find the unit price
46/23 = 2
The onions cost $2 per pound.
If x is the number of pounds, and we pay $30, then
2x = 30
x = 30/2
x = 15
Meaning 15 pounds of onions cost $30.
Write the quadratic equation whose roots are -6 and 5, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
= 0
Answers
Answer:
The equation is 3x²-6x+5
Given roots are-6,5
Sum of roots = -6+5 = -1
Product of roots = -6 x 5 = -30
Now the quadratic expression is
[tex]3x^{2}+x-30=0[/tex]
Hope this helps you dear;)
Have a good day :3
HELP PLEAZE
ILL GIVE BRAINLIEST
Answers
Answer:
153.86 in²
Step-by-step explanation:
The area of a circle is:
A = π r²
Radius is just half of the diameter so r = 7.
Substitute 3.14 for π.
Restate the equation:
A = 3.14 x 7² = 3.14 x 49
A = 153.86
The bumper car ride at the state fair has 3 red cars, 4 green cars, and 5 blue cars. Michelle is first in line for the ride and is assigned a car at random. Garth is next in line and is randomly assigned a car. What is the probability that both Michelle and Garth will drive a red bumper car? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Answers
Answer:
4.5 %
Step-by-step explanation:
Answer:
4.5%
Explanation:
1) red = 3
2) green = 4
3) blue = 5
Total bumper cars: (3 + 4 + 5) = 12 cars
Michelle gets red car:
3/12 = 1/4Remaining red cars: 3 - 1 = 2
Remaining total cars: 12 - 1 = 11
Garth get red car:
2/11Probability they both get red cars:
1/4 × 2/11 = 1/22 ≈ 4.5%Which is the slope-intercept form of the equation of the line with a slope
of 2 and a y-intercept of 5?
Oy-5=2(x-0)
Oy=2x-2
O y = 2x+5
Oy-0=2(x - 5)
Answers
Use the equation y=slope(x)+b
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 97m long and 76m wide. Find the area of the training field. Use the value 3.14 for pie , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
If the radius of the semi-circle is 38 m. Then the area of the training field will be 11,908.459 square meters.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 97 m long and 76 m wide.
Then the radius of the semi-circle will be
2r = 76
r = 38 m
Then the area of the training field will be
Area = area of rectangle + 2 x area of semi-circle
Area = 97 x 76 + 2 x (1/2) x π x 38²
Area = 7372 + 4536.459
Area = 11908.459 square m
More about the geometry link is given below.
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An arc subtends a central angle measuring \dfrac{3\pi}{5}
5
3π
start fraction, 3, pi, divided by, 5, end fraction radians.
What fraction of the circumference is this arc?
Answers
Answer:
3/10 of the circumference
Step-by-step explanation:
Take the fraction between the central angle and the total degree measure of the circle, which is 2π.
(3π/5)/2π3π/10π3/10 of the circumferenceSolve 2x2 + 3x − 5 = 0 by factoring.
x=1, 52
x=1, −52
x=1
x=−52
Answers
x=-5/2 or x
= 1
the points at which a quadratic equation intersects the x-axis
Answers
The points at which a quadratic equation intersects the x-axis are referred to as x intercepts or zeros or roots of quadratic equation
Given :
The points at which a quadratic equation intersects the x-axis
The points at which the any quadratic equation crosses or touches the x axis are called as x intercepts.
At x intercepts the value of y is 0.
So , the points at which a quadratic equation intersects the x-axis is also called as zeros or roots of the quadratic equation .
The points at which a quadratic equation intersects the x-axis are referred to as x intercepts or zeros or roots of quadratic equation
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Triangle ABC has vertices A(-4, 3), B(2, 3) , C(-5, 1). A dilation with a scale factor of 5 and center at the orgin is appiled to this triangle.
What are the coordinates of C' in the dilated image? Enter your answer by filling in the boxes
Answers
Answer:
C' (- 25, 5 )
Step-by-step explanation:
since the dilatation is centred at the origin, then multiply each of the coordinates by the scale factor 5
C (- 5, 1 ) → C' (5 × - 5, 5 × 1 ) → C' (- 25, 5 )
PLEASE HELPPP THANK U SO MUCH
Answers
Answer:
396 = 341q-333
Step-by-step explanation:
396 is (396 =)
the quantity q times 341 (341q)
333 subtracted from (-333)
Answer:
341q - 333 = 396
Step-by-step explanation:
multiply q and 341, you get 341q
a number that is subtracted from another number is the same as saying 2 is subtracted from 5 gives you 3, which can be laid out as 5 - 2 = 3
therefore your equation will be 341q - 333 = 396
extra information :
341q = 396 + 333
341q = 729
q = 729/341
q = 2.137829912
In a video game, the player can choose a character from 4 animal characters and 3 human characters. Players can also let the computer randomly select a character for them. The player will have the computer randomly select his character. What is the probability it will pick a human character? Enter your answer as a fraction in simplest form in the box. PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
The probability of selecting the human characters will be equal to 3 / 7.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
The player can choose a character from 4 animal characters and 3 human characters.The probability will be calculated as:-
Probability = 3 / (3+4)
Probability = 3 / 7
Therefore the probability of selecting the human characters will be equal to 3 / 7.
To know more about probability follow
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Solve for x: Answer: -13x+8 = -8x - 7 Submit Answe
Answers
[tex]-13x+8=-8x-7\\\\8=5x-7\\\\15=5x\\\\3=x[/tex]
the value of x is 3.
Answer: X=3
Step-by-step explanation:
the diameter of circle x is 15 cenimeters. thediameter of circle y is 20 centimenters which measurement is closest to the diffrence between the circumference of circle x and the circumference of circle y in centimenters.
Answers
Answer:
15.7cm
Step-by-step explanation:
the circumference of x=L1=2π =15cm
L2=2π =20cm
L2-L1
=20π-15π
=5π
=5×3.14
=15.70cm
I need the answer soon please help. 20 points
Divide. −3 6/8 Enter your answer as a mixed number, in simplified form, in the box.
Answers
Answer:
The solution is in the image
Koda is making birdhouses for a park.
The instructions tell him how many of each wooden shape is needed for one birdhouse.
Complete each statement to adjust the number of shapes for each new situation if he follows the given instructions.
Answers
Koda who is making birdhouses for a park needs 16 trapezoids for 8 birdhouses, 12 rectangles for 3 birdhouses and 8 triangles when she has 4 square,
What is regular Pentagon?Regular Pentagon is the closed shaped polygon which has 5 sides equal in measure and 5 interior angles equal in measure.
Koda is making birdhouses for a park. For one birdhouse she required 2 trapezoids, 1 square 2 triangles and 4 rectangles.
For the 8 birdhouse, the number of trapezoids she need is,
Trapezoids=2 x 8
Trapezoids=16
For the 3 birdhouse, the number of rectangle she need is,
Rectangle =4 x 3
Rectangle=12
The number of birdhouse when she use 4 square,
Bird house=4 x 1
Bird house=4
Thus, the number of triangle for 4 birdhouse is,
Triangle=2 x 4
Triangle=8
Hence, Koda who is making birdhouses for a park needs 16 trapezoids for 8 birdhouses, 12 rectangles for 3 birdhouses and 8 triangles when she has 4 square,
Learn more about the Regular Pentagon here;
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An equation for the line
Answers
Answer:
y=-1/3x
Step-by-step explanation:
if it’s going down by one there should be one on top on since it’s going over by 3 it should be 3 on the bottom
Suvam fixed the price of a watch as Rs. 1200 and he sold it allowing a discoiunt of 15% and made a profit of Rs. 120. What was the cost price of the watch? Find it.
Answers
1200-180= 1020
to find the cost price use the discounted price and take it away from the original, then use the profit take away the discounted price.
1020-120=900
the cost price of the watch is Rs. 900
there are 11 clowns and 3 elephants. how many is all together?
Answers
Answer:
14
Step-by-step explanation:
in fgh, m f=60 degrees g= 68 degrees. which side of fgh is the shortest
Answers
Answer:
h=52 and h is the shortest
Step-by-step explanation:
180-f-g=h step 1. -f from 180
180-60=120 step 2. -g from 120
120-68= 52
h=52 degrees
CAN SOMEONE HELP ME PLS?
Answers
Answer:
x = 8
[tex]\overline{AC}[/tex] = 30
[tex]\overline{CD}[/tex] = 10
Step-by-step explanation:
Triangle [tex]\triangle ABC[/tex] and triangle [tex]\triangle DEC[/tex] are similar because they have 2 congruent angles. We can find the scale factor between them by comparing the length of [tex]\overline{BC}[/tex] and [tex]\overline{EC}[/tex] in a fraction, resulting in us finding the scale is 3:1 from [tex]\triangle ABC[/tex] to [tex]\triangle DEC[/tex].
Now we can solve for x using a proportion.
[tex]\frac{3}{1} = \frac{x+22}{x+2}[/tex] | Cross multiply
3x+6 = x+22 | Subtract x from both sides
2x+6 = 22 | Subtract 6 from both sides
2x = 16 | Divide both sides by 2
x = 8
Now we can solve for [tex]\overline{AC}[/tex] and [tex]\overline{CD}[/tex] by substitution.
[tex]\overline{AC}[/tex] = x + 22 = 8 + 22 = 30
[tex]\overline{CD}[/tex] = x + 2 = 8 + 2 = 10
These are your answers
- Kan Academy Advance
A line contains the following points left to right: r, t, u, s. the space between r and t is 12 units. the space between r and s is 24 units. if tu = 6 units, what must be true? su ut = rt rt tu = rs rs su = ru tu us = rs
Answers
Given thet SU = UT = 6 units, hence 6 + 6 = 12 showing that the expression SU + UT = RT is TRUE. Option A is correct
Measure of line segmentsA line is defined as the distance between two points
From the given line, RT = TU = 12 unitsSince the point T bisects RT and TU = 6 units, hence the point U bisects TS.
The sum of the segment SU and UT will be RT
SU + UT = RTGiven that SU = UT = 6 units, hence 6 + 6 = 12 showing that the expression SU + UT = RT is TRUE
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someone help this is so confusing
Answers
I mean im prob in a lower grade then you so i'd say b?
Need to know this asap number 6 and 7
Answers
The equation that does not assign one value to y is [tex]\frac 5y = 7x + \frac{10}{2y}[/tex] and the points that do not represent a function is (c)
The equation that does not assign one value to yTo do this, we simply make y the subject of formula.
So, we have:
[tex]\frac 5y = 7x + \frac{10}{2y}[/tex]
Simplify
[tex]\frac 5y = 7x + \frac{5}{y}[/tex]
Subtract 5/y from both sides
[tex]0 = 7x[/tex]
Rewrite as:
[tex]x = 0[/tex]
This means that the value of x is 0 irrespective of the value of y
Hence, the equation that does not assign one value to y is [tex]\frac 5y = 7x + \frac{10}{2y}[/tex]
The points that do not represent a functionFor a set of point to represent a function, the points must represent a one-to-one or many-to-one relationship.
From the list of options, option (3) represents a one-to-many relationship.
This is so because one x value has 3 y values
Hence, the points that do not represent a function is (c)
Read more about functions and relations at:
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SOMEONE PLEASE HELP ME I WILL LOVE YOU FORVER
Answers
Answer:
A. OEO, EOE, EEE, EEO, OOE, OEE
A (probability). [tex]\frac{3}{4}[/tex]
B. OEO, EOE
B (probability). [tex]\frac{1}{4}[/tex]
C. EOE, EEE, OOE, OEE
C (probability). [tex]\frac{1}{2}[/tex]
hope this helps:)
Answer:
A. OEO, EOE, EEE, EEO, ------- (probability). 3/4
B. OEO, EOE ------(probability). 1/4
C- EOE --------------(probability). 1/4 aswell
Step-by-step explanation:
Sorry it took so long
I hope this helps C:
arrange the following in order 9,09 909,09 0,099 0,909 0,0099 9,0099 9,909
Answers
Answer:
0.0099, 0.099,0.909, 9.0099, 9.09, 9.909, 909,09
Step-by-step explanation:
Here they are from least to greatest. Hope this helps. :)
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x − 3).
Which statement describes how the graph of h is different from the graph of g?
A.
The graph of h is the graph of g vertically shifted up 3 units.
B.
The graph of h is the graph of g horizontally shifted right 3 units.
C.
The graph of h is the graph of g horizontally shifted left 3 units.
D.
The graph of h is the graph of g vertically shifted down 3 units.
Answers
Answer:
B
Step-by-step explanation:
given f(x) then f(x ± a) is a horizontal translation of f(x)
• if + a , then a shift to the left of a units
• if - a then a shift to the right of a units
h(x) = g(x - 3)
then h is the graph of g shifted right 3 units
a random survey. of seventh and eighth graders was conducted to determine the number of each student has the results are shown statement about populations is not supported by information in the graph
Answers
Answer:
I believe the answer is 8th graders.
Step-by-step explanation:
3. In which quadrant do lines land m Intersect?
m
A. Quadrant !
B. Quadrant II
C. Quadrant III
D. Quadrant IV
Answers
Answer:
Quadrant 3 so the answer should be c
Which of the following BEST describes how to use the addition property of equality to isolate the variable y
below?
y-12 = 14
A. add 12 to the left side of the equation only
B. subtract 12 from the left side of the equation only
C. add 12 to both sides of the equation
D. subtract 12 from both sides of the equation
Please select the best answer from the choices provided
Ο Α
ОВ
С
Answers
Answer: C) add 12 to both sides
Reason:
We add 12 to the left side to undo the -12, which will get y by itself.
We must do the same thing to both sides to keep things balanced.
