Answer:
See below.
Step-by-step explanation:
Call the sum of the first n terms S.
S = a + ar + ar^2 + ar^3 + ... + ar^(n -1)
Multiply both sides by r.
Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^n
No subtract S - Sr.
S = a + ar + ar^2 + ar^3 + ar^4 + ... + ar^(n -1)
(-) Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^(n - 1) + ar^n
-------------------------------------------------------------------
S - Sr = a - ar^n
S(1 - r) = a(1 - r^n)
S = a(1 - r^n)/(1 - r)
S = a(r^n - 1)/(r - 1)
a + ar + ar^2 + ar^3 + ... + ar^(n -1) = a(r^n - 1)/(r - 1)
PLEASE ANSWERRR! FIRST CORRECT ANSWER WILL VOTE BRAINLIEST
For a certain value of k, the system
x + y + (k-1) = 2,
6x + 2y - 3z = 1
kx - z = -3
has no solutions. What is this value of k?
In matrix form, the given system is written as
[tex]\begin{bmatrix}1&1&0\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3-k\\1\\-3\end{bmatrix}[/tex]
and the system has no solution is the coefficient matrix is singular. The determinant is
[tex]\begin{vmatrix}1&1&0\\6&2&-3\\k&0&-1\end{vmatrix} = -3k+4[/tex]
and this is zero when k = 4/3.
On the other hand, in case you are missing a factor of z in the first equation, so that the system should read
x + y + (k - 1) z = 2
6x + 2y - 3z = 1
kx - z = -3
reframing it as a matrix equation gives
[tex]\begin{bmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}2\\1\\-3\end{bmatrix}[/tex]
Then the determinant of the coefficient matrix is
[tex]\begin{vmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{vmatrix} = -2k^2-k+4[/tex]
and the determinant is zero at two values, k = (-1 ± √33)/4.
Need help! Please answer quickly! :)
Answer: a
Step-by-step explanation:
Tìm giá trị lớn nhất giá trị nhỏ nhất
Cos(x+π/3)+ cos(x-π/3)
Answer:
GTLN : 1 GTNN: -1
Step-by-step explanation:
Ta có:
[tex]y=cos(x+\frac{\pi }{3} ) + cos(x-\frac{\pi }{3} ) \\ = 2.cosx.cos\frac{\pi }{3} \\ = cosx[/tex]
mà [tex]-1\leq cosx \leq 1[/tex]
Nên Max [tex]y=1[/tex] , [tex]x[/tex] ∈ [tex]R[/tex]
Min [tex]y = -1[/tex], [tex]x[/tex] ∈ [tex]R[/tex]
please answer this!!!
Answer:
A
Step-by-step explanation:
As the angles are equal, AB=BC, 16x-7=12x+1, 4x=8, x=2.
John read the first 144 pages of a novel, which was 3 pages less than 1/3 of the novel. Write an equation to determine the total number of pages (p in the novel.
Find the total number of pages in the novel.
Answer: 441 pages
Step-by-step explanation:
[tex]\frac{1}{3}p-3=144\\\frac{1}{3}p=147\\3(\frac{1}{3})p=147(3)\\p=441[/tex]
If a translation of (x,y) (x+6,y-10) is applied to figure ABCD, what are the coordinates of D?
Image of figure ABCD is missing and so i have attached it.
Answer:
D_new = (-1, - 12)
Step-by-step explanation:
From the figure attached, the current coordinates of D are; (-5, -2)
Now, we are told the figure undergoes a translation of (x,y) (x+6,y-10)
Thus, this means we add 6 to the x value and subtract 10 from the y-value.
Thus, new coordinate of D is;
> (-5 + 6, -2 - 10)
> (-1, - 12)
Answer:
1, -12
Step-by-step explanation:
D = -5, -2
|
-5 + 6 = 1
|
-10 and -2 is -12
1, -12
did it on edge, got it right.
which of the following expressions is equal to -3x^2-27?
Answer:
6
[tex] \sqrt{2} [/tex]
La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6, la probabilidad de que apruebe un estudiante B es 0.4 y la probabilidad de que ambos estudiantes aprueben es 0.3. ¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?
Answer:
0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.
Step-by-step explanation:
La probabilidad condicional :
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
En el cual:
P(B|A) es la probabilidad de que ocurra el evento B, dado que A sucedió.
[tex]P(A \cap B)[/tex] es la probabilidad de que ocurran tanto A como B.
P(A) es la probabilidad de que ocurra A.
En esta pregunta :
Evento A: Estudiante A aprueba.
Evento B: Estudiante B aprueba.
La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6
Entonces [tex]P(A) = 0.6[/tex]
La probabilidad de que ambos estudiantes aprueben es 0.3
Entonces [tex]P(A \cap B) = 0.3[/tex]
¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.6} = 0.5[/tex]
0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.
13
Simplify the following expression and evaluate for x=36
b
0.02(1.4x - 300)-0.2(2.4x+10)+0.552x
answer:
Answer:
0.028x-6-0.48x-2+0.552x
(0.028-0.48+0.552)x-6-2
0.1x-8
The simplified expression, when evaluated for x=36, is -4.4, when following expression and evaluate for x=36 b= 0.02(1.4x - 300)-0.2(2.4x+10)+0.552x
To simplify the expression and evaluate it for x=36, let's break it down step by step:
0.02(1.4x - 300) - 0.2(2.4x + 10) + 0.552x
First, let's simplify the terms within each set of parentheses:
0.02 * (1.4 * 36 - 300) - 0.2 * (2.4 * 36 + 10) + 0.552 * 36
Next, perform the multiplications and additions/subtractions within each set of parentheses:
0.02 * (50.4 - 300) - 0.2 * (86.4 + 10) + 0.552 * 36
0.02 * (-249.6) - 0.2 * (96.4) + 19.872
Now, evaluate the remaining multiplications:
-4.992 - 19.28 + 19.872
Finally, perform the additions and subtractions:
-4.992 - 19.28 + 19.872 = -4.4
Therefore, the simplified expression, when evaluated for x=36, is -4.4.
To know more about simplified , here
https://brainly.com/question/28595186
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Select the correct answer from the drop-down menu.
A
The diagram shows a stage in the construction of a line perpendicular to GH through point A.
The next step in this construction is
Reset
Next
2021 Edmentum. All rights reserved.
The diagram is missing and so i have attached it.
Answer:
Next step is;
to keep the same compass width and draw an arc centered at H crossing the previous arc in the image.
Step-by-step explanation:
A perpendicular line is to be drawn to line GH through point A.
The steps are;
1. Identification of the two end points of the line which has been done.
2. Place one leg of the compass at point G and draw a small arc above the line GH. This has been done.
3. Without changing the span of the compass, place the same leg of the compass at point H and draw another small arc above the line GH to intersect the previously drawn small arc.
4. Make use of a straight object to connect the point of intersection of the two small arcs to the point A.
This line is the perpendicular line to GH.
In the figure attached, they have just finished point 2 I wrote above. Thus, the next step is point 3.
Answer:
to keep the same compass width and draw an arc centered at H crossing the previous arc in the image.
Step-by-step explanation:
please help!!!
What is the volume of this regular prism?
48.55 cubic inches
55.8 cubic inches
9.7 cubic inches
24.28 cubic inches
Answer:
V = 24.28 in ^3
Step-by-step explanation:
The area of the base is
A =5/2 × s × a where s is the side length and a is the apothem
A = 5/2 ( 2.13) * .87
A = 4.63275
The volume is
V = Bh where B is the area of the base and h is the height
V = 4.63275 ( 5.24)
V =24.27561 in^3
Rounding to the hundredth
V = 24.28 in ^3
5. Solve each of the following quadratic equations using the Quadratic Formula (Express all roots as integers or as real numbers rounded to one decimal place)
a) 2x2 – 3x - 10 = 0
b) 3x2 - 8x + 4 = 0 (answer pls:)
For the remaining questions, show your work.
6. Solve each of the following equations.
a. - 5 = -3 + a
b.Зc + 2 = -22
Step-by-step explanation:
6a.
[tex] - 5 = - 3 + a[/tex]
[tex] - 2 = a[/tex]
6b.
[tex]3c + 2 = - 22[/tex]
[tex]3c = - 24[/tex]
[tex]c = - 8[/tex]
Find the volume of a sphere
with a radius of 6. Use 3.14 for n and round
the answer to the nearest whole number
Answer: Approximately 904
volume = (4/3) · π · r³
r = 6π = 3.14(4/3) · 3.14 · 6³ = (4/3) · 3.14 · 216 = (4/3) · 678.24 = 904.32 ≈ 904
Answer:
904 units^3
Step-by-step explanation:
The formula for finding the volume of a sphere is V = 4/3 πr³
π is assumed to be 3.14, and the radius is 6.
V = 4/3 * 3.14 * 216
V = 4.18666666 * 216
Volume = 904.32, which can be rounded to 904 units cubed
Which series represents this situation? 1+1*7+1*7^ 2 +...1*7^ 6; 1+1*7+1*7^ 2 +...1*7^ 7; 7+1*7+1*7^ 2 +... 1*7^ 6; 7+1*7+1*7^ 2 +...1*7^ 7
Answer:
Step-by-step explanation:
The series is missing from the question. I will answer this question with a general explanation by using the following similar series:
[tex]\sum\limits^6_{n=0} 7^n[/tex]
Required
The series
To do this, we simply replace n with the values
[tex]\sum\limits^6_{n=0}[/tex] means n starts from 0 and ends at 6
[tex]\sum[/tex] means the series is a summation series
So, we have:
[tex]\sum\limits^6_{n=0} 7^n = 7^0 + 7^1 + 7^2 + ...... + 7^6[/tex]
[tex]\sum\limits^6_{n=0} 7^n = 1 + 7 + 7^2 + ...... + 7^6[/tex]
it's emergency pls.
Answer:
see above there is the answer sorry for rough
The area of a square is given as (s3)6.
What is its perimeter?
Step-by-step explanation:
what does this problem description really say ? what is the area of that square ?
36 ?
s3×6 ?
s³×6 ?
5³×6 ?
2³×6 ?
(5×3)×6 ?
(2×3)×6 ?
and these are just the options that I can see right away without really thinking about it.
in any case, the solution is to draw the square root of the area, and then multiply the result by 4.
why ?
because the area of a square is the square of the length of one of its side - like for any rectangle the area is length×width, but in a square length = width, so the area is length×length = length².
therefore, sqrt(area) = sqrt(length²) = length.
and the perimeter of the square is the way all around the whole square (4 sides), which is then
length + length + length + length = 4×length
from all the possibilities I listed up there, only 36 and (2×3)×6 lead to nice round numbers.
as the area would be in both cases 36.
sqrt(36) = 6
and the perimeter would be 6×4 = 24
HELP ME pleaseeee help help
Step-by-step explanation:
a. x+10.
b. (5)(x)(x+10)=V
c. 5×8×18=720
d. 5,8,18
e. Yes, the dimensions all stay the same so the volume should be the same.
How can you use what you know about 5(2) to find 5(-2)?
Please help
Answer:
-10
Step-by-step explanation:
5(2) or fives times two is positive ten. The rule about multiplying with negatives is a negative times a positive is a negative. We take the multiplication answer from 5(2)=10 and apple the nagative from 5(-2). Hope this helps:)
A soccer player stands at one corner of a field and kicks a soccer ball 95 yards to the opposite corner. If the field is 76 yards long, what is the width?
= 57 yards.
Step-by-step explanation:
95 yards is the diagonal of the field
76 yards is the length
Find the width.
This set-up will for a right angled triangle with a length of 76 yards and Hypotenuse of 95 yards. Therefore the height will represent the width of our Rectangle.
[tex]{b}^{2} = {c}^{2} - {a}^{2} \\ {b}^{2} = {95}^{2} - {76}^{2} \\ {b}^{2} = 9025 - 5776 \\ \sqrt{ {b}^{2} } = \sqrt{3249} \\ b = 57yards[/tex]
What is the circumference of a circle with a diameter of 9 feet? Use 3.14 for
TL
d = 9ft
O A. 28.26 ft
PREVIOU
the formula for calculating the circumference is [tex]\pi[/tex] x diameter
so, 3.14 x 9 = 28.26ft (a)
Answer:
C = 28.26 ft
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
C = 3.14 *9
C = 28.26 ft
David bought a used Dodge Challenger for $14,000. The value of the car depreciates 11% per year from the time he bought the car. Write a function that represents the value of David's car, V(t), after t years.
Answer:
V(t) = 14,000(0.89)^t
Step-by-step explanation:
Present value of the Dodge Challenger = $14,000
Present percentage value = 100%
Depreciation value = 11%
Number of years = t
Future value = V(t)
V(t) = Present value of the Dodge Challenger(Present percentage value - Depreciation value)^t
= 14,000(100% - 11%)^t
= 14,000(89%)^t
= 14,000(0.89)^t
V(t) = 14,000(0.89)^t
f(x) = 2x + 7 with domain: x = {2, 3, 5, 9}
Answer:
2(2)+7=11
2(3)+7=13
2(4)+7=15
2(5)+7=17
2(9)+7=25
Step-by-step explanation:
2(2)+7
4+7=11
2(3)+7
6+7=13
2(4)+7
8+7=15
2(5)+7
10+7=17
2(9)+7
18+7=25
PLEASE HELP I NEED THIS TURNED IN BY TOMORROW AND I DONT KNOW WHAT TO DO!!!!
Answer:
Don't write the " ^ " that I'm typing, that's just showing its to the power of 2 (squared)
1. x^2 + y^2 = 100
2. (x+1)^2 + (y-8)^2 = 25
3. (x+5)^2 + (y+5)^2 =20
4. x^2 + y^2 = 85
5. x^2 + (y+2)^2 = 40
graph 6) middle of circle (dot) at origin (0,0), 5 out in every direction
graph 7) middle of circle (dot) at (-2, 1), 2 out in every direction
graph 8) middle of circle (dot) at (0, -3), 1 in every direction
graph 9) middle of circle (dot) at (1, 1), 4 in every direction
Step-by-step explanation:
Hope these are right, I just kind of banged them out real quick :)
WHO KNOWS HOW TO DO THIS!!!!!
Answer:
Step-by-step explanation:
Scale factor is 2. 6/3=2, 8/4=2. So it’s 1/2
Simplify (square root 3)(^5 square root 3)
Answer:
[tex]3^{\frac{7}{10} }[/tex]
Step-by-step explanation:
[tex]\sqrt{3} *\sqrt[5]{3}[/tex] = 3^1/2 x 3^1/5 = 3^(1/2 +1/5) = 3^7/10
Answer:
Step-by-step explanation:
Exponent law: [tex]a^{m}*a^{n}=a^{m+n}[/tex]
[tex](\sqrt{3} ) )*(\sqrt[5]{3})= 3^{\frac{1}{2}}*(3^{\frac{1}{5}})\\\\=3^{\frac{1}{2}+\frac{1}{5}}\\\\=3^{\frac{1*5}{2*5}+\frac{1*2}{5*2}}\\\\= 3^{\frac{5}{10}+\frac{2}{10}}\\\\=3^{\frac{5+2}{10}}\\\\=3^{\frac{7}{10}}[/tex]
A sinusoidal graph has a maximum at the point (–40, 3) and a midline of y = – 12. Determine the amplitude of the graph.
Answer:
15
Step-by-step explanation:
The amplitude of y=sin(x) is 1 with a maximum of y=1 and a minimum of y=-1. It's amplitude is 1 because that is the distance the max( y=1 )is from the mid line (y=0) or the distance the min( y=-1 ) is from the mid line (y=0).
So we just need to find the distance the mid line, y=-12, and the max,y= 3, is from each other.
3--12=3+12=15
Find the value of that makes m
||
n.
m
n
xº
2xº
82,92,76,72,92,74,80 and 78
What is the median
Answer:
Step-by-step explanation:
we have 8 choises 8 its even number so
we can write 8= 2*4
X=4 ss the answear between the fiveth and sixeth choise 72+92/2 AND YOU WILL FIND THE ANSWEAR
I'm unsure if I got the correct answer, mind if you help?
Answer:
Yes, you got the correct answer, it's y=-4
