100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!

If cos(x) = -5/6, and x lies in quadrant"II", then exact values are:

sin(2x) = (-5√11)/(18);

cos(2x) = 7/18;

tan (2x) = -5√11/7.

We know that, Cos(x) = -5/6 and "x" is in quadrant II, so, we can use the Pythagorean identity to find sin(x):

sin(x) = √(1 - cos²(x)) = √(1 - (-5/6)²) = √(1 - 25/36) = √(11/36) = √11/6

Using the double angle trigonometry identities for sine and cosine, we find sin(2x) and cos(2x):

Substituting the value of Sin(x) and Cos(x),

We get,

sin(2x) = 2sin(x)cos(x) = 2(√11/6)(-5/6) = (-5√11)/(18);

cos(2x) = cos²(x) - sin²(x) = (-5/6)² - (11/6) = 25/36 - 11/36 = 14/36 = 7/18;

Finally, we find tan(2x) by using the identity:

tan(2x) = sin(2x)/cos(2x) = (-5√11/18) / (7/18) = -5√11/7.

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Answer:

15h-6k+12m

Step-by-step explanation:

The perimeter of the triangle is the sum of all of its side lengths

P=a+b+c

If a=5h-4k

b=10h+7m

c=5m-2k

Then the formula would be

P=(5h-4k)+(10h+7m)+(5m-2k)

P=15h-6k+12m

Hope this helps!

Answer:

(x-3)(x+4)

Step-by-step explanation:

This way is how it s done in Greece. If u don't understand don't read the explanation Δ=β2-4αγ=81-32=49

χ1,2=-1+-7^2=3

=-4

Answer: 189 m^2

Step-by-step explanation:

Area = (Diagonal 1 x Diagonal 2) ÷ 2

There were 64 players at the start of the tournament.

To determine the number of players at the start of the tournament

We need to work backwards from the final round to the first round.

In the final round, there will be only two players remaining since the winner of that match will be declared the overall champion.

In the penultimate (fifth) round, there will be four players remaining.

These four players must have come from the previous round, where there were eight players.

Continuing this pattern, in the fourth round, there will be eight players, and in the third round, there will be 16 players.

In the second round, there will be 32 players, and in the first (initial) round, there will be 64 players.

Therefore, there were 64 players at the start of the tournament.

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Answer:

x =  7, y = 3, z = -4

Step-by-step explanation:

Therefore, the slope of line s is equal to (d + b) / (a - c).

In mathematics, the slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those same two points. In other words, the slope is the change in the y-coordinate divided by the change in the x-coordinate. If the slope is positive, the line is increasing from left to right and has an upward direction. If the slope is negative, the line is decreasing from left to right and has a downward direction. If the slope is zero, the line is horizontal. If the slope is undefined, the line is vertical. The concept of slope is important in various fields of mathematics, science, and engineering, as it helps to describe the relationship between two variables and make predictions based on that relationship. It is also used in calculus to find the rate of change of a function, and in geometry to find the equation of a line or the angle between two lines.

Here,

Since line s is parallel to line t, it has the same slope as line t. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, the points on line t are (a, -b) and (-c, d), so the slope of line t is:

slope of t = (d - (-b)) / (-c - a)

slope of t = (d + b) / (a - c)

Since line s is parallel to line t, it has the same slope as line t:

slope of s = (d + b) / (a - c)

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Answer:

To find the perimeter of a regular pentagon, you need to know the length of one side and the number of sides. In a regular pentagon, all sides have the same length and the shape has 5 sides.

Let's say the length of one side of the regular pentagon is 's'.

The formula for the perimeter of a regular pentagon is:

Perimeter = 5s

This is because a regular pentagon has 5 sides of equal length, so you can simply add the length of each side together 5 times.

Therefore, the perimeter of a regular pentagon with a side length 's' is 5s.

Step-by-step explanation:

The difference between the adjustable-rate mortgage (ARM) and the  fixed-rate mortgage is $176,494.80.

First, find the total amount paid on the adjustable-rate mortgage would be :
= ( 5 years x 12 months x 2, 506.43 payment ) + ( 10 x 12 x 3, 059. 46 ) + ( 5 x 12 x 3, 646.76) + ( 5 x 12 x 3, 630.65 )

=  $ 1, 172, 971. 20

Then we can find the total payment for the fixed - rate mortgage :

= Monthly payment x Number of years

= 2, 767. 99 x 30 years x 12 months

= $ 996, 476. 40

The difference is:

= 1, 172, 971.20 - 996, 476. 40

= $ 176,494. 80.

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The ratio of the two arc lengths is equal to a / b. (Correct choice: B)

In this problem we must determine the ratio of two arc lengths, that is, the ratio between two circular arcs. The length of a circular arc is described by the following expression:

s = θ · r

Where:

s - Arc length

θ - Angle, in radians.

r - Radius

And the ratio of the length JK to the length MN is:

JK / MN = (θ · a) / (θ · b)

JK / MN = a / b

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After 4 years, the investment of $700 at 4% compounded daily results in a future value of $821.45.

The future value represents the present value or investment compounded at an interest rate periodically for a certain number of years.

The future value can be determined using the FV formula or an online finance calculator.

N (# of periods) = 1,460 days (4 years x 365)

I/Y (Interest per year) = 4%

PV (Present Value) = $700

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $821.45

Total Interest = $121.45

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The scale factor between a square of dimensions 7 by 7 and a scaled copy of dimensions 21/2 by 21/2 is 3/2 or 1.5.

We know that the dimensions of the square on the left are 7 by 7, and the dimensions of the square on the right are 21/2 by 21/2.

To find the scale factor, we can divide the dimensions of the square on the right by the dimensions of the square on the left

scale factor = (21/2) / 7

We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor, which is 7

scale factor = (21/2) / 7 = (21/2) * (1/7) = 3/2

Therefore, the scale factor is 3/2, or 1.5.

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Answer: y = -|x + 1| + 1

Step-by-step explanation:

This is a "V" shaped graph, so we know it uses the absolute value function. This is the parent function:

    y = |x|

This represents the possible transformations:

➜ a is amplitude

➜ h is horizontal shift

➜ k is vertical shift

    f(x) = a | x - h | + k

Next, we see it is shifted one unit upwards.

    y = |x| + 1

Then, we see it is also shifted one unit left.

➜ Note that this shift is -h units, so we will use positive for moving left.

    y = |x + 1| + 1

Lastly, we see this graph is flipped and has a negative slope, or amplitude.

    y = -|x + 1| + 1

Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.

Given data:

From the figure:

m∠RST  = m∠QST + m∠QSR

Put the values

70 = 2x + 3x - 10

5x = 80

x = 16

Thus,

m∠QSR = 3x - 10  = 3(16) - 10

m∠QSR = 38

Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

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Complete question:

If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.

The figure is attached:

16

48

32

38

Answer: 27.33

Step-by-step explanation: If you use a calculator to do the hard stuff the rest is a breeze

Time taken by final lesson is 48 minutes and time consumption will not be affected if first lesson takes less time to finish.

Given that;

The time to finish five lessons = 4 hours

Then one lesson takes = 4/5 hours to finish

(a) Since  each lesson takes equal amount of time

Therefore,

The time taken by final lesson in minutes = (4/5)x60

                                                                      = 48 minutes

(b) Since each lesson has own capacity of time so the time consumption for other lesson is not affected if first lesson takes less time.

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The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.

:: Radius of trundle wheel = 30 cm = 0.3 meter (as 100 cm = 1 m)

:: No. of rotations = 48

:: Circumference of a circle = ( 2 x π x r )

where, r is radius of the circle

So, as,

Distance between junctions = [ (circumference of trundle wheel) x (no. of rotations) ]

Therefore,

Distance = (2 x π x 0.3) x (48)

Distance = 2 x (3.14) x 0.3 x 48

Distance = 90.432 meters

When rounded off to the nearest meter,

Distance = 90 meters.

So, The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.

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Answer:

Four units left and one unit up

Step-by-step explanation:

Since we're subtracting from x, the figure is going to go toward the left side of the coordinate plane, and since we're adding to y, the figure is going to go up.

The missing parameters of the regular polygons are listed below:

Case 1: θ = 45°, a = 10.864 cm

Case 2: θ = 72°, s = 5.812 cm

In this problem we must determine missing parameters of regular polygons, that is, polygons with sides of equal length. All parameters are summarized below:

Central angle

θ = 360 / n

Relationship between apothema and side length

a = s / [2 · tan (180 / n)]

Where:

Now we proceed to find missing parameters:

Case 1: s = 9 cm, n = 8

θ = 360 / 8

θ = 45°

a = (9 cm) / [2 · tan (180 / 8)]

a = 10.864 cm

Case 2: a = 8 cm, n = 5

θ = 360 / 5

θ = 72°

s = 2 · a · tan (180 / n)

s = 2 · (8 cm) · tan (180 / 5)

s = 5.812 cm

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Answer:

Step-by-step explanation: 0+0=0

Answer:

0

Step-by-step explanation:

0+0= nothing that why.

Based on the information, we identified that the scale used in the construction is approximately 1:35.2.

To find the scale used in the construction of the Crazy Horse Monument, we need to divide the height of the actual monument by the height of the model. Let's use the following formula to calculate the scale:

The height of the actual monument is 563 feet and the height of the scale model is 16 feet. Substituting these values in the formula, we get:

Simplifying the fraction, we get:

Therefore, the scale used in the construction of the Crazy Horse Monument is approximately 1:35.2.

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The integral for this problem has the result given as follows:

[tex]\int_2^5 -8f(x) dx = 168[/tex]

The integral over the largest region for this problem is given as follows:

[tex]\int_2^9 f(x) dx = -14[/tex]

The integral can be divided into two smaller regions, as follows:

[tex]\int_2^9 f(x) dx = \int_2^5 f(x) dx + \int_5^9 f(x) dx[/tex]

Hence the integral from x = 5 to x = 9 is given as follows:

[tex]-14 = \int_2^5 f(x) dx + 7[/tex]

[tex]\int_2^5 f(x) dx = -21[/tex]

Multiplying -21 by -8, the result of the integral is given as follows:

[tex]\int_2^5 -8f(x) dx = 168[/tex]

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The decimal used to figure the price of their clothing is 2.1

The improvement in Larry's test score written as a decimal is 1.52

Markup = 210%

= 210/100

= 21/10

= 2.1

Larry's increased test score percentage = 152%

= 152/100

= 1.52

In conclusion, the price of clothing and Larry's test score in decimals is 2.1 and 1.52 respectively.

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Using the continuously compounded interest formula, the amount of debt owed after 5 years is $ 8988.18

The continuous compounding interest formula is given by P = Peⁿˣ where

Since Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously? To determine that, we use the continuously compounded interest formula.

Given that

Substituting the values of the variables into the equation, we have that

P = Peⁿˣ

P = $7000e⁰°⁵ ˣ ⁵

P = $7000e⁰°²⁵

P = $7000(1.28)

P = $ 8988.18

So, the amount of debt owed is $ 8988.18

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The vertices that produces the circuit of lowest cost is A and D. So, the correct answer is A) and D).

To apply the repeated nearest neighbor algorithm, we need to start at a vertex and repeatedly choose the nearest neighbor until all vertices have been visited. Then, we return to the starting vertex to complete the circuit.

Starting at vertex A, we can follow the path A-DE-BE-C-AD-BC-E-A. The total cost of this circuit is 3 + 1 + 13 + 7 + 6 + 5 + 3 = 38. Starting at vertex B, we can follow the path B-E-DE-BC-AD-C-A-B. The total cost of this circuit is 1 + 3 + 7 + 6 + 5 + 15 + 10 = 47.

Starting at vertex C, we can follow the path C-BC-AD-DE-E-B-CA-C. The total cost of this circuit is 5 + 6 + 1 + 13 + 3 + 15 = 43. Starting at vertex D, we can follow the path D-AD-BC-C-E-DE-BD-DA. The total cost of this circuit is 6 + 5 + 7 + 3 + 10 + 11 = 42.

Starting at vertex E, we can follow the path E-DE-BE-C-BC-AD-CA-E. The total cost of this circuit is 1 + 13 + 7 + 5 + 6 + 15 = 47. Therefore, the circuits with the lowest cost are those starting at vertex A and vertex D, both with a total cost of 38 and 42 respectively. So, the correct option is A) and D).

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The volume of each cup shown above are as follows;

Volume of small cup = 50.24 in³.

Volume of medium cup = 127.56 in³.

Volume of large cup = 226.08 in³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the parameters, we have:

Volume of small cylinder, V = 3.14 × 2² × 4

Volume of small cylinder, V = 50.24 in³.

Volume of medium cylinder, V = 3.14 × 2.5² × 6.5

Volume of medium cylinder, V = 127.56 in³.

Volume of large cylinder, V = 3.14 × (6/2)² × 8

Volume of large cylinder, V = 226.08 in³.

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The other value of x where g(x) = 15 is 16 in the absolute value function

Since the vertex of the absolute value function is at (10,0), the equation for the function can be written as:

g(x) = a|x - 10|

To find the value of a, we can use the fact that the function passes through the point (4,15):

15 = a|4 - 10|

15 = 6a

a = 2.5

So the equation for the absolute value function is:

g(x) = 2.5|x - 10|

To find another value of x where g(x) = 15, we can set the equation equal to 15 and solve for x:

2.5|x - 10| = 15

|x - 10| = 6

x - 10 = 6 or x - 10 = -6

x = 16 or x = 4

Therefore, there are two possible values of x where g(x) = 15: x = 16 and x = 4.

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If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.

To solve this problem, we need to use the formula for exponential growth:

A = P(1 + r)ᵗ

where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.

Plugging these values into the formula, we get:

A = 60(1 + 0.015)¹⁰

A ≈ 71

t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.

Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.

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To solve the problem, we need to find Julian's average speed, given that he started biking from a position behind the simulated biker at a speed of 20 km/h, and after 15 minutes, his position was reported as -214 km.

We can use the formula for average speed:

Average speed = total distance / total time

To find the total distance, we need to calculate the displacement of Julian from the initial position of -d (where d is the distance between Julian and the simulated biker when he started biking) to the position of -214 km after 15 minutes.

Displacement = final position - initial position

Displacement = (-214 km) - (-d) = d - 214 km

The total distance covered by Julian is equal to the absolute value of the displacement, since the direction of the motion does not matter when computing distance.

Total distance = |d - 214 km|

To find the total time, we need to convert 15 minutes to hours:

Total time = 15 minutes / 60 minutes/hour = 0.25 hours

Now we can substitute the values into the formula for average speed:

Average speed = total distance / total time

Average speed = |d - 214 km| / 0.25 hours

Since Julian was traveling at a constant speed of 20 km/h, we can also express the distance in terms of time:

Average speed = (20 km/h) x t / 0.25 hours

where t is the time Julian biked in hours.

Setting the two expressions for average speed equal to each other, we can solve for t:

|d - 214 km| / 0.25 hours = (20 km/h) x t / 0.25 hours

|d - 214 km| = 20 km/h x t

Solving for t:

t = |d - 214 km| / 20 km/h

Now we can substitute this expression for t into either expression for average speed:

Average speed = (20 km/h) x t / 0.25 hours

Average speed = |d - 214 km| / 0.25 hours

Substituting the expression for t:

Average speed = |d - 214 km| x 4 / |d - 214 km|

Simplifying:

Average speed = 80 km/h

Therefore, Julian's average speed so far has been 80 km/h.