Khanacademy Unit: Sequences
Which one of them is right?

Answer:

Let's define:

s1 = (3, 4)

s2 = (-1, 1)

s3 = (2, 0)

The system will be linearly dependent if we can write one of the vectors as a linear combination of the other two, so for example:

s1 = a*s2 + b*s3

where a and b are real numbers.

So let's try to solve this:

(3, 4) = a*(-1, 1) + b*(2, 0)

Note that the second term in the left only modifies the x-component. And the y-component in the left is 4, so we can conclude that a = 4 (because the first term is the only that has an y-component different than zero)

(3, 4) = 4*(-1, 1) + b*(2, 0)

(3, 4) = (-4, 4) + b*(2, 0)

Now we need to solve:

3 = -4 + b*2

3 + 4 = b*2

7 = b*2

7/2 = b

Then the linear combination is:

s1 = 4*s2 + (7/2)*s3

(3, 4) = 4*(-1, 1) + (7/2)*(2, 0)

Then the set is linearly dependent.

Answer:

-1 over 2

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

The line joins (-2, 2) and (0, 1).

Remember that slope equals change in y all divided by the change in x.

Here,

change in y = 1 - 2 =- 1

change in x = 0 -(-2) = 2

Thus, slope =- 1/2

Answer:K=-2

Step-by-step explanation:

becuase you do the opposite of +9 which is -9 and you do 7-9 which is -2 so K=-2

Answer:

90

Step-by-step explanation:

Let the whole number be x.

100% is to x as 70% is to 63

100/x = 70/63

10/x = 10/9

10x = 90 * 10

x = 90

Answer: 90

Step-by-step explanation:

0.7x = 63, x = 63/0.7 = 90

Step-by-step explanation:

the answer is in the image above

Answer:

mean of data is 141.2

Step-by-step explanation:

mean of data = sum of data / no of data

=98 + 208 + 189 + 94 + 117 / 5

=706 / 5

=141.2

Answer:

Step-by-step explanation:

98 + 208 +189 +94 +1117 =709

706/5 = 141.2

Hope this helps!

Answer:

x=63

Step-by-step explanation:

Because we know that the total angle is a right angle (see the square in the top right of the problem), and 25 and x+2 constitute as the only two angles making up the total angle, we can say that 25 and x+2 are complementary, meaning they add up to 90 degrees. We can then write our equation as follows:

25 + (x+2) = 90

27+x=90

Subtract 27 from both sides

x=63

Answer: See explanation

Step-by-step explanation:

From the information given, the following can be deduced:

Let rate of jet in still air be J

Let rate of wind be W

The formula for distance:

d = rt

Therefore, r = d/t

When, flying against the wind, then the Jet flies at a rate of J - W which will be:

= 1590mi/3hrs

= 530mph

When flying with the wind the jet will fly at a rate of J+W which will be:

= 8240mi/8hrs

= 1030 mph

Their average rate will be:

J = (530+1030)/2

= 1560/2

J = 780 mph

Since J - W = 530

Therefore, so

780 - W = 530

W = 780 - 530

W = 250 mph

The Jet in still air flies at a rate of 780 mph and the wind speed is 250 mph

Step-by-step explanation:

sum of 5 times a number and -2, + 8n

becomes:

5n + (-2) + 8n, or

5n -2 +8n, or. 13n - 2

Answer:

30

Step-by-step explanation:

You use polynomial division to divide all the numbers on the numerator by the denominator.

Answer:

The "Standard Form" for writing down a Linear Equation is

Ax + By = C

A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

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

y = 4/5x + 2

Multiply both sides by 5 to clear the fraction

5y = 4x + 10

Subtract 4x from both sides

-4x + 5y = 10     This is answer D, BUT A shouldn't be negative

Multiply both sies by -1

4x - 5y = -10    This is correct Standard Form, BUT it is not one of the choices

Answer D is closest to being correct

Answer:

-5/2 because there is -5y/2 but we have to take coefficient only so -5/2

Answer:

Because we know that here we have an oscillation, we can model this with a sine or cosine function.

P = A*cos(k*t) + M

where:

k is the frequency

A is the amplitude

M is the midline

We know that at t = 0, we have the lowest population.

We know that the mean is 129, so this is the midline.

We know that the population oscillates 25 above and below this midline,

And we know that for t = 0 we have the lowest population, so:

P = A*cos(k*0) + 129 = 129 - 25

P = A + 129 = 129 - 25

A = -25

So, for now, our equation is

P = -25*cos(k*t) + 129

Because this is a yearly period, we should expect to see the same thing for t = 12 (because there are 12 months in one year).

And remember that the period of a cosine function is 2*pi

Then:

k*12 = 2*pi

k = (2*pi)/12 = pi/6

Finally, the equation is:

P = -25*cos(t*pi/6) + 129

Now we want to find the lowest population was in April instead:

if January is t = 0, then:

February is t = 2

March is t = 3

April is t = 4

Then we would have that the minimum is at t = 4

If we want to still use a cosine equation, we need to use a phase p, such that now our equation is:

P = -25*cos(k*t + p) + 129

Such that:

cos(k*4 + p) = 1

Then:

k*4 + p = 0

p =  -k*4

So our equation now is:

P = -25*cos(k*t  - 4*k) + 129

And for the periodicity, after 12 months, in t = 4 + 12 = 16, we should have the same population.

Then, also remembering that the period of the cosine function is 2*pi:

k*12 - 4*k = 2*pi

k*8 = 2*pi

k = 2*pi/8 = pi/4

And remember that we got:

p = -4*k = -4*(pi/4) = -pi

Then the equation for the population in this case is:

P = -25*cos( t*pi/4 - pi) + 129

Answer:

The answer is "Option a".

Step-by-step explanation:

Dispute C comes under factual dispute because the words Vacaville or Victorville are two different places and they are arguing about the fact that's why option a is correct.

Answers:

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

Explanation:

We're given these three clues

Clue 3 is what we'll start with. Since Mrs. Gray is a doctor, this means that the doctor owns either a white horse or a brown horse. The doctor can't own a gray horse because the names can't match up (eg: the last name Gray with gray horse), due to clue 1.

If Mrs. Gray owned a brown horse, then she'd be a teacher (clue 2). But clue 3 says she's a doctor. We have a contradiction if Mrs. Gray owns the brown horse. Therefore, Mrs. Gray owns the white horse.

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

After we concluded the last section, we now know the following:

In short, we've just crossed "Mrs. Gray", "doctor", and "white horse" from the list.

Based on clue 1, we know that Mrs. Brown cannot possibly own the brown horse. Therefore, she must own the gray horse. So Mrs. White must own the brown horse.

Since Mrs. White owns the brown horse, she must be the teacher (clue 2). That leaves "lawyer" as the last profession, and that's assigned to Mrs. Brown.

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

Side note: I apologize for being a bit wordy, but I wanted to be very careful in the logical sense as to approach this problem. There's probably a much quicker efficient way to do this.

Diagram A and Diagram B do not form a triangular prism

Answer:

1059

Step-by-step explanation:

33 · 32 + 12 ÷ 4

PEMDAS

Multiply and divide first from left to right

1056 + 3

Then add

1059

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{33\times32+12\div4}\\\\\mathsf{33\times32= \boxed{\bf 1,056}}\\\\\mathsf{\bold{1,056}+12\div4}\\\\\mathsf{12\div4=\boxed{\bf 3}}\\\\\mathsf{1,056+\bf 3}\\\mathsf{= \boxed{\bf 1,059}}\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 1,059}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite40:)}[/tex]

Equations:

x + y = 50

x = y - 18

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

Add and solve for "x"::

2x = 32

x = 16

-----

Solve for "y"::

16 + y = 50

y = 34

ANSWERS ARE IN BOLD

Answer:

14

Step-by-step explanation:

sqrt(25) = 5

sqrt(81) = 9

5 + 9 = 14

Answer:

5.83095189485

Step-by-step explanation:

Its so long

Answer:

Step-by-step explanation:

64

128°

Step-by-step explanation:

The measure of the intercepted arc is twice the measure of the inscribed angle in a circle. Since the inscribed angle is given as 64°, that means that the intercepted arc x is 2×64° = 128°

Answer:

Step-by-step explanation:

question no . 5

ratio of angle L

take angle as reference angle

using cos rule

cos L = base / hypotenuse

= 4/5

ratio of angle N

take angle N as reference angle

using sin rule

sin N = opposite / hypotenuse

= 4/5

for measure of angle L

cos L = 4/5

cos L = 0.8

L = [tex]cos^{-1}(0.8)[/tex]

L = 36.9

for meanure of angle N

sin N = 4/5

sin N = 0.8

N = [tex]sin^{-1}(0.8)[/tex]

N = 53.1

Answer:

by using middle term break method

Step-by-step explanation:

9x^2 + 12x + 4

9x^2+ (6 + 6)x + 4

9x^2 + 6x + 6x + 4

3x(3x + 2) + 2(3x + 2)

(3x + 2)(3x + 2)

(3x + 2)^2

Step-by-step explanation:

[tex]\huge\mathfrak\pink{Answer}[/tex]

Total number of students= y

(25/100) xy= 200

25 xy = 200 x 100

25y 20000

y = 20000/25

y 800

total number of students = 800

Step-by-step explanation:

[tex]\mathfrak\pink{Answer}[/tex]

Total number of students= y

(25/100) xy= 200

25 xy = 200 x 100

25y 20000

y = 20000/25

y 800

total number of students = 800

Answer:

if you still need the answer its B here the explenation in a picture:

Step-by-step explanation:

Answer:

1) Yes, it is a right angle triangle

2)Yes, it is a right angle triangle

3) No, they are not similar.

Step-by-step explanation:

Dimension of triangle A = 48, 55 & 73

Dimension of triangle B = 36, 77 & 85

For any of the triangles to be a right angled one, then;

c = √(a² + b²)

Where a,b & c are side dimensions of a triangle.

Thus;

Triangle A: c = √(48² + 55²)

c = √5329

c = 73

This tallies with what we are given and so it is a right angled triangle.

Triangle B: c = √(36² + 77²)

c = √(7225)

c = 85

Similar to the third side dimension of 85, thus it is true.

For Triangle A & B to be similar, the ratio of the 3 corresponding sides must be in a whole number ratio.

Thus, we have;

48/36 = 1.5

55/77 = 5/7

73/85 = 73/85

Since the ratios are not similar, then we can say that the triangles are not similar.

Answer:

<ABC = 15

< BAC = 150

Step-by-step explanation:

<C = <B since this is an isosceles triangle.  We know this because AC = AB

<C = 15 so <ABC = 15

The sum of the angles of a triangle is 180

A + B+ C = 180

A + 15+15 = 180

A +30 =180

A = 180-30

A = 150

< BAC = 150

Answer:

It's answer is 93i +558....

Answer:

The height is 8cm

Step-by-step explanation:

Given

[tex]L_A = 240cm^2[/tex] --- lateral area

[tex]a = 12cm[/tex] --- base lengths

Required

The height of the pyramid

The lateral area of a square pyramid is:

[tex]L_A = a\sqrt{a^2 + 4h^2[/tex]

So, we have:

[tex]240 = 12\sqrt{12^2 + 4h^2[/tex]

[tex]240 = 12\sqrt{144 + 4h^2[/tex]

Divide both sides by 12

[tex]20 = \sqrt{144 + 4h^2[/tex]

Square both sides

[tex]400 = 144 + 4h^2[/tex]

Collect like terms

[tex]4h^2 = 400 - 144[/tex]

[tex]4h^2 = 256[/tex]

Divide by 4

[tex]h^2 = 64[/tex]

Take square roots

[tex]h = 8[/tex]