using diagonals from a common vertex, how many triangles could be formed from a 14-gon?

The solution to the system of equations is x = 31/7 and y = 1/7.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two parts, the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

We can solve this system of equations using the elimination method. We will eliminate one of the variables by adding or subtracting the equations to get an equation with just one variable.

Multiply the first equation by 4 and the second equation by 3 to get:

16x + 12y = 76

9x + 12y = 45

Subtract the second equation from the first to eliminate y:

16x + 12y - (9x + 12y) = 76 - 45

7x = 31

Solve for x by dividing both sides by 7:

x = 31/7

Substitute the value of x into either equation to solve for y. Let's use the first equation:

4x + 3y = 19

4(31/7) + 3y = 19

3y = 19 - 124/7

3y = 3/7

y = 1/7

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Complete question:

Solve the equation for x and y:

4x+3y=19

3x+4y=15

Answer:

answer is 2 into 2 into twenty three

Step-by-step explanation:

2×2×23

√2^2×23

2√23

Answer: The square root of 92 is approximately 9.59166304663. Rounding this to the nearest tenth gives 9.6. Therefore, the square root of 92 rounded to the nearest tenth is 9.6.

Step-by-step explanation:

You would need to make a 94 on the next quiz to have a mean quiz score of 90.

If 90 is the desired mean, then you have to multiply it by the number of quizzes

5 x 90 = 450 is the total in the 5 quizzes.

Now, add the scores of the first four quizzes.

88 + 95 + 93 + 80 = 356

Then, take the amount of the 5 quizzes and subtract it from the amount of the total 4 quizzes.

450 - 356 = 94

Answer:

answer: 7

Step-by-step explanation:

u have to find the median by finding the middle of all of those numbers which will me seven

Answer: There are 7 marbles in the bag and in the first attempt, all 7 marbles are there. After one marble is taken away, then we have 6 marbles to choose from. Therefore we will multiply 7*6 = 42.

Hence, there are 42 possible outcomes.

Answer:

D. -3, -7

Step-by-step explanation:

Answer:

The zeroes are -2 and 4.

Step-by-step explanation:

x^2 - 2x - 8 = 0

(x + 2)(x - 4) = 0

x + 2 = 0 or x - 4 = 0

x = -2, 4

The general form of the equation is ax^2 + bx + c = 0.

The sum of the zeroes should be equal to -b/a:-

-2 + 4 = 2

and -(-2)/1 = 2

Verified

The product of the zeroes should be c/a = -8:-

-2 * 4 = -8.

Verified.

Answer:

A) 0

Step-by-step explanation:

1.5+(-1 x (.5 + .25)) / .5

1.5+(-1 x .75) / .5

1.5 + -0.75 / .5    Because of order of operations division comes first

1.5 + (-1.5)

1.5 - 1.5

0

The value of x that will make ∆ABC similar to ∆ RST is 12

Similar triangles are triangles with similar shapes but their sizes are not necessarily thesame. The ratio of the corresponding sides of similar triangles are equal.

This means ,

2x+6/36 = 40/48 = 25/x+18

therefore, 2x+6/36 = 40/48

48( 2x+6) = 36× 40

96x + 288 = 1140

96x = 1140-288

96x = 1152

divide both sides by 96

x = 1152/96

x = 12

therefore the value of x that will make the two triangles similar is 12

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Answer:

x = - 1, 6

Step-by-step explanation:

the denominator of h(x) cannot be zero as this would make h(x) undefined

equating the denominator to zero and solving gives the values of x that cannot be in the domain of h(x)

x² - 5x - 6 = 0

(x + 1)(x - 6) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 6 = 0 ⇒ x = 6

then x = - 1, 6 are values not in the domain of h(x)

Answer: 5

Step-by-step explanation:

If Cather added the ages of a crowd of both 18-year-olds and 22-year-olds and got 290, we can write that as 18x+22y=290. Knowing that there were 10 18-year-olds, we can plug 10 in for x.

18 times 10 + 22y = 290

So, first, we should multiply.

18 times 10 is 180, leaving us with 180+22y=290

Next, we should subtract both sides by 180.

So, 22y=110

Finally, we need to divide both sides by 22.

Leaving us with the answer of 5.

Answer:

5

Step-by-step explanation:

10×18=180

290-180=110

110/22=5

To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to the power 6.

Powers of 10 are used in scientific notation to indicate extremely big or extremely tiny quantities. A number is written as the result of a coefficient (a number between 1 and 10) and a power of 10 when it is expressed in scientific notation. The number represented by the power of 10 is the distance the decimal point must be moved to convert a number to standard form (i.e., a number without exponents).

To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to 6.

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Answer:

I think 496

Step-by-step explanation:

Divide

Both of the two triangles are similar by SSS similarity postulate.

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.

Looking at the 2 given triangles, we can see the ratio if corresponding sides as:

39/13 = 3

39/13 = 3

21/7 = 3

Since the ratios of the corresponding sides of both triangles are the same, then they are both Similar by SSS similarity postulate.

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Manuel purchased 1.75 pounds of corn kernels.

An equation is a mathematical statement that shows the equality between two expressions. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. An equation can be written in many different forms, but the most common form is: Left-hand side = Right-hand side

In the given question,

Let's use x to represent the number of pounds of corn kernels Manuel purchased.

We know that Manuel bought 2.5 pounds of sunflower seeds, and that both the sunflower seeds and corn kernels cost $2.20 per pound.

The total amount Manuel spent on the sunflower seeds and corn kernels was $9.35, so we can write the equation: 2.2(2.5) + 2.2x = 9.35

Simplifying the left side of the equation, we get: 5.5 + 2.2x = 9.35

Subtracting 5.5 from both sides, we get: 2.2x = 3.85

Dividing both sides by 2.2, we get: x = 1.75

Therefore, Manuel purchased 1.75 pounds of corn kernels.

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The probability that the component survives 200 hours is approximately 0.9802. The probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.

What is probability?

Probability is a numerical representation of the likelihood or chance of a specific event occurring. It is typically expressed as a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

To determine the probability that the component survives 200 hours, we need to calculate the survival function, which is the probability that the component lasts longer than 200 hours. We can use the formula:

[tex]$$ S(t) = e^{-\int_0^t z(u) du} $$[/tex]

where [tex]$S(t)$[/tex] is the survival function and [tex]$\int_0^t z(u) du$[/tex] is the integral of the failure rate from 0 to [tex]$t$[/tex].

In this case, the failure rate is [tex]$z(t) = 2.0\times10^{-6}t/\text{hour}$[/tex] for [tex]$t > 0$[/tex]. Integrating this from 0 to 200 gives:

[tex]$$ \int_0^{200} z(t) dt = \int_0^{200} (2.0\times10^{-6}t) dt =[/tex] [tex]\left[\frac{(2.0\times10^{-6})}{2}t^2\right]_0^{200} = 0.02 $$[/tex]

Substituting this into the survival function formula gives:

[tex]$$ S(200) = e^{-\int_0^{200} z(t) dt} = e^{-0.02} \approx 0.9802 $$[/tex]

Therefore, the probability that the component survives 200 hours is approximately 0.9802.

To determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, we need to use the conditional probability formula:

[tex]$ P(T > 400|T > 200) = \frac{P(T > 400 \cap T > 200)}{P(T > 200)} $$[/tex]

We can calculate the numerator using the survival function:

[tex]$ P(T > 400 \cap T > 200) = S(400) $$[/tex]

To find [tex]$S(400)$[/tex], we need to integrate the failure rate from 0 to 400:

[tex]$$ \int_0^{400} z(t) dt = \int_0^{400} (2.0\times10^{-6}t) dt = \left[\frac{(2.0\times10^{-6})}{2}t^2\right]_0^{400} = 0.16 $$[/tex]

Substituting this into the survival function formula gives:

[tex]$$ S(400) = e^{-\int_0^{400} z(t) dt} = e^{-0.16} \approx 0.8534 $$[/tex]

To find the denominator, we can use the survival function we found earlier:

[tex]$ P(T > 200) = S(200) = e^{-0.02} \approx 0.9802 $$[/tex]

Substituting these values into the conditional probability formula gives:

[tex]$ P(T > 400|T > 200) = \frac{S(400)}{S(200)} \approx \frac{0.8534}{0.9802} \approx 0.8703 $$[/tex]

Therefore, the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.

1) The probability that the component survives 200 hours is approximately 0.9802.

2) The probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.

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Complete question:

1. A component with time to failure [tex]$\mathbf{T}$[/tex]  has failure rate[tex]$z(t)=2.0*10^{-6}$[/tex]t/hour for [tex]$t \ge 0$[/tex]

1) Determine the probability that the component survives 200 hours

2) Determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours Note that the failure rate in this problem is not constant, but a function of time [tex]${\mathbf{}}t$[/tex].

2. Consider a computer system called [tex]$3\mathrm{P2M}$[/tex]  in the following figure. The system consists of three processors and two shared memories communicating over a shared bus, as shown in the following Figure. The [tex]$3\mathrm{P2M}$[/tex] system is operational as long as at least two processors can communicate with at least one of the two memories over the bus. a) Construct the fault tree model of this system b) Find all the minimal cut sets c) Assume all the components fail exponentially with the following failure rates: processors (P1, P2, P3): 0.0001/hour; memories (M1, M2): 0.0001/hour; bus: 0.000001 /hour. Find the system reliability at mission time [tex]$t=100$[/tex] hours.

Answer:

( a + 2 ) ( a - 15 )

Step-by-step explanation:

a² - 13a - 30

a² + 2a - 15a - 30

( a² + 2a ) - ( 15a - 30 )

a ( a + 2 ) - 15( a + 2 )

( a + 2 ) ( a - 15 )

The y -intercept of the parabola y = x^2 + 2x + 10 is (0, 10)

the y-intercept represents the value of y when x=0. In the equation y = x^2 + 2x + 10, the x^2 and 2x terms create a parabola that opens upwards. As x approaches infinity or negative infinity, the value of y also increases towards infinity.

The y-intercept of a graph is the point at which the graph crosses the y-axis, which is where x=0. To find the y-intercept of the parabola y = x^2 + 2x + 10, we substitute x=0 into the equation, which gives

y = 0^2 + 2(0) + 10

y = 10

Therefore, the y-intercept of the parabola is (0, 10), which means the graph crosses the y-axis at the point (0, 10).

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The given question is incomplete, the complete question is:

Find the y -intercept of the parabola y = x^2 + 2x + 10

Answer: 15 nickels, 63 dimes, 44 quarters

Step-by-step explanation:

x=number of nickels

4x+3=number of dimes

4x+3-19=number of quarters

Solve the following equation:

x+4x+3+4x+3-19=122

9x-13=122

x=15

Plug x back into the expressions:

Number of nickels=15

Number of dimes:

4(15)+3

63

Number of quarters:

4(15)+3-19

44

Check the picture below.

so if we cut the pyramid like a pie with a knife from the top and open it up, it'd look more or less like that picture, so its area is just the area of four triangles with a base of 4 and a height of 3 and a 4x4 square.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(4)(3) \right]}~~ + ~~\stackrel{square}{(4)(4)}}\implies 24+16\implies \text{\LARGE 40}~yd^2[/tex]

Answer:

We need to find the number of points of intersection between the line with equation y = -3/4x + 25/4 and the circle. The equation of the circle is not given, so we cannot directly solve for the intersection points. However, we can use the fact that the intersection points must satisfy both the equation of the line and the equation of the circle.

Let (x, y) be a point on the circle. Then the coordinates satisfy the equation of the circle, which we will assume is (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius. Substituting y = -3/4x + 25/4, we get:

(x - a)^2 + (-3/4x + 25/4 - b)^2 = r^2

This is a quadratic equation in x, which we can expand and simplify:

(x^2 - 2ax + a^2) + (-3/2)x^2 + (15/2)x - 3bx + (625/16) + b^2 - (25/2)b + (625/16) - r^2 = 0

Simplifying further, we get:

(-5/2)x^2 + (-2a - 3b + 15/2)x + (2a^2 - 25/2b + 125/8 - r^2) = 0

This is a quadratic equation in x, with coefficients that depend on the center and radius of the circle. We can use the quadratic formula to solve for x, and then substitute into y = -3/4x + 25/4 to get the corresponding value of y.

The discriminant of the quadratic equation is:

(-2a - 3b + 15/2)^2 - 4(-5/2)(2a^2 - 25/2b + 125/8 - r^2)

Simplifying and factoring, we get:

(4a + 6b - 15)^2 - 25(4a^2 - 50b + 250/8 - 2r^2)

This is a quadratic expression in b, which tells us whether the equation has real solutions (i.e., whether the line intersects the circle). If the discriminant is positive, then the equation has two real solutions, which means the line intersects the circle at two points. If the discriminant is zero, then the equation has one real solution, which means the line is tangent to the circle. If the discriminant is negative, then the equation has no real solutions, which means the line does not intersect the circle.

Without knowing the equation of the circle, we cannot determine the discriminant and therefore the number of intersection points. Therefore, the answer is D: "There is not enough information to determine the number of points of intersection."

Step-by-step explanation:

is a pineapple

Step-by-step explanation:this is becuase you should work it out youself you silly goose

Answer:

circle is not a function.

Step-by-step explanation:

there are certain rules to define a mapping as function, one of them is function should not have more than 1 value at a given x.

for illustration purpose consider the below diagram,

as you can see in the given circle at x = 2, there are two different values of y, therefore equation of circle doesn't qualify as a function. half circle can be defined as a function (by restricting the range to only positive or negative values).

Hopefully you found the answer helpful

Therefore, the length of the perpendicular side x is approximately 12.64 feet, rounded to two decimal places.

A trigonometric ratio is a mathematical function that relates the sides of a right triangle to its angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Each of these ratios is defined as the ratio of two sides of the triangle. Sine (abbreviated as sin) is the ratio of the length of the side opposite an acute angle to the length of the hypotenuse. That is, sin(theta) = opposite/hypotenuse. Cosine (abbreviated as cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. That is, cos(theta) = adjacent/hypotenuse. Tangent (abbreviated as tan) is the ratio of the length of the opposite side to the length of the adjacent side. That is, tan(theta) = opposite/adjacent.

Here,

We can use the trigonometric ratio of sine to solve for x in this problem.

Sine is defined as the ratio of the length of the opposite side (in this case, x) to the length of the hypotenuse (21 feet):

sin(37°) = x/21

We can solve for x by multiplying both sides of the equation by 21:

x = 21 sin(37°)

Using a calculator to evaluate sin(37°), we get:

sin(37°) ≈ 0.6018

Substituting this value into the equation, we get:

x ≈ 21(0.6018)

x ≈ 12.64

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To graph the function f(x) = 2sin(x)-2, we can start by plotting the y-intercept (0, -2).

Next, we can use the amplitude of 2 to mark the highest and lowest points of the graph. The highest point will be 2 units above the midline at y = 0, and the lowest point will be 2 units below the midline at y = -4.

To establish the period of the function, we need to identify the distance between one complete cycle of the graph. Since sine has a period of 2pi, we can see that the period of our function is also 2pi.

Starting from the y-intercept, we can mark a point on the graph that is one-quarter of the way through a cycle, at x = pi/2. The sine function will be at its maximum value of 1 at this point, so the graph will be at y = 0 + 2

The Surface area of Pyramid is equal to Option (B) [tex]72 m^2[/tex] when base is square and their are 4 triangles.  

The surface area of a pyramid is the total area of all its faces. The formula to calculate the surface area of a pyramid depends on the shape of its base.

To find the surface area of this pyramid we should add area of all 4 triangles and 1 square base.

Area of Base = 4m * 4m

                      = [tex]16m^2[/tex]

Area of Triangle = 1/2 *4* 7

                           = [tex]14m^2[/tex]

Surface Area of Pyramid = Area of Base + 4 * (Area of Triangle)

                                         = [tex]16m^2 + 4(14m^2)[/tex]

                                         = [tex]72 m^2[/tex]

Therefore, Surface area of Pyramid is equal to  [tex]72 m^2[/tex].

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Answer: The area of the rectangular prism would be S.A. = 66m²

Step-by-step explanation: :)

What is the surface area of this rectangular prism?

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces. The surface area of this rectangular prism = l x b

We have given

4 rectangles with area

A₁ = 3m × 4m  = 12 m²

2 rectangles with area

A₂ = 3m × 3m = 9 m²

Therefore the Surface Area of the rectangular prism is:

S.A. = 4A₁ + 2A₂

S.A. = 4(12) + 2(9)

= 48 + 18

= 66

Hence, the net surface area of the rectangular prism would be 66 meters sq.

As a result, the hotel has 208 single rooms and 112 double rooms. We can now use these two equations to find the values of x and y.

An equation in mathematics is a claim that two mathematical expressions are equivalent. In an equation, the two expressions on either side are separated by the equals sign (=). As in the following equation: 3x + 2 = 11 declares that the formula 11 is identical to the formula 3x + 2. Finding the value of x that causes the equation to be true is the first step towards solving this equation. By first removing 2 from both sides of the equation and then dividing by 3, we may find x in this situation: 3x + 2 - 2 = 11 - 2 (subtracting 2 from both sides) (subtracting 2 from both sides) .3x = 9 (simplifying the right side) (simplifying the right side) .

given

Assume that there are x single rooms and y double rooms at the hotel.

We may create an equation since we are aware that there are 320 rooms in the hotel overall:

x + y = 320 (Equation 1) (Equation 1)

We can create another equation based on sales since we also know the prices for each type of accommodation and the overall sales:

40x + 65y = 15,600 (Equation 2) (Equation 2)

We can now solve for x and y using these two equations. To accomplish this, one method is to solve for x in Equation 1 and replace it in Equation 2:

x + y = 320

x = 320 - y

Equation 2 using x = 320 - y as a replacement:

12,800 - 40y + 65y = 15,600

25y = 2,800 y = 112

40x + 65y = 15,600

40(320 - y) + 65y

= 15,600

There are 112 double rooms in the hotel. In order to determine the number of single rooms, we can reenter this value into Equation 1 as follows:

x + y = 320

x + 112 = 320

x = 208

As a result, the hotel has 208 single rooms and 112 double rooms. We can now use these two equations to find the values of x and y.

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Step-by-step explanation:

To find F^-1(x), we need to solve for x in terms of f(x) using the given equation for f(x):

f(x) = 4(3x+2)

First, we can simplify the expression inside the parentheses:

f(x) = 12x + 8

Next, we can solve for x by isolating it on one side of the equation:

f(x) - 8 = 12x

(x is isolated)

x = (f(x) - 8) / 12

Therefore, F^-1(x) = (x - 8) / 12.

Answer:

2550

Step-by-step explanation:

Step-by-step explanation:

To multiply decimals, we can simply multiply the numbers as if they were whole numbers and then count the total number of decimal places in the factors. In this case, we have:

25.5 x 10 x 10 = 255 x 10

Now, we multiply 255 by 10 as if they were whole numbers:

255 x 10 = 2550

Finally, we count the total number of decimal places in the factors, which is two (one in 25.5 and one in 10). Therefore, the answer should have two decimal places, so we can add a decimal point to the result and place two zeros after it:

25.5 x 10 x 10 = 2550.00

Therefore, 25.5 x 10 x 10 = 2550.00.