Arianys wants to ride her bicycle 55.5 miles this week. She has already ridden 19 miles. If she rides for 5 more days, which equation could be used to determine, m, the average number of miles she would have to ride to meet her goal? A. 19m = 55.5 - 5 B. 5m = 19 - 55.5 C. m = 55.5-19/5 D. 55.5 = 19m + 5​

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE

As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.

So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.

Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.

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The complete question is given below:

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:

"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."

The equation of the line is y=x+12.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The points are

(-3,9)=[tex](x_{1} ,y_{1} )[/tex] and (-9,3)=[tex](x_{2} ,y_{2} )[/tex]

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

We have to Write the equation of the line.

According to given question we have,

Equation of line passing through the point (-3,9) and  (-9,3).

Slope of the line=

[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\\=\frac{3-9}{-9+3} \\\\=\frac{-6}{-6} \\\\=1[/tex]

⇒y−9=1(x+3)

⇒y-9=x+3

Add 9 on both sides we get,

y=x+12

∴ y=x+12 which is in the form y=mx +c is the required equation.

Therefore, the equation of the line is y=x+12.

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y = x + 12

What is equation of a line?

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.

y-y₁=m(x-x₁)

mm₁=-1

Points (-3,9) and  (−9,3).

Slope of the line m = (y₂ - y₁)/(x₂ - x₁)

m = (3-9)/(-9+3)

m = 1

Now  equation of line passing through two points

(y - y₁)/(y₂ - y₁) = m*(x - x₁)/(x₂ - x₁)

(y - 9)/(3-9) = 1*(x - 3)/(-9+3)

y - 9 = x + 3

y = x + 12

Therefore, the equation of line is y = x + 12

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By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.

We find a point in rectangular form, that is, a point of the form (x, y). Unit circles are circles with a radius 1 that are commonly used to represent graphically angles. The given point is in the units if and only if its norm is equal to 1. The norm of the point is determined by using the Pythagorean theorem:

r = √[(√11 / 6)² + (5 / 6)²]

r = √[(11 / 36) + (25 / 36)]

r = √(36 / 36)

r = √1

r = 1

By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.

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Answer: The pattern is that you -1 then -2 then -3.

Step-by-step explanation:

If you got 9, 8, 6, 3. You would be subtracting 1 then 2 then 3 then 4 then on and on.

No. of pennies and nickels are 53 and 29 respectively

Let the number of pennies be x

Let the number of nickels be y

Value of pennies = $0.01x

Value of nickels = $0.05y

It is given that value of pennies and nickels = $1.98

Therefore the equation will be,

0.01x + 0.05y = 1.98

x + 5y = 198------(1)

Also, the number of pennies is five less than twice of nickels

x = 2y - 5

2y - x = 5 -------(2)

Adding equations (1) and (2) we get,

(x + 5y) + (2y - x) = 203

7y = 203

y = 29

Substituting the value of y in equation (1) we get,

x = 53

Therefore, the no. of pennies is 53 and the no. of nickels is 29

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Using exponent power property, ³√x²y³ = x^r y^s, where x and y are non-negative real numbers.

r, the exponent of x, is: 2/3

s, the exponent of y, is: 1

According to the Power of a Power Property, you can multiply the exponents if one exponent is increased to a higher exponent. This characteristic may be used to resolve the equation (3 x 2) 3.

³√x²y³ = x^r y^s

Cubing on both sides,

x²y³ = x^3r y^3s

As base is same, equating the powers

⇒ 2 = 3r; r = 2/3

⇒ 3 = 3s; s = 1

The expression

³√x²y³ = x^ry^s

where x and y are non-negative real numbers.

r, the exponent of X, is:

s, the exponent of y, is:

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The function g that is finally graphed after the transformations are applied is g(x) = -5f(-x) - 10

The function is given as:

f(x)

Next, we apply the transformations

So, we have:

(1) reflect about the x-axis;

This is represented as

(x, y) = (x, -y)

So, we have

g(x) = -f(x)

(2) shift down 2 units;

This is represented as

(x, y) = (x, y - 2)

So, we have

g(x) = -f(x) - 2

(3) stretch vertically by a factor 5;

This is represented as

(x, y) = (x, 5y)

So, we have

g(x) = 5(-f(x) - 2)

Evaluate

g(x) = -5f(x) - 10

(4) reflect about the y-axis.

This is represented as

(x, y) = (-x, y)

So, we have

g(x) = -5f(-x) - 10

Hence, the function g that is finally graphed after the following transformations are applied is g(x) = -5f(-x) - 10

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Bonjour,

Answer:

16 2/3 = 50/3

Step-by-step explanation:

16 2/3 = 16.6666666…

Change the percent to a decimal number by moving the decimal two places to the left.

Call this x = 0.16666666…

10x = 1.66666666…

100x 16.66666666…

Subtract 100x - 10x = 15

90x = 15

x = 15/90 = 1/6

16 2/3 % = 1/6

So S.P of the product is 10.4% .

We have been given C.P of a product is E950 and loss percentage is 6%,.

So the starting price is the the price for which something actually sells.

And the cost price represents the specific value that represents unit price purchased. This value is used as a key factor in determining profitability, and in some stock market theories it is used in establishing the value of stock holding.

A saving account has a rate of interest of 10 denoted by our which we can write equal to 0.1 in decimal form and we have to calculate the effective annual yield yield if the interest is calculated quarterly, that means we have the number of compounds per year denoted by M equal to four. The effective yield denoted by capital Y is given by the formula one plus are divided by M. Hold raised to the Power M -1. After putting in the values of R and M we get one plus 0.1 divided by four. Hold raised to the Power 4 -1, equal to one plus 0.25 raised to the power four minus one which is equal to 1.025 raised to the Power 4 -1. On simplifying this further, we get the value equal to 0.1038. Now this value is in the decimal form to convert it into percentage. We will multiply this value by 100. That means we have like 0.1038 multiplied by 100 Which gives us 10.38. And after rounding it off to one decimal place, we get the value 10.4%.

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Answer:

1. acute

2. right

3. straight

Step-by-step explanation:

Answer: -7/24

Step-by-step explanation:

move 2/3 to the opposite side of the equal sign which then changes the equation to...

3/8-2/3 = r

then change the denominators for both of them to 24.

so it would be 9/24 - 16/24

9-16 = -7

so it would be -7/24

[tex]\cfrac{2}{3}\left( \cfrac{9}{10} \right)\left( \cfrac{1}{2} \right)\implies \cfrac{2}{3}\cdot \cfrac{9}{10}\cdot \cfrac{1}{2}\implies \cfrac{9}{3}\cdot \cfrac{1}{10}\cdot \cfrac{2}{2}\implies 3\cdot \cfrac{1}{10}\cdot 1\implies \cfrac{3}{10}[/tex]

Answer:

1/2

Hope this helps with your question :)

Triangle A'B'C' is the result of dilation about the origin with a scale factor of 2 / 3 on triangle ABC. (Translation: Pippa was right)

Herein we find a picture a graph with two proportional right triangles, which means that the small triangle is the consequence of a rigid transformation. The kind of rigid transformation used is a dilation around the origin, whose formula is shown below:

P'(x, y) = k · P(x, y)

Where k is the scale factor.

There is a dilation if and only if each point is scaled by the same factor. If we know that A(x, y) = (3, 9), A'(x, y) = (2, 6), B(x, y) = (9, 9), B'(x, y) = (6, 6), C(x, y) = (3, 3) and C'(x, y) = (2, 2), then the scale factor for each point is:

Point A

(2, 2) = k · (3, 3)

k = 2 / 3

Point B

(6, 6) = k · (9, 9)

k = 2 / 3

Point C

(2, 2) = k · (3, 3)

k = 2 / 3

Then, triangle A'B'C' is the result of dilation about the origin with a scale factor of 2 / 3 on triangle ABC.

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The scaled triangles perimeter is 1/3 the size of the original triangles perimeter

All of the sides of the triangle known as the Scalene Triangle are of various lengths. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.

A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional planar object having three sides and three angles. There are three edges and three vertices on it.

According to the given values;

original:

hieght=24   slant=  24    lenght=24

Scaled:

hieght=8  slant=  8   lenght=8

Looking at the dimension of both triangles,

The relationship between the original and the scaled copy is : 1/3*original

Hence, the perimeter is:1/3*perimeter(original)

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if you look at the part where the first part connects with the second part:

y = 5 if x < - 2

y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

When we graph over intervals like (a, b) or [a, b] or something like that, we use dots to define the end of the intervals, and to denote that the function ends abruptly or we have a jump.

In this case, you can see that between the end and the second part and the beginning of the third part there is a jump, so the use of dots is correct there, but if you look at the part where the first part connects with the second part:

y = 5 if x < - 2

y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

That is the only error with the graph.

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Answer:

11

Step-by-step explanation:

9 + 2 = 11

Best explanation I can give for this.

Answer: 11

Step-by-step explanation: bc i used a calculater

Answer: The orthocenter and varicenter  of an equilateral triangle are the same point?

Step-by-step explanation

Answer: De nuevo, puedes ver que el baricentro, el ortocentro y el circuncentro son todos el mismo punto para un triángulo equilátero. Tenemos un centro más para comparar, el incentro. Como habrás sospechado, el incentro es el mismo punto que los otros tres para un triángulo equilátero.

Step-by-step explanation:

πr² an example of a model.

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).

Here, the area of a circle is calculated by the use of formula πr² where π is a constant 3.14 and r is a variable. Therefore this formula is used to find the area.

Thus, πr² an example of a model.

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Answer:

85%

Step-by-step explanation:

Total no. of matches played,

→ x = 20 matches

No. of matches they won,

→ y = 17 matches

Now the win percentage will be,

→ (y/x) × 100

→ (17/20) × 100

→ 0.85 × 100

→ 85%

Hence, the percentage is 85%.

The result obtained are-

A frequency table is merely a "t-chart" or two-column table that illustrates the numerous possible outcomes and associated frequencies demonstrated in a sample.

Part 1: Smallest value;

As the frequency table is continuous distribution with a initial value of 4.

Thus, the smallest value of the table is 4.

Part 2: largest value;

As the frequency table is continuous distribution with a final value of 48.

Thus, the largest value of the table is 48.

Part 3: Median

The median is the number in the middle of a sorted list of numbers, and it is more descriptive of the data set than that of the average.

For even number of frequencies.

median = n/2

median = 12/2 = 6

Thus, the 6th term is the median.

median = 24.

Part 4: first quartile {Q1}

When data points are organized in increasing order, the lower quartile, or the first quartile (Q1), is indeed the value at which 25% of them are found.

Thus, Q1 = 12.

Part 3: third quartile {Q3}

When arranged in increasing order, the upper quartile, as well as third quartile (Q3), has been the value at which 75% of data points are found.

Q3 = 36.

The result for the frequency distribution is obtained.

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Step-by-step explanation:

work is shown and pictured

The first graph that we have in this question is the graph that can be used to model the relationship that we have in this table.

In this table we can see that what we are having is a linear equation. First we have to check the slope that lies in any two of the points

This would be;

( 112.5- 75) / ( 3- 2)  = 37.5 and

( 150 -112.50) / ( 4-3) = 37.50

We can have the equation of a straight line as:  y = mx + c

y = 37.50x + c, x = 2

then c = 75 - 75 =0

When plotted on the graph we would have the first graph as the best solution. Hence option 1 is right

Option 1 best fits the graph

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No, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.

Here,

A function f defined on [ 4 , 5 ].

We have to find, is it possible to f is continuous on [ 4 , 5 ], is non-constant, and takes on only integer values.

What is Intermediate value theorem?

Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b] with its domain having values f(a) and f(b) at the endpoints of the interval, then the function takes any value between the values f(a) and f(b) at a point inside the interval.

Now,

A function f defined on [ 4 , 5 ].

Assume that the function,

f :  [ 4 , 5 ] → Z is a non constant continuous function.

Then, f(4) and f(5) both are integers and not equal to each other.

By, Intermediate value theorem;

Function f takes all real numbers between f(4) and f(5) at least once.

These would contain all non integers rational and irrational number between f(4) and f(5), contradicting the assumption that function takes only integer values.

Hence, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.

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Answer:

x = 4       y = 21

Step-by-step explanation:

16x - 23 = 10x + 1

16x - 10x = 23 + 1

6x = 24

24/6 = x

x = 4

16(4) - 23 = 41

41 + (180 - 62) + y = 180

41 + 118 + y = 180

y = 21

{ 0,2,4,6,8} is  the complement of the set.

What is natural number in math?

Is zero a natural number?

u = {0, 1, 2, 3, 4, 5, 6, 7, 8}

Odd number less than 8  = { 1,3,5,7 }

complement =  {0, 1, 2, 3, 4, 5, 6, 7, 8} -  { 1,3,5,7 }

                     = { 0,2,4,6,8}

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Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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