A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A. 120 metres
B. 180 metres
C. 324 metres
D. 150 metres

Answer:

(2,-1)

Step-by-step explanation:

The solution of the system of equations 2x + 3y = 1 and 5x + 2y = 8 is x = 2 and y = -1.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.

And simultaneous equation is the system of equation.

Given:

System of equations,

2x + 3y = 1,  {equation 1}

And 5x + 2y = 8.    {equation 2}

To find the solution:

Multiply 5 to the equation 1 and multiply 2 to the equation 2.

And then subtract the equation 2 to the equation 1.

We get,

11y = -11

y = -1

And 2x = 4

x = 2

Therefore, the solution is x = 2 and y = -1.

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Looking at the shape, you should be able to tell immediately that this will be an absolute value function. Noticing that it is both 1 over and 1 up, you will get the equation y = - | x + 1 | + 1

Answer:

y=-|x+1|+1

Step-by-step explanation:

Answer:

If "m" stands for meters, then thats not possible.

Step-by-step explanation:

if m is meters then i would say 0.075 meters i’m pretty sure

Answer:

7:2:8.

Step-by-step explanation:

The income form the raffle = £350

Income from the quiz = 14*4 = £56 + £44 = £100

Income from membership fees = 20*20 = £400.

The ratio of raffle : quiz : fees

= 350:100:400

Dividing each number by 50:

= 7:2:8   in simplest form.

Answer:

A ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

Step-by-step explanation:

Given : The table shows a darts club's income in 2017 from a raffle, a quiz and membership fees.

To find : Express as a ratio the income from the raffle to the income from the quiz to the income from membership fees ?

Solution :

The raffle amount is £350.

Quiz, entry fees is 14 at £4 each and refreshment is £44.

The quiz amount is £[tex]14\times 4[/tex]+£44=£56+£44=£100

Membership fees=20 at £20 each.

The membership amount is £[tex]20\times 20[/tex]=£400

Now, the ratio of income from the raffle to the income from the quiz to the income from membership fees is

The ratio of raffle : quiz : membership

[tex]R= 350:100:400\\\\R= 35:10:40\\\\R=7:2:8[/tex]

Therefore, a ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

Answer:

Step-by-step explanation:

[tex]METHOD\ \#1\\\\\text{Put b = 3 to each equation and check equality:}\\\\A.\ 3-24b=75\\L_s=3-24(3)=3-72=-69\\R_s=75\\L_s\neq R_s\\\\B.\ 65+9b=38\\L_s=65+9(3)=65+27=92\\R_s=38\\L_s\neq R_s\\\\C.\ -2b+30=24\\L_s=-2(3)+30=-6+30=24\\R_s=24\\L_s=R_s\\\\D.\ 102b-21=-55\\L_s=102(3)-21=306-21=285\\R_s=-55\\L_s\neq R_s[/tex]

[tex]METHOD\ \#2:\\\\\text{Solve each equation:}\\\\A.\\3-24b=75\qquad\text{subtract 3 from both sides}\\-24b=72\qquad\text{divide both sides by (-24)}\\b=-3\neq3\\\\B.\\65+9b=38\qquad\text{subtract 65 from both sides}\\9b=-27\qquad\text{divide both sides by 9}\\b=-3\neq3\\\\C.\\-2b+30=24\qquad\text{subtract 30 from both sides}\\-2b=-6\qquad\text{divide both sides by (-2)}\\b=3\\\\D.\\102b-21=-55\qquad\text{add 21 to both sides}\\102b=-34\qquad\text{divide both sides by 102}\\b=-\frac{1}{3}[/tex]

The equation y = 11x + 1 is a linear equation. All three ordered pairs, (0, 1), (1, 12), and (-1, -10), satisfy this equation.

The equation y = 11x + 1 represents a linear equation. To determine which ordered pairs satisfy this equation, we substitute the x and y values into the equation and check if the equation holds true. Let's check each option:

Based on the calculations, we can see that all three ordered pairs are valid solutions for y = 11x + 1.

Answer:

The correct answer option is (5, -6).

Step-by-step explanation:

We know that the following are the coordinates of a point:

[tex] ( - 5 , - 6 ) [/tex]

If this point is reflected through y axis, we are to find the coordinates of its image?

If a point is reflected through y-axis, the sign of the x coordinate is changed so we get:

[tex] ( - 5 , -6 ) [/tex] [tex] \implies [/tex] (5, -6)

The answer is:

The first option,

[tex]y=-\frac{1}{2}x-3;x<-2[/tex]

To answer the question, we need to look for an inequality that fits with the following description:

- Negative slope, since the segment "a" is decreasing.

- x- axis interception at x equal to -6

- One of its point is located at (-2,-2)

- The segment exists from -∞ to -2.

So, checking we have:

Firs option

[tex]y=-\frac{1}{2}x-3[/tex]

With,

[tex]x<-2[/tex]

- Finding the y-axis component when x is equal to -2, we have:

[tex]y=-\frac{1}{2}*(-2)-3\\y=1-3=-2[/tex]

We have that one of the points of the segments is located at (-2,-2)

- Finding the "x" intercept, we have:

[tex]0=-\frac{1}{2}x-3\\\\\frac{1}{2}x=-3\\\\x=2*-3=-6[/tex]

Also, (from the inequality and the graph) we know that, the given segment exists from the negative infinite numbers to -2.

Hence, we can know that the first option meets all the requirements:

[tex]Slope=-\frac{1}{2}[/tex]

[tex]x-axis_{interception}=-6[/tex]

[tex]Point(-2,-2)[/tex]

and from the inequality, we know that the segment exists from -∞ to -2.

Have a nice day!

Answer:

8/15

Step-by-step explanation:

Well to add fractions you have to have the same denominator so you would multiply your 1/3 by 5 to be 5/15 then you can add.

3/15 + 5/15 = 8/15

1 over 3 would change to 5 over 15 to make the denominators equal then you add the numerators and you get 8 over 15

Is it equal to the measure if angle C

In an isosceles triangle, the measure of the vertex angle (Angle B in this case) is equal to the measure of the other base angle. This is because in an isosceles triangle, the angles opposite the equal sides are also equal.

In an isosceles triangle ABC, Angle B, the angle between the two sides of equal length, is known as the vertex angle. The two base angles of an isosceles triangle are always equal. Therefore the measure of Angle B will be equal to the measure of Angle C. This property comes from the fundamental characteristics of an isosceles triangle, where two sides are of equal length and the angles opposite these equal sides are also equal.

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Answer:

2970

Step-by-step explanation:

2700+ 270

270 because that is 10% of 2700

2700 because that is 75 x 36

I think 5x represents 90 degrees.

5x = 90

x = 90/5

x = 18

ANSWER

[tex]x = 18 \degree[/tex]

EXPLANATION

A semicircle subtends an angle of 90° at the circumference.

From the diagram, the semicircle subtends an angle of (5x)° at the circumference.

We equate this angle to 90° and solve for x.

This implies that,

[tex]5x = 90 \degree[/tex]

Divide both sides by 5.

[tex]x = \frac{90}{5} [/tex]

[tex]x = 18 \degree[/tex]

Answer:

The answer would be eight.

Step-by-step explanation:

The range is the difference between the largest and smallest number you need to make sure you have them in order or it won’t work.

Answer:

the answer is eight

Step-by-step explanation:

Answer:

B [tex]log_{2} 42[/tex]

Step-by-step explanation:

Due to the product rule of logarithms, we can combine them as such. Then it will simplify to our answer.

[tex]log_{2} 6+log_{2} 7=log_{2} (6*7)\\\\log_{2} 42[/tex]

The single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex]  is [tex]log_{2} 42[/tex]. The correct answer is option B.

To express [tex]log_2^{6} + log_2^{7}[/tex] as a single logarithm, we can use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

Simplifying the expression within the logarithm, we get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex]. The correct answer is option B.

Logarithms are used to simplify complex mathematical calculations involving large numbers. They allow us to break down a number into its constituent parts and perform operations on those parts more easily. In this problem, we are asked to express the sum of two logarithms as a single logarithm. To do this, we use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

We simplify the expression on the right-hand side of the equation to get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex].

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Answer:

4

Step-by-step explanation:

a linear function is

y = ax + b

so, for the first pair of x, y

8.5 = 2a + b

b = 8.5 - 2a

the second pair

15.25 = 5a + b

let's use the substitution information from the first pair :

15.25 = 5a + 8.5 - 2a

6.75 = 3a

a = 2.25

b = 8.5 - 2×2.25 = 8.5 - 4.5 = 4

so, we get as linear function

y = 2.25x + 4

that means the y-intercept (x = 0) is at y = 4

y = 2.25×0 + 4 = 4

The y-intercept of this function will be at (0, 4).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

In the table below, x represents miles traveled and y represents the cost to travel by train.

Miles (x)    Cost (y)

   2            8.50

   5           15.25

   8          22.00

  12          31.00

Then the linear equation will be

y - 8.50 = [(31.00 - 8.50) / (12 - 2)] (x - 2)

y - 8.50 = 2.25(x - 2)

y - 8.50 = 2.25x - 4.5

          y = 2.25 + 4

The graph of the equation is given below.

Then the y-intercept of this function will be at (0, 4).

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Answer:

36g + 81

Step-by-step explanation:

9 is your multiplier.  Multiply each of the two terms inside the parentheses by this 9, one at a time:  

36g + 81

Answer:

9 (4g + 9) = 9*(4g) + 9* (9) = 36g + 81

Step-by-step explanation:

Answer:

59.5

Step-by-step explanation:

The middle number of the number set is 59.5 because the number in between 59 and 60 is 59.5

The median of the data set: 46, 88, 28, 73, 63, 55  is 59.

Arranging in ascending order :  28, 46,55, 63, 73,88,

A number of terms are odd, then the median is the middle number i.e., 59.

⇒(55+63)/2=59

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer:  12

Step-by-step explanation:

2/3  = 8/12

1/4 = 3/12

8/12 + 3/12 + 11/12

amy & anna ate 11 and david had 1

Answer:

There were 12 donuts in the box.

Step-by-step explanation:

We are given the following information in the question:

Let x be the number of donuts in the box.

Then, according to the question

Number of donuts eaten by Amy = [tex]\frac{2x}{3}[/tex]

Number of donuts eaten by Anna = [tex]\frac{x}{4}[/tex]

Number of donuts eaten by David = 1

Total number of donuts =

Number of donuts eaten by Amy + Number of donuts eaten by Anna + Number of donuts eaten by David

[tex]\Rightarrow \frac{2x}{3} + \frac{x}{4} + 1 = x[/tex]

Solving the above equation:

[tex]11x + 12 = 12x\\x =12[/tex]

Thus, there were 12 donuts in the box.

Check the picture below.

I'm pretty sure that question 1 is 254.5 m but i'm not entirely sure about my answer to question 2. sorry i couldn't be more help to you :( good luck!

Answer:

True

Step-by-step explanation:

The numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.

A triangle with sides of lengths 20, 21, and 29 is a right triangle.

Three numbers can be the sides of a triangle if the sum of two of them is greater than the third. So, since

20+21 > 29,

20+29 > 21, and

21+29 > 20

Are trivially true, they can be the sides of a triangle.

The given numbers are a Pythagorean triplet and can be the dimensions of a right triangle.

20,21 and 29 is a Pythagorean triplet, since

[tex]20^2+21^2=29^2[/tex]

So you also know that they form a right triangle.

Hence, the numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

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Answer:

x = (8.75 - 2 5/6) / 7.1 + (4 1/2 + 2 2/3) / 4 3/10

x = 2.5

Answer:

2  1/2

Step-by-step explanation:

Order of operations rules require that we do any work within parentheses first.  Thus, calculate (8.75 - 2  5/6); it is (5  11/12).  Next, calculate (4  1/2 + 2  2/3); it is ( 7  1/6).  So what we have now looks like:

(5  11/12) / 7.1  + (7  1/6) / (43/10)    (Note that 4  3/10 = 43/10)

Performing the two indicated divisions, we get:

5/6 + 1  2/3.

Since the LCD here is 6, we add:    5/6 + 1  4/6, which comes out to

                                                          1  9/6, or 1 + 1  1/2, or    2  1/2 (answer)

Down

The formula for a quadratic equation is y = ax^2 + bx + c. In this case, a = -4, b = 8, and c = 12. The direction of the parabola can be determined by a. If a is positive, the parabola opens upwards, and if a is negative, the parabola will open downwards.

Answer:

The answer is 48pi

Step-by-step explanation:

what you have to do is you have to do 8*6=48 and there you go your answer

Answer:

48pi

Step-by-step explanation:

Answer:

Yes, the following equation is a quadratic function in vertex form

Step-by-step explanation:

we know that

The quadratic function of the vertical parabola into vertex form is equal to

[tex]y=a(x-h)^{2} +k[/tex]

where

(h,k) is the vertex of the parabola

If the coefficient a is > 0 ----> the parabola open upward (vertex is a minimum)

If the coefficient a is < 0 ----> the parabola open downward (vertex is a maximum)

in this problem we have

[tex]y=4(x-2)^{2} +6[/tex]

The squared term contain the x-coordinate of the vertex

[tex]h=2[/tex]

The constant term is the y-coordinate of the vertex

[tex]k=6[/tex]

The vertex is the point (2,6)

The coefficient is equal to

[tex]a=4[/tex] ----> open upward (vertex is a minimum)

ANSWER

y=10

x=5

EXPLANATION

The base angles of an isosceles triangle are equal.

This implies that:

8y-7=73°

Add 7 to both sides:

8y=73+7

8y=80°

y=10°

Interior angles of a triangle sums up to 180°

73+73+6x+4=180

150+6x=180

6x=180-150

6x=30

Divide both sides by 6

x=5

Step-by-step explanation:

[tex]8^{2x-4}=8^{5x+1}\iff2x-4=5x+1\qquad\text{add 4 to both sides}\\\\2x=5x+5\qquad\text{subtract 5x from both sides}\\\\-3x=5\qquad\text{divide both sides by (-3)}\\\\\boxed{x=-\dfrac{5}{3}}\\\\================================[/tex]

[tex]2^{x+6}=16^{3x+4}\\\\2^{x+6}=(2^4)^{3x+4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{x+6}=2^{4(3x+4)}\iff x+6=4(3x+4)\qquad\text{use the distributive property}\\\\x+6=(4)(3x)+(4)(4)\\\\x+6=12x+16\qquad\text{subtract 6 from both sides}\\\\x=12x+10\qquad\text{subtract 12x from both sides}\\\\-11x=10\qquad\text{divide both sides by (-11)}\\\\\boxed{x=-\dfrac{10}{11}}\\\\================================[/tex]

[tex]\left(\dfrac{1}{2}\right)^x=2^{x+3}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^{-1})^x=2^{x+3}\\\\2^{-x}=2^{x+3}\iff -x=x+3\qquad\text{subtract x from both sides}\\\\-2x=3\qquad\text{divide both sides by (-2)}\\\\\boxed{x=-\dfrac{3}{2}}\\\\================================[/tex]

[tex]36^{2x}=216^{3x-1}\\\\(6^2)^{2x}=(6^3)^{3x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\6^{(2)(2x)}=2^{3(3x-1)}\iff(2)(2x)=3(3x-1)\qquad\text{use the distributive property}\\\\4x=(3)(3x)+(3)(-1)\\\\4x=9x-3\qquad\text{subtract 9x from both sides}\\\\-5x=-3\qquad\text{divide both sides by (-5)}\\\\\boxed{x=\dfrac{3}{5}}\\\\================================[/tex]

[tex]p\%=\dfrac{p}{100}\\\\100\%-12.6\%=87.4\%=\dfrac{87.4}{100}=0.874\\\\8\ years\to(0.874)^4\approx0.584\to58.4\%\\\\\text{After 8 years, the car will be worth 58.4}\%\ \text{of the initial price.}[/tex]

Answer:

10/24 and 15/36, more answers possible

Step-by-step explanation:

if you multiply both the numerator and denominator by the same number, it will always be equivalent to 5/12, as you can simplify it back to that fraction.

5/12, multiply both by two, and you have 10/24

5/12, multiply both by three, and you have 15/36

10/24 and 15/36 are fractions equivalent to the given fraction.

10/24: This is equivalent to 5/12 because it can be reduced to 5/12 by dividing both the numerator and the denominator by 2.

15/36: This is another fraction equivalent to 5/12 since it can be reduced to 5/12 by dividing both the numerator and denominator by 3.

c = 2x + 3. The third side of the triangle is 2x + 3.

The key to solve this problem is using the perimeter of a triangle equation which is P = a + b + c, where a, b, and c are the sides of the triangle.

We know that the perimeter P = 3x² + 7x, let's suppose a = 6x - 7, b = 3x² - x + 4, and c is the unknow.

Clearing c from the equation:

c = P - (a + b)

c = 3x² + 7x - (6x - 7 + 3x² - x + 4)

c = 3x² + 7x - 6x + 7 - 3x² +x - 4

Grouping the equal terms:

c = 3x² - 3x² + 7x + x - 6x + 7 - 4

c = 0 + 8x - 6x + 3

c = 2x + 3