Simplify the expression cos2x−2cos2x+1 .

Part A: The student that simplified the give trigonometrical identity expression incorrectly is student B.

Part B: The correct complete solution is shown below

From the question, we are to determine the student that simplified the expression incorrectly.

Part A:

The student that simplified the expression incorrectly is student B.

The student is went wrong in step 3.

From step 2, the student divided (1 + tan²θ) by (tanθ/cotθ). The student is supposed to divide [(1 + tan²θ)/tanθ] by cotθ

Part B:

The correct solution is shown below

[(1 + tan²θ)/tanθ] ÷ cotθ

(sec²θ/tanθ) ÷ cotθ

Which can be written as:

(sec²θ/tanθ) ÷ 1/tanθ

Then,

(sec²θ/tanθ) × tanθ/1

= sec²θ/1

= sec²θ

Hence, the correct simplified expression is sec²θ

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Answer:180 square inches

Step-by-step explanation:

18*6+9*8=180

The linear equation representing the situation is y = 0.75x - 2.25, and according to this equation, the height of the sprout after 14 days would be 8.25 inches.

To create a linear equation that represents the relationship between the height of the bean sprout and the number of days after planting.

Therefore, the slope of the line is:

slope = change in height / change in days = (7.5 - 3) / (13 - 7) = 1.5

The intercept of the line can be found by substituting one of the data points into the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope, x1 and y1 are the coordinates of one of the data points. We choose the first data point (7, 3):

y - 3 = 1.5(x - 7)

y - 3 = 1.5x - 10.5

y = 1.5x - 7.5

Therefore, the linear equation that represents the relationship between the height of the bean sprout (y) and the number of days after planting (x) is:

y = 1.5x - 7.5

To find the height of the sprout after 14 days, we substitute x = 14 into the equation:

y = 1.5(14) - 7.5

y = 10.5

Therefore, the height of the sprout after 14 days is predicted to be 10.5 inches.

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The total number of miles driven by the two brothers is 2,220 miles.

Average speed is the ratio of total distance and time. It measures how fast an object is moving with respect to time.

Average speed = distance / time

In order to determine the formula for distance from the formula of average speed, multiply both sides of the equation by time.

Distance = time x average speed.

The distance that Kevin covered  = 65 x 12 = 780 miles

The distance that Jeffery covered  = 60 x 24 = 1440 miles

The total distance is the sum of the distance covered by Kevin and the distance covered by Jeffery.

Total distance = 1440 + 780 = 2,220 miles

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Answer:

The third one

Step-by-step explanation:

if you look at it, and actually solve it its 88.

Answer:    c=2πr

Step-by-step explanation:

because im just that guy

Answer:

c=62.8

Step-by-step explanation:

diameter=20

radius=10

c=2πr

c=2×22/7×10

c=62.8

Step-by-step explanation:

We can simplify the given expression using the rules of absolute values:

l-80-20l – 100 + l-100l

= -(20l + 80) - 100 + 100 (since |x| = -x when x is negative)

= -20l - 80

= -20(l + 4)

Therefore, the simplified expression is -20(l + 4).

Answer:

100

Step-by-step explanation:

[tex] | - 80 - 20| - 100 + | - 100| \\ = | - 100| - 100 + | - 100| \\ = 100 - 100 + | - 100| \\ = | - 100| \\ = \boxed{100}[/tex]

____________

hope it helps!

Therefore , the solution of the given problem of expressions comes out to be Q = Q0 e(ln(0.9)/24)t this is the formula for the block's mass at any moment t.

Calculations such as joining, random subdivision, variable multiplier, and elimination are required. They would accomplish the following if they were united: An  algorithm, some information, and a mathematical equation. Numerical information, formulas, elements, and arithmetic operations like additions, erasures, errors, and categories are all included in a declaration of truth. Words and phrases can be evaluated and analysed.

Here,

Let's write Q for the radioactive material's mass at any moment t. (t). We can write: Because the substance decays at a rate proportional to its mass.

=> -kQ = dQ/dt

where k is a measure of ratio. This first-order differential equation can be solved by separating the variables, and it is separable:

=>-k dt Equals dQ/Q

By combining both parts, we obtain:

=>Q = -kt + C, where

where C is the integration constant. We can use the original assumption that the material has a mass of Q grammes at time t = 0 to determine C:

=> ln(Q) = C

When we add this to the prior solution, we obtain:

=> Q = -kt + ln, where (Q0)

where Q0 is the starting mass of the material.

=> 0.9Q0 = Q(24) = Q0 e^(-k*24)

After finding k, we obtain:

=> k = ln(0.9)/(-24) (-24)

Using this value of k as a substitute in the preceding equation, we obtain:

=> (ln(0.9)/24)t - ln(Q) + ln (Q0)

If we simplify, we get:

=> Q = Q0 e(ln(0.9)/24)t

This is the formula for the block's mass at any moment t.

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The distance KT and angle of elevation of the pole's top, K, with respect to the ground, D, are;

KT is about 6.2 cm

DN = 30 m

The angle of elevation of K from D is  0.23°

The angle created between a horizontal line and the line of sight of a viewer gazing up at an object is known as the angle of elevation.

The two vertical poles are MT and NK

The height of MT = 8 cm

The height of NK = 12 cm

From the top of the pole MT, point T, to the top of the pole NK, point K, there is a 40-degree elevation difference.

The poles' height differences are 12 cm - 8 cm, or 4 cm.

The distance KT can be found as follows;

Therefore;

sin(40°) = 4/KT

KT = 4/(sin(40°)) ≈ 6.2

The distance KT is approximately 6.2 cm

According to the information in the question, the distance is DN = 30 m.

The base of the poles MT and NK is on the same level ground as point D.

ND=30m

Hence, the trigonometric ratio for tangent may be used to get the angle of elevation,, of the top of the pole NK, (point K), from D as follows;

tan(θ) = NK/ND

tan(θ) = (12 cm)/(30 m) = 0.12/30 = 0.004

θ = arctan(0.004) ≈ 0.23°

K is elevated from d at an angle of roughly 0.23°.

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Answer:

The equation in general form is x² + y² - 4x - 10y - 20 = 0

Answer:

x² + y² -  4x - 10y - 20 = 0

Step-by-step explanation:

The general equation of circle is
x² + y² + ax + by + c = 0

where a, b and c are constants

To convert the standard form of the equation (x - 2)² + (y - 5)² = 7² into general form, expand the squares and the constant on the right side and adjust the terms to have 0 on the right side

(x - 2)² = x² - 4x + 4
(y - 5)² = y² - 10y + 25

7² = 49

(x - 2)² + (y - 5)² = 7²
= x² - 4x + 4 + y² - 10y + 25 = 49

Subtract 49 from each side to get 0 on the right:
x² - 4x + 4 + y² - 10y + 25 - 49 = 0

Simplify the constant terms
4 + 25 - 49 = 29 - 49 = -20

Required equation is

x² + y² -  4x - 10y - 20 = 0

Using the multiplier formula, the eventual change in aggregate expenditure due to the inflow of R10 billion into South Africa and using the marginal propensity to consume (MPC) is R6 billion.

The multiplier formula is used to compute the amount of new income generated from the flow of extra income.

The multiplier formula uses the MPS (marginal propensity to save) to compute the multiplier as follows:

M = 1 / MPS

The marginal propensity to save gives the proportion of income that will be saved.

The marginal propensity to save (MPS) = 0.4

M = 1 / MPS

M = 1/0.4)

= 2.5

Change in aggregate expenditure = R25 billion (2.5 x R10 billion)

Thus, we expect the aggregate expenditure in South Africa to increase by R25 billion following the inflow of R10 billion investment.

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There are 6 possible outcomes for each roll of the cube, since there are 6 letters on the cube. Out of the 6 letters, there are 3 consonants (S, L, V) and 3 vowels (O, E, D).

To find the probability of rolling two consonants, we need to multiply the probability of rolling a consonant on the first roll (3/6) by the probability of rolling a consonant on the second roll (also 3/6), since the rolls are independent events.

(3/6) * (3/6) = 9/36 = 1/4

Therefore, the probability of rolling two consonants is 1/4, which can also be expressed as 25%.

Inequality y 5x - 7 has solutions (-5, -3), (-4, 2), and (-1, 0).

In order to address an inequality • You can multiply or divide each side by the same positive amount; • You can add the same amount to each side; • You can take the same amount away from each side. If you multiply or divide each side by a negative value, the inequality sign must be reversed.

Let's examine each point individually:

(-5, -3)

y ≥ 5x - 7

-3 ≥ 5(-5) - 7

-3 ≥ -32

The inequality is true, so (-5, -3) is a solution.

(-4, 2)

y ≥ 5x - 7

2 ≥ 5(-4) - 7

2 ≥ -27

The inequality is true, so (-4, 2) is a solution.

(1, -2)

y ≥ 5x - 7

-2 ≥ 5(1) - 7

-2 ≥ -2

The inequality is not true, so (1, -2) is not a solution.

(-1, 0)

y ≥ 5x - 7

0 ≥ 5(-1) - 7

0 ≥ -12

The inequality is true, so (-1, 0) is a solution.

(3, 0)

y ≥ 5x - 7

0 ≥ 5(3) - 7

0 ≥ 8

The inequality is not true, so (3, 0) is not a solution.

(4, 1)

y ≥ 5x - 7

1 ≥ 5(4) - 7

1 ≥ 13

The inequality is not true, so (4, 1) is not a solution.

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Answer:

The solutions to the given system of equations are:

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=-x^2+4\\y=2x+1\end{cases}[/tex]

To solve the given system of equations, substitute the second equation into the first equation:

[tex]\implies 2x+1=-x^2+4[/tex]

Add x² to both sides:

[tex]\implies x^2+2x+1=4[/tex]

Subtract 4 from both sides:

[tex]\implies x^2+2x-3=0[/tex]

Factor the quadratic equation:

[tex]\implies x^2+3x-x-3=0[/tex]

[tex]\implies x(x+3)-1(x+3)=0[/tex]

[tex]\implies (x-1)(x+3)=0[/tex]

Apply the zero product property:

[tex](x-1)=0 \implies x=1[/tex]

[tex](x+3)=0 \implies x=-3[/tex]

Substitute the found values of x into the second equation and solve for y:

[tex]x=1 \implies y=2(1)+1=3[/tex]

[tex]x=-3 \implies y=2(-3)+1=-5[/tex]

Therefore, the solutions to the given system of equations are:

Answer:

distance traveled in 1 hour = x/3

To find the distance traveled in 9 hours, we can multiply the distance traveled in 1 hour by 9:

distance traveled in 9 hours = (x/3) * 9

Simplifying this expression gives:

distance traveled in 9 hours = 3x

Therefore, the car will travel 3 times the distance it travels in 3 hours when it travels for 9 hours.

a.) The area covered by algae for 10 days after it was spotted would be = 35.7 m²

The area covered by the algae when it was first spotted = 12.5 m²

For every week(7 days) = 2(12.5)

But 10 days = x

Make X the subject of formula;

X = 10× 2(12.5)/7

X = 250/7

X = 35.7 m²

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Answer:

A
b
D

Step-by-step explanation:

The sun revolves around the Earth." Statements 1 and 4 are true.

As the question asks for statements that are not true, I will go through each statement and determine if it is true or false. Statement 1: "Water boils at 100 degrees Celsius."

This statement is true. Water boils at 100 degrees Celsius at sea level under normal atmospheric conditions.

Statement 2: "The moon is made of cheese." This statement is not true. The moon is not made of cheese. It is primarily composed of rock and does not contain any dairy products.

Statement 3: "The sun revolves around the Earth." This statement is not true.

The Earth revolves around the sun in an elliptical orbit. The concept that the Earth is at the center of the solar system and the sun revolves around it was disproven by the heliocentric model proposed by Nicolaus Copernicus in the 16th century.

Statement 4: "Gravity only exists on Earth." This statement is not true. Gravity exists everywhere in the universe. It is a fundamental force that attracts objects with mass towards each other.

While the strength of gravity may vary depending on the mass of the objects and their distance apart, it is present throughout the universe.

To summarize, the statements that are not true are: 2. "The moon is made of cheese." 3. "The sun revolves around the Earth." Statements 1 and 4 are true.

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The z-scοre is prefer tο have cοmpared tο yοur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race is -2.50.

When a value is given a Z-scοre, it shοws hοw far οff frοm the standard deviatiοn it is. The amοunt οf standard deviatiοns a given data pοint is abοve οr belοw the mean is represented by the Z-scοre, alsο knοwn as the standard scοre. The level οf variability within a particular data cοllectiοn is effectively reflected in the standard deviatiοn.

We knοw that ,

=> z=(x-µ)/σ

If we have z scοre less it means we cοmplete the race in less time as cοmpare tο οthers.

Sο, z scοre -2.50 is least as per given all the οptiοns. sο ,we wοuld yοu prefer -2.50 cοmpared tο οur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race.

Hence the z-scοre is -2.50.

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the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.

a. The exponential growth equation to represent the price y of a new HD television t years from now is:

y = $2500[tex](1 + 0.04)^t[/tex]

where t is the number of years from now.

b. To predict when a new HD television will cost $3000, we can set y = $3000 and solve for t:

$3000 = $2500[tex](1 + 0.04)^t[/tex]

1.2 = [tex]1.04^t[/tex]

ln(1.2) = t ln(1.04)

t = ln(1.2) / ln(1.04)

t ≈ 3.97

Therefore, a new HD television will cost $3000 approximately 4 years from now.

c. To determine when the amount in Jason's savings will exceed the cost of a new television, we can use the formula for continuous compound interest:

A = [tex]Pe^(rt)[/tex]

where A is the amount in savings after t years, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.

In this case, P = $2200, r = 0.047 (since the annual interest rate is 4.7%), and we want to find the time t when A = $2500. Plugging these values into the formula, we get:

$2500 = $2200[tex]e^(0.047t)1.13636 = e^(0.047t)[/tex]

ln(1.13636) = 0.047t

t = ln(1.13636) / 0.047

t ≈ 7.22

Therefore, the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.

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Answer:

-6 and -7

Step-by-step explanation:

-6 + -7 = -13

-6 * -7 = 42

The length of the diameter of the circle of the radius 4 cm is 8 cm and other solutions are added below

See attachment for the circle

This is calculated as

Diameter (d) = 2 * Radius (r)

So, we have

d = 2 * 4 cm

d = 8 cm

The number of 90° sectors that will fit inside the circle is

Sectors = (360°/90°)

Sectors = 4

See attachment for the circle

The shape created inside the circle by joining the ends of five equally spaced radii is a regular pentagon.

The length (L) of one chord is

L = 2 × r × sin(c/2)

For 6 chords created by the 5 radii, we have

Total length = 6 × 2 × r × sin(c/2)

Where

c = 360/6 = 60

So, we have

Total length = 6 × 2 × 4 × sin(60/2)

Evaluate

Total length = 24 cm

Each sector of 90° in a circle has an angle of

Angle = (360/6)°

Angle = 60°

If sectors of 45° were used, the shape created inside the circle by joining the ends of the radii would be a nonagon

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Answer:

Step-by-step explanation:

x² + 4x-21

x²-5x-2

x² + 3x + 7

x² + 4x-21

x²-5x-2

x² + 3x + 7

x²-x-1

x²-x-1

The answer of the given question based on Statistics to find minimum monthly premium payments is option D) Plan 2, since it has lower monthly premium payments.

Probability is  measure of  likelihood or chance of an event occurring. It is expressed as  number between 0 and 1, where 0 indicates an impossible event and 1 indicates  certain event

Assuming that the coverage details are similar, we can compare the monthly premium payments for each plan based on the different categories of coverage:

Individual: Plan 1 has a monthly premium of $87.32, while Plan 2 has a monthly premium of $11.77. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Spouse: Plan 2 has a monthly premium of $735.00, while Plan 1 has a monthly premium of $890.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Child: Plan 2 has a monthly premium of $606.00, while Plan 1 has a monthly premium of $750.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Family: Plan 2 has a monthly premium of $1,400.00, while Plan 1 has a monthly premium of $1,600.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Based on these comparisons, we can see that Plan 2 has a lower monthly premium for all categories of coverage. Therefore, the answer is option D: Plan 2, since it has lower monthly premium payments.

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The value of x in the infinite geometric series, x = (7 ± i√107) / 26.

We can start by simplifying the left-hand side of the equation:

-1 + 1/x + x + x² + ...+ xⁿ + ...

= -1 + (1/x) * (1/(1 - x))

Using the formula for the sum of an infinite geometric series:

1 + r + r² + ... = 1/(1 - r) for |r| < 1

We can simplify the left-hand side further:

= -1 + (1/x) * (1/(1 - x))

= -1 + (1/(x - x²))

Now we have:

-1 + (1/(x - x²)) = 10/3

Multiplying both sides by 3(x - x²), we get:

-3(x - x²) + 3 = 10(x - x²)

Simplifying, we get:

13x² - 7x + 3 = 0

Using the quadratic formula, we can solve for x:

x = (7 ± √(7² - 4133)) / (2*13)

x = (7 ± i√(107)) / 26

Since the expression is defined only for |x| < 1, we can discard the solution with the plus sign, leaving:

x = (7 - √(-143)) / 26

x = (7 - 3i√13) / 26

Therefore, the solution for x is x = (7 ± i√107) / 26.

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Answer:

Below

Step-by-step explanation:

I suppose you are looking for the ORIGINAL price

x = original

 32% is .32 in decimal

    so    .32 * x = $ 179.20

                     x = 179.20/.32 = $ 560.

Answer: 9.2 x 105

Step-by-step explanation: