It takes a bus 6 hours to take a trip. The train takes only 4 hours to make the same trip. The train travels at a rate of speed that is 25 mph more than the speed of the bus. What is the rate of the bus and the rate of the train? State what x represents, state the equation, and then state the answer.

Answer:

-45

Step-by-step explanation:

The question is asking for the sum of the sequence. Therefore, there is no such thing as a "radians" answer.

When you evaluate the sum, you should get -45 as your answer. To find so, you simply plug in 1 as n and other numbers then add the result.

The sum telescopes. Consider the N-th partial sum of the series,

[tex]S_N=\displaystyle\sum_{n=1}^N\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)[/tex]

[tex]S_N=\bigg(\tan^{-1}\sqrt1-\tan^{-1}\sqrt2\bigg)+\bigg(\tan^{-1}\sqrt2-\tan^{-1}\sqrt3\bigg)+\bigg(\tan^{-1}\sqrt3-\tan^{-1}\sqrt4\bigg)+\cdots+\bigg(\tan^{-1}\sqrt N-\tan^{-1}\sqrt{N+1}\bigg)[/tex]

Notice how [tex]\tan^{-1}\sqrt2[/tex] is added, then immediately subtracted. The same goes for [tex]\tan^{-1}\sqrt3[/tex], then [tex]\tan^{-1}\sqrt4[/tex], and so on, up to [tex]\tan^{-1}\sqrt N[/tex]. This leaves us with

[tex]S_N=\tan^{-1}\sqrt1-\tan^{-1}\sqrt{N+1}[/tex]

The value of the given sum is obtained as [tex]N\to\infty[/tex]. We get

[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\lim_{N\to\infty}S_N=\tan^{-1}1-\lim_{N\to\infty}\tan^{-1}\sqrt{N+1}[/tex]

To compute the limit, recall that [tex]\tan^{-1}x[/tex] has a range of [tex]\left(-\frac\pi2,\frac\pi2\right)[/tex]; in particular, [tex]\tan^{-1}x\to\frac\pi2[/tex] as [tex]x\to\infty[/tex]. So we have

[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\frac\pi4-\frac\pi2=\boxed{-\frac\pi4}[/tex]

Answer:

For Example say a number is in scientific form, 4.10x10^5, to write this in standard form you can either do 10^5=100,000x4.10=410,000, or you could simply take 4.10 and move the decimal place 5 places to the right, and you would get the same answer, 410,000.

Step-by-step explanation:

Answer:

#1 true

#2 false

false

Step-by-step explanation:

Answer: sqrt(85)/2

Step-by-step explanation:

Remember that the length of the diameter is twice that of the radius.

The first step would be finding the distance between the two points using the distance formula[tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}[/tex].

The distance of diameter = [tex]\sqrt{85}[/tex]

The distance of the radius would be half that, so [tex]\frac{\sqrt{85}}{2}[/tex]

Answer:

x=52

I think it is the answer

Answer:

I think the answer is 4)may be negative

Answer:

u=(9-6w)÷-2

Step-by-step explanation:

Answer:

u = 3w - 4.5

Step-by-step explanation:

Step 1: -2u + 6w = 9 - Solve for u by isolating the variable u.

Step 2: Subtract 6w both sides

-2u = 9 - 6w

Step 3: Divide by -2 both sides

u = ( 9 - 6w ) / ( -2 )

u = 3w - 4.5

Have a good day!! :)

Answer: 6 dollars

Step-by-step explanation:

Answer:

addition property of equality

inverse property of multiplication

Step-by-step explanation:

7y − 15 = −29

Add 15 to each side using the addition property of equality

7y -15+15 = -29+15

7y = -14

Divide each side by 7 using the inverse property of multiplication

7y/7 = -14/7

y =2

Answer:

[tex]\Large \boxed{\mathrm{Addition \ Property \ of \ Equality}} \\\\\\ \Large \boxed{\mathrm{Inverse \ Property \ of \ Multiplication}}[/tex]

Step-by-step explanation:

[tex]\sf 7y-15=-29[/tex]

Using the additive property of equality, we add 15 to both sides of the equation.

[tex]\sf 7y-15+15=-29+15[/tex]

[tex]\sf 7y=-14[/tex]

Using the inverse property of multiplication, we divide both sides of the equation by 7.

[tex]\displaystyle \sf \frac{7y}{7} =\frac{-14}{7}[/tex]

[tex]\sf y = -2[/tex]

Answer:

its 10.5 cm

Step-by-step explanation:

its what I got off of khan

The base area of the oblique triangular prism is 10.5 square cm

The volume is given as:

Volume = 63 cubic cm

The height of the prism is:

Height = 6 cm

The base area of the prism is then calculated using:

Area = Volume/Height

So, we have:

Area = 63/6

Evaluate

Area = 10.5

Hence, the base area of the triangular prism is 10.5 square cm

Read more about volume at:

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The answer is explained in the photo I have linked.

Answer:

95.50

Step-by-step explanation:

a constant is a number not attached to a variable

in this case the variables are c and w

95.50 is the only one without a variable

Answer:

$22.50

Step-by-step explanation:

Let's write what we know.

$10 a month bonus

+ $0.50 / per item of the month

$2 per compliment

We can write an equation:

T = Total bonus for the month

i = number of item of the month sales

c = number of compliments

T = $10 + $0.50i + $2c

i = 17

c = 2

Plug in the values:

T = $10 + $0.50i + $2c

T = $10 + $0.50( 17 )+ $2( 2 )

T = $10 + $8.50 + 4

T = $22.50

Her bonus for this month is $22.50

Jenae bonus for this month is $22.50.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given that Jenae works at a clothing store and gets a bonus of $10 a month, plus $0.50 every time she sells the item of the month.

$10 a month bonus + $0.50 / per item of the month

$2 per compliment

We can write an equation;

T = Total bonus for the month

i = number of item of the month sales

c = number of compliments

T = $10 + $0.50i + $2c

i = 17

c = 2

Plug in the values;

T = $10 + $0.50i + $2c

T = $10 + $0.50( 17 )+ $2( 2 )

T = $10 + $8.50 + 4

T = $22.50

Hence, Jenae bonus for this month is $22.50.

Learn more about equations here;

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Answer:

Step-by-step explanation:

Like terms have same variables and exponents

12b and 7b are like terms

15 & -8  are like terms

12b + 15 + 7b - 8 + 7x = 12b + 7b + 15 - 8 + 7x

                                   = 19b + 7 + 7x

Answer:

Step-by-step explanation:

12b+7b+15-8+7x

19b+15-8+7x

Answer: 12.07 ounce/gallon.

Step-by-step explanation:

given data:

desired ratio = 90grams / liter of water.

ratio In ounce/ gallon

first we convert our grams to ounce

= 98grams / 28.35

= 3.175 ounce.

converting liter to gallons

= 1/3.8

=0.263 gallons

therefore;

= 3.175 ounce / 0.263 gallons

= 12.07 ounce/gallon.

Answer:

Step-by-step explanation:

The sum of all exterior angles of any regular polygon is 360°.

= [tex]\frac{360}{57} \\\\= 120/19\\or\:6.315[/tex]

The number of sides should be a natural number not in fraction or decimal

Answer:

none of them are right

Step-by-step explanation:

a is 254.6153846153846.

b is 25.96078431372549

c is 2.570873786407767

d is 0.0262178217821782

if b would to be 2,648 divided by 100* it would correct but sadly none of them are correct.

Answer:

The only option that comes close is option 2.

Explanation:

Put everything into your calculator as you see it:

26,480 / 104 = 254.61

2,648 / 102 = 25.96

264.8 / 103 = 2.57

2.648 / 101 = 0.02

Answer:

40.8696% increase (40.9%)

if x =7 then plug in 7 for x

4(7) - 2((7)+a) = 8

28 - 14 -2a = 8

14 - 2a = 8

-2a = -6

a = 3

Answer:

Step-by-step explanation:

Answer:

Given, a number is x.

The question says 8 is decreased by a number. So which is x.

Decreased by here means subtracting "a number" from the "other number".

According to the question, the algebraic expression will be given by-

8-x

Regards!

Answer:

x = 30 degrees

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees.

This means that 2x + 2 + 3x + x - 2 = 180.

We can then combine like terms, getting 6x = 180.

We can then divide both sides by 6, getting x = 30 degrees.

Answer:

x = 30

Step-by-step explanation:

Every triangle equals 180. So make an equation first:

2x + 2 + 3x + x - 2 = 180

Next Combine Like Terms:

6x = 180

Then Divide by 6 On Both Sides:

x = 30

Step-by-step explanation:

The domain of a graph is all of the possible x values, and the range is all possible y values.

7. The graph goes on for both the x and y values, so the domain is (-inf, inf) and the range is (-inf, inf).

8. In this case, the domain is also (-inf, inf), but the range is [-2, inf) as there are no y values less than -2.

9. The domain is [-2, 2], as the x values only range from -2 to 2. The range is [-3, 3] as the y values range from -3 to 3.

10. The domain is (-inf, inf) because all x values are possible. The range is [-1, 1], as there are no y values greater than 1 or less than -1.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

You have one orange and your friend gives you another, then you will have 2.

Hope this helps ;) ❤❤❤

Answer:

A

Step-by-step explanation:

if we had a economic turn down, basically people would lose money, so that means the consumers, so the producers will have a bunch of left over products because the people can't afford to buy as much, which means the company loses money, which means the employees must be let go of so the business doesn't go out of business

A] Economic Downturn could influence Employer to reduce number of workers at business.

Economic Downturn is a slowdown in economic activities for a considerable period of time. It is characterised by low demand by consumers & low production levels in businesses.

This situation implies that a rational employer would reduce the workers employed, as there is lesser demand & need of production.

Better educated workers, new location' opening, high demand of goods : are rather likely to increase employment levels instead of decreasing.

To learn more, refer https://brainly.com/question/1253307?referrer=searchResults

Answer:

B.  16

Step-by-step explanation:

x² − 8x = 10

x² − 8x + (-4)² = 10 + (-4)²

x² − 8x + 16 = 10 + 16 --------- added 16 to both sides.

to finish the equation..

x² − 8x + 16 = 26

(x - 4)² = 26

[tex]\sqrt(x - 4)^2 = \sqrt{26}[/tex]

x = [tex]\sqrt{26} + 4[/tex]

x = [tex]4 - \sqrt{26}[/tex]

Answer:

[tex]\Huge \boxed{\mathrm{B. \ 16}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]x^2-8x=10[/tex]

The equation is in the form ax² + bx = -c. The value of b in the equation is -8.

To complete the square, we need to add (b/2)² = (-8/2)² =  -4² = 16 to both sides.

[tex]x^2-8x+16=26[/tex]

Factoring left side of the equation.

[tex](x-4)^2 =26[/tex]

Taking the square root of both sides.

[tex]x-4=\pm\sqrt{26}[/tex]

Adding 4 to both sides.

[tex]x=4\pm\sqrt{26}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

5,170

Step-by-step explanation:use rounding number calculater for extra help

Answer:

Total earning in the summer = $1440

Step-by-step explanation:

Earning per hour for Samuel = $7.50

No. of hours worked in a day = 6

Earning for a day = Earning per hour for Samuel *No. of hours worked in a day

Earning for a day =  $7.50 *6 = $45

___________________________________________________

No of days worked in a week by Samuel = 4

Earning for week = Earning for a day *No of days worked in a week by Samuel

Earning for week =  $45*4 = $180

_____________________________________________________

No. of weeks worked in summer = 8

Total earning in the summer = Earning for week *No. of weeks worked in summer

Total earning in the summer =  $180*8 = $1440  (Answer)

Answer:

a.  L.B. = 20.5

b.  U.B. = 21.5

Step-by-step explanation:

Length is measured 21 cm correct to 2 significant figures

a.  Lower bound of 21

  =  20.5 < 21

  = 20.5

b. Upper bound of 21

   = 21 < 21.5

   = 21.5

Answer:

a.  L.B. = 20.5

b.  U.B. = 21.5

Step-by-step explanation:

Answer:20

Step-by-step explanation: