A train moves at a speed of 90 km/hr. How far will it travel in 36 minutes?

Answer:

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Answer:

25[tex]\sqrt{3}[/tex] +60

Step-by-step explanation: The first thing you need to do is realize that, this figure is a isosceles trapezoid due to the markings on each side.

So now we know both sides are 10.

We also know the the top two angles are congruent to each other and so are the bottom two angles due to the trapezoid being isosceles.

So the top two angles are 120 degrees and bottom two angles are 60 degrees.

It seems like we can't find the sides, let's try drawing two lines from each top angle all the way down to form two right triangles.

Wow, these two triangles are special right triangles in the form of

30 - 60 - 90 degrees.

shorter side = n

longer side = n[tex]\sqrt{3}[/tex]

hypotenuse = 2n

So, 2n = 10

n = 5 for the short side

The bottom base is 4[tex]\sqrt{3}[/tex] + 5 + 5 = 10 + 4[tex]\sqrt{3}[/tex]

The longer side is  5[tex]\sqrt{3}[/tex].

The area of trapezoid = (base1 + base2)/2 * height

= (4[tex]\sqrt{3}[/tex] + 10 + 4[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (10 + 8[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (5+4[tex]\sqrt{3}[/tex])*5[tex]\sqrt{3}[/tex] = 25[tex]\sqrt{3}[/tex] +60

So, 25[tex]\sqrt{3}[/tex] + 60 is our answer.

Answer:

  60 +25√3

Step-by-step explanation:

In the figure of the isosceles trapezoid below, the angles at C and D are supplementary to the given angle, so are 60°. That makes triangle BDE a 30°-60°-90° right triangle, which has side length ratios ...

  DE : BE : BD = 1 : √3 : 2 = 5 : 5√3 : 10

Triangle BDE can be relocated to the other end of the figure to become triangle CAD'. Then the area of concern is that of the rectangle with height 5√3 and length 5+4√3. The area is then ...

  Area = lh = (5√3)(5 +4√3) = 5·5√3 +5·4·3

  Area = 60 +25√3 . . . square units

_____

In the figure, 6.93 = 4√3, and 8.66 = 5√3, 16.93 = 10+4√3.

Answer:

See below.

Step-by-step explanation:

(a)

To multiply two polynomials, multiply every term of the first polynomial by every term of the second polynomial. Then combine like terms.

[tex] (\dfrac{1}{2}x - \dfrac{1}{4})(5x^2 - 2x + 6) = [/tex]

[tex] = \dfrac{1}{2}x \times 5x^2 - \dfrac{1}{2}x \times 2x + \dfrac{1}{2}x \times 6 - \dfrac{1}{4} \times 5x^2 + \dfrac{1}{4} \times 2x - \dfrac{1}{4} \times 6 [/tex]

[tex]= \dfrac{5}{2}x^3 - x^2 + 3x - \dfrac{5}{4}x^2 + \dfrac{1}{2}x - \dfrac{3}{2}[/tex]

[tex] = \dfrac{5}{2}x^3 - \dfrac{9}{4}x^2 + \dfrac{7}{2}x - \dfrac{3}{2} [/tex]

(b)

No. Since the binomials are different, the product of two different binomials and the same trinomial will give different results.

Answer:

Step-by-step explanation:

We will use the addition rule of probability of two events to solve the question. According to the rule given two events A and B;

p(A∪B) = p(A)+p(B) - p(A∩B) where;

A∪B is the union of the two sets A and B

A∩B is the intersection between two sets A and B

Given parameters

P(A)=15

P(A∪B)=1225

P(A∩B)=7100

Required

Probability of event B i.e P(B)

Using the expression above to calculate p(B), we will have;

p(A∪B) = p(A)+p(B) - p(A∩B)

1225 = 15+p(B)-7100

p(B) = 1225-15+7100

p(B) = 8310

Hence the missing probability p(B) is 8310.

Answer:

B) Range

Step-by-step explanation:

Hope this will help you

Answer:

Range

Step-by-step explanation:

I hope this will help buddy

Answer:

26.5 liters

Step-by-step explanation:

We know that 1 gallon is 4 quarts, and 1 gallon is approx. 3.78 liters. There's 7 days in a week, so 7 gallons of water is being flowed through. Multiplying 3.78  by 7, we get 26.46 liters per week. Rounding to the nearest tenth, and we get 26.5 liters.

Answer:

D) y=-4

Step-by-step explanation:

we can multiply the first equation by -3 to cancel out the x's

and then add the first equation and the second equation

9x-21y=48

-9x+5y=16

0x-16y=64

y=-64/16=-4

Answer:

5, 12, 13

Step-by-step explanation:

Pythagoras theorem ⇒ Perpendicular² + Base² = Hypotenuse²

5² + 12² = 13²

25 + 144 = 169

Thus 5, 12, 13 is a Pythagorean triple.

r=I × 100÷pxt

8200×100÷ 11406×4

820000÷. 45624

17.97

make me brainliest .

Answer: 17.5 miles

Step-by-step explanation:

P=price, L=length

Firm A:

P=2L+10

Firm B:

P=2.40L+3

2.40L+3=2L+10

L=17.5

The fare would be the same for 17.5 miles for both firms.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here, Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey . let the fixed component of the fare be k and charge for travelling per mile be x then we have,     20=5x+k. . . (1)

                                                   30=10x+k. . . .(2)

solving these two equations we get x=2 and k = 10

Now let the length of the journey that both firm charge the same is equal to  L and given here that firm B charges a pickup fee of £3 and then £2.40 for each mile travelled. Thus forming the equations we get

2L+10=2.40L+3

0.40L=7

      L=17.5

Hence, The fare would be the same for 17.5 miles for both firms.

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The expression of 0.785 in the form p/q is 157/200

The ratio is defined as a way of dividing a variable by another variable.

Given the decimal number 0.785, to convert to fraction, we will place divide 785 by 1000 (since the decimal is on thousandth)

0.785 = 785/1000

Express in its simplest form

785/1000 = 157/200

Hence 0.785 written in the form p/q is 157/200 where p = 157 and q = 200.

Learn more on ratio here: https://brainly.com/question/19473677

Answer:

Top left: 6

Bottom left: 8

Top right: 7

Bottom right: 3

Step-by-step explanation:

To solve this problem, we need to look at the table to see what missing information we need to solve for. On the table, it asks us how many students:

On the first intersection (top left), we are asked how many students played an instrument and sport. That is easy to solve because the information they provide us already gives us that number: 6.

On the second intersection (bottom left), things get a little more challenging. The information states that 14 students in total play sports, so that is not the number of people who only play sports. Since 14 people in total play sports and 6 people play both an instrument and sport, we subtract 6 from 14 to get our answer, 8.

On the third intersection (top right), it asks us how many people play an instrument but doesn't play a sport. Let's look at the remaining values first. There is: 6, 8, 3. When we add those together, we get 17, and when we subtract that from the total (24), we get our answer: 7.

On the last intersection (bottom right), the information already provides us with the answer to how many people don't play anything: 3.

Answer:

Step-by-step explanation:

I can't believe I'm doing this for 5 points, but ok!

For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:

[tex]\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right][/tex]  and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):

[tex](7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)][/tex] which gives us:

392 + 36 - 192 - [48 + 504 - 112] which simplifies to

236 - 440 which is -204

On to the second one:

[tex]\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)][/tex] which gives us:

-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to

-417 - 124 which is -541, choice c.

Now for the third one:

[tex]\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)][/tex] which gives us:

[tex]-126+48-90-[-280+54-36][/tex] which simplifies to

-168 - (-262) which is 94, choice c again.

Now for the last one. I'll show you the set up for the matrix equation; I solved it using the inverse matrix. So I'll also show you the inverse and how I found it.

[tex]\left[\begin{array}{cc}-4&-5&\\-6&-8\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-5\\-2\\\end{array}\right][/tex] and I found the inverse of the 2 x 2 matrix on the left.

Find the inverse by:

* finding the determinate

* putting the determinate under a 1

* multiply that by the "mixed up matrix (you'll see...)

First things first, the determinate:

|A| = (-4*-8) - (-6*-5) which simplifies to

|A| = 32 - 30 so

|A| = 2; now put that under a 1 and multiply it by the mixed up matrix. The mixed up matrix is shown in the next step:

[tex]\frac{1}{2}\left[\begin{array}{cc}-8&5\\6&-4\end{array}\right][/tex]  (to get the mixed up matrix, swap the positions of the numbers on the main axis and then change the signs of the numbers on the minor axis). Now we multiply in the 1/2 to get the inverse:

[tex]\left[\begin{array}{cc}-4&\frac{5}{2}\\3&-2\\\end{array}\right][/tex] Multiply that inverse by both sides of the equation. This inverse "undoes" the matrix that's already there (like dividing the matrix that's already there by itself) which leaves us with just the matrix of x and y. Multiply the inverse matrix by the solution matrix:

[tex]\left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{cc}-4&\frac{5}{2} \\3&-2\end{array}\right] *\left[\begin{array}{c}-5&-2\\\end{array}\right][/tex] and that right side multiplies out to

x = 20 - 5 which is

x = 15 and

y = -15 + 4 which is

y = -11

(It works, I checked it)

Step-by-step explanation:

C(x) = 2.50 + 5(0.40x)

<=> C(x) = 2.50 + 2.00 x

The required expression for the taxi charges is C(x) = $2.50 + 0.4  * x/5.

Given that,
A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. To determine an expression for the cost of the ride, if travel x miles in the taxi with no traffic delays to determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the number of miles be x,
The total charge be C(x)
Now accoding to the condition total charge could be the sum of the cost of every fifth mile and $2.40. So, every fifth mile = x / 5
Now,
C(x) = 2.40 + 0.40 * x/5

Thus, the required expression for the taxi charges is C(x) = $2.50 + 0.4  * x/5.

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Answer:

Option(A)

Step-by-step explanation:

From the graph attached,

Quadrilateral USTR has been transformed to get the image quadrilateral U'S'T'R'.

Coordinates of point U → (-2, 6)

Coordinates of point U' → (3, 3)

Coordinates of U and U' show that quadrilateral USTR has been shifted by 5 units to the right and 3 units down.

Rule to be followed for the translation,

U(-2, 6) → U'[(-2 + 5), (6 - 3)]

U(x, y) → U'[(x + 5), (y - 3)]

Therefore, Option (A) describes the correct rule of transformation.

Answer:

6x+2-1x+5=42

Step-by-step explanation:

Answer:

6x+2-x-5=42

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The colony will follow an exponential equation. y(x) = 8000*(2)^(t/210). Plug in t=630 and you will get y(x) = 64000

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)[/tex]

And the we know that if the discriminant is

***** [tex]\Delta[/tex] < 0, meaning 8-3k<0, meaning

[tex]\boxed{k>\dfrac{8}{3}}[/tex]

then, there is no real solution.

***** [tex]\Delta = 0[/tex], meaning

[tex]\boxed{k=\dfrac{8}{3}}[/tex]

There is 1 solution.

***** [tex]\Delta[/tex] > 0, meaning

[tex]\boxed{k<\dfrac{8}{3}}[/tex]

There are 2 solutions.

Thank you

PS: To give more details...

[tex]8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}[/tex]

Answer:

50 cars

Step-by-step explanation:

Let's define p as the number of people and c the number of cars.

We know that p / c = 3/5 or in other words, there are 5 cars every 3 people. If we have 30 people means that p = 30 which implies 30/c = 3/5 which implies c = 5/3 * 30 = 50.

Answer:

Step-by-step explanation:people=30=3/5

30/5=6*3=18

car=30=5/3

30/3=10

10*5=50

so there are 50 cars there

Answer:

7 : 18

Step-by-step explanation:

1. Convert to the same units (cents)

70 cents = 70 cents

$1.80 = 180 cents

2. Simplify

70 : 180 (divide both by ten)

7 : 18

7 and 18 cannot be simplified any further.

Answer:

x=-2 and x = 5

Step-by-step explanation:

The solutions to the equation are where the graph crosses the x axis

We can see that the graph crosses at x=-2 and x = 5

Answer:

x = -2

x = 5

Step-by-step explanation:

The answer is found when the graph crosses the x-axis

Hope this helps :D

Answer:

Step-by-step explanation:

#1) [tex]\arcsin \left(0.64958\right)=0.70703\dots \quad \begin{pmatrix}\mathrm{Degrees:}&40.51^{\circ \:}\end{pmatrix}[/tex]

∡C =62.49

[tex]\frac{\left(\sin \left(27^{\circ \:}\right)\right)}{3}=\frac{\sin \left(54^{\circ \:}\right)}{x}\quad :\quad x=\frac{3\left(\sqrt{5}+1\right)}{\sin \left(27^{\circ \:}\right)\cdot \:4}\quad \left(\mathrm{Decimal}:\quad x=5.34603\dots \right)[/tex]

Answer:

[tex]{x, y} = {-\frac{2}{3}, \frac{5}{3}}[/tex]

Step-by-step explanation:

7x + 4y = 2

x + y = 1

// Solve equation [2] for the variable  y  

 [2]    y = -x + 1

// Plug this in for variable  y  in equation [1]

  [1]    7x + 4•(-x +1) = 2

  [1]    3x = -2

// Solve equation [1] for the variable  x  

  [1]    3x = - 2  

  [1]    x = - 2/3  

// By now we know this much :

   x = -2/3

   y = -x+1

// Use the  x  value to solve for  y  

   y = -(-2/3)+1 = 5/3  

Solution :

{x,y} = {-2/3,5/3}

Answer:

b

Step-by-step explanation:

16x10=160

Answer:

[tex]\large \boxed{e^{i\pi}+1=0}[/tex]

Step-by-step explanation:

Hello, please consider the following.

For any x real number,

[tex]e^{ix}=cos(x)+i\cdot sin(x)\text{, right? So}\\\\e^{i\pi}=cos(\pi)+i\cdot sin(\pi)\\\\e^{i\pi}=-1+i\cdot 0=-1\\\\\text{ We add 1 to both sides of the equation.}\\\\\large \boxed{e^{i\pi}+1=0}\\[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

x = 1/8

Step-by-step explanation:

[tex]\log _2\left(x\right)=-3\\\\\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c\\\\\log _2\left(x\right)=-3\quad \Rightarrow \quad \:x=2^{-3}\\\\Simplify\\\\x=\frac{1}{8}[/tex]

Answer:

45

Step-by-step explanation:

c(x)=2x^2-4x-3

Let x= -4

c(-4)=2(-4)^2-4(-4)-3

      = 2(16) +16-3

       =32+16-3

         45

Answer:

45

Step-by-step explanation:

c(-4) = 2(-4)² - 4(-4) - 3

       = 2(16) + 16 - 3

       = 32 + 13

       = 45

Answer:

4.76 g/cm³

Step-by-step explanation:

Density formula = mass / volume

1. Set up the equation and solve

50.0 / 10.5 = 4.76

Answer: y = 7

Step-by-step explanation: