Two trains leave towns 1542 kilometers apart at the same time and travel toward each other. one train travels 11 km/h slower than the other. if they meet in 6 hours, what is the rate of each train?

Rate of the slower train:

Rate of the faster train:

Answer:

[tex]\sqrt[2]{8}[/tex]

Step-by-step explanation:

Remember the basic format of a fraction raised to a fractional exponent:

[tex]a^\frac{b}{c}=\sqrt[b]{a^c}[/tex]

Some terms to keep in mind are the following:

(a) is the base

(c) is the exponent

(b) is the index

Apply this information to the given problem:

[tex]2^\frac{3}{2}[/tex]

In this case, (2) is the base, and the index; (3) is the exponent. Apply the general format of the fraction exponent to change the expression from an exponent to a radical.

[tex]2^\frac{3}{2}=\sqrt[2]{2^3}[/tex]

Simplify the term under the radical:

[tex]\sqrt[2]{2^3}=\sqrt[2]{8}[/tex]

Answer:

The equation is true.

Step-by-step explanation:

In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation.  Please note that each side is named with respect to the angle is it across from.

Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

One is given the following equation,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

As per the attached reference image, one can state the following, using the right angle trigonometric ratios,

[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]

Substitute these values into the given equation. Then simplify the equation to prove the idenity,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]

[tex]1+(-1)=0[/tex]

[tex]1-1=0[/tex]

[tex]0=0[/tex]

Answer:

66%

Step-by-step explanation:

[tex]-10x\:+\:\left(20\cdot \left(1-x\right)\right)=\:0[/tex]

x = [tex]\frac{2}{3}[/tex] = .666 = 66%

Answer: l,j,k

Step-by-step explanation:

Answer:

sorry I don't know

sorry I Don't know

Answer:

V = 276.32 ft^3

Step-by-step explanation:

Volume of a cylinder is

V = pi r^2 h

The diameter is 4 so the radius is d/2 = 4/2 = 2

V = (3.14) ( 2)^2 * 22

V = 276.32 ft^3

Answer:

The answer is "25 ml".

Step-by-step explanation:

Dose[tex]= 500 \ mg\\\\[/tex]

Solution [tex]= 100\ \frac{mg}{teaspoonful}\\\\[/tex]

Calculating the Conversions:

Teaspoonful [tex]= 5 \ ml \ \text{(Ounce = 30 ml = 6 Tablespoonsful)}[/tex]

[tex]\therefore\\\\Solution = \frac{100\ mg}{ 5\ ml} = 20\ \frac{mg}{ml}\\\\Dose \ volume = \frac{500\ mg}{ 20\ \frac{mg}{ml}} = 25\ ml[/tex]

Answer: 56

Step-by-step explanation:

Let x be the number that is supposed to be subtracted from 61.

Given

61 - x = 5

Add both sides by x

61 - x + x = 5 + x

61 = 5 + x

Subtract 5 on both sides

61 - 5 = 5 + x - 5

x = 56

Hope this helps!! :)

Please let me know if you have any questions

Answer:

DE=27

EF=13

DG=13

GF=27

Step-by-step explanation:

12x+3=5x+17

12x-5x=17-3

u'll get 14 then simply it by the numbe of X u'll get 2 then replace the X with the number

Answer: 5 and 7

Step-by-step explanation:

Given

Sum of the integers is 12

Product of the integers is 35

Suppose the integers are [tex]x[/tex] and [tex]y[/tex]

[tex]\Rightarrow x+y=12\\\\\Rightarrow y=12-x\\\Rightarrow xy=35\\\text{Substitute y}\\\Rightarrow x(12-x)=35\\\Rightarrow 12x-x^2=35\\\Rightarrow x^2-12x+35=0\\\Rightarrow x^2-7x-5x+35=0\\\Rightarrow (x-7)(x-5)=0\\\Rightarrow x=5\ or\ 7[/tex]

[tex]\therefore \text{y can be }7\ or\ 5[/tex]

Hence, the numbers are 5 and 7.

Answer:

Option D, 52

Answered by GAUTHMATH

Answer:

y = 2x -4

Step-by-step explanation:

2y = 4x - 8

Divide each side by 2

2y/2 = 4x/2 - 8/2

y = 2x -4

Answer:

let the polynomial be

f(x)=x³+2kx+2

is divided by

g(x)=x+2

hence

(x+2) is a factor of f(x)

so comparing with x-a we get a=-2

so

f(a)=0

f(-2)=(-2)³+2*-2*k+2

0=-8-4K+2

4k=-6

K=-6/4

k=-3/2

again

when divided by x+1

g(x)=x+1

hence

x+1 is a factor

so a=-1

f(-1)=-(1)³+2*-1*k+2

0=-1-2k+2

0=1-2k

k=1/2

The value of k is 1/2 when divided by x+1

and

K =-3/2 when divided by x+2

Answer:

-60

Step-by-step explanation:

Step-by-step explanation:

5.

[tex]3\cdot 10^{8} : 1000 = 3\cdot 10^{8} : 10^{3} =3 \cdot 10^{8-3} =3 \cdot 10^{5}[/tex]

Answer:   [tex]3 \cdot 10^{5}[/tex]

6.

[tex]\dfrac{0.0046}{0.000000000513} =\dfrac{46 \cdot 10^{-4} }{5.13 \cdot 10^{-10} } =\dfrac{46 \cdot 10^{-4-(-10)}}{5.13} =\dfrac{46 \cdot 10^{6}}{5.13} \approx 9 \cdot 10^{6}[/tex]

Answer:   [tex]9 \cdot 10^{6}[/tex]

Answer:

15x^9

Step-by-step explanation:

A=l x w

5x^4 times 3x^5 is basically 3*5*x^4*x^5

when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9

Answer:

Total number of students in the college = 200 student

Step-by-step explanation:

Given:

Number of student make dean's list = 67 student

Percentage of student make dean's list = 33.5% of all student

Find:

Total number of students in the college

Computation:

Total number of students in the college = Number of student make dean's list / Percentage of student make dean's list

Total number of students in the college = 67 / 33.5%

Total number of students in the college = 67 / 0.335

Total number of students in the college = 200 student

Answer:

"97" is the appropriate answer.

Step-by-step explanation:

Given:

Number of trees,

= 485

Orchards of trees,

= 5

The number of trees in each orchard will be:

= [tex]\frac{Number \ of \ trees}{Orchards \ of \ trees}[/tex]

= [tex]\frac{485}{5}[/tex]

= [tex]97[/tex]

Answer:

The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.

Answer:

SA=2πrh+2πr2=2·π·12·3+2·π·122≈282.7cm2

Answer:

C. Kiometers per hour. I think

Answer:

x = ±i ,  x=1

Step-by-step explanation:

(x^2+1)(x-1)=0

Using the zero product property

x^2 +1 = 0   x-1= 0

x^2 = -1       x=1

Taking the square root of the equation on the left

sqrt(x^2) = sqrt(-1)

x = ±i   where  i is the imaginary number

We still have x=1 from the equation on the right

Answer:

6.75x + 5.50y = 186.75

Step-by-step explanation:

The stuffed mushrooms cost 6.75 dollars and the tomato bread costs 5.50 dollars.

Answer:

186.75

Step-by-step explanation:

6.75x+5.50y=186.75

Answer:

try 14n

Step-by-step explanation:

Answer:

[tex]r \: = 2sin2 \theta \\ = > r = 2.2sin\theta.cos\theta \\ = > r = 4sin\theta.cos\theta \: \\ \\ \sf \: we \: know \: that \: \\ x = r \: cos\theta \: \therefore \: cos\theta = \frac{x}{r} \\ \\ y = r \: sin\theta \: \therefore \: sin\theta = \frac{y}{r} \\ \\ \sf \: now \\ \\ r = 4 \times \frac{y}{r} \times \frac{x}{r} \\ = > {r}^{3 } = 4xy \\ \\ \sf \: again \: \: r = \sqrt{ {x}^{2} + {y}^{2} } \\ \\ = > {( \sqrt{ {x}^{2} + {y}^{2} } })^{3} = 4xy \\ = > {( {x}^{2} + {y}^{2} })^{ \frac{3}{2} } = 4xy \\ = > {( {x}^{2} + {y}^{2} })^{3} = 16 {x}^{2} {y}^{2} [/tex]

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Given:

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]              ...(i)

Surface area of a sphere:

[tex]A=4\pi r^2[/tex]                      ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

[tex]V=\dfrac{28}{3}\times A[/tex]

[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]

Multiply both sides by 3.

[tex]4\pi r^3=112\pi r^2[/tex]

[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]

[tex]r=28[/tex]

Using (i), the volume of the sphere is:

[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]

[tex]V\approx 91989[/tex]

Using (ii), the surface area of the sphere is:

[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]

[tex]A=9856[/tex]

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.

Answer:

The volume of the cube is 21952.

Step-by-step explanation:

V = L x W x H

because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:

V= S^3

(S standing for side)

we know the height is 28 and as all sides measure the same we use the equation:

V= 28^3

28^3 = 21952

So, V= 21952

Answer:

you can plug it back into the original equation to see if it fits the solution. if not then you have another solution you need to solve for.

Answer:

if we're talking on linear equations, then the two equations would intersect at one point. or when you solve it, it'll be only 1 number that can fit that equation.

p.s.: sub to #gauthmath# sub reddit if ya can ^^

Answer:

678

Step-by-step explanation:

12*11=132

11*9=99

12*9=108

132+99+108=339

339*2=678

[tex] \bf \: f(x) = \frac{3}{2} \times {2}^{x} \\ \\ = > \bf \: f(0) = \frac{3}{2} \times {2}^{0} = \frac{3}{2} \times 1 = \frac{3}{2} = 1.5 \\ \\ = > \bf \: f(1) = \frac{3}{2} \times {2}^{1} = 3 \\ \\ = > \bf \: f(2) = \frac{3}{2} \times {2}^{2} = 6 \\ \\ = > \bf \: f( - 1) = \frac{3}{2} \times {2}^{ - 1} = \frac{3}{2} \times \frac{1}{2} = \frac{3}{4} = 0.75 \\ \\ = > \bf \: f( - 2) = \frac{3}{2} \times {2}^{ - 2} = \frac{3}{2} \times \frac{1}{4} = \frac{3}{8} = 0.375[/tex]

Answer:

17.y=-x+12

18.y=-1/4x+7

Step-by-step explanation:

17.a Solve for y (y=-5+x)

17. b Reciprocal (y=-1x-5)

17. c Subsitute equation into (8,-1) (-1=-13=y=x+12)

18.a Subtract y values and x values= (6-4)/(4-12)=2/-8=-1/4, this will be your slope

18. b Plug in -1/4 into either of the two ordered pairs to find y value=(12,4)=(4=-3)=y value=7.

18. c=y=-1/4x+7