Answers:
First term = 1Last term (37th term) = 109=======================================================
Explanation:
a1 = first term
a2 = second term
a3 = third term
and so on, until we reach a37 to represent the 37th term
We don't know the first term, but we'll call it x for now. We'll also let d be the difference between each adjacent term, aka the common difference.
Meaning that,
a1 = xa2 = a1+d = x+da3 = a2+d = (x+d)+d = x+2da4 = a3+d = (x+2d)+d = x+3dand so on, until,
a35 = x+34da36 = x+35da37 = x+36d---------------------
Add up the first three terms (a1 through a3) and set the sum equal to 12
Then do a bit of algebra to get
a1+a2+a3 = 12
(x)+(x+d)+(x+2d) = 12
3x+3d = 12
3(x+d) = 12
x+d = 12/3
x+d = 4
x = 4-d
Do the same for the last three terms, but the sum here is 318
a35+a36+a37 = 318
(x+34d)+(x+35d)+(x+36d) = 318
3x+105d = 318
3(x) + 105d = 318
3(4-d)+105d = 318 .... replace x with 4-d; isolate d
12-3d+105d = 318
102d+12 = 318
102d = 318-12
102d = 306
d = 306/102
d = 3
The common difference is 3. It means each term is increasing by 3.
Use this value of d to find x
x = 4-d
x = 4-3
x = 1
The first term is 1. That makes the second term x+d = 1+3 = 4, then the third term is x+2d = 1+2*3 = 7, and so on.
The sum of the first three terms is 1+4+7 = 12. That helps partly confirm the answer.
Also we have,
a35 = x+34d = 1+34(3) = 103a36 = x+35d = 1+35(3) = 106a37 = x+36d = 1+36(3) = 109 is the last term (37th term)Or you could note that the 35th term is 103, and then you increase by 3 each time to get the remaining two terms.
The last part of the confirmation is adding up those three last terms: 103+106+109 = 318, so the answer is fully verified at this point.
Side note: An arithmetic sequence never ends. There technically is no "last term"; however, since we're confined to focusing on these specific 37 terms, we can get away with using the phrasing.
What is the length of the hypotenuse
Answer:
15
Step-by-step explanation:
The Pythagorean's Theorem states that a^2 + b^2 = c^2, so 81 + 144 = 225, and 225 square rooted is 15.
Answer:
15
Step-by-step explanation:
So, to find the hypotenuse you must use the pythagreons theorm:
A^2+B^2=C^2
Now, we knowt hat A and B is the side lengths.(9 and 12)
The hyoptenuse is C.
So, lets plug in our values for A and B, and find C:
A^2+B^2=C^2
=
9^2+12^2=C^2
Now lets square each number except for C, since its a unknown value:
81+144=C^2
Now combine the 144 and 81:
225=C^2
Finally, square root both sides so C^2 becomes C:
15=C
So the answer for the hyotenuse is 15!
Hope this helps!
one side of a triangle is 50 and the other side is 120 what is the length of the third side?
this is exterior angle theorem.
I think it 10
Hope that helps
HELP ME I will give brainliest to whoever is RIGhT
Answer:
B)
Step-by-step explanation:
The following tables show the values of linear , quadratic, and exponential functions for various values of . Indicate which function type corresponds to each table. Justify your choice. с у Y X у 6 1 1 71 56 6 1 14 9 2 9 2 28 N N 28 12 3 3 14 14 3 15 4 4 4 7 56 21 D B
Answer:
Step-by-step explanation:
Consecutive differences in Table A are constant (9−6=12−9=15−12=3), indicating a linear function. Consecutive quotients in Table B are constant (147=2814=5628=2) indicating an exponential function. Similarly the constant quotient for Table D is 1/2. Neither consecutive differences nor quotients are constant in Table C, and its ordered pairs are related by the equation y=x2+5. So, Table A should be labeled "linear", Table B and D, "exponential", and Table C, "quadratic".
Find the volume of an construction cone if it has a radius of 4 inches and a height of 16 inches.
Answer:
≈ 268 or 85.3π
Step-by-step explanation:
V = 1/3πr²h
V = 1/3 x 3.14 x 4² x 16
V ≈ 267.9467 or 268
also can be considered 85.3π
Write a sentence in which the relative frequency of the letter E (or e) is exactly 10%.
Answer:
I'd try to do that, but it cannot be done.
Step-by-step explanation:
The above sentence contains 30 letters, including 3 "e"s, so the frequency of e is 3/30 = 0.1 = 10%
PLEASE ANSWER PLZ PLZ
Answer:
Your answer is -5/2.
Step-by-step explanation:
Use the slope equation. (Refresh if you cant see below.)
[tex]\frac{y_2-y_1}{x_2-x_1}\\\text{Substitute two points into the equation. We can use the first two, (3, 5), and (5, 0).}\\\frac{0-5}{5-3}\\\text{Subtract.}\\-\frac{5}{2}[/tex]
The length of segment PK is 4 units and the length of segment PQ is 2 units. What is the approximate
perimeter of shaded triangle PQL
A 10.0 units
B 9.5 units
C 9.0 units
D 8.5 units
Answer:
9.5
Step-by-step explanation:
X-3<9
What’s the answer to this everbody should know
Answer:
x<12
Step-by-step explanation:
Let's solve your inequality step-by-step.
x−3<9
Step 1: Add 3 to both sides.
x−3+3<9+3
x<12
Answer:
x<12
2. What is a line of symmetry?
(1 Point)
Answer:
Step-by-step explanation:
I believe you're refering to an "axis of symmetry." This is most often seen in quadratic equations. If the parabolic graph opens up or down, the axis of symmetry is the vertical line passing through the vertex, and the graph is symmetrical about this axis. The same applies to a parabolic graph that opens left or right.
If y = ax^2 + bx + c, the equation of the axis of symmetry is x = -b / (2a).
9. The quotient of n and -4 is 5. What is the
value of n?
Answer:
n=-20
Step-by-step explanation:
Answer:
n = -20
Step-by-step explanation:
n/-4 = 5
n/-4 (-4) = 5(-4)
n = -20
-20/-4 = 5
Pls help fast will give brainliest
Answer:
y= -2x+ 5
Step-by-step explanation:
parallel with y= -2x+ 1 means the lines have the same slope m= -2
from point (-1, 7) we go with a slope of -2 until we find the y-intercept (0, 5)
y= mx+b is the general formula
y= -2x+ 5
Which value(s) is a solution for the inequality
f < 4?
Answer:
665
Step-by-step explanation:
kmnbvcxsdrftyuiol,m nbvcxsdftgyhuio
Answer:
s = s
f < 4 = s
Step-by-step explanation:
Question b quick 10 points
Volume is expressed in
Answer:
Cubic Units
Step-by-step explanation:
HELP MEEEEEEEEEEEEEEE!
Answer: go
Step-by-step explanation:
Helppppppoppp please 10 points !!!
Answer:
2x+27+x+27=180
3x+54=180
3x=180-54
x=126/3
x=42
angle B=x+27
=42+27
=69 degree
Step-by-step explanation:
Answer:
B=69
Step-by-step explanation:
Supplementary angles have a sum of 180. Set up your formula as
180=(2x+27)+(x+27)
180=2x+27+x+27
180-27-27=3x
126=3x
126/3=x
42=x
Now substitute 42 in place of x for Angle B
Angle B = x+27
B = 42+27
B=69
Check your work by doing the same for Angle A
Angle A = (2x+27)
A=2*42+27
A=84+27
A=111
Now add both together and if you did it right, your answer is 180
69+111 = 180
Which of the following shows the quadratic formula correctly used to solve the
polynomial equation 3x^2 - 2 =11x
[tex]3{x}^{2} - 2 = 11x \\ + 11x \: \: \: \: \: \: + 11x \\ 3 {x}^{2} + 11x- 2 = 0 \\ quadratic \: formula \: goes \: fom \: this \: : a {x}^{2} + bx + c = 0 \\ to \: this : x = \frac{- b \ \frac{ + }{ \: } \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
so now you just plug in the numbers to their corresponding letter:
[tex]x = \frac{ - 11 \frac{ + }{ \: } \sqrt{ {11}^{2} - 4(3)( - 2)} }{2(3)} [/tex]
If each unit on the graph measures 1 inch, how far is the
inchworm from the ladybug? (Hint: The Pythagorean
theorem can be used because the x-axis, y-axis, and z-
axis each intersect at a right angle.)
O 5 in.
O 7 in.
0 12 in.
25 in.
Answer:
A. 5
Step-by-step explanation:
just did the quiz on .
Edgar pay $67.86 for 7.8 pounds of fertilizer. What is the price per pound of fertilizer?
(Write in dollars & cents.)
Answer:
He pays $8.70
Step-by-step explanation:
You would do $67.86 divided by 7.8 lbs
Logan inherited $8,000 from his grandmother. He split the money and placed the amounts in the two accounts below. Find the total amount of money he will have in the accounts combined after 5 years. x Account A: earns 7% interest compounded quarterly x Account B: earns 5.5% interest compounded annually
Answer:
What i got was 3000 please mark wrong if it not right
Step-by-step explanation:
I need help with this problem this is so hard for me please
Answer:
angle 2=81 degree
angle 1 =126 degree
Step-by-step explanation:
The function r(n) = 5n² + 1 represents the value of the nth term in a sequence.
What is the sum of the 1st and 3rd terms of the sequence?
Step-by-step explanation:
a_n=5n²+1
➜a_1=5(1)²+1
➜5×1+1
➜5+1
➜6➜a_3=5(3)²+1
➜5×9+1
➜45+1
➜46There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get? (enter your answer as a fraction or mixed number)
Write a number sentence that represents the problem.
Answer:
0.3
Step-by-step explanation:
yushhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
0.3
Step-by-step explanation:
djdjwinqwp9dejnedm
What is the equation of a circle with a radius of 6 and a center at ( -2 , 3 )?
Answer:
Solution given:
centre(h,k)=(-2,3)
radius(r)=6 units
we have
equation of a circle is:
(x-h)²+(y-k)²=r²
(x+2)²+(y-3)²=6²
(x+2)²+(y-3)²=36 is required equation of a circle.
Find the missing lengths of the leg AND the hypotenuse in simpilest radical form.
Answer:
Above picture is the solution for your question
Step-by-step explanation:
Use relation of trignometric ratios
Carol measured her windows for new curtains. She measured the width to be 34 in when it was actually 36 inches. Which was carols approximate percent error in her window measurement .
A. 2.0%
B. 2.8%
C. 5.6%
D. 5.9%
Answer:5.9
Step-by-step explanation: Clarification from teacher
Anna is solving this equation:
7 - 3(2x - 5) = -(3x + 7)
Anna uses the distributive property for her first step.
Which equation shows the correct result of Anna using the distributive property?
O A. 7-6x - 5 = -3x + 7
B. 7 - 6x + 5 = -3x - 7
C. 7 - 6x - 15 = -3x + 7
D. 7 - 6x + 15 = -3x - 7
Answer:
7-6x+15=-3x-7
29=3x
x=29/3
the asnwer is D
Nico practiced drums 1.5 fewer hours than he practiced piano. If Nico practiced the piano for 4 hours, how many hours did Nico practice the drums
Answer:
2.5 hours
Step-by-step explanation:
4 - 1.5 = 2.5
You must subtract 1.5 from the amount of hours he plays piano, which is 4. This is because he spends 1.5 hours less playing drums than he does playing piano.
Sonia has a hat collection. The ratio of white hats to
blue hats in her hat collection is 10:9. Which ratio is
equivalent to 10:9?
Answer:
20:18 30:27 40:36 etc..
Step-by-step explanation:
To find equivalent ratios you multiply both 10 and 9 by the same number to find equivalent ratios.