write the standard form of the equation of the circle that passes through the origin, (2.8,0), and (5,2)

Answer:

Step-by-step explanation:

Given is the probability distribution of a random variable X

X 4 5 6 7 Total

P 0.2 0.4 0.3 0.1 1

x*p 0.8 2 1.8 0.7 5.3

x^2*p 3.2 10 10.8 4.9 28.9

a) E(X) = Mean of X = sum of xp = 5.3

[tex]Var(x) = 28.9-5.3^2=0.81[/tex]

Std dev = square root of variance = 0.9

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

b) For sample mean we have

Mean = 5.3

Variance = var(x)/n = [tex]\frac{0.81}{{36} } \\=0.0225[/tex]

c) [tex]P(\bar X <5.5)\\= P(Z<\frac{5.5-5.3}{\sqrt{0.0225} } \\= P(Z<1.33)\\=0.908[/tex]

The mean and the variance from the data about the cherries will be 5.3 and 0.81.

The required mean from the information given will be:

= (4 × 0.2) + (5 × 0.4) + (6 × 0.3) + (7 × 0.1)

= 0.8 + 2.0 + 1.8 + 0.7

= 5.3

The variance will be calculated thus:

= (4² × 0.2) + (5² × 0.4) + (6² × 0.3) + (7² × 0.1) - (5.3)²

= 3.2 + 10 + 10.8 + 4.9 - (5.3)²

= 0.81

The variance is 0.81.

The probability that the average number of cherries in 36 cherry puffs will be less than 5.5 will be:

= P(x = 4( + P(x = 5)

= 0.2 + 0.4

= 0.6

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Answer:

The answer to your question is cos A = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Process

1.- Write the formula

[tex]cos A = \frac{adjacent side}{hypotenuse}[/tex]

2.- Identify the legs of the triangle

opposite side = 12

adjacent side = 9

hypotenuse = 15

3.- Substitute the values in the formula

[tex]cos A = \frac{9}{15}[/tex]

4.- Simplification and result

[tex]cos A = \frac{3}{5}[/tex]

Explanation of finding the value of cos A using trigonometric identities and scalar products.

Cosine function: The value of cos A can be determined using trigonometric identities. For example, from the given expressions like cos 4A=8cos^4A-8cos^2A+1, we can find the value of cos A for specific angles.

Trigonometric identities: By manipulating the given equations and using trigonometric relationships like 1 - cos A = 2sin^2A, you can solve for cos A for different angles.

Scalar products: Understanding the concept of scalar products involving cosine functions like AB cos(θ) will help in applying trigonometry in real-world applications.

Answer: 52/57

Step-by-step explanation:please see attachment for explanation

Final answer:

The question involves calculating the probability of selecting at least 2 business majors from a group, using complementary probability and combinations. The probability that at least 2 of the 4 students selected are business majors is approximately [tex]\(0.1608\).[/tex]

Explanation:

To find the probability that at least 2 of the 4 students selected are business majors, we can calculate the probability of exactly 2, 3, and 4 students being business majors, and then sum these probabilities.

First, let's find the probability of selecting exactly 2 business majors and 2 non-business majors:

1. Probability of selecting 2 business majors: [tex]\( \frac{{14 \choose 2}}{{21 \choose 4}} \)[/tex]

2. Probability of selecting 2 non-business majors:[tex]\( \frac{{7 \choose 2}}{{21 \choose 4}} \)[/tex]

Then, we can find the probability of selecting exactly 3 business majors and 1 non-business major:

1. Probability of selecting 3 business majors: [tex]\( \frac{{14 \choose 3}}{{21 \choose 4}} \)[/tex]

2. Probability of selecting 1 non-business major: [tex]\( \frac{{7 \choose 1}}{{21 \choose 4}} \)[/tex]

Finally, we find the probability of selecting all 4 business majors:

1. Probability of selecting 4 business majors: [tex]\( \frac{{14 \choose 4}}{{21 \choose 4}} \)[/tex]

Now, we sum up these probabilities:

[tex]\[\text{Probability of at least 2 business majors} = \text{Probability of selecting exactly 2} + \text{Probability of selecting exactly 3} + \text{Probability of selecting all 4}\][/tex]

[tex]\[\text{Probability of at least 2 business majors} = \left( \frac{{14 \choose 2}}{{21 \choose 4}} \times \frac{{7 \choose 2}}{{21 \choose 4}} \right) + \left( \frac{{14 \choose 3}}{{21 \choose 4}} \times \frac{{7 \choose 1}}{{21 \choose 4}} \right) + \left( \frac{{14 \choose 4}}{{21 \choose 4}} \right)\][/tex]

[tex]\[= \left( \frac{{91}}{{5985}} \times \frac{{21}}{{5985}} \right) + \left( \frac{{364}}{{5985}} \times \frac{{7}}{{5985}} \right) + \left( \frac{{1001}}{{5985}} \right)\][/tex]

[tex]\[= \left( \frac{{1911}}{{5985^2}} \right) + \left( \frac{{2548}}{{5985^2}} \right) + \left( \frac{{1001}}{{5985}} \right)\][/tex]

[tex]\[= \frac{{1911 + 2548 + 1001}}{{5985^2}}\][/tex]

[tex]\[= \frac{{5460}}{{5985^2}}\][/tex]

[tex]\[\approx 0.1608\][/tex]

So, the probability that at least 2 of the 4 students selected are business majors is approximately [tex]\(0.1608\).[/tex]

Answer:

The ad is about the price of a house which is sufficient for two families to live in it along with the contact details to purchase this house.

According to the ad, the total cost of the home is $190,000. It is sufficient for two families. It may be double story as well. To purchase this house, one can call at the given number which is 212-123-4567. This can be the original number or the format by the editor to show original number. Actual area of the house is not mentioned in the ad.

Answer:

E(x) = 15 minutes

Step-by-step explanation:

The random variable X (waiting time)  has a uniform distribution between the interval [0,30], because it is just as likely that you arrive in any time and then your waiting time is minimum 0 minutes and maximum 30 minutes

The expected value  of a random variable uniform is:

E(x) = [tex]\frac{a+b}{2}[/tex]

      Where a and b are the interval's extremes

Thus

E(x) = [tex]\frac{0+30}{2}[/tex]

E(x) = 15 minutes

The probability that a randomly chosen adult from the survey has no desire to take skiing lessons is 57/80, or as a decimal, 0.7125.

Out of a sample of 400 adults, 115 expressed an interest in taking skiing lessons. Therefore, to find the number of adults who have no interest in skiing lessons, we subtract the number interested (115) from the total number surveyed (400).

The calculation is as follows: 400 - 115 = 285 adults who have no interest in taking skiing lessons. The probability that a randomly selected adult has no desire to take skiing lessons is the number of adults with no interest divided by the total number surveyed. This gives us:

       Probability = 285 / 400

        Probability = 57 / 80

If we want to express this as a decimal rounded to the nearest millionth, we perform the division:

Probability = 0.7125

This result is already rounded to the fourth decimal place, which is more precise than rounding to the nearest millionth.

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

2x+9y=5

9y = - 2x + 5

y = -2x/9 + 5/9

Comparing with the slope intercept form, slope = -2/9

If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (4,-9) is 9/2

To determine the intercept, we would substitute m = 9/2, x = 4 and y = -9 into y = mx + c. It becomes

- 9 = 9/2×4 + c = 18 + c

c = - 9 - 18 = - 27

The equation becomes

y = 9x/2 - 27

What is the average rate of change of the function on the interval from x = 0 to x = 5 ; f(x)= 1\2 (3)^x

Answer:

Average rate of change of the function on the interval from x = 0 to x = 5 is 24.2

Solution:

Given function is:

[tex]f(x) = \frac{1}{2}(3^x)[/tex]

We have to find the average rate of change of function from x = 0 to x = 5

The formula for average rate of change can be expressed as follows:

[tex]{A\left( x \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}}[/tex]

So for rate of change of function from x = 0 to x = 5 is:

[tex]{A\left( x \right) = \frac{{f\left( 5 \right) - f\left( 0 \right)}}{{5 - 0}}}[/tex]

Let us find f(0) and f(5)

To find f(0), substitute x = 0 in f(x)

[tex]f(0) = \frac{1}{2}(3^0) = \frac{1}{2}[/tex]

To find f(5), substitute x = 5 in f(x)

[tex]f(5) = \frac{1}{2}(3^5) = \frac{1}{2}(243) = \frac{243}{2}[/tex]

Therefore,

[tex]A(x)=\frac{\frac{243}{2}-\frac{1}{2}}{5-0}=\frac{242}{\frac{2}{5}}=\frac{242}{2} \times \frac{1}{5}=24.2[/tex]

Therefore average rate of change of the function on the interval from x = 0 to x = 5 is 24.2

Answer:

  30 seats

Step-by-step explanation:

The problem statement tells you 30 seats are broken.

___

It does not say 30 seats in each row are broken.

Answer:

Step-by-step explanation:

Abby's car gets approximately 24 miles per gallon. This means that for every 24 mile that her car covers, it uses 1 gallon of gas. She is planning a 1200 mile trip. This means that the number of gallons of gas that she would need would be 1200/24 = 50 gallons.

One average price of 1 gallon of gas is $4.20. The total amount that she would spend in buying 50 gallons of gas would be

50 × 4.2 = $210

Abby needs 50 gallons of gas for her 1200-mile trip. At $4.20 per gallon, the total cost will be $210. This calculation helps Abby budget for her fuel expenses.

Abby needs to calculate the amount of fuel and the cost for a 1200-mile trip with her car that gets approximately 24 miles per gallon. Here's how to find out:

To find the number of gallons Abby needs, divide the total trip distance by her car's miles per gallon (MPG):

1200 miles / 24 MPG = 50 gallons

Multiply the number of gallons by the cost per gallon:

50 gallons x $4.20 per gallon = $210

Abby should plan to buy 50 gallons of gas for her 1200-mile trip, costing about $210 at $4.20 per gallon.

Answer:

Option b ) 2.310

Step-by-step explanation:

Given that the function is

[tex]y = sin (x-sinx)[/tex]

For finding when the tangent is parallel to x axis, we must find the least positive value of x for which y' i.e. derivative =0

Differentiate y with respect to x using chain rule.

[tex]y' = cos(x-sinx) * (1-cosx)[/tex]

Equate this to 0

Either one factor should be zero.

[tex]cos(x-sinx)=0\\x-sinx =\frac{\pi}{2} \\[/tex]

x=2.31 satisfies this

For the other root,

[tex]1-cos x =0\\cos x =1\\x =0\\[/tex]

Since positive least value is asked we can say

x =2.310

Option b

Answer:

A. 14%.

B. [tex]\frac{43}{50}[/tex]

Step-by-step explanation:

We have been given that a running back was the MVP (most valuable player) in 0.14 of the first 50 Super Bowls.

A. To find the percent, when the MVPs were running backs, we need to convert 0.14 into percent by multiplying by 100 as:

[tex]0.14\times 100=14\%[/tex]

Therefore, 14 percent of the MVPs were running backs.

B. To find the fraction of the MVPs were not running backs, we will subtract 0.14 from 1 to find the MVPs, who were not running backs. Finally, we will convert the answer into fraction as:

[tex]1-0.14=0.86[/tex]

Now, we will multiply and divide 0.86 by 100 as:

[tex]0.86\times \frac{100}{100}=\frac{86}{100}[/tex]

Reduce the fraction by dividing numerator and denominator by 2:

[tex]\frac{43}{50}[/tex]

Therefore, [tex]\frac{43}{50}[/tex] of the MVPs were not running backs.

14% of the MVPs in the first 50 Super Bowls were running backs. Yet, 43 out of 50 MVPs (or 86%) were not running backs.

The running back was the MVP in 0.14 of the first 50 Super Bowls according to the question. To find the percent of the MVPs that were running backs, we simply convert the 0.14 to percentage by multiplying it by 100. Hence, 14% of the MVPs were running backs.

For the fraction of the MVPs that were not running backs, we need to calculate the remaining part not covered by the running backs. Given as 1 (entirety) minus 0.14 gives 0.86. In fraction terms, this is same as 86/100 which simplifies to 43/50.

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Answer:

1. with the aid of a saw

2.No

Step-by-step explanation:

A. The  9‘ x 9‘ can be divided into two with the aid of a saw .

we have to take into account the area of the shape wic 9'x9'. and then saw the piece at the middle.

b.there are two sides to the second answer

1. the area of the smaller pieces will be smaller than the area of the larger piece

2. when the smaller pieces are placed side by side aain , tere area combined together will be the same as the original piece

Answer:

Part A. Using a handsaw.

Part B. Yes, the area of the two smaller pieces together equal the are of the large piece

Step-by-step explanation:

Part A. Explain how Oscar can divide it into two smaller pieces of plywood?

He can use a handsaw and cut the plywood in two smaller pieces of several measures, not necessarily the two smaller pieces need to be equal.

Part B. Would the area of the smaller pieces equal the area of the large piece?

Yes, the area of the two smaller pieces together equal the are of the large piece.

i. Let's suppose we have two pieces of 4.5 feet by 9 feet, then the combined area of these two pieces would be:

A = 4.5 *9 + 4.5 * 9

A = 40.5 + 40.5 = 81 ft² that is the same than 9 * 9 = 81 ft²

ii. Now let's suppose we divide the plywood into a piece of 6 ft by 9 ft and a second one of 3 ft by 9 ft, then the combined area of these two pieces would be:

A = 6 * 9 + 3 * 9

A = 54 + 27 = 81 ft² that is the same than 9 * 9 = 81 ft²

iii. Finally, let's suppose we divide the plywood into a piece of 1 ft by 9 ft and a second one of 8 ft by 9 ft, then the combined area of these two pieces would be:

A = 1 * 9 + 8 * 9

A = 9 +72 = 81 ft² that is the same than 9 * 9 = 81 ft²

Answer:

The answer to your question is x = 17.32; y = 8.67

Step-by-step explanation:

Process

1.- Use trigonometric functions to find x and y

   a) sin Ф = [tex]\frac{opposite side}{hypotenuse}[/tex]

      Ф = 60°

      opposite side = 15

      hypotenuse = ?

     [tex]hypotenuse = \frac{opposite side}{sin \alpha }[/tex]

     [tex]hypotenuse = \frac{15}{sin 60}[/tex]

     [tex]hypotenuse = \frac{15}{0.87}[/tex]

            hypotenuse = 17.32

     b) cosФ = [tex]\frac{y}{hypotenuse}[/tex]

         [tex]y = hypotenuse x cos 60[/tex]

         [tex]y = 17.32 x 0.5[/tex]

                y = 8.67

Answer:

a) yes we should get suspicious

b) smallest percentage to like all three sports= 60

Step-by-step explanation:

Let the total professors be =100

n(tennis) = 60

n( bridge) = 65

n( chess)= 50

n( T U B) = 45, n(BU C) = 45, n(T UC)=45

n( T U B U C)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) +  [tex]n(T\cap B\cap C)[/tex]

100 = 60 + 65 + 50 - 45-45-45 +   [tex]n(T\cap B\cap C)[/tex]

 [tex]n(T\cap B\cap C)[/tex] = 60

Therefore,

a) yes we should get suspicious

b) smallest percentage to like all three sports= 60

Final answer:

The given information suggests that we should be suspicious if told that 20% of all college professors like all three recreations. The smallest percentage who could like all three recreations is 0%.

Explanation:

(a) Yes, we should be suspicious if told that 20% of all college professors like all three recreations. This is because the given information states that 45% of college professors like any given pair of recreations. If 20% of them like all three, it means that the remaining 25% (45% - 20%) would have to like two recreations, which contradicts the given data.

(b) The smallest percentage who could like all three recreations is 0%. Since the information states that 50% of college professors like chess and 65% like bridge, it means that at most, 50% (the percentage who like chess) can like both chess and bridge. Therefore, there is no overlap between those who like chess and bridge, and those who like tennis. Hence, the smallest percentage who could like all three recreations is 0%.

Answer:

  6/11

Step-by-step explanation:

Assuming all students are accounted for, the fraction that is female is ...

  female/total = 18/(15+18) = 18/33 = 6/11

Answer:

the vertices (1,1,1), (1,0,0), (0,1,0) and (0,0,1) form a tetrahedron. The length of each side is √2

Step-by-step explanation:

The cube has 8 vertices: (0,0,0), (1,1,0), (0,1,0), (1,0,0), (0,0,1), (0,1,1), (1,0,1), (1,1,0) and (1,1,1). The first four of them are the vertices of the bottom square and the last four are the vertices of the upper square of the cube.

We will take two non-consecutive vertices from each square. For the upper one we take (1,1,1) as the problem suggests, and (0,0,1), which is not consecutive from (1,1,1) and its distance is √2. The non consecutive vertices from the bottom square respect to the vertex (1,1,1) are (0,0,0), (0,1,0) and (1,0,0).

We take (0,1,0) and (1,0,0) because (0,0,0) is consecutive from (0,0,1) hence its distance from it is not √2, but 1.

Note that we take (1,1,1), (0,0,1), (0,1,0) and (1,0,0). If we take any two vertices and compare them toguether we will notice that both of those vertices differ in two places and are equal in the other. In the places where they differ one has the value 1 and the other 0, so the distance between those vertices is √(1²+1²) = √2.

Thus, the vertices (1,1,1), (1,0,0), (0,1,0) and (0,0,1) form a tetrahedron.

Final answer:

Explaining how to find the vertices of a cube forming a regular tetrahedron and confirming why all cube edges have the same length.

Explanation:

To find the four vertices of a cube that form a regular tetrahedron starting with (1, 1, 1), we can consider the cube's diagonals. The vertices of the regular tetrahedron can be located at the center of each face of the cube, which are at coordinates (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2).

The length of an edge of a cube is the distance between two adjacent vertices. To calculate the edge length, we can use the distance formula. Since all edges of a cube connect two adjacent vertices, they have the same length due to the cube's symmetry.

Therefore, all edges of the cube have the same length because each connects two adjacent vertices with equal coordinates.

Sandy would be able to make 5,333 earrings with a gold bar of 1,000 grams.

Given that;

Sandy has 2 grams of gold, and each earring requires 3/16 grams of gold.

Now for the number of earrings she can make, divide the total amount of gold she has by the amount of gold needed for each earring.

[tex]\text {Number of earrings} = \dfrac{\text {Total gold} }{\text {Gold per earring} }[/tex]

[tex]\text {Number of earrings} = \dfrac{\text {2} }{\text {3/16} }[/tex]

To divide by a fraction, multiply by its reciprocal:

[tex]\text {Number of earrings} = \text {2} \times \dfrac{16}{3}[/tex]

Now, let's simplify the calculation:

[tex]\text {Number of earrings} = \dfrac{32}{3}[/tex]

Therefore, Sandy can make 10 earrings with 2 grams of gold, leaving 2 grams remaining.

When she had a gold bar of 1,000 grams, use the same approach to find out how many earrings she can make:

[tex]\text {Number of earrings} = \dfrac{\text {1000} }{\text {3/16} }[/tex]

[tex]\text {Number of earrings} = 5333[/tex]

So, Sandy would be able to make 5,333 earrings with a gold bar of 1,000 grams.

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Sandy could make about 5,333 earrings from 1,000 grams of gold by dividing 1,000 grams by the weight of gold in each earring (3/16 grams), which equates to multiplying 1,000 by the reciprocal of 3/16

To solve this, we need to figure out how many times 3/16 grams goes into 1,000 grams. To do this, we divide 1,000 by 3/16.

However, when dividing by a fraction, it's often easier to multiply by its reciprocal (flip the fraction) instead. So we'll turn 1,000 into 1,000/1, and multiply by 16/3 (the reciprocal of 3/16).

Therefore, Sandy could make about 5,333 earrings from 1,000 grams of gold.

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Answer:

There are Even, Odd and None of them and this does not depend on the degree but on the relation. An Even function: [tex]f(-x)=f(x)[/tex] And Odd one: [tex]-f(x)=f(-x)[/tex]

Step-by-step explanation:

1) Firstly let's remember the definition of Even and Odd function.

An Even function satisfies this relation:

[tex]f(-x)=f(x)[/tex]

An Odd function satisfies that:

[tex]-f(x)=f(-x)[/tex]

2) Since no function has been given. let's choose some nonlinear functions and test with respect to their degree:

[tex]f(x)=x^{2}-4, g(x)= x^{5}+x^{3}[/tex]

[tex]f(x)=x^2 -4\Rightarrow f(-x)=(-x)^{2}-4\Rightarrow f(-x)=x^{2}-4\therefore f(x)=f(-x)[/tex]

[tex]g(-x)=-(x^{5}+x^{3})\Rightarrow g(-x)=-x^{5}-x^{3}\Rightarrow g(-x)=-g(x)[/tex]

3) Then these functions are respectively even and odd, because they passed on the test for even and odd functions namely, [tex]f(-x)=f(x)[/tex] and [tex]-f(x)=f(x)[/tex] for odd functions.

Since we need to have symmetry to y axis to Even functions, and Symmetry to Odd functions, and moreover, there are cases of not even or odd functions we must test each one case by case.

Final answer:

The degree of a polynomial indicates whether it is even or odd based on the highest power of x. Even functions exhibit symmetry across the y-axis, while odd functions show symmetry with respect to the origin. The derivative of an even function is odd due to the horizontal flip property during differentiation, and the integral of an odd function over a symmetric interval is zero.

Explanation:

To determine whether the degree of a function is even or odd, and whether the function itself is even or odd, one must understand the definitions and properties of even and odd functions. An even function satisfies the property f(-x) = f(x), implying symmetry across the y-axis. A classic example is the cosine function, cos x, or any power function x^n where n is an even number. Conversely, an odd function is defined by the property f(-x) = -f(x), indicating symmetry with respect to the origin. The sine function, sin(x), and x^n where n is odd, are examples of odd functions.

Regarding derivatives, it is interesting to note that the derivative of an even function results in an odd function due to the horizontal flip property of the derivative. This is because differentiation involves a limit process that inherently flips the sign of any even function's symmetric components, resulting in an odd function.

Moreover, both even and odd functions display specific behaviors when integrated over symmetric intervals: the integral of an odd function is zero due to its antisymmetric nature while even functions do not necessarily share this property. For instance, when considering a function expressed as a product, such as f(x) = (x^3 - 3x)e^{-x^2}, where one function is odd and the other even, the resulting function will be odd, based on the product of their respective eigenvalues with respect to the inversion operator.

Answer:

  18] not a function; (1, 5), (1, -1)

  19] is a function

Step-by-step explanation:

The graph of a function will pass the "vertical line test." That is, a vertical line will not intersect the graph at more than one point.

18] There are an infinite number of points where a vertical line will cross the graph twice. Two that are recognizable are the ones at the vertical extremes: (1, 5) and (1, -1). This relation is not a function.

__

19] None of the points on the graph are vertically aligned, so the relation is a function.

Answer:

Jill is most correct and it should be $33

Step-by-step explanation:

Total number of seats = x =20000+13000+17000

x =50000

Total cost of seats as per the price;

a = 20*20000

a =400,000

b = 30*13000

b =390,000

c = 50*17000

c =850,000

Average  = (a + b + c) /x

Average = (400,000+390,000+850,000)/50,000

Average cost = 1,640,000/50,000

Average cost = $32.8

Answer:

(fоgоh)(x)=2x³+1

Step-by-step explanation:

Function composition is an operation where two functions, say f(x) and g(x), a new function h(x)=(fоg)(x)=f(g(x)) is generated. In this operation, the function g is applied to the result of the function f. Hence, function f:X→Y and g:Y→Z are joined to form a new function h:X→Z

Given [tex]f(x)=x+1[/tex]

[tex]g(x)=2x[/tex]

[tex]h(x)=x^{3}[/tex]

(fоgоh)(x)=[tex]f(g(h(x)))[/tex]

               =[tex]f(g(x^{3}))[/tex]

               =[tex]f(2x^{3})[/tex]

               =2x³+1

Only problem is with the simplifying.

We all know that 5/5 = 1, it is natural to  assume (x+a)/(x+a) is also 1, but in some cases where x+a=0, it is undefined. In this equation, where they simplify (x-2) and (x-6), you must say that x is not 2 nor 6 or, you just delete 0/0 which is undefined.

Therefore the only solution would be x=-1

The error that the student made in the rational equation simplification is that; She made 6 and -1 to be a solution but 6 is not a solution but only x = -1 because 6 makes the function undefined

         From the simplification of the rational equation, the solution the person got is; x = 6 or -1

         Now, when we put 6 for x in the rational equation, it is discovered that the denominator becomes zero for two of the expressions.

Now, when the denominator of a fraction is zero, that fraction is said to be undefined.

         Whereas when x = -1, we don't get an undefined function. Thus, the mistake the student made is that 6 is not a solution but only x = -1

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Answer:

Step-by-step explanation:

The aquarium is 2 1/2 miles from her hotel. Converting 2 1/2 miles into improper fraction, it becomes 5/2 miles.

She walks 1/4 mile to the bus stop, takes the bus for 1 3/4 miles. Converting 1 3/4 miles to improper fraction, it becomes 7/4 miles. Therefore the total distance covered by walking and boarding the bus would be

1/4 + 7/4 = 8/4 = 2 miles

She walks the rest of the way to the aquarium. Therefore, the distance that Clara walked after getting off the bus would be

5/2 - 2 = 1/2 miles

Answer:

Option C)  Any three numbers, each of which is squared is correct

Step-by-step explanation:

By using Pythagorean Theorem:

 Pythagorean theorem is also called as Pythagoras' theorem. It is a fundamental relation among the three sides of a right triangle.

It states that the length of the square of hypotenuse side is equal to the sum of the lengths of the squares of the opposite side and adjacent side.

[tex]a^{2}+b^{2}=c^{2}[/tex]  

where c is the length of the hypotenuse side and a and b are the lengths of the  opposite and adjacent sides of  triangle's.

Therefore Option C)  Any three numbers, each of which is squared is correct

Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem.

Pythagorean triples are sets of three whole numbers (a, b, and c) that satisfy the equation a² + b² = c². This equation is derived from the Pythagorean theorem, which relates the lengths of the legs of a right triangle to the length of the hypotenuse. In a Pythagorean triple, the square of the larger numbers is equal to the sum of the squares of the smaller numbers. For example, the triplet (3, 4, 5) is a Pythagorean triple because 3² + 4² = 5² (9 + 16 = 25).

Answer:

[tex]Months =\frac{3784}{214 /month}=17.682months\approx 18 months[/tex]

As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months

Step-by-step explanation:

Notation

[tex]P_f =792[/tex] current mortgage payment

[tex]P_i = 578[/tex] reduced mortgage payment

R= 3784 represent the rfinancing charges

Solution to the problem

In order to solve this question we need to find first the difference between the two mortgage payments like this:

[tex]P_f- P_i = 792-578=214[/tex]

And then since the refinancing charges is $3784 we can find the number of months that we will need to remain in the house like this:

[tex]Months =\frac{3784}{214 /month}=17.682months[/tex]

As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months

Answer:

B.a vertical shift of 9 units up

Step-by-step explanation:

Given [tex]f(x) = 4x-2\\g(x) = 4x+7[/tex]

[tex]g (x) = f (x) + k[/tex]

It means shifting [tex]f (x)\ k[/tex] unit vertically.

Now, we will find the value of [tex]k[/tex] for the given function

[tex]g(x) = 4x+7\\\\add\ 2\ and\ subtract\ 2\\\\g(x) = 4x+7+2-2\\g(x) = 4x-2+9\\\\We\ have\ f(x)=4x-2\\\So,\ g(x)=f(x)+9[/tex]

[tex]k=9[/tex]

Hence, vertical shift of 9 units.

Answer:

C. a horizontal shift of 9 units left

Step-by-step explanation:

Look at this helpful chart:

Vertical Translations

translation up k units: g(x) = f(x) + k, where k > 0

translation down k units: g(x) = f(x) – k, where k > 0

Horizontal Translations

translation left k units:  g(x) = f(x + k), where k > 0

translation right k units:  g(x) = f(x – k), where k > 0

The change happening in Martina's graph is therefore a horizontal translation to the left.

Answer:

a) the number of miles in 1 kilometer

Step-by-step explanation:

The car converts from miles/hour to kilometers/hour, if we see the time measurement (hours) it stays the same in both units.

So to make the conversion it is enough to know how many miles are in one kilometer.

For example, lets convert 10miles/hour to kilometers/hour.

there are 0.621371 miles in 1 kilometer, so if we divide 10miles/hour by 0.621371 we get kilometers/hour units:

[tex]\frac{10miles}{hour} (\frac{1kilometer}{0.621371miles} )=16.0934\frac{kilometers}{hour}[/tex]

Thus to make the conversion between the two units is needed the number of miles in 1 kilometer.

Good evening ,

Answer:

Step-by-step explanation:

GE=2×ZE

Since ZE=XY then ZE=5

therefore GE=2×5=10.

:)