Two trains leave the station at the same time, one is heading west and the other is east. The westbound train travels 10 miles per hour slower than the eastbound train. If the two trains are 900 miles apart after 5 hours, what is the rate of the westbound train? Do not do any rounding.

Answer:

Step-by-step explanation:

To find the speed of a cyclist, divide the distance traveled by the time taken.

In this case, the speed is:

3.75 miles ÷ 0.3 hours = 12.5 miles per hour (mph)

So, the cyclist was traveling at a speed of 12.5 mph.

Answer:

Step-by-step explanation:

Answer should be 12.5 mph.

Answer:

The first table(top row, leftmost) represents a function

Step-by-step explanation:

In a function y = f(x), the value for y must be unique for a value of x

In other words, you cannot have two different values of y for the same x

We see that only the first table(top row, leftmost) satisfies this requirement

So that is the answer

Second table has two values for x = -5

Third table has two values of x = -2

Fourth table has two  values for x = -4

Answer:

Step-by-step explanation:

2nd one because if you use logic it works

btw this is a real answer

The number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.

For the first five digits to form an increasing series, we can choose the first digit in 9 ways (it can't be 0), the second digit in 8 ways, the third digit in 7 ways, the fourth digit in 6 ways, and the fifth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the first five digits.

For the last five digits to form a decreasing series, we can choose the sixth digit in 9 ways (it can't be 0), the seventh digit in 8 ways, the eighth digit in 7 ways, the ninth digit in 6 ways, and the tenth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the last five digits.

Therefore, the number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series, and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.

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The equivalent expression is (t - 2)² - 1

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

4t²-16t+12

Divide through the equation by 4

So, we have the following representation

t² - 4t + 3

Take the coefficient of t

k = -4

Divide by 2

k/2 = -2

Square it

(k/2)^2 = 4

So, we have

t² - 4t + 3 + 4 - 4

Rewrite as

t² - 4t + 4  + 3 - 4

Express as squares

(t - 2)² - 1

Hence, the expression is (t - 2)² - 1

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Answer:  NO/MN   =     QR/PQ

Answer:

[tex]\frac{NO}{MN}[/tex] = [tex]\frac{QR}{FQ}[/tex]

Step-by-step explanation:

∠ 0 ≅ ∠ R and ∠ M ≅∠ F

thus Δ NOM ≅ ∠ QRF ( by the AA postulate )

the ratios of corresponding sides are in proportion, so

[tex]\frac{NO}{MN}[/tex] = [tex]\frac{QR}{FQ}[/tex]

The equation 3y + 7 = x does not represent a direct proportion.

The constant of proportionality is a value that describes the relationship between two variables in a proportional relationship. For example, if y is proportional to x, and y = 2 when x = 4, then the constant of proportionality would be 0.5 (since 2/4 = 0.5). The constant of proportionality is often represented by the letter "k".

A direct proportion is a relationship between two variables where their ratio is always constant.

In the equation, 3y + 7 = x, the relationship between x and y is not fixed, so it does not represent a direct proportion.

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Using Pythagorean theorem and the vertices given, the two triangle are similar

Two triangles are similar if and only if the ratios of their corresponding sides are equal. So, to determine if triangle ABC is similar to triangle XYZ, we need to compare the ratios of corresponding sides.

One way to do this is to calculate the lengths of the sides in both triangles and compare the ratios. For example, the length of side AB in triangle ABC can be found using the Pythagorean theorem:

AB = √((0-(-3))^2 + (10-6)^2) = √(3^2 + 4^2) = √25 = 5

Similarly, the length of side XY in triangle XYZ can be found:

XY = √((2-(-1))^2 + (7-3)^2) = √(3^2 + 4^2) = √25 = 5

Next, we can compare the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ. If the ratios are equal for all corresponding sides, then the triangles are similar.

In this case, we find that the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ are all equal, so triangles ABC and XYZ are similar.

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Step-by-step explanation:

(g–f)

multiply by nine

9(g–f)or 9g–9f

Answer:

To make the smallest number with the cards 3, 2, 4, and 7, you can arrange them as 2, 3, 4, 7 to get the number 237.

To make the number closest to 5000, arrange the cards as 7, 4, 2, 3 to get the number 7243.

Step-by-step explanation:

So the slope of the scenario is $28 per hour, which indicates that the expense of the tour increases by $28 for every extra hour spent on it.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, while the y-intercept is (0, 7).

Here,

In this situation, the slope represents the rate of change in the cost of the tour with respect to the time spent on the tour. The slope of the situation can be calculated as the change in cost divided by the change in time.

Since the one-time fee is a fixed cost, it does not change with respect to the time spent on the tour. Therefore, the slope can be calculated as the rate of change in the cost due to the hourly fee of $28.

The slope can be represented as:

slope = Δcost/Δtime = $28/hour

So, the slope of the situation is $28 per hour, which means that for every additional hour spent on the tour, the cost of the tour increases by $28.

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The best description is skew right. (the date is missing in this question)

A distribution is right skewed if it has a “tail” on the right side of the distribution.

here, we have,

The cumulative relative frequency graph shows that

The slope between 0 and 4 is substantially steeper than the curve between 6 and 14.

Then

Because most of the data values are between 0 and 4 (where the histogram's highest bar appears) and relatively few values lie between 6  and 14 the histogram's distribution should be skewed to the right, resulting in low bars tailing to the right side of the highest bars.

Because there are more data values between 0 and  4 than between 6 and 14 we can conclude that skewed right is the best description of the histogram's form. Hence, the it is skewed right.

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Answer: that is shading 10/12 of the figure

Step-by-step explanation:

Shading 5/6 of the figure means that 5 out of the 12 equal pieces would be colored or filled in. To visualize this, imagine the figure being divided into 12 equal slices, like a pizza. If 5 of those slices were to be filled in with color, they would represent 5/6 of the total figure.

The simplified expression is equal to 2/3.

        2m⁰ * n⁶ / (3n⁵)

       2 * n⁶ / (3n⁵)

        2 * n / (3n) = 2/3

So the simplified expression is equal to 2/3.

The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.

For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.

In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.

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Answer:

£ 3125

Step-by-step explanation:

Tax amount on  £ 2665 = 20% of 2665

                                       = 0.2 * 2665

                                       =  £ 533

Rest amount = 3672 - (972 + 2665)

                     = 3672 -3637

                     =  £ 35

Tax amount of  £ 35 = 40% * 35

                                 = 0.4 * 35

                                 = 14

Total tax = 533 + 14

               =  £ 547

Money left after paying tax = 3672 - 547

                                              =  £ 3125

Answer:

Below

Step-by-step explanation:

Slope of BLACK line = rise/run =   9  / 3 = m =  3  

  y intercept = b = 2       Line eq =  y = mx+ b    y = 3x +2

Slope of BLUE line   similarly is  9 / -3  = m = -3

   and b = 8

     y = mx + b      y = -3x + 8

The value of the expression is 94.9

Algebraic expressions are expression with variables, terms, coefficients, factors and constants.

They are also made up of mathematical operations, such as;

From the information given, we have that;

8.3x + 7.5y

When x = 3 and y = 4

Substitute the values into the formula

8.3(3) + 7.5(4)

expand the bracket

24.9 + 60

Add the values

84. 9

Hence, the value is 84.9

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The summation of the series ¹³∑ₙ₎ ₁ (3n - 1) is 260.

Given the summation in the question;

¹³∑ₙ₎ ₁ (3n - 1)

First, we split the summation into smaller summations that fits the summation rule.

¹³∑ₙ₎ ₁ (3n - 1) = 3 ¹³∑ₙ₎ ₁ (n) + ¹³∑ₙ₎ ₁ (- 1)

Now, lets evaluate 3 ¹³∑ₙ₎ ₁ (n).

Using the formula for the summation of a polynomial with degree 1

ⁿ∑ₐ₎ ₁ (a) = n( n + 1 ) / 2

Plug in the values

3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(13+1))/2)

3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(14))/2)

3 ¹³∑ₙ₎ ₁ (n) = (3) (182/2)

3 ¹³∑ₙ₎ ₁ (n) = (3) (91)

3 ¹³∑ₙ₎ ₁ (n) = 273

Next, evaluate ¹³∑ₙ₎ ₁ (- 1)

Using the formula for the summation of a constant

ⁿ∑ₐ₎ ₁ (c) = cn

Plug in the values

¹³∑ₙ₎ ₁ (- 1) = (-1)(13)

¹³∑ₙ₎ ₁ (- 1) = -13

Now, we add the results of the summation.

273 - 13

260

Therefore, the sum of the series is 260.

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It should be noted that it is possible to construct a matrix with linearly independent columns. This means that no one column can be represented as a linear combination of the other columns. In this case, the columns are said to span the space of the matrix.

It is also possible to construct a matrix with linearly independent rows. This means that no one row can be represented as a linear combination of the other rows.

In this case, the rows are said to span the space of the matrix. In general, the rows and columns of a matrix may or may not be linearly independent, depending on the specific matrix and the basis used to represent it.

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Answer:

This question is asking for a construction problem, which involves using a pair of compasses and a ruler to draw the triangle DEF and then measure certain aspects of the triangle, such as the length of DF, the height of XF, and the locus of a point 2cm from E. It also requires bisecting the angle D.

Step-by-step explanation:

a. To construct the triangle DEF, use the compasses to draw arcs with radii of 3cm and 7cm from points D and E respectively, so that the arcs intersect. Then, connect the points of intersection with a straight line to form the side DE. Next, use the compasses to draw an arc with a radius of 8cm from point F and intersect it with the previous arcs. Connect the points of intersection with a straight line to form the side DF. Finally, use the ruler to connect the points D, E, and F to form the triangle. To draw the perpendicular line at X, draw a line segment parallel to DE passing through the midpoint X, and then use the compasses to draw arcs centered at X and intersecting the sides DE and DF. Connect the points of intersection to form the perpendicular line at X.

b. Measure the length of DF using a ruler.

c. Measure the height of the triangle XF by measuring the distance from X to DF.

d. The locus of the point that is 2cm from E can be found by drawing an arc with a radius of 2cm centered at E and intersecting the sides DE and DF. The points of intersection represent the points that are 2cm from E.

e. To bisect the angle D, use the compasses to draw two arcs centered at D that intersect the sides DE and DF. Connect the points of intersection to form the bisector of angle D.

It is important to note that these steps are only a general guide and may need to be adjusted slightly depending on the specifics of the problem.

1) 2x + 5y = 17

+ 6x – 5y = -9

────────

8x = 8

divide both sides by 8 :

Answer : x = 1 (one solution)

2) (3x – y = 0) * 4

(4x + 2y = 14) * 3

12x – 4y = 0

- 12x + 6y = 14

────────
-10y = -14

Divide both sides by -10

Answer : y = 1.4 (one solution)

3) 6x + 5y = 39

- 3x + 5y = 27

────────
3x = 12

Divide both sides by 3

Answer : x = 4 ( one solution )

4) 4x – 7y = 3

+ x – 7y = -15

────────
5x = -12

Divide both sides by 5

Answer : x= -2.4 (one solution)

The point of intersection of the two equations will be ( 0, 3 ). The correct option is C.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the two equations are y= 2x+3 and y=-3x+3. The value of x and y will be calculated as:-

y= 2x+3

y=-3x+3

Equate the equations and solve,

2x + 3 = - 3x + 3

2x +3x = 0

x = 0

The value of y is,

y = 2x+3

y = 2 x 0 + 3

y = 3

Therefore, the two equations points of intersection will be ( 0, 3 ). The right answer is C.

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For the quadratic equations -

1) f(x) = x² - 16x + 3 → Vertex form is y = 3(x - 8)² - 61 and vertex is (8,-61).

2) f(x) = 4x² + 24x - 7 → Vertex form is y = 4(x + 3)² - 43 and vertex is (-3,-43).

3) f(x) = -2x² - 8x + 9 → Vertex form is y = -2(x + 2)² + 17 and vertex is (-2,17).

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic equation is written in the form ax² + bx + c = 0.

The vertex form of a quadratic equation is -

y = a(x - h)² + k

The first equation is - f(x) = x² - 16x + 3.

Here, a = 1, b = -16 and c = 3

The formula for h is -

h = -b/2a

h = -(-16)/2(1)

h = 16/2

h = 8

The formula for k is -

k = c - (b²/4a)

k = 3 - [(-16)²/4(1)]

k = 3 - (256/4)

k = 3 - 64

k = -61

So, the vertex form is -

y = a(x - h)² + k

y = 3(x - 8)² - 61

The vertex is written as (h,k).

The vertex is (8,-61).

Therefore, the vertex form and vertex is y = 3(x - 8)² - 61 and (8,-61) respectively.

The second equation is - f(x) = 4x² + 24x - 7.

Here, a = 4, b = 24 and c = -7

The formula for h is -

h = -b/2a

h = -(24)/2(4)

h = -24/8

h = -3

The formula for k is -

k = c - (b²/4a)

k = -7 - [(24)²/4(4)]

k = -7 - (576/16)

k = -7 - 36

k = -43

So, the vertex form is -

y = a(x - h)² + k

y = 4(x + 3)² - 43

The vertex is written as (h,k).

The vertex is (-3,-43).

Therefore, the vertex form and vertex is y = 4(x + 3)² - 43 and (-3,-43) respectively.

The third equation is - f(x) = -2x² - 8x + 9.

Here, a = -2, b = -8 and c = 9

The formula for h is -

h = -b/2a

h = -(-8)/2(-2)

h = 8/-4

h = -2

The formula for k is -

k = c - (b²/4a)

k = 9 - [(-8)²/4(-2)]

k = 9 - (64/-8)

k = 9 + 8

k = 17

So, the vertex form is -

y = a(x - h)² + k

y = -2(x + 2)² + 17

The vertex is written as (h,k).

The vertex is (-2,17).

Therefore, the vertex form and vertex is y = -2(x + 2)² + 17 and (-2,17) respectively.

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The total amount due on November 15th would be $1667.81

Let's first calculate the trade discount amount:

Suggested list price: $1400

Trade discount rate: 40/10 = 4%

Trade discount amount: $1400 x 4% = $56

After deducting the trade discount, the price becomes:

$1400 - $56 = $1344

Next, let's calculate the cash discount:

Amount after trade discount: $1344

Cash discount rate: 8/10 = 8%

Cash discount amount: $1344 x 8% = $107.52

After deducting the cash discount, the price becomes:

$1344 - $107.52 = $1236.48

Finally, let's calculate the total amount due:

Amount after cash discount: $1236.48

Markup rate: 35%

Markup amount: $1236.48 x 35% = $431.33

Total amount due: $1236.48 + $431.33 = $1667.81

So, the total amount due on November 15th would be $1667.81.

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The rate of change between 2015 and 2016 was 1.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

We have been given the data

Year║Winning time (minutes)

2015║55

2016║54

2017║50

2018║51

2019║56

The rate of change = 2016 - 2015 / 55 - 54

= 1/1= 1

Thus, the answer is 1.

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The probability of getting 2 same colour balls in a row = 41/81

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

Probability of an event P(E)

= [ No of favorable outcomes ]/ Total No of outcomes

Here we have

There is a bag filled with 5 blue and 4 red marbles.  

Number of balls = 5 + 4 = 9  

Marble is taken at random from the bag,

The probability of getting the red ball = 4/9  

The probability of getting the blue ball = 5/9

The color is noted and then it is replaced.

Another marble is taken at random.  

The probability of getting the red ball 2nd time = 4/9  

The probability of getting the blue ball 2nd time = 5/9    

The probability of getting red ball in 2 attempts = (4/9)(4/9) = 16/81

The probability of getting blue ball in 2 attempts = (5/9)(5/9) = 25/81  

Hence the probability of getting 2 of the same color

= 16/81 + 25/81

= 41/81  

Therefore,

The probability of getting 2 same colour balls in a row = 41/81

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Answer:

Step-by-step explanation:

No, the number of students at Lake View Middle School is not proportional to the number of teachers.

Proportionality between two quantities means that they maintain a constant ratio, regardless of their actual values. In this case, if the number of students and teachers were proportional, we would expect the ratio of students to teachers to remain constant as the total number of students or teachers changes.

However, in this scenario, the ratio of students to teachers is not constant. The ratio is 48:2, which simplifies to 24:1. This means that there are 24 students for every 1 teacher. If the number of students at the school were to double to 96, we would expect the number of teachers to double as well if they were proportional. However, this would mean that there would be 4 teachers assigned to the students, which is twice the original number of teachers assigned to the original number of students.

Therefore, the number of students at Lake View Middle School is not proportional to the number of teachers, because the ratio of students to teachers is not constant, and it changes as the total number of students or teachers changes.

Answer: maybe go to quizly

Step-by-step explanation: just type geometric formulas quizly in the search bar

answer you can go to kahn acadamy

Step-by-step explanation:

please add me on brainlist

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Area of a rectangle is given by :

[tex]\qquad \sf  \dashrightarrow \: area = l \times b[/tex]

[ l = Length, and b = width ]

[tex]\qquad \sf  \dashrightarrow \: x {}^{2} + 3x = (x + 3)(b)[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \dfrac{ {x}^{2} + 3x }{x + 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \dfrac{ {x(}x^{} + 3) }{x + 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: b = x[/tex]

Next problem ~

[tex] \textsf{Number of stoppers fixed per minute = 25 } [/tex]

[tex] \textsf{1 stopper is fixed in = 1/25 minutes} [/tex]

[tex] \textsf{2250 stoppers are fixed in = 1/25 × 2250 = 90 minutes } [/tex]

Now, convert it into hours~

[tex]\qquad \sf  \dashrightarrow \:60 \: \: min = 1 \: \: hr[/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: min = \dfrac{1}{60} \: \: hrs[/tex]

[tex]\qquad \sf  \dashrightarrow \: 90 \: \: min = \dfrac{1}{60} \times 90 \: \: hrs[/tex]

[tex]\qquad \sf  \dashrightarrow \: 90 \: \: min = \dfrac{3}{2} \: \: hrs[/tex]

[tex]\qquad \sf  \dashrightarrow \: 90 \: \: min = 1.5 \: \: hrs[/tex]

So, in total it would take 1.5 hours to fix stoppers on 2250 bottles.

Answer:

[tex]3=e[/tex]

Step-by-step explanation:

I know this might be late but I can help if you still need it

So in the equation [tex]2=e-1[/tex], we need [tex]e[/tex] by itself. To do that we need to add [tex]1[/tex] to each side. We do this because the side that [tex]e[/tex] is on, the [tex]1[/tex] is being subtracted and we need to do the opposite of subtraction which is addition.

[tex]2=e-1[/tex]

[tex]+1[/tex]     [tex]+1[/tex]

So the new equation:

[tex]3=e[/tex]

Hope this helped!
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