perimeter of a triangle
​

The domain of the function is Domain: (-2, 2). The range is:

Range: (-2, 2). The given graph does not have exactly one output for one input value. Hence, the given is not a function.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

The domain of the function are the input values or the x-coordinate of the graph. From the given graph the domain is:

Domain: (-2, 2)

The range of the function are the output values, or the y-coordinate of the graph. From the given graph the range is:

Range: (-2, 2)

We know that a function is a relationship between inputs where each input is related to exactly one output.

The given graph does not have exactly one output for one input value.

Hence, the given is not a function.

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The estimated cost for constructing the house in New Orleans, Louisiana of the given square feet is option A. $113,750.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that, construction rate per square feet is $65.

We have to find the estimated cost for a two-story home of 950 ft2 on the first floor and 800 ft² on the second floor.

Total area of the plot = 950 ft² + 800 ft²

                                   = 1750 ft²

Estimated cost can be calculated by multiplying total area with the construction rate per square feet.

Estimated cost = 1750 ft² × $65

                         = $113,750

Hence the estimated cost is $113,750.

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Answer:

last option

number of students in class plus new students

The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

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The correct options are a) ∠ R corresponds to ∠ P'QQ'  and d) side RQ corresponds to QQ'

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given that, a triangle PQR is being dilated to form a new triangle P'Q'Q following a rule: (x, y) → (2x, 2y)

This show that, the scale factor is 2 and the dilation is an enlargement,

We know that, dilation transformation makes similar figures, and in similar figures, the corresponding angles and ratio of corresponding sides are equal,

Here, the corresponding angles are:

∠ P = ∠ P'

∠ PQR = ∠ P'Q'Q

∠ R = ∠ P'QQ'

And, the corresponding side:

P'Q'/PQ = P'Q/PR = Q'Q/QR

Therefore, true statements are;

a) ∠ R corresponds to ∠ P'QQ'  

d) side RQ corresponds to QQ'

Hence, the correct options are a) ∠ R corresponds to ∠ P'QQ'  and d) side RQ corresponds to QQ'

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Answer:

[tex] \color{grey}{ \boxed{\sf x < \frac{1}{2} }}[/tex]

Solve..

Let's solve your inequality step-by-step.

[tex] \sf{3(6x+10)<39} [/tex]

Step 1: Simplify both sides of the inequality.

[tex] \sf{18x+30<39}[/tex]

Step 2: Subtract 30 from both sides.

[tex] \sf18x+30−30<39−30 \\ \sf18x<9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

Step 3: divide by 18

[tex] \sf{x <\frac{9}{18} = \frac{9 \times 1}{9 \times 2} } \\ \\ \sf x < \frac{1}{2} [/tex]

The solutions to the equations of the triangle is given by x = 86 and the value of y = 56

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the equation is

3x - 5y = -22   be equation (1)

Now , the measure of ∠A = ( y - 18 )°

The measure of ∠B = y°

The measure of ∠C = x°

Now , for a triangle

∠A + ∠B + ∠C = 180°

Substituting the values in the equation , we get

y - 18 + y + x = 180

On simplifying the equation , we get

2y + x = 198   be equation (2)

Multiply equation (2) by -3 , we get

-6y - 3x = -594   be equation (3)

Adding equation (3) and equation (1) , we get

-5y - 6y = -594 - 22

-11y = -616

Divide by -11 on both sides of the equation , we get

y = 56

Substitute the value of y in equation (2) , we get

2 ( 56 ) + x = 198

x + 112 = 198

Subtracting 112 on both sides of the equation , we get

x = 86

Hence , the solution to the equation is ( 86 , 56 )

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Thus, a vector function that represents the curve of intersection of the cone and the plane is: [tex]r(t) = tcos(t), 1 +\sqrt{ (1 - t^2)}, 1 -\sqrt{ (1 - t^2)}, tsin(t)[/tex]

The vector function that represents the curve of intersection of a cone and a plane can be found by equating the equation of the cone and the equation of the plane, and then solving for x and y in terms of z.

Given the cone  [tex]z = \sqrt{(x^2 + y^2)}[/tex]  and the plane  [tex]z = 1 + y[/tex] , we have:

[tex]\sqrt{(x^2 + y^2) }= 1 + y[/tex]

Squaring both sides, we get:

[tex]x^2 + y^2 = (1 + y)^2 = 1 + 2y + y^2[/tex]

Solving for y, we get:

[tex]x^2 + y^2 - 2y = 1[/tex]

[tex]y^2 - 2y + x^2 - 1 = 0[/tex]

Using the quadratic formula, we get:

[tex]y = 1 + \sqrt{(1 - x^2)} , 1 + \sqrt{(1 - x^2)}[/tex]

Thus, a vector function that represents the curve of intersection of the cone and the plane is:

[tex]r(t) = tcos(t), 1 +\sqrt{ (1 - t^2)}, 1 -\sqrt{ (1 - t^2)}, tsin(t)[/tex]

where t varies between -1 and 1.

The resulting curve is a circle with center (0, 1, 0) and radius 1, which lies in the xy-plane and is perpendicular to the z-axis.

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The multiplication of the expression given is 60x² - 28x - 8.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is (5x + 1) (12x - 8).

We have to multiply the expressions and simplify.

For any numbers or algebraic expressions, a, b, c and d,

(a + b) (c + d) = ac + ad + bc + bd

(5x + 1) (12x - 8) = (5x × 12x) + (1 × 12x) + (5x × -8) + (1 × -8)

                         = 60x² + 12x - 40x - 8

                         = 60x² - 28x - 8

Hence the multiplication of the given expression gives 60x² - 28x - 8.

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The number of longboards that will be defective based on the defective longboards in the month can be predicted to be 2, 500 longboards.

The number of longboards that would be defective for the other skateboarding company is 2, 446 longboards.

To find the defective longboards, first find the percentage of the longboards that were produced in the month. Then multiply this result with the number of longboards to be produced :

= 204 / 10, 200 x 125, 000

= 2 % x 125, 000

= 2, 500 longboards

The same procedure can be used for the other skateboarding company to find the defective products to be:

= 225 / 11, 500 x 125, 000

= 2, 446 longboards

The product for the second company therefore has fewer defects.

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The electric field at points on the y-axis above the uppermost charge is given by [tex]E= kq/(a^{2}+y^{2} )^{(3/2)} ,ex=0, ey=kq/(a^{2}+y^{2} )^{(3/2)}[/tex].

The electric field at points on the y-axis above the uppermost charge can be calculated by finding the electric field due to each of the three charges and summing them. This calculation requires the use of Coulomb's law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The electric field due to a single charge is proportional to the charge and inversely proportional to the square of the distance from the charge to the point at which the field is being calculated.

By using the equations for the electric field due to each charge and the vector sum of their electric fields, an expression for the electric field at points on the y-axis above the uppermost charge can be obtained. The final expression would likely be a function of q, a, x, y, and the Coulomb constant k.

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The solution is (FoF) (0) = -8, when f(x) = 3x-2.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

f(x) = 3x-2

i.e. fof(x)

 =3(3x-2)-2

=9x-8

so. fof(0)

   =9*0-8

   = -8

Hence, The solution is (FoF) (0) = -8, when f(x) = 3x-2.

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(i) the coordinates of the vertex S = Q + QS = (-1, -1) + (2, 2) = (1, 1).

(ii) the coordinates of the point of intersection of the diagonals PR and QQS is point (-1, 0).

(i) The coordinates of the vertex S can be found by shifting the vector PQ to QS. The vector PQ is given by Q - P = (-1 - (-3), -1 - (-1)) = (2, 0). The vector QS can be found by shifting PQ by 2 units vertically, so QS = (2, 2). To find the coordinates of S, we add the vector QS to the point Q: S = Q + QS = (-1, -1) + (2, 2) = (1, 1).

(ii) The point of intersection of the diagonals PR and QS can be found by finding the midpoint of each diagonal and checking if they are equal. The midpoint of PR is given by ( (1 + -3)/2 , (1 + -1)/2 ) = (-1, 0). The midpoint of QS is given by ( (1 + -1)/2 , (1 + 1)/2 ) = (0, 1). Since the midpoints are equal, the diagonals PR and QS intersect at the point (-1, 0).

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The time complexity of constructing a heap of n elements is no better than O(nlogn).

The correct statement is that heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time.

Heap sort is an efficient sorting algorithm that uses a heap data structure to store the data elements. The heap is a complete binary tree structure where the root node is the largest element in the heap and each node contains a value that is less than or equal to its parent node. The heap is constructed in a bottom-up fashion, meaning that each leaf node is compared to its parent node and swapped if it is larger. This ensures that the root node is always the largest element in the heap.

The complexity of heap sort is O(nlogn), since the heap is constructed in O(n) time but the sorting operation requires O(nlogn) time. This is because, for each element in the heap, the sorting algorithm must compare it to its parent node and swap if necessary. Therefore, the overall time complexity of the algorithm is O(n) + O(nlogn) = O(nlogn).

The complexity of constructing a heap of n elements is also O(nlogn), since each element must be compared to its parent node and swapped if necessary. This process must be repeated for each element in the heap, so the time complexity is O(n) + O(nlogn) = O(nlogn). Therefore, the time complexity of constructing a heap of n elements is no better than O(nlogn).

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Answer:

yes

Step-by-step explanation:

a)

The value of k is 0.61.

b)

The population in 2010 is 739013.

The population in 2015 is 15604434.

c)

In 5.2 years, the population will reach 2.5 million.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

P = 1657.5 [tex]e^{kt}[/tex]

P is the population in t years.

Now,

In 2000, t = 0,

a)

In 2005, t = 5 and P = 1940,000

So,

P = 1657.5 [tex]e^{kt}[/tex]

1,940,000 = 1657.5 [tex]e^{5k}[/tex]

1940000/1657.5 = [tex]e^{5k}[/tex]

1170.44 = [tex]e^{5k}[/tex]

Taking logs on both sides.

log 1170.44 = 5k

3.07 = 5k

k = 0.61

b)

In 2010, t = 10

So,

kt = 0.61 x 10 = 6.1

P = 1657.5 [tex]e^{6.1}[/tex]

P = 1657.5 x 445.86

P = 739012.95

P = 739013

In 2015, t = 15

So,

P = 1657.5 [tex]e^{9.15}[/tex]

P = 1657.5 x 9414.44

P = 15604434

c)

P = 2.5 million = 2,500,000

Now,

P = 1657.5 [tex]e^{6.1}[/tex]

Solve for t.

2,500,000 = 1657.5 [tex]e^{0.61t}[/tex]

2500000/1657.5 = [tex]e^{0.61t}[/tex]

1508 = [tex]e^{0.61t}[/tex]

Taking logs on both sides.

log 1508 = 0.61t

3.18 = 0.61t

t = 3.18/0.61

t = 5.21

t = 5.2

Thus,

a)

k = 0.61

b)

P = 739013 in 2010

P = 15604434 in 2015

c)

In 5.2 years, the population will reach 2.5 million.

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QRST is a Rhombus, then:

Rhombus is a parallelogram with all congruent sides. Rhombus' diagonals are perpendicular and bisects its angles. Rhombus has 4 congruent right angles created from its perpendicular diagonals and form 2 pairs of two congruent isosceles triangle.

RT bisects of QRS because every diagonals on rhombus bisect their repsective angles.

QS is perpendicular to RT because both QS and RT are rhombus' diagonals and diagonals in rhombus are perpendicular with each other.

QS bisects RT because QS divide rhombus QRST into 2 congruent triangles, QRS and QTS. Since both triangles' height are half of RT, then QS bisects RT.

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The Taylor expansion of cos(x) around x=0 is [tex]cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) +[/tex]......

We would use this expansion to calculate the cosine of a given angle with an error tolerance of 0.1%.

To do this, we must first write a function taylorcosine() which takes two arguments: the angle (in radians) and the relative percentage error. The function should then return two values: the Taylor approximation for the cosine of the angle, and the number of terms required in the Taylor series to reach this level of error.

For example, if we want to find the approximate value of cos(3π) with an error tolerance of 0.1%, we would call the function as follows:

[tex]val, nsteps = taylorcosine(3π, 1e-3)[/tex]

To find the percentage relative error, we must multiply the relative error by 100.

We can also use the bisection method to determine the roots of a function. To do this, we must write a function myBisection() which takes

three arguments: the function handle, an array containing the lower and upper limits of the starting interval, and the maximum allowable relative error. The return value of the function is the estimate of the root.

For example, if we want to find the root of f(x) = x^2 - 3x + 2, with an initial bracket of [1.3, 0] and an error tolerance of 1%, we would call the function as follows:

root = [tex]myBisection(f, [1.3, 0], 1%)[/tex]

The error is defined as the absolute value of the ratio of the difference between the old and the new estimates of the root and the new estimate of the root.

Error = [tex]|x_new/x_new - x_old|/x_new[/tex]

By writing the taylorcosine() and myBisection() functions, we can calculate the cosine of an angle with a given error tolerance, and determine the roots of a function with a given error tolerance, respectively.

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At this point, the vector "intvector" will contain all of the integers read from input minus five.

int x = 0;

vector<int> intvector;

while (x != 0)

{

   cin >> x;

   intvector.push_back(x - 5);

}

First, we create a variable to store the integer from input, "x", and a vector to store the integers minus five, "intvector". Then, we create a while loop that runs until the value of "x" is equal to zero. Inside the loop, we read an integer from input and store the value in "x". Then, we subtract five from "x" and add the resulting value to the vector "intvector". This loop will run until the value of "x" is equal to zero.  At this point, the vector "intvector" will contain all of the integers read from input minus five.

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The sample size required to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02 is 685.

Population is the term typically used to refer to the number of people in a single area.

To estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02.

we can use the formula for sample size in a proportion estimation problem:

n = (Z^2 * p * (1 - p)) / E^2

Plugging in the values:

n = (1.96^2 * 0.17 * (1 - 0.17)) / (0.02^2)

n = 684.2

Since n must be a whole number, we round up to the next integer:

n = 685

So, the sample size required to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02 is 685.

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Note that the rates that are unit rates are given as follows:

Note that a unit rate is a rate in which the second term equals 1. It represents a comparison of a quantity to 1.

Since:

Therefore, it is right or correct to state that 2/4,  9/1, and 10:1 are unit rates.

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Yes, that is correct. A system of linear equations with fewer equations than unknowns is often referred to as an underdetermined system.

In this type of system, there are infinitely many solutions or no solutions, and it is not possible to determine a unique solution for the variables.

When a system of equations has more variables than the equation, therefore, it has fewer rules to curb the variables, giving the variables more freedom to take up values from their respective domain(Usually it is a set of real numbers), in such a condition the system of equations has infinite solutions. This kind of system is known as an underdetermined system.

Hence, the system of equations doesn't have a unique solution.

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Answer:

Step-by-step explanation:

3 (w - 2) ≥ 10

3w - 6 ≥ 10

3w ≥ 16

w ≥ 16/3

(a) Chebyshev's theorem states that at least 75% of lifespan fall between 748 and 1112 hours.

(b) Chebyshev's theorem states that at least 56% of all lifetimes fall between the average lifespan minus the standard deviation and the average lifetime plus the standard deviation. Additional information, such as the mean and standard deviation of the lifespan, would be required to calculate the exact interval.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

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The speed of Usain Bolt is given by the equation S = 23.25 miles per hour

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as S

Now , the value of S is

The speed at which Usain Bolt won the gold medal = 34.1 feet per second

So , the speed at which Usain Bolt won the gold medal in miles per hour is calculated by dividing the value by 1.467

Substituting the values in the equation , we get

The speed of Usain Bolt S = ( speed of Usain / 1.467 ) miles per hour

On simplifying the equation , we get

The speed of Usain Bolt S = 34.1 / 1.467

The speed of Usain Bolt S = 23.25 miles per hour

Therefore , the value of S is 23.25 mph

Hence , the equation is S = 23.25 miles per hour

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When 2, 325 is rounded to the nearest thousand, the result would be 2, 000.

To round a number to the nearest thousand, identify the place value of the rounding digit, which is the thousandth place (the third digit from the right).

Then, look at the digit to the right of the rounding digit. If this digit is 5 or greater, then round up the rounding digit by adding one to it. If the digit is less than 5, keep the rounding digit as it is.

The number 2, 325 would therefore be rounded to 2, 000 because the digit " 3 " is less than 5.

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Answer:

-18 and -27 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

The value of all trigonometric functions can be found with the help of a triangle,

from the diagram of the point and reference triangle needed to answer the problem.

Plot the point (2,-3) which is in quadrant 4

Draw a right triangle such that one leg is resting on the x axis and the other leg is perpendicular to the x axis. The hypotenuse goes from (0,0) to (2,-3).

The horizontal leg is 2 units long. So a = 2

The vertical leg is 3 units long. So b = 3

The hypotenuse is unknown but we can use the pythagorean theorem to find it. We'll call it c for now

Use the Pythagorean theorem to find c

   [tex]a^2+b^2=c^2\\\\2^2+3^2=c^2\\\\c=\sqrt{13}\\[/tex]

The hypotenuse is sqrt(13) which is shown in the attached image (Fi

Using figure 1, now refer to figure 2 to compute the ratios for sine, cosine, and tangent

Figure 3 shows how to compute the ratios for cosecant, sectant, and cotangent

With figure 1, the leg furthest from angle theta is the opposite side (in this case -3). The leg closest to the angle theta is 2 units long.

[tex]Sin\theta=\frac{3}{\sqrt{13}}\\\\cos\theta = 2/\sqrt{13}\\\\tan\theta=3/2\\\\same\ as,\\cot\theta=2/3\\sec\theta=\sqrt{13}/2\\cosec\theta=\sqrt{13}/3[/tex]

The complete question is -

A point on the terminal side of an angle in standard position is given. Find the exact value of each of the six trigonometric functions of θ.

Point given: (2,-3)

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