In order to find the value of sin K in △JKL, which of the following ratios needs to be used?


A
JLJK

B
KLJL

C
JKKL

Consider the [tex]n[/tex]-th partial sum of a geometric series with first term [tex]a[/tex] and common ratio [tex]r[/tex] between consecutive terms. Then the sum of the first [tex]n[/tex] terms of this series is

[tex]S = a + ar + ar^2 + \cdots + ar^{n-1}[/tex]

Multiply both sides by [tex]r[/tex], then subtract [tex]rS[/tex] from [tex]S[/tex] and solve for [tex]S[/tex].

[tex]rS = ar + ar^2 + ar^3 + \cdots + ar^n[/tex]

[tex]S - rS = a - ar^n[/tex]

[tex]\implies S = \dfrac{a(1-r^n)}{1-r}[/tex]

In the given series, we have [tex]a=1[/tex] and [tex]r=2[/tex]; then the sum of the series with [tex]n=8[/tex] terms is

[tex]S = \dfrac{1-2^8}{1-2} = 2^8 - 1 = \boxed{255}[/tex]

They are both really the same. so they should hold the same. All that happened is one moved a 1/2 inch over to the length from the height.  

Answer:

above me is maybe a yes or no

Step-by-step explanation:

brainlles to above me

Answers:

==================================================

Explanation:

Problem 1

This is false because the A and B should swap places. It should be [tex](AB)^{-1} = B^{-1}A^{-1}[/tex].

The short proof is to multiply AB with its inverse [tex](AB)^{-1}[/tex]  and we get: [tex](AB)*(AB)^{-1} = (AB)*(B^{-1}A^{-1}) = A(B*B^{-1})*A^{-1} = A*A^{-1} = I[/tex]

The fact we get the identity matrix proves that we have the proper order at this point. The swap happens so that B matches up its corresponding inverse [tex]B^{-1}[/tex] and the two cancel each other out.

Keep in mind matrix multiplication is not commutative. So AB is not the same as BA.

-------------------------

Problem 2

This statement is true if and only if AB = BA

(A+B)^2 = (A+B)(A+B)

(A+B)^2 = A(A+B) + B(A+B)

(A+B)^2 = A^2 + AB + BA + B^2

(A+B)^2 = A^2 + 2AB + B^2 ... only works if AB = BA

However, in most general settings, matrix multiplication is not commutative. The order is important when multiplying most two matrices. Only for special circumstances is when AB = BA going to happen. In general,  AB = BA is false which is why statement two breaks down and is false in general.

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Problem 3

This statement is true.

If A and B are invertible, then so is AB.

This is because both [tex]A^{-1}[/tex] and [tex]B^{-1}[/tex] are known to exist (otherwise A and B wouldn't be invertible) and we can use the rule mentioned in problem 1. Make sure to swap the terms of course.

Or you can use a determinant argument to prove the claim

det(A*B) = det(A)*det(B)

Since A and B are invertible, their determinants det(A) and det(B) are nonzero which makes the right hand side nonzero. Therefore det(A*B) is nonzero and AB has an inverse.

So if we have two invertible matrices, then their product is also invertible. This idea can be scaled up to include things like A^4*B^3 being also invertible.

If you wanted, you can carefully go through it like this:

and so on until you build up to A^4*B^3. Therefore, we can conclude that A^m*B^n is also invertible. Be careful about the order of multiplying the matrices. Something like A*AB is different from AB*A, the first of which is useful while the second is not.

So this is why statement 3 is true.

-------------------------

Problem 4

This is false. Possibly a quick counter-example is to consider these two matrices

[tex]A = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}[/tex]

both of which are invertible since their determinant is nonzero (recall the determinant of a diagonal matrix is simply the product along the diagonal entries). So it's not too hard to show that the determinant of each is 1, and each matrix shown is invertible.

However, adding those two mentioned matrices gets us the 2x2 zero matrix, which is a matrix of nothing but zeros. Clearly the zero matrix has determinant zero and is therefore not invertible.

There are some cases when A+B may be invertible, but it's not true in general.

-------------------------

Problem 5

This is true because each A pairs up with an [tex]A^{-1}[/tex] to cancel out (similar what happened with problem 1). For more info, check out the concept of diagonalization.

Answer: -72 I think

Step-by-step explanation:

Hope this helps :)

The weight of the new student is 27 kg.

Average weight

= total weight ÷total number of students

Let the total weight of the 35 students be y kg and the weight of the new student be x kg.

[tex]45 = \frac{y}{35} [/tex]

y= 35(45)

y= 1575 kg

New total number of students

= 35 +1

= 36

Total weight

= total weight of 35 students +weight of new students

= y +x

[tex]44.5 = \frac{y + x}{36} [/tex]

[tex]44.5 = \frac{1575 + x}{36} [/tex]

36(44.5)= 1575 +x

1602= x +1575

Subtract 1575 from both sides:

x= 1602 -1575

x= 27

Thus, the weight of the new student is 27 kg.

Answer:

y=1.2x-3

Step-by-step explanation:

I had this as an rsm problem a few weeks ago and forgot how to solve it lol hope this helps

Answer:

[tex]\displaystyle y = -2x + 8[/tex]

Step-by-step explanation:

Perpendicular equations have OPPOCITE MULTIPLICATIVE INVERCE RATE OF CHANGES [SLOPES], so ½ becomes −2. Now, proceed with plugging the information into the Slope-Intercept Formula:

[tex]\displaystyle 2 = -2[3] + b \hookrightarrow 2 = -6 + b; 8 = b \\ \\ \boxed{y = -2x + 8}[/tex]

I am joyous to assist you at any time.

Answer:

7,14,21,28,35,42,49,56,63,70

Step-by-step explanation:

just add 7 lol anyways here ya go :)

Answer:

1.6 is how much each person gets

hope this will helpful to you

Answer:

C

Step-by-step explanation:

Answer:

The answer is 7680

Step-by-step explanation:

First you multiply 32 by 4(the usual formula) which gives you 128. However, the time changes the some things. So then you must multiply 128 by 60 (60 minutes in one hour). Which gives you 7680

hope i helped :D

Answer:

Slope = 20

y-intercept = 60

Step-by-step explanation:

Slope formula is given as [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Pick two points on the line and use their coordinates. Let's pick (1, 80) and (2, 100).

Let,

[tex] (1, 80) = (x_1, y_1) [/tex]

[tex] (2, 100) = (x_2, y_2) [/tex]

Plug the values above into the formula for slope:

[tex] m = \frac{100 - 80}{2 - 1} = \frac{20}{1}} = 20 [/tex]

Slope of the graph is 20.

The y-intercept is the point where the line intercepts the y-axis. Thus, y-intercept = 60.

Answer:

-------------------------------

[tex]35000 \times \frac{15}{100} = 350 \times 15 = 5250[/tex]

Answer:

48 then it would be 32? im not sure that what i caculated

Step-by-step explanation:

Answer:

1+x it means I plus the rest

Answer:

96

Step-by-step explanation:

commom difference = d

a₆ + a₇ = 16

a₅ + a₈ = (a₆ - d) + (a₇ + d) = a₆ + a₇ = 16

a₄ + a₉ = (a₆ - 2d) + (a₇ + 2d) = a₆ + a₇ = 16

Similarly,

a₃ + a₁₀ = 16, a₂ + a₁₁ = 16, a₁ + a₁₂ = 16

so

a₁ + a₂ + ... + a₁₁ + a₁₂ = 6 x 16 = 96

Answer:

The conductor checked on the passengers 12 times.

Step-by-step explanation:

To find how many times the conductor checks on the passengers, you must do

8 divided by 2/3

because you have to find how many 2/3 (times checked by conductor) are in 8 hours.

8/1 ÷ 2/3

Switch the two numbers of 2/3 or find the reciprocal which is

3/2

and change ÷ to ×

Now solve.

8/1 x 3/2 =  24/2 (8x3=24 and 1x2=2)

which Simplified is

12/1 or 12

Check your answer:

12/1 x 2/3 = 24/3 = 8

The conductor checked on the passengers 12 times.

Answer:

AAS

Step-by-step explanation:

There are two congruent angles, but the congruent side is not included between the two angles.

Answer:

i think it's b4

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

because it is the right answer

Answer:

8 weeks

Step-by-step explanation:

265-30 = 240

240/30(per week)=8

Answer is 8 weeks

Answer:

No.

Step-by-step explanation:

Translation is a type of rigid transformation. It simply moves the figure around the coordinate plane, so the size doesn't change.

well, a right-triangle will have one angle that is 90°, and using the pythagorean theorem, we also know that the longest side is really the root of the sum of the square of the other two.  After all that mouthfull let's check

[tex]\stackrel{longest}{16}~~ = ~~\sqrt{\underset{short}{13^2}~~ + ~~\underset{short}{4^2}}\implies 16=\sqrt{169+16} \\\\\\ 16=\sqrt{185}\implies 16^2=185\implies 256~~ \ne ~~185\qquad \leftarrow \textit{nope, it isn't}[/tex]

Answer:

x = 95

Step-by-step explanation:

The total degree of a circle is 360. The twp arcs on each side of the parallel lines are equal.

Subtract 135 and 35 from your total

360 - 135 - 35 = 190

Divide your answer by 2

190 ÷ 2 = 95

 [tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]

______________________________

 [tex]\bold{Solution~Steps:}[/tex]

[tex]1.)~Multiply~the~parenthesis:[/tex]

[tex]2.)~Subtract~the~parenthesis:[/tex]

[tex]3.)~Subtract~on~the~side~without~an~equal:[/tex]

______________________________

 [tex]\bold{Answer:}[/tex]

______________________________

 [tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~-TotallyNotTrillex}[/tex]

Answer:

2(x+2)

Step-by-step explanation:

(2x²+10x+12)/(x+3)=(2(x²+5x+6))/(x+3)=(2(x²+2x+3x+6))/(x+3)=(2(x(x+3)+2(x+3)))/(x+3)=(2(x+3)+(x+2))/(x+3)=2(x+2)

i hope you understand (well it's math)

Answer:

undefined

Step-by-step explanation:

(y2-y1)/(x2-x1)

replacing x and y with the given value:

(-4-1)/(8-8)

-5/0

the slope is undefined because the run is 0

Step-by-step explanation:

The diagonals of a square bisect each other, are perpendicular to each other, bisect opposite angles and are congruent.