Complete the statements to find the measurements of ∠a and ∠b .

15. Length of the radius is 4√11 inches.16.

16. Length of the chord is 6√51 cm.17

17.  Length of AB is 117.4 cm.

15. Given a chord is 20 inches long and is 24 inches from the center of the circle.

Let O be the center of the circle, and AB is the chord which is 20 inches long. Also, let OP be perpendicular to AB. Hence, OP is the perpendicular bisector of AB. Therefore, AO = BO = 12 inches. Hence, we have to find radius OP.

Using Pythagoras theorem, we have  [tex]$OP=\sqrt{OA^2-AP^2}=\sqrt{12^2-10^2}=4\sqrt{11}$[/tex] inches

Answer: Length of the radius is 4√11 inches.16. Given the diameter of a circle is 30 cm long and the distance from the chord to the center of the circle is 9 cm.

We know that the distance of the chord from the center of the circle is 9 cm and diameter is 30 cm.

The distance of the chord from the center of the circle bisects the chord i.e., PE = EF. We have to find the length of chord CD.

Now, we know that OP = 15 cm (half of diameter)and OE = 9 cm

Therefore, we have, EP = OP - OE = 6 cm

Triangle EPC is a right-angled triangle using Pythagoras theorem, we have, [tex]$EC = \sqrt{PC^2+EP^2}=\sqrt{15^2-6^2}=3\sqrt{51}$[/tex]

Similarly, triangle FPD is a right-angled triangle, using Pythagoras theorem, we have, [tex]$FD = \sqrt{PD^2+PF^2}\\=\sqrt{15^2-6^2}\\\=3\sqrt{51}$[/tex]

Therefore, we have, CD = EF = EC + FD = $3\sqrt{51}+3\sqrt{51}=6\sqrt{51}$ cm

Answer: Length of the chord is 6√51 cm.17. Given in circle O, the radius is 36 cm long and mAB = 140°.

We know that the angle subtended at the center of a circle is twice the angle subtended at the circumference of the circle.

Therefore, [tex]$\angle AOB = 2\angle ABB=280$[/tex]°

We know that angle in a semicircle is a right angle.

Therefore, [tex]$\angle AOB = 90$[/tex]°

So, 280° + 90° = 370° is the total angle in circle O

Therefore, we have 370° = [tex]$2\pi r$[/tex] (circumference of circle)

where r is the radius of the circle.

We know that [tex]$\pi=\frac{22}{7}$[/tex]

Hence, [tex]$370=2\frac{22}{7}r$[/tex]

Solving the above equation, we have,

[tex]$r = \frac{370\times 7}{44}= 62.5$[/tex] cm

So, the length of AB = 2r sin (AB/2)

= [tex]$2\times 62.5 \sin(70)$[/tex]

= [tex]$2\times 62.5 \times 0.9397$[/tex]

= 117.4 cm (approx)

Answer: Length of AB is 117.4 cm (approx).

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Answer:

2(2) + 1   =  5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2*2=4+1=5

The correct statements are:

1. If the product AB = 0 (zero matrix), then either A = 0 or B = 0.

4. BC = CB.

Explanation:

1. If the product of two matrices AB equals the zero matrix, it implies that at least one of the matrices A or B (or both) must be the zero matrix for the product to result in zero.

4. The statement BC = CB states that the order of multiplication of matrices B and C does not affect the resulting matrix. This property holds true for matrices of any size as long as the dimensions are compatible for matrix multiplication.

The other statements are not necessarily true in general:

2. Both BC and CB being square matrices is not guaranteed. The product of two matrices can result in a square matrix only if the number of columns of the first matrix is equal to the number of rows of the second matrix. In this case, B has 3 columns and C has 2 rows, so BC and CB are not square matrices.

3. The matrix A + BC is not defined since the addition of matrices requires them to have the same dimensions. In this case, A is a 2×2 matrix, while BC is a 2×3 matrix, so they cannot be added together.

5. The statement A = A12​ = I2​ implies that matrix A is equal to the 2×2 identity matrix I2​. However, this is not necessarily true as the given information does not provide any details about the values or properties of matrix A.

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Dime Thickness = 0.135 cm. Dollar Thickness = 1.0992 x 10^-2 cm. To calculate the thickness of a dime is times greater than the thickness of a dollar bill, we need to divide the thickness of a dime by the thickness of a dollar bill:0.135 cm / 1.0992 x 10^-2 cm = 12.3 times.

Therefore, the thickness of a dime is 12 times greater than the thickness of a dollar bill. Round off the answer to the nearest whole number is 12.

To calculate the thickness of a dime is times greater than the thickness of a dollar bill, we need to divide the thickness of a dime by the thickness of a dollar bill. To do that, let's use the given values to find out the ratio of the thicknesses of a dime and a dollar bill.

Thickness of a dime = 0.135 cmThickness of a dollar bill = 1.0992 x 10^-2 cmLet us divide the thickness of a dime by the thickness of a dollar bill to find the ratio of thicknesses.0.135 cm / 1.0992 x 10^-2 cm= 12.3 timesTherefore, the thickness of a dime is 12 times greater than the thickness of a dollar bill.

The answer should be rounded off to the nearest whole number, which is 12. So, it can be concluded that the thickness of a dime is 12 times greater than the thickness of a dollar bill.

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Answer:

D. g(x)=5x^2

Step-by-step explanation:

This is the graph, if you need help go to desmos.com

Answer:

D

Step-by-step explanation:

If you plug the x coordinate into the 4 possible answers, only one gives you the correct y coordinate.

Answer A:  if X=1 then 1 squared is still 1 and 1 times 25 means Y=25 (wrong)

Answer B: If X=1 then 1 times 5 is 5 and 5 squared is 25 so Y=25 (wrong)

Answer C: if X=1 then 1 squared is still 1 and 1 times 1/5 is 1/5 so Y=1/5 (wrong)

Answer D: if X=1 then 1 squared is still 1 and 1 times 5 is 5 so Y=5 (Correct)

Answer:

a) perimeter = 8π + 6 + 8 + 10

= (8π + 24) ft

= about 49.13 ft

8(3.14) + 24 = about 49.12 ft

b) area = π(4^2) + 10(8) + (1/2)(6)(8)

= (16π + 104) ft²

= about 154.27 ft²

16(3.14) + 104 = about 154.24 ft²

The function U = sin(x) cosh(y) + cos(x) sinh(y) is a solution of Laplace's equation Uxx + Uyy = 0.

In order to determine whether each of the given functions is a solution of Laplace's equation

Uxx + Uyy = 0 or not, we need to differentiate the given functions twice w.r.t. x and then twice w.r.t. y, respectively, and then add these values.

If the sum equals to zero, then the function is a solution of Laplace's equation Uxx + Uyy = 0.

Now, let's differentiate each function with respect to x and y twice one by one.

(1) u = In(Vx2 + y2)

Differentiating with respect to x:

u_x = 2x / (x^2 + y^2),

u_xx = (2(x^2 + y^2) - 4x^2) / (x^2 + y^2)^2

Differentiating with respect to y:

u_y = 2y / (x^2 + y^2),

u_yy = (2(x^2 + y^2) - 4y^2) / (x^2 + y^2)^2

Now, u_xx + u_yy = [(2(x^2 + y^2) - 4x^2) / (x^2 + y^2)^2] + [(2(x^2 + y^2) - 4y^2) / (x^2 + y^2)^2] = 0 + 0 = 0.

Hence, the function u = In(Vx2 + y2) is a solution of Laplace's equation

Uxx + Uyy = 0.(2) u = x2 - y2

Differentiating with respect to x:

u_x = 2x, u_xx = 2

Differentiating with respect to y:

u_y = -2y, u_yy = -2

Now, u_xx + u_yy = 2 - 2 = 0.

Hence, the function u = x2 - y2 is a solution of Laplace's equation Uxx + Uyy = 0.(3) u = x2 + y2

Differentiating with respect to x: u_x = 2x, u_xx = 2

Differentiating with respect to y: u_y = 2y, u_yy = 2

Now, u_xx + u_yy = 2 + 2 = 4 ≠ 0. Hence, the function u = x2 + y2 is not a solution of Laplace's equation

Uxx + Uyy = 0.(4) u = e-x cos(y) – e-Y cos(x)

Differentiating with respect to x: u_x = -e-x cos(y) + e-Y sin(x), u_xx = e-x cos(y) + e-Y cos(x)

Differentiating with respect to y: u_y = -e-x sin(y) + e-Y cos(x), u_yy = e-x cos(y) + e-Y cos(x)Now, u_xx + u_yy = (e-x cos(y) + e-Y cos(x)) + (e-x cos(y) + e-Y cos(x)) = 2(e-x cos(y) + e-Y cos(x)).

This is not equal to 0.

Hence, the function u = e-x cos(y) – e-Y cos(x) is not a solution of Laplace's equation Uxx + Uyy = 0.(5) u = x3 + 3xy2

Differentiating with respect to x: u_x = 3x2 + 3y2, u_xx = 6x

Differentiating with respect to y: u_y = 6xy, u_yy = 6x

Now, u_xx + u_yy = 6x + 6x = 12x ≠ 0.

Hence, the function u = x3 + 3xy2 is not a solution of Laplace's equation Uxx + Uyy = 0.(6) u = sin(x) cosh(y) + cos(x) sinh(y)

Differentiating with respect to x: u_x = cos(x) cosh(y) - sin(x) sinh(y), u_xx = -sin(x) cosh(y) - cos(x) sinh(y)

Differentiating with respect to y: u_y = sin(x) sinh(y) + cos(x) cosh(y), u_yy = sin(x) cosh(y) + cos(x) sinh(y)

Now, u_xx + u_yy = (-sin(x) cosh(y) - cos(x) sinh(y)) + (sin(x) cosh(y) + cos(x) sinh(y)) = 0 + 0 = 0.

Hence, the function U = sin(x) cosh(y) + cos(x) sinh(y) is a solution of Laplace's equation Uxx + Uyy = 0.

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Answer:

$0.67

Step-by-step explanation:

Divide 8(dollars) by 12 (donuts) and you get  0.66666666666666666666666666666667

But, round it and you get .67

Answer:

(113^6*37^3*54^12)

hope it helps you

Answer:

41 minutes

Step-by-step explanation:

The average value of the position function from t = 2 seconds to t = 5 seconds is approximately: Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]

To find the equation of the velocity function, we need to find the antiderivative of the acceleration function. The antiderivative of 2 sin(t) is -2 cos(t), and the antiderivative of 1 is t.

So, the velocity function v(t) is given by integrating the acceleration function:

v(t) = INT(2 sin(t) + 1) dt

[tex]= -2 cos(t) + t + C[/tex]

Since the initial velocity is v(0) = 0, we can substitute this value into the equation to find the constant C:

[tex]0 = -2 cos(0) + 0 + C\\0 = -2(1) + C\\C = 2[/tex]

Therefore, the equation of the velocity function is:

[tex]v(t) = -2 cos(t) + t + 2[/tex]

To find the position function, we integrate the velocity function:

[tex]s(t) = INT(-2 cos(t) + t + 2) dt\\= -2 sin(t) + 0.5t^2 + 2t + D[/tex]

Since the initial position is s(0) = 3, we substitute this value into the equation to find the constant D:

[tex]3 = -2 sin(0) + 0 + 0 + D\\3 = 0 + 0 + D\\D = 3[/tex]

Therefore, the position function is:

[tex]s(t) = -2 sin(t) + 0.5t^2 + 2t + 3[/tex]

To find the average value of the position function from t = 2 seconds to t = 5 seconds, we use the formula for the average value of a function over an interval:

Average value =[tex](1 / (b - a)) * INT(a, b) f(t) dt[/tex]

In this case, the interval is from t = 2 seconds to t = 5 seconds, so we have:

Average value =[tex](1 / (5 - 2)) * INT(2, 5) (-2 sin(t) + 0.5t^2 + 2t + 3) dt[/tex]

Evaluating the definite integral:

Average value = [tex](1 / 3) * [(-2 cos(t) + (1/6)t^3 + t^2 + 3t) EVAL(2, 5)][/tex]

Average value =[tex](1 / 3) * [(-2 cos(5) + (1/6)(5^3) + 5^2 + 3(5)) - (-2 cos(2) + (1/6)(2^3) + 2^2 + 3(2))][/tex]

Calculating the values:

Average value ≈[tex](1 / 3) * [(-2 cos(5) + 125/6 + 25 + 15) - (-2 cos(2) + 8/6 + 4 + 6)][/tex]

Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]

Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is approximately:

Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]

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Answer:

x < 15

Step-by-step explanation:

Step 1: Write inequality

-x/3 + 10 > 5

Step 2: Solve for x

An isoquant is a curve that represents all the various combinations of two factors of production that can produce a particular level of output. The formula for the given production function is

F(k,l)=.75L+K, where Q=1. Now, we will draw the isoquant for the given function.

The graph of the isoquant will be plotted with the help of two axes, K and L, where K represents capital, and L represents labor.

Steps to draw the Isoquant for the given production function F(k,l)=.75L+K:

Here's the graph of the Isoquant for the given production function:

F(k,l)=.75L+K where Q=1:

f(k, l) = 0.75L + Kf(k, l) = 0.75L + KQ = 1

Isoquant1 = 1; K = 1 - 0.75L0.75(4) + 1 = 1 + 0.75(0)1 + 0 = 0.75(3) + 1= 1 + 2.25

Isoquant0.75(1) + 1 = 1 + 0.75(2)0.75 + 1 = 1 + 1.5= 1 + 0.75(1)

Isoquant0.75(0) + 1 = 1 + 0.75(4)1 + 0 = 3

isoquant's graph indicates the various combinations of two factors of production, labor, and capital, that can produce a particular level of output, Q = 1.

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There are 1680 ways the teaching assistants can be chosen to grade the exam.

To determine the number of ways the teaching assistants can be chosen to grade the exam, we need to consider the number of choices available for each question and multiply them together.

For the first question, there are eight teaching assistants available. Therefore, there are 8 choices for the first question.

For the second question, since one assistant has already been assigned to the first question, there are seven remaining assistants available. Thus, there are 7 choices for the second question.

Similarly, for the third question, there are six remaining assistants available after two have been assigned to the previous questions. Hence, there are 6 choices for the third question.

Lastly, for the fourth question, there are five remaining assistants available after three have been assigned to the previous questions. Therefore, there are 5 choices for the fourth question.

To determine the total number of ways, we multiply the number of choices for each question:

Total ways = 8 * 7 * 6 * 5 = 1680

Therefore, there are 1680 possible approaches to select the teaching assistants to grade the exam.

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Answer:

QET

FWR

Step-by-step explanation:

Colinear means lying on the same line.

Answer:

Well nah

Step-by-step explanation:

Answer:

Lol no

Step-by-step explanation:

Answer:

okay so to figure out a perfect square a number has to be outlined by itself. 8 is not. 4 is because 2 times itself is 4. 81 is because 9 time itself is 81. 44 is not. 49 is because 7 times itself is 49. 125 is not. 150 is not. 144 is because 12 times itself is 144.

Square 3, multiply -2 and subtract -4 from the result. Therefore, option C is the correct answer.

The given function is f(x) = -2x²-4.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Substitute x=3 in f(x) = -2x²-4, we get

f(3) = -2(3)²-4

Square 3, multiply -2 and subtract -4 from the result. that is

f(3) = -2×9-4

= -22

Square 3, multiply -2 and subtract -4 from the result. Therefore, option C is the correct answer.

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To create a system of constraints that defines a parallelogram, we need to establish conditions that satisfy the properties of a parallelogram: opposite sides are parallel and equal in length, and opposite angles are congruent.

Here's an example of a system of constraints that represents a parallelogram:

Let's consider a parallelogram with vertices (x, y):

1. Constraint 1: Opposite sides are parallel.

  This can be represented by the equation: y = ax + b, where a is the slope and b is the y-intercept.

2. Constraint 2: Opposite sides are equal in length.

  This can be represented by the equation: [tex](x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2[/tex] are the coordinates of two opposite vertices.

3. Constraint 3: Opposite angles are congruent.

  This can be represented by the equation: [tex]m_1 = m_2[/tex], where [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of two adjacent sides.

By combining these three constraints, we can define a system of equations that represents a parallelogram. The specific values of a, b, ([tex]x_1, y_1[/tex]), and ([tex]x_2, y_2[/tex]) will determine the properties and shape of the parallelogram.

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Answer:

she can feed 2,220 people with 555555 pancakes.

Step-by-step explanation:

Answer:20 people

Step-by-step explanation:

we can solve the problem by setting a simple proportion.

We know that 22 pancakes can feed 8 people, so we have to find the number x which corresponds to the number of people that can be feeded with 55 pancakes:

Solving the proportion, we find

So, 55 pancakes can feed 20 people.

Answer:

6. b

7. d

8. a

9. c

10.around 40

Step-by-step explanation:

no idea but i think i did my best

Answer:

6 and -6

Step-by-step explanation:

Since they're 12 units apart that means one of them is 6 and the fact they're opposites means the other is -12

Answer:

x ≈ 2.30277563

Step-by-step explanation:

Answer:

585

Step-by-step explanation:

divide 780 by 12

780/12=65

The answer you get is her speed, so 65miles/hour

So if she did this for nine hours, multiply 65 by 9

65*9=585

Answer:

The correct answer is c, Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

We want to study the possible solutions of a system of equations where one equation is a parabola and the other equation is a line.

We will see that the correct option is A:

"Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9."

-----------------------------------------

Here we have the system of equations:

Isabel claims that one of the solutions to the system must always be the vertex of the parabola.

Now, the solutions of the system are the points where both graphs intersect, so to find the solutions we can write:

(x + 3)^2 = y = m*x + 9

Then the solutions can be found by solving:

(x + 3)^2  = m*x + 9

Now, the vertex of the parabola is at x = 0, so to test Isabel claim, we can evaluate the above expression in x = 0 to get:

(0 + 3)^2  = m*0 + 9

3^2 = 9

9 = 9

This is true, so Isabel is correct, there will always be a solution and that solution is the vertex of the given parabola.

Then the correct option is:

A: Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9.

(Option B is incorrect because the y-intercept of line B is written incorrectly there).

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Answer:

[tex]\dfrac{4}{3}x[/tex]

Step-by-step explanation:

Given that:

Rate of bottle filling for Machine B = [tex]x[/tex]

Rate of filling of Machine B is 1.5 times the rate of Machine A.

Let the rate of bottle filling for Machine A = [tex]y[/tex]

As per question statement:

[tex]x=1.5y\\\Rightarrow y=\dfrac{2}{3}x[/tex]

Now, combined rate of both the machines, i.e. A and B = [tex]x+y[/tex]

[tex]\Rightarrow x+\dfrac{2}{3}x\\\Rightarrow \dfrac{5}{3}x[/tex]

Bottle filling Rate of new Machine = [tex]3x[/tex]

It is given that both the machines are replaced by the new machine.

Now, increase in the rate can be calculated by subtracting the combined rate of both the machines from the bottle filling rate of new machine.

i.e.

[tex]3x-\dfrac{5x}3\\\Rightarrow \dfrac{9x-5x}{3}\\\Rightarrow \bold{\dfrac{4x}{3}}[/tex]

So, the following expression shows the increase in rate:

[tex]\dfrac{4}{3}x[/tex]

Answer:

You will pay $2,302 back.

Step-by-step explanation:

Compound interest occurs when the interest is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

We are given the following conditions: Principal amount P=$1,690, duration=5 1/2 years, interest rate r=5.7% compounded semi-annually.

Note we don't actually have the value of n or t because they must be taken from the duration and the compounding period.

The interest compounds semi-annually i.e. twice a year. Thus, n=2.

The interest rate is converted to decimal r=0.057 and we apply the formula:

[tex]{\displaystyle A=1,690\left(1+{\frac {0.057}{2}}\right)^{2*5.5}}[/tex]

[tex]{\displaystyle A=1,690\left(1+0.0285\right)^{11}}[/tex]

A=$2,302

You will pay $2,302 back.

=========================================================

Explanation:

Point C is located at (-2, -3).

When we apply an x axis reflection, the x coordinate stays the same and the y coordinate flips from negative to positive.

The x axis reflection rule is [tex](x,y) \to (x,-y)[/tex]

So that's how we go from (-2,-3) to (-2,3)

Answer:

-2,3

Step-by-step explanation:

Reflection in the x -axis:

A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is. (x,y)→(x,−y) .

There is a 38.29% likelihood that at most five goblets must be chosen to find four that are not seconds.

a. Among six randomly selected goblets, the likelihood that only one is a second is calculated as follows:[tex]P(only one is a second) = P(X = 1) = (6C1 x 0.1 x 0.9⁵) = 0.47 or 47%[/tex]Therefore, Among six randomly selected goblets,

The likelihood that at least two are seconds is calculated as follows[tex]:P(at least 2 seconds) = 1 - P(0 second or 1 second)P(0 second or 1 second) = P(X = 0) + P(X = 1) = (6C0 x 0.1⁰ x 0.9⁶) + (6C1 x 0.1 x 0.9⁵) = 0.531P(at least 2 seconds) = 1 - P(0 second or 1 second) = 1 - 0.531 = 0.469 or 46.9%[/tex]Therefore, it is 46.9% likely that at least two of the six selected goblets are seconds.c. If goblets are examined one by one, the probability that at most five must be selected to find four that are not seconds is calculated as follows:

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