Here are 2 points in the plane.
Using only a straightedge,can you find points in the plane that are the same distance from points A and B. Explain your reasoning

The CSC of the expression \(\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)\) is mathematically given as

\(\csc (\theta)=-\frac{8 \sqrt{55}}{55}\)

This is further explained below.

Generally, the equation for the Problem is mathematically given as

\(\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)\)

Therefore

To find the \($\csc (\theta)$\) between the x-axis and the line between the points (0,0) and \(\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right),\) draw the triangle between the three points \((0,0),\left(\frac{3}{8}, 0\right)$, and $\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)$\)

Opposite \($:-\frac{\sqrt{55}}{8}$\)

Adjacent :\($\frac{3}{8}$\)

Find the hypotenuse using the Pythagorean theorem \($c=\sqrt{a^2+b^2}.\)

\($\csc (\theta)=\frac{\text { Hypotenuse }}{\text { Opposite }}$\)

therefore

\(\csc (\theta)=\frac{1}{-\frac{\sqrt{65}}{8}}$.\)

\(\frac{1}{-\frac{\sqrt{55}}{8}}\)

Simplify\(\csc (\theta)\)

\(\csc (\theta)=-\frac{8 \sqrt{55}}{55}\)

Approximate the result.

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To solve the problem we must know about the slope of a line.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

\(m = \dfrac{(y_2-y_1)}{(x_2-x_1)}\)

The slope of the line passing through the points (-8,5) and (7,0) is \(\dfrac{-1}{3}\).

Given to us

Points can be written as,

\(y_2 = 0\\y_1 = 5\\x_2=7\\x_1 = -8\)

We know that the slope of a line whose two points are given is written as,

\(m = \dfrac{(y_2-y_1)}{(x_2-x_1)}\)

Substituting the value, we get,

\(m = \dfrac{(0-5)}{[7-(-8)]}\\\\m = \dfrac{(0-5)}{[7+8]}\\\\m = \dfrac{(-5)}{[15]}\\\\m= \dfrac{-1}{3}\)

Hence, the slope of the line passing through the points (-8,5) and (7,0) is \(\dfrac{-1}{3}\).

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Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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Answer:

the square root of 55, or 7.42

Step-by-step explanation:

Use the Pythagorean Theorem, or  a²+b²=c², where a and b are the sides or "legs" of the triangle and c is the hypotenuse.

a is 3, b is x, and c is 9

If you plug that into the equation, you get 3²+x²=8²

We can make this 9+x=64 by squaring the 3 and 8.

Then we can subtract 9 from each side to get x=55.

Finally, take the square root of 55 to get √55 or 7.42.

I hope this helped!

9514 1404 393

Answer:

  any real number

Step-by-step explanation:

The value of 7^0 is 1, so the equation is ...

  1^x = 1

This is true for any value of x. Possible values of x are "any real number."

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.

In probability function, the value of b = \(\frac{\pi}{2}\).

What is Probability?

Probability is the measure of the likelihood of a given event occurring. It is usually expressed as a number between 0 and 1, where 0 indicates an impossibility of the event occurring and 1 indicates a certainty that the event will occur. Probability theory is an important part of mathematics, and is used in a variety of applications, from predicting weather patterns to assessing the risk of a financial investment.

For f(x) to be a probability density function, the total area under the graph of the function should be equal to 1. This implies that the integral of f(x) from 1 to 3 should be equal to 1. This gives us the equation

\(\int1^3 (x^2 - b) dx = 1\)

Solving the integral, we get b = 4.

For h(x) to be a probability density function, the total area under the graph of the function should be equal to 1. This implies that the integral of h(x) from -b to b should be equal to 1. This gives us the equation

\(\int-b^b cos x dx = 1\)

Solving the integral, we get b = \(\frac{\pi}{2}\).

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The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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The value of DE is 6 units long.

Since triangles ABC and DEF are similar, we know that their corresponding sides are proportional. In other words, the ratio of any corresponding side lengths in the two triangles is the same.

We can use this fact to set up the following proportion:

DE/BA = EF/BC

Substituting the given values, we get:

DE/9 = 12/18

Simplifying the right side of the equation, we get:

DE/9 = 2/3

To solve for DE, we can cross-multiply:

DE = 9 x 2/3 = 6

Therefore, DE is 6 units long.

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To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

The width of the rectangular rug is 13 feet and the length of the rectangular rug is 26 feet.

Area of a rectangle formula: A = L * W. A

rectangle's length and width are multiplied to produce its area.

A is the area, L is the length, and W is the width or girth, where

A = L * W.

The corresponding sides of the rectangular rug and the rectangular floor must be proportional if they are alike.

Let's use "x" to represent the rug's width. The floor measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet according to the details provided. Since the rug and the surface are comparable, we can establish the following ratio:

Rug width/floor width = rug length/floor length

x / 26 = rug's length / 32

We can cross-multiply and then solve for "x" to find the answer:

32x = 26 * Rug's length

x =  (26 * Rug Length) / 32

\(= \frac{26 * 16}{32} \\= \frac{26}{2} \\= 13\)

Therefore x ( the width of the rug) is = 13 feet.

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Complete question:

The rectangular rug is similar to the rectangular floor. If the floor of the room measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet, what is the width of the rug?

The sentence with proper subject-verb agreement is the student as well as the teacher want to go to the museum. In this sentence, the subject is what we call a compound subject, meaning that the verb refers and agrees with more than just one singular word.

The compound subject is "student" and "teacher" and they are connected by "as well as", which functions as a coordinating conjunction would. That's why the verb should conjugate in its plural form.

Option A is incorrect because the structure inside parentheses is not related to the verb and does not influence its conjugation. Options C and D have a verb in the singular form for a compound subject - that would demand a plural conjugation.

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Answer:

That's the answer and I hope it helps. Thanks and have a great time.

Answer:

Explanation:

Here, we want to get the cost of one of the chairs

From what we are given, the three chairs cost $1,680

The cost of each of the chairs will be the cost of the 3 divided by 3

Mathematically, we have that as:

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

The discount percent is 18.75%

Step-by-step explanation:

The amount of money that was lost in this discount is $150, to calculate the percent, you subtract the original price by the discounted price, and then divide the difference by the original price and multiply that by 100% to get the discount percent. \(\frac{150}{800}\) * 100% equals 18.75%, so that would be the discount percent.

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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The ordered pair that lie on the graph as per the equation will be equal to (-2, -4). Hence, option B is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given information in the question,

The given equation is,

f(x) = 2(x + 4) - 8

Let's check as per the points given in the question,

A. (24, 1)

f(x) = 2(24 + 4) - 8

f(x) = 48

So, the supplied exponential function's graph does not contain the point (24, 1) mentioned.

B. (-2, -4)

f(x) = 2(-2 + 4) - 8

f(x) = 4 - 8

f(x) = -4

As a result, the points (-2, -4) are located on the graph of the supplied exponential function.

C. (2, 256)

f(x) = 2(2 + 4) - 8

f(x) = 4

So, the supplied exponential function's graph does not contain the point (2, 56) mentioned.

D. (8, 0)

f(x) = 2(8 + 4) - 8

f(x) = 16

So, the supplied exponential function's graph does not contain the point (8, 0) mentioned.

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Answer:

0

Step-by-step explanation:0 times anything is still 0

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

i think it would be b

Step-by-step explanation:

Answer:

3x - 5y = 22 -----(1)

y = -5x + 32  ------(2)

substitute (2) in (1)

3x - 5(-5x +32) =22

3x + 25x - 160 = 22

28x = 182

x = 6.5

option C

Answer:

here is the Answer The population will be 799,500 people

Step-by-step explanation:

The scale factor of the dilation for the rectangle ABCD is found as 3.

The ratio of the scale of an original thing to a new object that is a representation of it but of a varying design is known as a scale factor (bigger or smaller).

The rectangle A'B'C'D' is created by dilation of rectangle ABCD.

We shall calculate the ratio of the rectangle's lengths in order to get the scale factor.

A:(1,5) and B:(4,5).

Length of side AB = 4 - 1 = 3

And,

A':(3,15) and B': (12,15).

Length of the side A'B' = 12-3 = 9

Ratio of the sides

AB : A'B' = 3 : 9

AB : A'B' = 1 : 3.

Thus, the scale factor of the dilation for the rectangle ABCD is found as 3.

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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.

2)The snow days to days ratio is 20:1

3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.

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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.

2)The snow days to days ratio is 20:1

3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.

Define ratio?

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Answer:

7250%

Step-by-step explanation:

To express 72 1/2 as a percentage, you need to convert it to a decimal first and then multiply by 100.

72 1/2 is equivalent to 72.5 as a decimal.

To convert it to a percentage:

72.5 * 100 = 7250

Therefore, 72 1/2 is equal to 7250% when expressed as a percentage.

let me know it is helpful for you or not

Answer:

95

Step-by-step explanation:

The equation to solving this would be 203 - (9 multiply 12). If you multiply 9 and 12 you get 108. Minus 108 from 203 and you get 95.

Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

Answer:

The length of the road after 35 days is of 79 miles.

Step-by-step explanation:

The length of the road, after d days, is given by:

\(L(d) = 44 + d\)

What is the length of the road after 35 days?

This is l when d = 35. So

\(L(35) = 44 + 35 = 79\)

The length of the road after 35 days is of 79 miles.