Martina solved the equation x+14=44
x
+
14
=
44
. Her work is shown.

What error did Martina make?

Answer: We can use the double angle identity for tangent, which states that:

tan(2θ) = 2tan(θ) / (1 - tan²(θ))

to simplify the expression.

Let θ = 6 degrees, then we have:

tan(2θ) = tan(12 degrees)

tan(2θ) = 2tan(θ) / (1 - tan²(θ))

tan(12 degrees) = 2tan(6 degrees) / (1 - tan²(6 degrees))

We can use the tangent half-angle identity to find tan(6 degrees), which states that:

tan(θ/2) = sin(θ) / (1 + cos(θ))

Letting θ = 12 degrees, we get:

tan(6 degrees) = sin(12 degrees) / (1 + cos(12 degrees))

We can then use the double angle identity for sine, which states that:

sin(2θ) = 2sin(θ)cos(θ)

to simplify sin(12 degrees). Letting θ = 6 degrees, we get:

sin(12 degrees) = 2sin(6 degrees)cos(6 degrees)

We can use the half-angle identity for cosine to find cos(6 degrees), which states that:

cos(θ/2) = √((1 + cos(θ)) / 2)

Letting θ = 12 degrees, we get:

cos(6 degrees) = √((1 + cos(12 degrees)) / 2)

Substituting these values into the original expression, we get:

tan(12 degrees) = 2tan(6 degrees) / (1 - tan²(6 degrees))

tan(12 degrees) = 2(sin(12 degrees) / (1 + cos(12 degrees))) / (1 - (sin²(12 degrees) / (1 + cos(12 degrees))²))

tan(12 degrees) = 2(2sin(6 degrees)cos(6 degrees) / (1 + cos(12 degrees))) / (1 - (4sin²(6 degrees)cos²(6 degrees) / (1 + cos(12 degrees))²))

tan(12 degrees) = (4sin(6 degrees)cos(6 degrees)) / (1 + cos(12 degrees) - 4sin²(6 degrees)cos²(6 degrees))

This is the simplified expression using the double angle identity.

Step-by-step explanation:

Answer:

1. 15

2. 26

3. ≈ 7.62

4. 8

5. ≈ 23.24

6. √2

7. ≈ 19.42

8. 18

9. x≈10.29 y≈5.83

Step-by-step explanation:

Use a²+b²=c² throughout the problems and plug in the given sides and hypothenuse.

1. 9²+12²=c²

81+144=225

√225 = 15

2. 10²+24²=c²

100+576=676

√676=26

3. 7²+3²=c²

49+9=58

√58 ≈ 7.62

4. a²+6²=10²

a²+36=100

a²=64

x=8

5. a²+6²=24²

a²+36=576

a²=540

x≈ 23.24

6. 1²+1²=c²

1+1=2

x=√2

7. a²+8²=21²

a²+64=441

a²=377

x≈ 19.42

8. a²+24²=30²

a²+576=900

a²=324

x=18

9. for x:

9²+5²=x²

81+25=106

√106 ≈10.29

x ≈10.29

for y:

5²+3²=y²

25+9=34

√34 ≈5.83

y ≈5.83

When the outside temperature is 30°F, the sales are estimated to be $414.73.

The outside temperature is approximately 78.03°F, the sales are estimated to be $1,993.33.

It refers to a physical property of matter that reflects how hot or cold an object is relative to other objects or a standard scale. Temperature is typically measured in units such as Celsius (°C), Fahrenheit (°F), or Kelvin (K).

When the outside temperature is 30°F, the sales are estimated to be:

y = 32.92(30) - 572.87

y = 987.60 - 572.87

y = $414.73

Therefore, when the outside temperature is 30°F, the sales are estimated to be $414.73.

When the outside temperature is x, the sales are estimated to be $1,993.33, we can solve for x as follows:

1,993.33 = 32.92x - 572.87

2,566.20 = 32.92x

x ≈ 78.03°F

Therefore, when the outside temperature is approximately 78.03°F, the sales are estimated to be $1,993.33.

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Selecting the first tile (1st) and selecting the secοnd tile (2nd) are independent events.

The prοbability οf selecting an even number οn a single draw is 2/5 οr 0.4, as there are twο even numbers (2 and 4) οut οf a tοtal οf five pοssible numbers.

Since the events are independent, the prοbability οf selecting an even number οn bοth draws is the prοduct οf the prοbabilities οf selecting an even number οn each draw:

P(bοth even) = P(even οn first) × P(even οn secοnd) = 0.4 × 0.4 = 0.16

Sο the prοbability that the numbers οn bοth tiles are even is 16%.

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Answer:

m =  [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

First, we must rewrite 5x + 6y = - 18 to the form y = mx + b.

5x + 6y = -18

6y = -5x - 18

y = [tex]\frac{-5}{ 6}[/tex]x - 3

The equation of a perpendicular line to y = [tex]\frac{-5}{ 6}[/tex]x - 3 must have a slope that is the negative reciprocal of the original slope.

So, the slope of the perpendicular line is

m = [tex]\frac{6}{5}[/tex]

Answer: 6/5

Step-by-step explanation:

trust me

Answer:

The expression 4 in x + in 3 - in x can be simplified using logarithmic rules: 4 in x + in 3 - in x = in x^4 + in 3 - in x = in (x^4 * 3 / x) = in (3x^3) Therefore, the expression is equivalent to in (3x^3).

Answer:

(i) log 1 base 2 = log_{2} 1 =1.30103

Step-by-step explanation:

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The diameter of the hemisphere to the nearest tenth of a centimeter is 62.1 cm.

What is hemisphere?

A hemisphere is a three-dimensional geometric shape that consists of a half-sphere, which is a curved surface that is shaped like the surface of a ball, and a flat circular base that lies on a plane perpendicular to the sphere's axis of symmetry. A hemisphere can be thought of as the three-dimensional analogue of a circle.

The volume of a hemisphere is given by the formula:

V = (2/3)π[tex]r^3[/tex]

where V is the volume and r is the radius of the hemisphere.

We are given the volume of the hemisphere as 62617 [tex]cm^3.[/tex]

So, we have:

62617 = (2/3)π[tex]r^3[/tex]

Multiplying both sides by 3/2π, we get:

[tex]r^3[/tex] = 62617 * (3/2π)

Simplifying, we get:

[tex]r^3[/tex] = 29897.4152

Taking the cube root of both sides, we get:

r ≈ 31.04

The diameter of the hemisphere is twice the radius, so:

d = 2r ≈ 62.08

Rounding to the nearest tenth, we get:

d ≈ 62.1

Therefore, the diameter of the hemisphere to the nearest tenth of a centimeter is 62.1 cm.

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Answer: To complete the square, we need to add and subtract the square of half the coefficient of x:

x^2 - 4x = 2

x^2 - 4x + 4 = 2 + 4 (adding and subtracting 4)

(x - 2)^2 = 6

Now we take the square root of both sides:

x - 2 = ±√6

Adding 2 to both sides gives:

x = 2 ± √6

So the solutions are:

x = 2 + √6, 2 - √6

Step-by-step explanation:

This information can be used to understand the performance of the students and Evaluate their scores in relation to the overall group.

Suppose that the distribution of scores of 1,000 students who take a standardized intelligence test is a normal distribution. In this scenario, the distribution's mean is 470 and its standard deviation is 10.

A normal distribution, also known as a Gaussian distribution or bell curve, is a symmetric distribution where the majority of the data falls around the mean value. In this case, the mean score is 470, which represents the average intelligence score for the 1,000 students. The standard deviation, which is 10 in this case, measures the dispersion or spread of the data around the mean.

To interpret the scores, we can use the empirical rule, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Applying this rule:
- About 68% of the students scored between 460 (470-10) and 480 (470+10).
- Approximately 95% of the students scored between 450 (470-2*10) and 490 (470+2*10).
- Around 99.7% of the students scored between 440 (470-3*10) and 500 (470+3*10).

This information can be used to understand the performance of the students and evaluate their scores in relation to the overall group.

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Answer:

308 yards^2

Step-by-step explanation:

Area = length * width

Length = 20

Width = 15.4

20 * 15.4 = 308

Answer: 308 yards

Step-by-step explanation:

Answer:

215.95

Step-by-step explanation:

68.4+49.6+97.95

Answer:

x = 47

Step-by-step explanation:

All angles in a triangle ALWAYS add up to 180 degrees, so to find a missing angle, subtract what is already given. It will be 180 - (102+31), which is the same as 180-133 which equals 47. The basic rule is to subtract given angels from 180 to find the missing side.

Rule 1: The output is the square of the input. For example, if the input is 3, then the output would be 9 (3 squared).

Rule 2: The output is 90 greater than the input. For example, if the input is 3, then the output would be 93 (3 + 90).

These are the two rules you've provided, and they describe how to calculate the output (y) based on the input (x).
Rule 1: The output is the square of the input.
In this rule, when you have an input value (let's call it x), you square it (multiply it by itself) to get the output value (y). Mathematically, this can be written as:
[tex]y = x^2[/tex]
Rule 2: The output is 90 greater than the input.
In this rule, when you have an input value (x), you add 90 to it to get the output value (y).

Mathematically, this can be written as:
y = x + 90.

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Answer:

the diver will reach the surface of the water after 1/4 seconds.

Step-by-step explanation:

To find when the swimmer reaches the surface of the water, we need to set h(t) to zero since the surface of the water is at a height of zero feet.

0 = t - 4t^2

Simplifying the equation, we get:

4t^2 = t

4t^2 - t = 0

t(4t - 1) = 0

So, either t = 0 (which corresponds to the initial time when the swimmer is at the surface) or 4t - 1 = 0. Solving for t, we get:

4t - 1 = 0

4t = 1

t = 1/4

Therefore, the diver will reach the surface of the water after 1/4 seconds.

Answer: $939 and $689

Step-by-step explanation:

     We can create a system of equations to help us solve. Let x be one and y be the other paycheck.

           y = x - $250

           y + x = $1,628

     Next, we can solve the system of equations by graphing. The point of intersection is our solution. See attached. This gives us (939, 689), so one check was written for $939 and one was written for $689.

The next three terms are:

The value of y for the inverse variation when x = -12 is derived to be equal to 1.

Inverse variation is a mathematical relationship between two variables, in which an increase in one variable leads to a proportional decrease in the other variable. Mathematically, inverse variation can be expressed as y = k/x, where y and x are the two variables, k is a constant of proportionality, and the product of y and x is always equal to k.

when x = 6 and y = -2, then k is derived as:

-2 = k/6

k = -12 {cross multiplication}

when x = -12, y is derived as:

y = -12/-12

y = 1

Therefore, the value of y for the inverse variation when x = -12 is derived to be equal to 1.

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Using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

The square's four sides are equal to one another or congruent.

The square's opposing sides run parallel to one another.

The square's diagonals form a 90° angle with one another.

The square's two diagonals are equal to one another.

Area: s²

s² + (s+3)² = 1017

s² + s² + 9 = 1017

2s² = 1017 - 9

2s² = 1,008

s² = 1008/2

s² = 504

s = ²504

s = 22.44

Round off: 22 cm

Then, (s+3) = 22 + 3 = 25 cm

Therefore using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.

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The future value of Ted's investment after 30 years would be approximately $13,711.86.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

Ted can use the formula for the future value of an annuity to calculate the future value of his investment:

FV = Pmt x (([tex](1 + r)^{n}[/tex]) - 1) / r

Where:

FV = Future Value

Pmt = Payment per period (monthly in this case)

r = Interest rate per period (monthly in this case)

n = Number of periods (in this case, 30 x 12 = 360 months)

Substituting the given values, we get:

FV = $250 x (([tex](1 + 0.062/12)^{360}[/tex] - 1) / (0.062/12)

FV = $250 x (283.8576) / 0.0051667

FV = $13,711.86

Therefore, the future value of Ted's investment after 30 years would be approximately $13,711.86.

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Answer:

  [A]  Multiply the bottom equation by -3/2, then add the equations.

  [C]  Multiply the top equation by -3, then add the equations.

Step-by-step explanation:

You want to know a suitable "elimination" strategy for the two equations ...

The result of an elimination strategy is that one of the variables in the combined equations has a coefficient of 0. If we add the equations as a final step, the coefficients must be opposites for that to happen.

The ratios of variable coefficients in the top equation to those in the bottom equation are ...

A suitable elimination strategy will multiply one of the equations by a value that makes this ratio -1. Let's look at the choices.

Multiplying the bottom equation by -3/2 makes the ratio of x-coefficients be ...

  [tex]\dfrac{1}{3}\times\dfrac{1}{\left(-\dfrac{3}{2}}\right)}=-\dfrac{2}{9}\ne -1[/tex]

Multiplying the bottom equation by -3/2 makes the ratio of y-coefficients be ...

  [tex]\dfrac{3}{2}\times\dfrac{1}{\left(-\dfrac{3}{2}\right)}=-\dfrac{6}{6}=-1[/tex]

This is a suitable strategy for eliminating the y-variable.

This strategy is equivalent to multiplying the bottom equation by -3, then adding. This will make the x-coefficient ratio be ...

  [tex]\dfrac{1}{3}\times\dfrac{1}{\left(-3}\right)}=-\dfrac{1}{9}\ne -1[/tex]

Multiplying the bottom equation by -3 makes the ratio of y-coefficients be ...

  [tex]\dfrac{3}{2}\times\dfrac{1}{-3}=-\dfrac{3}{6}\ne-1[/tex]

Not a suitable strategy for elimination.

Multiplying the top equation by -3 makes the ratio of x-coefficients be ...

  [tex]\dfrac{1}{3}\times\dfrac{-3}{1}}=-\dfrac{3}{3}= -1[/tex]

This is a suitable strategy for eliminating the x-variable.

Choices A and C are suitable strategies for eliminating a variable.

Answer:

The linear speed of the vehicle is approximately 0.798 miles per hour.

Step-by-step explanation:

The circumference of a tire is given by the formula C = πd, where d is the diameter of the tire. So, the circumference of each tire is:

C = πd = π(32 inches) ≈ 100.53 inches

Now, to find the distance that the vehicle travels in one revolution of each tire, we use the circumference formula again:

distance traveled in one revolution = circumference of the tire = 100.53 inches

Since the tires are rotating at a rate of 800 revolutions per minute, the vehicle travels a distance of:

distance traveled in one minute = distance traveled in one revolution × number of revolutions per minute

= 100.53 inches/revolution × 800 revolutions/minute

= 80424 inches/minute

To convert this to miles per hour, we need to divide by the number of inches per mile and the number of minutes per hour:

speed = (80424 inches/minute) × (1 mile/63360 inches) × (60 minutes/1 hour)

≈ 0.798 miles/hour

Therefore, the linear speed of the vehicle is approximately 0.798 miles per hour.

Answer: 22

Step-by-step explanation:

The first one is 10.

The other 2 has 6, because 10-4=6

So

10+(6x2)=22

The interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.

Payment is the transfer of funds from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment can take various forms, including cash, check, credit card, money order, or electronic transfer. Payment can be made in person, over the phone, or online. The most important aspect of payment is that it is a legally binding contract between two parties. Payment is an important part of the economic system that facilitates the exchange of goods and services and helps to ensure that all parties involved receive what they expect from the transaction.

The interest on $58,254.26:
To calculate the interest on $58,254.26, we first need to determine the interest rate. Assuming that the interest rate is 3%, we can calculate the interest owed as follows:

Interest = Principal x Interest Rate x Time

Interest = $58,254.26 x 0.03 x 1/12

Interest = $146.38

b) The payment to principal:
To calculate the payment to principal, we need to subtract the interest from the total payment amount.

Payment to Principal = Total Payment – Interest

Payment to Principal = $329 - $146.38

Payment to Principal = $182.62

c) The new principal:
To calculate the new principal, we need to subtract the payment to principal from the original principal.

New Principal = Original Principal – Payment to Principal

New Principal = $58,254.26 - $182.62

New Principal = $58,071.64

In conclusion, the interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.

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The value of x for measure a base angle for the isosceles trapezoid is equal to 25°.

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

angle C is equal to angle D so;

3x + 1 = 76°

3x = 76° - 1 {subtract 1 from both sides}

3x = 75°

x = 75°/3 {divide through by 3}

x = 25°

Therefore, the value of x for measure a base angle for the isosceles trapezoid is equal to 25°.

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After looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics.

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

A number on the left of a number line is always smaller than a number on the right.

A number to the right is always greater than a number to the left, too.

So, the inequality we have is:

1/4 + 1 < 5

Now, after observing the given lines, we can easily tell that the number line (B) represents 1/4 + 1 < 5 perfectly.

Therefore, after looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.

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Complete question:

Which number line shows the solution to 1/4 + 1 < 5

The argument to symbols of the logic expression is shown below

From the question, we have the following parameters that can be used in our computation:

The argument in symbols can be expressed as:

p -> q

~p

Therefore, ~q

Where:

p = "It rains."

q = "I will watch the Real World marathon."

"->" denotes "implies".

"~" denotes "not".

So the argument can be read as "If it rains, then I will watch the Real World marathon. It did not rain.

Therefore, I did not watch the Real World marathon."

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The company's total expenses and revenues will both be $196 when 4 attendees register.

What is Algebraic expression ?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

Let's assume that the company's goal is to break even, which means that their total revenue should be equal to their total expenses.

Let's represent the number of attendees by "x." For the company to break even, the total revenue earned from x attendees must be equal to the total expenses incurred.

Total Expenses = Fixed Cost + Variable Cost

Fixed cost = Facility rent fee = $164

Variable cost = Books and supplies per attendee = $8

Total Expenses = $164 + $8x

Total Revenue = Price per attendee x Number of attendees = $49x

To find the break-even point, we set the total revenue equal to the total expenses and solve for x:

$49x = $164 + $8x

$41x = $164

x = 4

Therefore, the company needs to have 4 attendees to break even.

To calculate the total expenses and revenues, we can substitute x = 4 into the equations we derived above:

Total Expenses = $164 + $8(4) = $196

Total Revenue = $49(4) = $196

Therefore, the company's total expenses and revenues will both be $196 when 4 attendees register.

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