Answers
==========================================================
Explanation:
We start with one block at the very left side. This is algebraically written as [tex]a_1 = 1[/tex]. The small subscript '1' means we're dealing with the first term, and that is set equal to 1. In other words, the first term is 1.
The second term is three since we have three blocks as the next figure down the line. So [tex]a_2 = 3[/tex]. We can then see that [tex]a_3 = 6[/tex] and [tex]a_4 = 10[/tex]
The sequence of the first four terms are: 1, 3, 6, 10.
The notation [tex]a_n = a_{n-1} + n[/tex] tells us "to get the nth term [tex]a_n[/tex], we add the previous term ([tex]a_{n-1}[/tex]) to the value of n".
For example, if we wanted the third term, we would add the second term a2 onto the value of n = 2. In order to know a2, we need the diagram or you would have to use the recursive formula to find it.
Furthermore, it means that to find the fifth term [tex]a_5[/tex], we do the following
[tex]a_n = a_{n-1} + n\\\\a_5 = a_{5-1} + 5\\\\a_5 = a_{4} + 5\\\\a_5 = 10+5\\\\a_5 = 15[/tex]
The fifth figure will have 15 small little blocks to it. You can draw this out by copying the fourth figure, and then adding 5 smaller blocks to the very bottom portion. The sixth figure is basically a copy of the fifth one, but we have six little blocks along the bottom. This is the "plus n" being applied in the recursive formula.
So the 6th figure will have 15+6 = 21 blocks in total while the 7th figure has 21+7 = 28 blocks. This points us to choice (3).
Side note: These are known as triangular numbers. Note how the gaps between consecutive values of 1,3,6,10,15,21,28 is +2,+3,+4,+5,+6,+7.
Related Questions
Combine like terms to simplify the following polynomial.
6x + 7y – 9 – x + 8y + 5
A. 4x + 12y – 5
B. 42xy – 8xy – 45
C. 5x + 15y – 4
D. 13x + 7y – 4
Answers
Answer:
5x + 15 y - 4 (option C)
Step-by-step explanation:
Solve
6x + 7y – 9 – x + 8y + 5
Group like terms!
6x - x +7y +8y - 9 + 5 =
5x + 15 y - 4 (option C)
_____________________
#IndonesianPride - kexcvi
Please help me out with my work
Answers
c≈2.92
1.5^2+2.5^2=2.92
A square pyramid has a volume of 297 cubed feet. The width and length of the pyramid are
both 9. feet. Find the height of the pyramid.
Answers
Answer:
11
Step-by-step explanation:
H =V/(LxW)/3
H = 297/(9x9)/3
H = 297/(81)/3
H = 297/27
H = 11
Therefore, the height of the pyramid is 11ft square
Point B is a point of tangency. Find the radius r of Oc 6. 15 B
Answers
Answer:
o6.15 B
Step-by-step explanation:
You start at (1,-5). You move left 5 units. Where do you end?
Answers
Answer:
QUESTION:
You start at (1,-5). You move left 5 units. Where do you end?
ANSWER:
You end at (-4,-5)
Step-by-step explanation:
Hope that this helps you out! :)
If you have any questions please put them in the comment section below this answer.
Have a great rest of your day/night!
Please thank me on my profile if this answer has helped you.
1-5=-4
Moving left and right is x-axis
[50 POINTS] WILL MARK BRAINLIEST!!! Please solve the whole page with work!! It will be very much appreciated and I will heart the correct comment and give it 5 stars
Answers
Answer:
wait, it only 25 points...
Step-by-step explanation:
Can someone help me and solve for x
Answers
Answer:
x ≈ 14.6
Step-by-step explanation:
Assuming the triangle is right.
Using the sine ratio
sin55° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{12}{x}[/tex] ( multiply both sides by x )
x × sin55° = 12 ( divide both sides by sin55°
x = [tex]\frac{12}{sin55}[/tex] ≈ 14.6 ( to 1 dec. place )
Answer:
24? because the measure of 12 is half the size of x then the other half should be 12 too so i think 24. I AM VERY SORRY IF ITS WRONG!!!!!!!
Help!!! Thank you
Math xl
Answers
Answer:
A= 648 :)
Step-by-step explanation:
how do you solve 2x+4y=7 and -2x +3y=14
Answers
Answer:
y=3 x= -5/2
Step-by-step explanation:
simultaneous equations
2x + 4y = 7 ------ eq 1
-2x + 3y = 14 --------eq2
(different signs add)
(eq 2 + eq 1)
-2x +(-2x) = 0
4y+3y = 7y
7+14 = 21
7y= 21
(divide both sides by 7)
y= 21/7= 3
2x + 4(3) = 7
2x+ 12=7
2x = 7-12
2x = -5
x= -5/2
Solve 0 = 5x2 – 1.5x – 0.5 by using the graphing calculator to graph the related function. What are the solutions to the equation?
–0.5 and 0.2
–0.2 and 0.5
–0.5 and 0.5
–0.2 and –0.5
Answers
Answer:
b -0.2 and 0.5
Step-by-step explanation:
The equation of a circle centered at the orgin is x^2 + y^2 = 16. What is the radius of the circle
Answers
Given:
The equation of the circle is:
[tex]x^2+y^2=16[/tex]
To find:
The radius of the circle.
Solution:
The standard form of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
Where, (h,k) is the center and r is the radius.
We have,
[tex]x^2+y^2=16[/tex]
In can be written as:
[tex]x^2+y^2=4^2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]h=0[/tex]
[tex]k=0[/tex]
[tex]r=4[/tex]
Here, the center of the circle is the origin and the radius is equal to 4 units.
Therefore, the radius of the given circle is 4 units.
PLEASE HELP ITS DUE TONIGHT!
Answers
Answer:
2x = 7y
Step-by-step explanation:
2 Yogurts = $7
4 Yogurts = $14
6 Yogurts = $21
8 Yogurts = $28
10 Yogurts = $35
What is the equation of the line that passes through the point (-2, 0) and has a slope of -2?
Answers
Answer:
y=-2(x+2)
Step-by-step explanation:
plug in(-2,0) into y-y1=m(x-x1)
y=m(x+2)
slope =m=-2
y=-2(x+2)
Harold has a round trampoline with a radius of 1 yard. What is the trampoline's diameter?
Answers
Answer:
2 yards
Step-by-step explanation:
As per its definition, the diameter is the largest line that can be drawn from end to end of a circle, the diameter will always pass through the center of a cricle. The radius of a circle is a line drawn from the center of a circle to one of its sides. The diameter is always twice the measure of the raidus.
Applying this knowledge here, when given a radius of (1) yard, the diameter will be twice the length, and thus it will be (2) yards.
how can you tell if a function is linear by looking at the graph or the equation
Answers
how can I solve this 9x-5-(6-)
Answers
Answer:
9x - 5 = 6
9x = 6 + 5
9x = 11 (divide both sides by 9 to get x)
9x/9 = 11/9
x = 1.22222222222
WILL GIVE BRAINLIEST What is the slope of the table shown?
3
5
1
2
Answers
Answer:
2
Step-by-step explanation:
Slope is the change in y over the change in x
m = ( y2-y1)/(x2-x1)
= ( 7-1)/(3-0)
= 6/3
=2
for the function f(x) = x2 + 3 what is the value of f(-4)?
Answers
Therefore, the value of the equation [tex]f(x) = x^2 + 3[/tex] is [tex]19.[/tex]
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given equation is
[tex]f(x) = x^2 + 3[/tex]
when [tex]x=-4[/tex] so,
[tex]f(-4)=(-4)^2+3\\\\f(-4)=16+3\\\\f(-4)=19[/tex]
Hence, the value of the equation [tex]f(x) = x^2 + 3[/tex] is [tex]19.[/tex]
To know more about the equation
https://brainly.com/question/12788590
#SPJ2
Madison finished of her homework
before dinner. What percent of
Madison's homework is left to finish?
15%
Answers
Answer:
I didn't understand your question
10. The letter tiles shown are placed in a bowl. Matt selects
one tile from the bowl. What is the probability that Matt
will select one of the letters in the word "JUMP"?
Answers
Answer:
2/5 or 40% chance
Step-by-step explanation:
Subtract the following mixed numbers. Make sure your answer is in simplest form. (the answer choices are all mixed numbers.) 8 4/5 - 5 1/10
Answers
Answer:3 7/10
Step-by-step explanation:
“Josh drops his phone from a height of 50 feet. The situation is best modeled by h = -16t^2 +50, where h is the height in feet and t is the time in seconds. How long will it take for the phone to hit the ground? Round to the nearest tenth”
Answers
Answer:
hope this helps you out good luck
I need help whats dose d = ? 41 = 21d - 7
Answers
Answer:
[tex]\frac{16}{7}[/tex]
Step-by-step explanation:
We have: [tex]41 = 21d - 7[/tex]. We add 7, to get rid of the 7, to the other side. [tex]41+7=21d. \\41+7=48.\\48=21d.[/tex]
41÷21, is[tex]\frac{16}{7}[/tex]
Answer:
4
Step-by-step explanation:
Help me pls! Thnx if u do ✨✌️
Answers
are the two lines x+2y=7 and 2x+4y=21 parallel or perpendicular?
Answers
Answer:
They are parallel
Step-by-step explanation:
PLEASE HELP ILL GIVE BRAINLIEST ASAP
Answers
Answer:
hope you can figure it out from the but incase you can't it's D.
Step-by-step explanation:
10% off $40 would be $36 15% off $45 would be $38.25
$36 > $38.25
Find the are of the blue shaded region.
XTRA POINTS!!!
Plus brainliest!!!
No links or anything i will report you!!!!!
PLZ!!!!
Answers
Answer:
25π
Step-by-step explanation:
i hope u hav a gud day ^_^
Answer:
area = 73.37 cm²
Step-by-step explanation:
area of circle:
A = π5² = 78.5 cm²
area of 80° segment:
(80/360)(78.5) = 17.44 cm²
area of isosceles triangle w/ 5 cm legs and 80° angle:
sin 40° = b/5
0.6428 = b/5
b = 3.214
base = 2(3.21) = 6.43 (we only figured for one-half of the base)
cos 40° = h/5
0.7660 = h/5
height = 3.83
A = 1/2(6.43)(3.83) = 12.31 cm²
area of unshaded part:
17.44 - 12.31 = 5.13 cm²
area of total shaded part:
78.5 - 5.13 = 73.37 cm²
Please answer this. I would greatly appreciate it
No links, no fake answers or your getting reported.
Answers
Answer:
11.1 feet
Step-by-step explanation:
When you are given a right triangle with a given angle and side, you can use
trigonometric functions to calculate missing side lengths or inverse functions for angles based on this information.
These ratios can be remembered by the mnemonic:
SOH CAH TOA.
S O H → Sin (Sine) = Opposite / Hypotenuse
C A H → Cos (Cosine) = Adjacent / Hypotenuse
T O A → Tan (Tangent) = Opposite / Adjacent
______________________________________
The Opposite side is the side directly across from the angle, The adjacent (next to) side is the side other than the hypotenuse or opposite side, and the hypotenuse is the longest side.
Given that we are trying to find the adjacent side, we must use the cos (cosine) function because that can be multiplied by the hypotenuse to give us the adjacent side we are looking for.
Therefore, 36 [Hypotenuse Side] × cos(72°) = Adjacent Side.
Because: 36 = Hypotenuse Side.
cos(72)° = Adjacent Side / Hypotenuse Side.
36 × cos(72°) =
36 × 0.309016994374... = 11.12461179749... ≈ 11.1
PLEASE ANSWER HONESTLY (PLEASE BE HELPFULL I HAVE BEEN STUCK ON THIS PROBLEM) WILL MARK BRANIEST IF CORRECT. (no links my computer is slow and no ctrl c ctrol v if possible (see picture below and show work)
Answers
WORTH 40 POINTS
write an equation given the following transformations
a hyperbola that is moved left 2 and up 5
all the info i have. steps would be appreciated
Answers
Answer:
Step-by-step explanation:
In this section, we will focus on graphing hyperbolas that open left and right or ... To easily sketch the asymptotes we make use of two special line segments ... From the center (5,4), mark points 3 units left and right as well as 2 units up and down. ... standard form for the equation of a hyperbola given the following information.
