Elin chose C as the correct answer. Explain how she got her answer.

Answer:

Step-by-step explanation:

To find the equation of a circle given three non-collinear points, we can use the following steps:

Find the equations of the perpendicular bisectors of the line segments connecting the pairs of points.

Find the intersection point of the two perpendicular bisectors. This point is the center of the circle.

Find the distance between the center and any one of the three points. This distance is the radius of the circle.

Let's apply these steps to the given points:

Find the midpoint and slope of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18+(-7))/2, (-5+(-16))/2) = (-12.5, -10.5)

Slope of (-18, -5) and (-7, -16): (-16 - (-5))/(-7 - (-18)) = -11/11 = -1

Midpoint of (-18, -5) and (4, -5): ((-18+4)/2, (-5+(-5))/2) = (-7, -5)

Slope of (-18, -5) and (4, -5): (-5 - (-5))/(4 - (-18)) = 0

Midpoint of (-7, -16) and (4, -5): ((-7+4)/2, (-16+(-5))/2) = (-1.5, -10.5)

Slope of (-7, -16) and (4, -5): (-5 - (-16))/(4 - (-7)) = 11/11 = 1

The equations of the perpendicular bisectors passing through the midpoints are:

x + 12.5 = -1(y + 10.5) or x + y + 23 = 0

y + 5 = 0

Find the intersection point of the two perpendicular bisectors:

Solving the system of equations:

x + y + 23 = 0

y + 5 = 0

yields: x = -18, y = -5

So, the center of the circle is (-18, -5).

Find the distance between the center and any one of the three points:

Using the distance formula:

Distance between (-18, -5) and (-18, -5): sqrt(((-18)-(-18))^2 + ((-5)-(-5))^2) = 0

Distance between (-18, -5) and (-7, -16): sqrt(((-18)-(-7))^2 + ((-5)-(-16))^2) = sqrt(221)

Distance between (-18, -5) and (4, -5): sqrt(((-18)-4)^2 + ((-5)-(-5))^2) = 22

The radius of the circle is sqrt(221).

Therefore, the equation of the circle in standard form is:

(x + 18)^2 + (y + 5)^2 = 221

The standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5) is:

(x + 13)² + (y + 1)² = 41

From the question, we are to determine the standard equation of a circle with the given points

The given points are:

(-18;-5), (-7;-16) and (4;-5)

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle

and r is the radius.

Using the given points (-18, -5), (-7, -16), and (4, -5), we can find the equation of the circle as follows:

Find the midpoint of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18 + -7)/2, (-5 + -16)/2) = (-12.5, -10.5)

Midpoint of (-7, -16) and (4, -5): ((-7 + 4)/2, (-16 + -5)/2) = (-1.5, -10.5)

Midpoint of (-18, -5) and (4, -5): ((-18 + 4)/2, (-5 + -5)/2) = (-7, -5)

Find the equations of the perpendicular bisectors of the line segments:

Perpendicular bisector of the line connecting (-18, -5) and (-7, -16):

Slope of the line: (−16 + 5)/(-7 + 18) = -11/5

Slope of the perpendicular bisector: 5/11

Midpoint: (-12.5, -10.5)

Equation: y + 10.5 = (5/11)(x + 12.5)

Perpendicular bisector of the line connecting (-7, -16) and (4, -5):

Slope of the line: (-5 + 16)/(4 + 7) = 11/7

Slope of the perpendicular bisector: -7/11

Midpoint: (-1.5, -10.5)

Equation: y + 10.5 = (-7/11)(x + 1.5)

Perpendicular bisector of the line connecting (-18, -5) and (4, -5):

Slope of the line: 0

Slope of the perpendicular bisector: undefined (perpendicular bisector is a vertical line)

Midpoint: (-7, -5)

Equation: x + 7 = 0

Find the point of intersection of any two perpendicular bisectors:

Intersection of perpendicular bisectors 1 and 2:

y + 10.5 = (5/11)(x + 12.5)

y + 10.5 = (-7/11)(x + 1.5)

Solving for x and y, we get:

x = -13

y = -1

Thus,

The center of the circle is (-13, -1).

Find the radius of the circle:

Using the center (-13, -1) and one of the given points, say (-18, -5):

r² = (-18 - (-13))² + (-5 - (-1))²

r² = 25 + 16

r² = 41

Hence, the equation of the circle is:

(x + 13)² + (y + 1)² = 41.

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a) The value of the investment after 4 years is $5,544.90.

b) The value of the investment after 8 years is $6,849.42.

c) The value of the investment after 12 years is $8,453.35.

The formula for calculating the value of an investment that is compounded continuously is given by:

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

where A is the final value of the investment, P is the initial investment 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 period in years.

(a) To find the value of the investment after 4 years, we can substitute the given values in the formula as follows:

A = 4500[tex]e^{(0.05254)[/tex]

A = 4500[tex]e^{0.21[/tex]

A = 45001.2322

A = $5,544.90

(b) To find the value of the investment after 8 years, we can substitute the given values in the formula as follows:

A = 4500[tex]e^{(0.05258)[/tex]

A = 4500[tex]e^{0.42[/tex]

A = 45001.5221

A = $6,849.42

(c) To find the value of the investment after 12 years, we can substitute the given values in the formula as follows:

A = 4500[tex]e^{(0.052512)[/tex]

A = 4500[tex]e^{0.63[/tex]

A = 45001.8785

A = $8,453.35

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The number of real zeros for the function whose graph is shown include the following: D. 0.

In Mathematics and Geometry, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

This ultimately implies that, a polynomial graph touches the x-axis at real zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can reasonably and logically deduce that the real zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and it is non-existent on the graph above.

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The total number of chickens the farmer owns is 35.

A quantity or proportion can be expressed as a percentage of 100 by using the word "percentage." It is represented by the sign %.

For instance, when we state that 50 percent of a group of people are women, we mean that 50 out of every 100 people in the group are women.

We can deduce here the total chickens the farmer owns in % = 100%

Hens placed in a new coop = 20% = 7

Let the total number of chickens = x

Thus,

7 / x = 20 / 100

To solve for x, we can cross-multiply and simplify:

7 × 100 = 20 × x

700 = 20x

x = 35

Thus, the total number of chickens = 35.

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Thw correct option based on the information given about the parabola will be B. X.

The observed parabola has its vertex situated at (0, 0), declining until (0, 0) then again rising. Its equation falls in the form of f(x) = a(x - 0)² + 0, which simplifies to ax².

In order to detect the value of 'a' we can utilize any point on the parabola itself. Let's take (1, 1):

1 = a(1)²

1 = a

Therefore, the formula for the presented parabola is exsiting in the form of f(x) = x².

Now consider g(x) = (x + 1)² such that it's merely a horizontal movement of function f(x) = x². The vertex of g(x) stands at (-1, 0) and linearly declines until (-1, 1) prior to onching higher again. All this leaves us with option X as the only conceivable graph for g(x).

Therefore, the answer is B) X.

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The truth statements about the function f(x) = 14(0.87)^x is Growth; y = 0

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

f(x) = 14(0.87)^x

An exponential function is represented as

y = ab^x

Where

a = initial value

b = growth/decay factor

In this case, the exponential function is a decay function

This means that

The value of b is less than 1 i.e.

b = 0.87 and 0.87 < 1

Hence, the function is a decay function

Recall that

f(x) = 14(0.87)^x

So, we have

y = 0 as the the equation of the asymptote

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Answer:

B

Step-by-step explanation:

This is a linear function.

:D

The next "three-umbers" in the pattern "2,0,6,-4,10,-8,..." are 14, -12, and 18.

To find the next three numbers in the pattern 2, 0, 6, -4, 10, -8, we need to analyze the pattern and identify the rule for it.

The pattern seems to be alternating between adding and subtracting the "odd-multiples" of 2.

The pattern is as follows : 2 - (2×1) = 0,

0 + (2×3) = 6,

6 - (2×5) = -4,

-4 + (2×7) = 10,

10 - (2×9) = -8,

Using this rule, we can find the next three numbers in the pattern as follows:

Add 22 because : -8 + (2×11) = 14,

Subtract 26 because : 14 - (2×13) = -12,

Add 30 , because : -12 + (2×15) = 18,

Therefore, the next three numbers in the pattern are 14, -12, and 18.

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Answer:

Private saving (Sprivate) is equal to disposable income minus consumption:

Sprivate = Y - T - C = 15,000 - 3,000 - 9,000 = 3,000

Public saving (Spublic) is equal to government revenue minus government spending:

Spublic = T - G = 3,000 - 3,600 = -600

National saving (S) is equal to the sum of private and public saving:

S = Sprivate + Spublic = 3,000 - 600 = 2,400

Investment (I) is given by the investment function:

I = 3,900 - 100r

Equating investment to national saving gives:

I = S

3,900 - 100r = 2,400

Solving for r:

r = 15%

Therefore, the equilibrium real interest rate is 15%.

Substituting r = 15% into the investment function gives:

I = 2,400

Therefore, investment is 2,400.

Finally, to determine if the government has a budget surplus or deficit, we need to calculate the government's budget balance, which is equal to government revenue minus government spending:

Budget balance = T - G = 3,000 - 3,600 = -600

Since the budget balance is negative, the government of Flatland has a budget deficit.

Answer:

t ≈ 37.76 seconds (rounded to the nearest hundredth)

Step-by-step explanation:

To solve the problem, we can use the equation for the height of a projectile at time t: h(t) = - 16 * t^2 + v0 * t + y0

where v0 is the initial velocity and y0 is the initial height.

In this case, we have:          v0 = 600 ft/sec (upward)

                                             y0 = 160 ft (above the ground)

We want to find the time at which the projectile hits the ground, which is when h(t) = 0.

So we can set up the equation:   0 = -16 * t^2 + 600 * t + 160

We can solve for t using the quadratic formula:

                                           t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -16, b = 600, and c = 160.

Plugging in the values, we get:

                   t = (-600 ± sqrt(600^2 - 4(-16)(160))) / 2(-16)

                   t = (-600 ± sqrt(360000 + 10240)) / (-32)

                   t = (-600 ± sqrt(370240)) / (-32)

We can simplify this expression by taking the negative root since the positive root would give a negative time, which is not physically meaningful in this context: t = (-600 - 608.47) / (-32)

t ≈ 37.76 seconds (rounded to the nearest hundredth)

Therefore, the projectile will be in flight for about 37.76 seconds before hitting the ground.

Answer:

Here's a set of five numbers, each of which is divisible by 3:

{ 3, 6, 9, 12, 15 }

All the numbers in this set are multiples of 3, so they are all divisible by 3.

The appropriate statistic for testing the null hypothesis is given as  D (-2.20/0.07)

Coefficient for slope variable (Exercise time) = -2.20

Standard error of coefficient = 0.07

Therefore, the test statistic value to verify whether or not there is an apparent slope on a population regression line can be estimated as follows.

Test statistic = Coefficient for slope variable/Standard error of coefficient = -2.20/0.07

Therefore its correct answer is D (-2.20/0.07)

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Answer: To evaluate this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) and work from left to right:

(49)^(-2) * (34)^(-2)

First, we can simplify the exponents:

1/(49^2) * 1/(34^2)

Next, we can calculate the values of 49^2 and 34^2:

1/2401 * 1/1156

Then, we can multiply the fractions:

1/2785456

Therefore, the value of the expression (49)^(-2) * (34)^(-2) is approximately 0.000000359.

Step-by-step explanation:

The measure (in radians) of central angle θ in the circle below is π/3.

We have,

radius = 3 cm

Arc length = π

We can use the formula relating the arc length (s) to the central angle (θ) and radius (r) of a circle:

s = r Ф

Now,

π = 3 x Ф

Ф = π/3

Thus,

The measure (in radians) of central angle θ in the circle below is π/3.

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The graph that shows the solution set for the given inequality is the one in option B.

Here we want to identify the graph of the inequality:

|x| ≤ 3

So, the absolute value of x is smaller or equal to 3, that means that the graph of the solution set is a segment whose endpoints are closed circles at x = -3 and x = 3.

(We use closed circles because these values are also solutions for the inequality).

With that in mind, we can see that the correct option in this case will be graph B.

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Step-by-step explanation:

[tex] { ({4}^{ - 4} )}^{3} \\ = {4}^{ - 12} [/tex]

[tex] \frac{ {4}^{15} }{ {4}^{5} } \\ = {4}^{10} [/tex]

[tex] {4}^{ - 5} \times {4}^{ - 4} \\ = {4}^{ - 9} [/tex]

[tex] \frac{1}{ {4}^{ - 12} } \\ = {4}^{12} [/tex]

least to greatest

[tex]1)\: {4}^{ - 12} \\ 2) \: {4}^{ - 9} \\ 3) \: {4}^{10 } \\ 4) \: {4}^{12} [/tex]

Let x be the length of each of the equal sides of the isosceles triangle. Then the length of the base is x - 4. The perimeter of the triangle is the sum of the lengths of the three sides, which is:

x + x + (x - 4) = 3x - 4

We know that the perimeter is 32, so we can set 3x - 4 equal to 32 and solve for x:

3x - 4 = 32

Adding 4 to both sides gives:

3x = 36

Dividing by 3 gives:

x = 12

Therefore, one of the equal sides of the triangle is 12 inches long, and the length of the base is 12 - 4 = 8 inches.

So the three sides of the triangle are 12 inches, 12 inches, and 8 inches.

The correct equation to solve the problem is (C) 3x - 4 = 32.

By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).

In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."

Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

By adding the given vectors algebraically, we have the following:

[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)

[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)

[tex]\vec a + \vec b[/tex] = (3, 1).

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a) The percent change in Jennifer's account balance each month is 2.5%.

b) Based on the future value function, A(m)= 1750(1.025)^m, the account balance is increasing because the growth factor is 1.025 and not less than 1.

A growth function is a mathematical equation that shows a constant rate in increase or growth in value of the dependent variable.

A growth function is modeled by a growth factor greater than 1 while a decay function shows a decay.

Percentage change = 2.5% (1.025 - 1)

2.5% = 2.5 ÷ 100 = 0.025

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Answer:

C

Step-by-step explanation:

The area of a rectangle is 2 dimensions so it would be measured in square meters.

a = lwh

26241 = lw(17)  Divide both sides by 17

1542 = lw

The lw is he area of the base.

Helping in the name of Jesus.

The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at;

-3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

By substitution:

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537 respectively.

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The part of the cake with vanilla or lemon frosting is 1/5 by using arithmetic and algebraic expression.

Let's start by defining the variable "x" as the part of the cake with vanilla or lemon frosting.

According to the problem, Jonah uses vanilla frosting on 1/5 of the cake, which can also be written as x = 1/5.

Similarly, he uses lemon frosting on 2/5 of the cake, which can be written as x = 2/5.

We know that the sum of the parts of the cake with vanilla, lemon, and chocolate frosting should equal the whole cake. Since there are only three types of frosting, we can write:

x + x + chocolate frosting = 1

2x + chocolate frosting = 1

We also know that chocolate frosting covers the remaining part of the cake, which is 3/5. Therefore, we can write:

chocolate frosting = 3/5

Substituting this value into the previous algebraic expression, we get:

2x + 3/5 = 1

Subtracting 3/5 from both sides of the equation, we get:

2x = 2/5

x = 1/5

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This is a word problem involving supplementary angles. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.

Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:

x=6(180−x)−590

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

xx7xxx​=6(180−x)−590=1080−6x−590=490=7490​=70​

Therefore, the measure of the angle is 70°.

The number of bacteria present at 5 hours is (b) 148.413

From the question, we were given,

f(t) = eᵗ

Then  f(t) = number of bacterials present at a particular time t.

f(5) = number of bacterial present at 5 hours

So, we have

f(5) = e⁵

f(5) = 148.413

Then this can be written in the whole number as 148  which implies that the second option is correct because using f(t) = eᵗ to describes the growth of a colony of bacteria will provide us with the answer

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For the given data set of temperatures, the median temperature is 72.5 degree Fahrenheit.

In order to find the median temperature, we first need to arrange the temperatures in order from lowest to highest:

The temperatures arranged in order is : {66, 70, 72, 72, 73, 75, 79, 81}

There are 8 temperatures in total, which is an even-number, so the median will be the average of fourth and fifth day temperature.

In this case, the temperature of the fourth day is 72, and fifth day is 73,

The average will be = (72+73)/2 = 72.5,

Therefore, the median high daily temperature in the city is 72.5 degrees Fahrenheit.

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The given question is incomplete, the complete question is

The data set shown below represents the distribution of daily high temperatures in a city for 8 days.

79,73,72,70,72,66,81,75.

What is the median high daily temperature, in degrees Fahrenheit, in the city?

Answer:

[tex]\mathrm{Matrix \: Form:}[/tex]
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]

[tex]\mathrm{Determinant\; of \;coefficient \;matrix = - 6}[/tex]

Step-by-step explanation:

The system of linear equations provided in the question:
[tex]\begin{aligned}3x+2y+z &= 26\\ x-4y&=-11\\ 2x+z&=13\\\\\end{aligned}[/tex]

can be represented in matrix form as

[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]

The coefficient matrix is
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]

The determinant of this matrix can be obtained by the expansion formula:
[tex]\det \begin{pmatrix}a&b&c\\ \:d&e&f\\ \:g&h&i\end{pmatrix}=a\cdot \det \begin{pmatrix}e&f\\ \:h&i\end{pmatrix}-b\cdot \det \begin{pmatrix}d&f\\ \:g&i\end{pmatrix}+c\cdot \det \begin{pmatrix}d&e\\ \:g&h\end{pmatrix}[/tex]

Therefore
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]

[tex]= 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}[/tex]

[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc[/tex]

[tex]\det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix} = \left(-4\right)\cdot \:1-0\cdot \:0 = -4[/tex]

[tex]\det \begin{pmatrix}1&0\\ 2&1\end{pmatrix} = 1\cdot \:1-0\cdot \:2 = 1[/tex]

[tex]\det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix} = 1\cdot \:0-\left(-4\right)\cdot \:2 =8[/tex]

Finally,
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\\\\\\ = 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}\\\\\\= 3\left(-4\right)-2\cdot \:1+1\cdot \:8\\\\= -12 - 2 + 8\\\\= -6[/tex]

The sum of all the pets in the list is 11.

The average number of pets that the students own is 1.375.

It should be noted that to find the sum of all the pets in the list, we simply add up all the values:

0 + 1 + 2 + 3 + 1 + 2 + 0 + 2 = 11

Therefore, the sum of all the pets in the list is 11.

Since Cameron asked eight of his classmates, we divide the sum of pets by 8 to find the mean:

11 ÷ 8 = 1.375

Therefore, the average number of pets that the students own is 1.375.

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The measures of center can be used to summarize the number of pets that students own. Cueton asked eight of his classmates how many pets they own. The results are listed below.

0  1  2  3  1  2  0  2

What is The sum of all the pets in the list

What is the average number of pets that the students own