Answer:
A) 80,164
B) S_n = (n/2)(17 + n)
Step-by-step explanation:
A) Formula for the nth term of an arithmetic progression series is;
a_n = a + (n - 1)d
a is first term of the series and in this case it is 9.
Difference is d which is 1 since they are consecutive integers.
Thus, For the last term which is 400, we have;
400 = 9 + (n - 1)1
400 - 9 = n - 1
391 = n - 1
n = 391 + 1
n = 392
Thus,there 392 terms in this sequence.
Formula for sum of an AP is;
S_n = (n/2)(2a + (n - 1)d)
S_392 = (392/2)((2 × 9) + (392 - 1)1)
S_392 = 80,164
B) The last term here is k, so we can't know exactly how many terms are in this sequence. Thus, let the number of terms be n.
Now, as above,
a = 9
d = 1
Sum of this AP sequence is;
S_n = (n/2)((2 × 9) + (n - 1)1)
S_n = (n/2)(18 + n - 1)
S_n = (n/2)(17 + n)
Find NP from the rectangle
The diagonals of a rectangle are equal and bisect each other.
NQ= 2×5 =10
Using Pythagoras theoram,
PQ²+NP²=NQ²
4²+ NP²= 10²
NP²= 100-16
NP²= 84
NP =√84
NP=2√21 = 9.2what is the slope of p?
===========================================================
Explanation:
Start at the origin (0,0). Move 2 units up (rise) and move to the right 3 units (run) to arrive at the point (3,2).
This shows that the slope is rise/run = 2/3.
---------------------
You could also use the slope formula, which is,
m = (y2-y1)/(x2-x1)
You can use any two points from the orange line.
If x = 10, which lines are parallel? Check all that apply.
pls someone help me who ever answers with a good explanation how to solve it, gets brainliest
Answer:
BCDE
Step-by-step explanation:
You can see it in the image. Parallel = if the line keeps going and will never touch each other.
Find the volume of the prism.
4.8 m
10 m
7.2 m
Answer:
172.8 m^3
Step-by-step explanation:
Volume for triangualr prism formula:
1/2 • length • width • height
Use formula with given dimensions:
1/2 • 7.2 m • 10 m • 4.8 m = 172.8
Volume is measured in cubic meters
(meters in this situation)
FINAL ANSWER:
172.8 cubic meters
Hope this helps!
The volume of the given prism is 172.8 cubic centimeters.
The given prism is a triangular prism with base length of 7.2m.
Height of 4.8m
Length of 10m.
The formula for volume of prism is V=1/2 bhl
Plug in the values of length , breadth and height:
V=(1/2) × 10 × 4.8 × 7.2
V=5×4.8×7.2
V=172.8 cubic centimeters.
Hence, the volume of the given prism is 172.8 cubic centimeters.
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Which statement describes the behavior of the function f(x) = 2x/1-x2?
The graph approaches -2 as x approaches infinity.
The graph approaches 0 as x approaches infinity.
The graph approaches 1 as x approaches infinity.
The graph approaches 2 as x approaches infinity.
Answer:
Step-by-step explanation:
Please use parentheses around the denominator:
2x
f(x) = -------------- or f(x) = 2x / (1-x^2)
1 - x^2
to eliminate any ambiguity. The graph of this function passes thru the origin (0,0) and has vertical asymptotes at x = -1 and x = + 1. The function is negative on (-1,0) and positive on (0,1).
Additionally, there are two horizontal asymptotes. As x grows large and negative, f(x) approaches zero from above. As x grows large and positive, f(x) approaches zero from below.
The graph approaches -2 as x approaches infinity, this describes the behavior of the function f(x) = 2x/1-x2.
The behavior of the function [tex]f(x) = 2x/(1-x^2)[/tex] as x approaches infinity depends on the degree of the numerator and denominator. In this case, both the numerator and denominator have degree 1, so we can use the ratio of the leading coefficients to determine the behavior.
The leading coefficient of the numerator is 2, and the leading coefficient of the denominator is -1. Therefore, as x approaches infinity, the function approaches -2.
So, the statement that describes the behavior of the function is: "The graph approaches -2 as x approaches infinity."
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What is the value of y - X?
A. 20
D
B. 30
O
E.
о O
C. 45
Answer:
30
Step-by-step explanation:
that is the procedure above
Find an example for each of vectors x, y ∈ V in R.
n
for n = 2 or n = 3 such that
applies:
A
||x|| = max{|x1|, ..., |xn|}
||x|| =√n · max{|x1|, ..., |xn|}
(B)
||x + y|| = ||x|| + ||y||
||x + y|| < ||x|| + ||y||
(C)
||x · y|| = ||x|| · ||y||
||x · y|| < ||x|| · ||y||
(a) Both conditions are satisfied with x = (1, 0) for [tex]\mathbb R^2[/tex] and x = (1, 0, 0) for [tex]\mathbb R^3[/tex]:
||(1, 0)|| = √(1² + 0²) = 1
max{1, 0} = 1
||(1, 0, 0)|| = √(1² + 0² + 0²) = 1
max{1, 0, 0} = 1
(b) This is the well-known triangle inequality. Equality holds if one of x or y is the zero vector, or if x = y. For example, in [tex]\mathbb R^2[/tex], take x = (0, 0) and y = (1, 1). Then
||x + y|| = ||(0, 0) + (1, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2
||x|| + ||y|| = ||(0, 0)|| + ||(1, 1)|| = √(0² + 0²) + √(1² + 1²) = √2
The left side is strictly smaller if both vectors are non-zero and not equal. For example, if x = (1, 0) and y = (0, 1), then
||x + y|| = ||(1, 0) + (0, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2
||x|| + ||y|| = ||(1, 0)|| + ||(0, 1)|| = √(1² + 0²) + √(0² + 1²) = 2
and of course √2 < 2.
Similarly, in [tex]\mathbb R^3[/tex] you can use x = (0, 0, 0) and y = (1, 1, 1) for the equality, and x = (1, 0, 0) and y = (0, 1, 0) for the inequality.
(c) Recall the dot product identity,
x • y = ||x|| ||y|| cos(θ),
where θ is the angle between the vectors x and y. Both sides are scalar, so taking the norm gives
||x • y|| = ||(||x|| ||y|| cos(θ)|| = ||x|| ||y|| |cos(θ)|
Suppose x = (0, 0) and y = (1, 1). Then
||x • y|| = |(0, 0) • (1, 1)| = 0
||x|| • ||y|| = ||(0, 0)|| • ||(1, 1)|| = 0 • √2 = 0
For the inequality, recall that cos(θ) is bounded between -1 and 1, so 0 ≤ |cos(θ)| ≤ 1, with |cos(θ)| = 0 if x and y are perpendicular to one another, and |cos(θ)| = 1 if x and y are (anti-)parallel. You get everything in between for any acute angle θ. So take x = (1, 0) and y = (1, 1). Then
||x • y|| = |(1, 0) • (1, 1)| = |1| = 1
||x|| • ||y|| = ||(1, 0)|| • ||(1, 1)|| = 1 • √2 = √2
In [tex]\mathbb R^3[/tex], you can use the vectors x = (1, 0, 0) and y = (1, 1, 1).
Find the sum of the first 10 terms of the following series, to the nearest integer.
175, 70, 28, ...
Answer:
Step-by-step explanation:
you can see this is a geometric progression which a ratio of [tex]{2\over{5}}[/tex]. the sum of the firs n term is:
[tex]S=a_1\frac{(1-r^n)}{(1-r)}=175\frac{1-(\frac{2}{5})^{10}}{1-\frac{2}{5}}=291.6360832[/tex]
the nearest integer would be:
292
The sum of the first 10 terms of the series 175, 70, 28, ... is 291.636
What is geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number. This fixed number is called common ratio.. This progression is also known as a geometric sequence of numbers that follow a pattern.
Common ratio = (Any term) / (Preceding term)
What is sum of first "n" natural numbers?It means the sum of all the first "n" numbers in the series. The formula for first "n" natural numbers is
Sn = a + a r + ar2 + ar3 +…+ arn-1
or
Sₙ = a[(rⁿ – 1)/(r – 1)]
where "r" is called common ratio
"a" is called the first term in the series
From the given question the given series is 175, 70, 28, ...
70/175 = 0.4 (or) 28?70 = 0.4
As each succeeding term is produced by multiplying each preceding term by 0.4 .Here the common ratio (r) is 0.4
let first term "a" be 175
then Sₙ = 175[(0.4¹⁰-1)/(0.4 - 1)
Sₙ= 291.636
Thus the sum of the first 10 terms of the series 175, 70, 28, ... is 291.636
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Evaluate the function
Answer:
-2
Step-by-step explanation:
f(x) = 3x^2 + 5x - 14
substitute -3 inplace of x
f(-3) = 3*(-3)^2 + 5*(-3) - 14
=3*9 - 15 - 14
=27 - 15 - 14
= -2
Really struggling with this, can someone please help me out and give me a brief explanation?
Answer:
the answer is 220
Step-by-step explanation:
the formula for surface area of a rectangular prism is A=2(wl+hl+hw)
w = width
h= height
l = length
and when you have those lengths, you have to substitute.
The cost C of manning household is partly constant and partly varies as the number of people, the cost is 70,000 and for 10 people, the cost is 90,000 find the expression for C in terms of n ii. The weekly cost for 12 people
Answer:
4.196.754
Step-by-step explanation:
god bless stay safe po
Help please…………….6/11/21
9514 1404 393
Answer:
8
Step-by-step explanation:
The notation n=1 .. 8 means that n takes on all integer values from 1 to 8. Each value of n gives one term that is added to the series.
The number of terms is 8.
HW HELP ASAP PLZZZZZ
Answer:
4a
Step-by-step explanation:
4ax^2 + 4ax + 4a
here in every term there is 4 and a so take 4 and a common
4a(x^2 + x + a)
Q2
What is 23.3 x 0.463 correct to three decimal places?
Answer:
10.787
Step-by-step explanation:
Given :
23.3×0.463
After multiplying this equation ,
10.787
Therefore, answer will be 10.787
A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?
Answer:
504/8=63/6=10.5
10 rooms per floor with 3 leftover
For the equation, complete the solution. 8x + y = −7
(x, y) = , 1
Answer:
(x, y) = (-1, 1)
Step-by-step explanation:
8x + y = −7
for y = 1
8x + 1 = -7
subtract 1 from boh sides
8x = -8
divide bot sides by 8
x = -1
(x, y) = (-1, 1)
A baseball player hits a home run. A spectator observes the trajectory of the ball and expresses the height of the ball using the equation s(t)= -(t-15) + 225. Calculate the instantaneous velocity of the ball at t=4 seconds where the distance is measured in meters.
A. 44 m/sec
B. 30 m/sec
C. 26 m/sec
D. 22 m/sec
Answer:
The appropriate solution is Option D (22 m/sec).
Step-by-step explanation:
The given equation is:
[tex]s(t)= -(t-15)^2 + 225[/tex]
Now,
The instantaneous velocity at t = 4 will be:
= [tex][-2(t-15)(1)+0][/tex]
= [tex]-2(4-15)[/tex]
= [tex]-2\times (-11)[/tex]
= [tex]22 \ m/sec[/tex]
Thus, the above is the correct option.
Write an equivalent expression for: 5(5x - 9) *
Answer:
25x - 45
Step-by-step explanation:
5(5x - 9)
Distribute
5*5x - 5* (9)
25x - 45
Answer:
➛ 25 x - 45
Step-by-step explanation:
➛ 5 ( 5 x - 9 )
Using distributive property multiply both by 5
➛ 5 × 5 x - 5 × -9
➛ 25 x - 45
edafjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj
Answer:
fjjjjjjjjjjjjjj?
aefieoapowiejfie
Translate the percent sentence to a percent equation.
What number is 43% of 80?
Answer:
.43 · 80 = 34.4
Step-by-step explanation:
percentages into decimals = move decimal place to left two places
'of' means multiply in math
equations have equal (=) signs
What is the answer to part a and b?
Hi :), im really struggling with this. Just wanted to know if anyone can explain step by step for me please. Id really appreciate it.
Answer:
314 m²
Step-by-step explanation:
the formula for the surface area of a sphere (As) is
As = 4×pi×r²
the radius r (half of the diameter) is clearly indicated as 5m.
so, As = 4×3.14×5² = 4×3.14×25
I don't even need a calculator for this, as 4×25 = 100
so, As = 100×3.14 = 314
(you know, when multiplying by 10, the decimal point moves right one position. multiply by 100 it moves 2 positions, and so on).
Write an equation of the line passing through the given point and satisfying the given condition. Give the equation (a) in slope-intercept form and (b) in standard form.
(6, 1), perpendicular to 2x - y = 8
Answer:
I don't no answer sorry
Step-by-step explanation:
give me brainliest
Find the array to finish 976 divided by 8. NO LINKS!!!
Answer:
976 ÷ 8 =
8 groups of n = 976
n groups of 8 = 976
122
____
8 | 976
- 8
____
176
- 16
_____
160
- 160
______
0
Which scenario is modeled by the equation (x) (0.6) = 86 dollars and 46 cents?
Answer:
Answer: (C)A picnic table is on sale for 60 percent off.
Step-by-step explanation:
well someone copied me but okay :[
is 8x + 5x and 40x
Equivalent?
Explain why
Using ƒ = {(1, 0), (2, 3), (3, 6)}, give the range.
I need help with this
Blue whales eat an average of 5,000 pounds of fish daily, with a standard deviation of 850 pounds. Approximately what percentage of blue whales eat more than 6700
Answer:
2.13%
Step-by-step explanation:
assume that the distribution is approximately normal
[tex]\frac{6700-5000}{850} =2[/tex]
the value is 2 s.d. more than the mean
according to normal distribution, approximately 2.13% of the data is 2 s.d. more than the mean.
Solve for x: 12x+5=3x+35
Answer:
The answer would be 3.33.
Step-by-step explanation:
Simplifying 12x + 5 = 3x + 35
Reorder the terms: 5 + 12x = 3x + 35
Reorder the terms: 5 + 12x = 35 + 3x
Solving 5 + 12x = 35 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation. 5 + 12x + -3x = 35 + 3x + -3x
Combine like terms: 12x + -3x = 9x 5 + 9x = 35 + 3x + -3x
Combine like terms: 3x + -3x = 0 5 + 9x = 35 + 0 5 + 9x = 35
Add '-5' to each side of the equation. 5 + -5 + 9x = 35 + -5
Combine like terms: 5 + -5 = 0 0 + 9x = 35 + -5 9x = 35 + -5
Combine like terms: 35 + -5 = 30 9x = 30
Divide each side by '9'. x = 3.333333333
Simplifying x = 3.333333333
