using the centriod explain the relationship between point z and the triangle. justify with applicable theorem.
4. if the length of gu is 18 units, what is the length of gz?
5. if the length of zt is 4.8 units, what is the length of ot?
show all work

x = ±π/6 + πn, ±11π/12 + πn, where n is an integers are solutions of the equation  cos²x = sin²x + 1/2

To solve the equation cos²x = sin²x + 1/2, we can use the trigonometric identity sin²x + cos²x = 1.

Rearranging the equation, we have:

cos²x - sin²x = 1/2

Using the identity cos²x - sin²x = cos(2x), we can rewrite the equation as:

cos(2x) = 1/2

The solutions to this equation can be found by taking the inverse cosine (or arccosine) of both sides:

2x = ±π/3 + 2πn, ±11π/6 + 2πn, where n is an integer

Dividing both sides by 2, we get:

x = ±π/6 + πn, ±11π/12 + πn, where n is an integers

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A point on circle B with integer coordinates when r = 1 would be (5, 6).

We have, the radius of Circle A is 6 unit.

and, Radius of Circle B= 6/2= 3 unit

Using the center (2, 3) and the radius 3, we can calculate the coordinates of a point on circle B as follows:

x-coordinate = center x-coordinate + radius = 2 + 3 = 5

y-coordinate = center y-coordinate + radius = 3 + 3 = 6

So, a point on circle B with integer coordinates when r = 1 would be (5, 6).

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Answer:

Step-by-step explanation:24 ft

In the given graph there is zero slope of the line.

As shown the points on the line

The coordinates of points be,

(4, 2) and (4, -2)

Since we know that slope of line passing through the points,

(x₁ , y₁) and (x₂, y₂) is, m = (y₂ - y₁)/(x₂ - x₁)

Here,

(x₁ , y₁) = (4, 2)

(x₂, y₂) = (4, -2)

Now the slope be = (-2 - 2)/(4 - 4)

                              = -4/∞

                              = 0

Therefore,

There is zero slope.

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Answer:

To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.

One way to do this is to use the formula for the future value of an annuity, which is:

FV = Pmt x ((1 + r)^n - 1) / r

where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.

First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:

r = 7% / 12 = 0.00583

Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.

Finally, we can plug in the values into the formula for the future value of an annuity:

FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583

FV ≈ $141,535.15

Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.

Step-by-step explanation:

To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.

One way to do this is to use the formula for the future value of an annuity, which is:

FV = Pmt x ((1 + r)^n - 1) / r

where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.

First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:

r = 7% / 12 = 0.00583

Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.

Finally, we can plug in the values into the formula for the future value of an annuity:

FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583

FV ≈ $141,535.15

Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.

The volume of the moon can be shown to be 3.07% of the volume of the planet.

First, calculate the radius of the planet and the moon.

The radius (r) of the planet is half of its diameter:

r = 27, 998 mi / 2

= 13, 999 mi

The volume of the planet is V:

= 4 / 3 π ( 13, 999 mi)³

=  11, 493, 372, 846 cubic miles

The volume of the moon is:

V = 4 / 3 π (4,059.71 mi) ³

=  352, 432, 952 cubic miles

The Percent volume :

= ( Volume of moon / Volume of planet) x 100

= ( 352, 432 ,952 cubic miles / 11, 493,372,846 cubic miles) x 100

= 3.07 %

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The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except for the value x = -11/3.

The range of the reciprocal function f(x) = -7/(3x + 11), we need to determine the set of all possible values that f(x) can take.

The reciprocal of a number is obtained by taking the multiplicative inverse, which means that the reciprocal of a non-zero number a is 1/a.

We are looking for the range of the reciprocal function, so we need to consider the range of the expression (3x + 11).

The range of (3x + 11) is the set of all real numbers, except when the denominator becomes zero.

The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except when (3x + 11) equals zero.

To find the x-value when (3x + 11) equals zero, we solve the equation:

3x + 11 = 0

Subtracting 11 from both sides, we get:

3x = -11

Dividing by 3, we find:

x = -11/3

The reciprocal function is undefined at x = -11/3, as it would result in a division by zero.

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By the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.

Since, The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean μ and standard deviation σ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s = σ / √n.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The mean for the entire population is 5.7 years.

So, by the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.

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The calculated coordinates of point B on line AB is (-1, 0)

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

P =  (1,2)  

A = (2,4)

Also, we have

m : n = 1 : 2

The coordinates of point P are calculated using

P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

(1, 2) = 1/(1 + 2) * (1 * x + 2 * 2, 1 * y + 2 * 4)

Evaluate

(3, 6) = (x + 4, y + 6)

So, we have

x = -1 and y = 0

Hence, the coordinates of point B on line AB is (-1, 0)

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Step-by-step explanation:

Wherever the fxn = 0  is where it touches the x -axis

0=(x-5)^3 (x+2)^2   means that one or both of the factors is 0

     (x-5)^3    is zero at   x = 5

      (x+2)^2  is zero at    x = -2

sooo    5 and  -2  

The number of hydrogen atoms present in the sculpture of earth if the mass of earth is 829 kg is 4.145 × 10²⁹.

Given that,

Mass of the sculpture of the earth = 829 kg

We know that,

Mass of an hydrogen atom = 2 × 10⁻²⁷ kg

Number of hydrogen atoms = Mass of earth / Mass of hydrogen atom

                                              = 829 / 2 × 10⁻²⁷

                                              = 414.5 × 10²⁷

                                              = 4.145 × 10²⁹

Hence the required number of atoms is 4.145 × 10²⁹.

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Hello!

[tex]-5x - 7 > 3x + 1\\\\-5x - 3x > 1+7\\\\-8x > 8\\\\\boxed{x < -1}[/tex]

The traveler will need (y / x) dollars to purchase y yen.

To determine the number of dollars the traveler will need to purchase a certain amount of yen, we need to divide the desired amount of yen by the exchange rate.

Let's assume the traveler wants to purchase y yen.

and, the exchange rate is 1 dollar = x yen.

To find the number of dollars, we can set up the following equation:

y yen × (1 dollar / x yen) = (y / x) dollars

Therefore, the traveler will need (y / x) dollars to purchase y yen.

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To calculate the number of dollars needed to purchase a specific amount of Japanese yen, we'll need the exchange rate between the two currencies. However, the exchange rate provided in your question is missing. Please provide the exchange rate between the US dollar (USD) and the Japanese yen (JPY) so that I can help you calculate accurately.

The interest rate that satisfies the assumption is approximately 5.33%.

We have,

To find the interest rate that satisfies the assumption, we can use the formula for compound interest:

[tex]A = P \times (1 + r)^t[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case, we have:

P = $400

A = $684

t = 11 years

Let's substitute these values into the formula and solve for r:

$684 = $400 x [tex](1 + r)^{11}[/tex]

Dividing both sides by $400, we get:

[tex]1.71 = (1 + r)^{11}[/tex]

Now, we need to isolate (1 + r) by taking the 11th root of both sides:

[tex](1 + r) = 1.71^{1/11}[/tex]

Using a calculator, we find:

(1 + r) ≈ 1.0533

Subtracting 1 from both sides, we get:

r ≈ 0.0533

To express the interest rate as a percentage, we multiply by 100:

r ≈ 5.33%

Therefore,

The interest rate that satisfies the assumption is approximately 5.33%.

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Answer:

Because y is a common variable, we can assume that they are equal to each other.

Answer: [tex]\sf\$6.48[/tex]

Step-by-step explanation:

If a six-pack of cola is sold for $1.50, then the price per can is:

[tex]\sf\implies\$1.50 \div 6 = \$0.25[/tex]

A 24 pack of cola contains 24 cans, so the total cost of the 24 pack is:

[tex]\sf\implies 24 \times \$0.25 = \$6.00[/tex]

The sales tax is 8%, so the tax on the purchase is:

[tex]\sf\implies \dfrac{8}{100} \times \$6.00 = \$0.48[/tex]

Therefore, the total charge including sales tax is:

[tex]\sf\implies\$6.00 + \$0.48 = \$6.48[/tex]

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The graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).

To graph the given equations, we'll plot the points that satisfy each equation and then connect them to form a line.

Equation 1: y = -1

This equation represents a horizontal line passing through the y-coordinate -1. Regardless of the x-coordinate, the y-value remains constant at -1. Therefore, we plot a point at (0, -1) and draw a horizontal line through that point.

Equation 2: 3x - y = 4

To graph this equation, we can rewrite it in terms of y:

y = 3x - 4

Now we can choose a few x-values, substitute them into the equation, and solve for y to obtain the corresponding y-values. Let's select three x-values: -2, 0, and 2.

For x = -2:

y = 3(-2) - 4

y = -6 - 4

y = -10

For x = 0:

y = 3(0) - 4

y = -4

For x = 2:

y = 3(2) - 4

y = 6 - 4

y = 2

Now we have three points: (-2, -10), (0, -4), and (2, 2). Plotting these points on the graph, we can draw a line connecting them.

In summary, the graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).

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Answer:

a)

Step-by-step explanation:

the function is 11x6=66+13=79x¹=79

hope it helps

The marksman hit 54% of the targets last year when expressed as a percentage, based on hitting 27 out of 50 targets from a distance of 100 yards.

From the given information, we know that a marksman hit 27 out of 50 targets last year from a distance of 100 yards.

To analyze this data, we can calculate the hit rate or success rate of the marksman. The hit rate is calculated by dividing the number of hits by the total number of attempts or trials.

Hit rate = Number of hits / Total number of attempts

In this case, the number of hits is 27, and the total number of attempts is 50.

Hit rate = 27 / 50

Simplifying the fraction, we get:

Hit rate = 0.54 or 54%

Therefore, the marksman had a hit rate of 54% last year.

This means that out of the 50 targets attempted from a distance of 100 yards, the marksman successfully hit 27 of them.

The hit rate serves as a measure of accuracy and effectiveness in target shooting. A higher hit rate indicates a higher level of skill and precision.

It's important to note that other factors such as weather conditions, visibility, and the difficulty level of the targets can influence the hit rate. Additionally, the marksman's skills may improve or vary over time, so this hit rate represents their performance specifically for the past year.

By analyzing the hit rate, we can gain insights into the marksman's accuracy and assess their proficiency in target shooting from a distance of 100 yards.

The question was incomplete. find the full content below;

Rewrite The Fraction In The Sentence Below As A Percentage.

From 100 Yards Away, A Marksman Hit 27/50 Of The Targets Last Year.

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The price per shirt when 100 shirts are sold is of $5.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the graph of the function, two points are given as follows:

(0, 20) and (20, 100).

Hence the slope is given as follows:

m = (100 - 20)/(20 - 0)

m = 4.

Hence the cost function is of:

y = 4x + 20.

For 20 shirts, the cost is of $100, hence the cost per shirt is given as follows:

100/20 = $5 per shirt.

The problem is given by the image presented at the end of the answer.

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To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }[/tex]

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }[/tex]

Now we solve for V₂:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }[/tex]

Where:

Now, we substitute the values in the formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}[/tex]

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

The solutions for the quadratic graph are (d) (-3, 0) and (1, 0)

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

The quadratic graph

The solutions for the quadratic graph are the points where the graph intersect the x-axis

These points are called the x-intercepts or the roots

Using the above as a guide, we have the following:

The point of intersection with the x-axis are (-3, 0) and (1, 0)

Hence, the solutions for the quadratic graph are (d) (-3, 0) and (1, 0)

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The volume of the hexagonal prism is 212.4 unit square

Prism is three-dimensional solid which has identical faces at both ends. It is a polyhedron, which means all faces are flat.

How to determine this

When an hexagonal prism has a base area = 36 units

Height = 5.9 units

Volume of Prism = Base area * Height

Volume of prism = 36 units * 5.9 units

Volume = 212.4 units square

Therefore, the volume of the hexagonal prism is 212.4 units square

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Using the formula for two events not mutually exclusive, the probability of ordering either one is given as 0.8.

Since we assume that the events are not mutually exclusive, this implies that the occurrence of event B is not affected by the probability of occurrence of event A.

Then, the probability of ordering either one is the sum of their individual probabilities minus the probability of ordering both.

The probability formula is:

p (chocolate or vanilla) = p (chocolate) + p (vanilla) - p (chocolate and vanilla)

p (chocolate) = 0.6

p (vanilla) = 0.5

p (chocolate or vanilla) = 0.6 + 0.5 - 0.6 * 0.5

= 1.1 - 0.3

= 0.8

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The area of the logo 1 in square feet is  38.465 ft²

Remember that the area of a circle of radius R is given by the formula:

A = 3.14*R²

Here we can see that the radius of the circle is (1/2 in), but we wat the are in square feet, so let's write that in feets.

1 in = 7ft, then:

(1/2 in) = (7/2 ft) = 3.5 ft.

Replace that in the formula for the area:

A = 3.14*(3.5 ft)²

A = 38.465 ft²

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Answer:

The answer is the third option

Step-by-step explanation:

When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.

So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.

37 and 1/2 % of 104 is 39 .

Given,

37 and 1/2 % of 104

Simplifying further,

Convert mixed fraction into simple fraction,

37 and 1/2 %  = 75/2%

Now,

75/2% of 104

= 75/2 ×1/100×104

=39 .

Hence 39 is the required answer.

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Size of the house should be 2900 ft².

Correct option is B.

We have,

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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complete question:

A house is listed for sale at $235,000, but the listing does not include square

footage of the house. Based on the comps, the line of best fit is

y=0.06x + 60.5. If the price is fair, what size (in square feet) should the house

be?

OA. 2850 ft2

OB. 2900 ft2

OC. 20,000 ft²

OD. 2350 ft²