A collection of 40 dimes and nickels
is worth $2.90. How many nickels are
there? (Hint: In your equation, use
290¢ instead of $2.90.)

[tex]\large\underline{\sf{Solution-}}[/tex]

Given integral is

[tex]\rm :\longmapsto\:\displaystyle\int\rm \frac{ {x}^{e - 1} + {e}^{x - 1} }{ {x}^{e} + {e}^{x} } \: dx[/tex]

To evaluate this integral, we use Method of Substitution.

So, Substitute

[tex]\rm :\longmapsto\: {x}^{e} + {e}^{x} = y[/tex]

[tex]\rm :\longmapsto\: \dfrac{d}{dx}({x}^{e} + {e}^{x}) = \dfrac{d}{dx}y[/tex]

[tex]\rm :\longmapsto\: {ex}^{e - 1} + {e}^{x} = \dfrac{dy}{dx}[/tex]

[tex]\rm :\longmapsto\:e( {x}^{e - 1} + {e}^{x - 1}) = \dfrac{dy}{dx}[/tex]

[tex]\rm :\longmapsto\:({x}^{e - 1} + {e}^{x - 1})dx = \dfrac{dy}{e}[/tex]

So, on substituting all these values in above integral, we get

[tex]\rm \:  =  \: \displaystyle\int\rm \frac{dy}{e \: y} [/tex]

[tex]\rm \:  =  \:\dfrac{1}{e} \displaystyle\int\rm \frac{dy}{ y} [/tex]

[tex]\rm \:  =  \:\dfrac{1}{e}log |y| + c[/tex]

[tex]\rm \:  =  \:\dfrac{1}{e}log \bigg| {x}^{e} + {e}^{x} \bigg| + c[/tex]

Hence,

[tex]\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int\rm \frac{ {x}^{e - 1} + {e}^{x - 1} }{ {x}^{e} + {e}^{x} } \: dx = \frac{1}{e}log \bigg| {x}^{e} + {e}^{x}\bigg| + c}}[/tex]

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LEARN MORE :-

[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf f(x) & \bf \displaystyle \int \rm \:f(x) \: dx\\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf kx + c \\ \\ \sf sinx & \sf - \: cosx+ c \\ \\ \sf cosx & \sf \: sinx + c\\ \\ \sf {sec}^{2} x & \sf tanx + c\\ \\ \sf {cosec}^{2}x & \sf - cotx+ c \\ \\ \sf secx \: tanx & \sf secx + c\\ \\ \sf cosecx \: cotx& \sf - \: cosecx + c\\ \\ \sf tanx & \sf logsecx + c\\ \\ \sf \dfrac{1}{x} & \sf logx+ c\\ \\ \sf {e}^{x} & \sf {e}^{x} + c\end{array}} \\ \end{gathered}\end{gathered}[/tex]

Answer:

There would be 2,120 dollars in that account

Answer:

Step-by-step explanation:

A=P(1 - r/n)^nt

A = 5,000 (1 - 0.03/1)^(1)12)

A = 5,000 (1 - 0.03)^2

A = 5,000 (0.9)^2

A = $5,314.06

Answer:

the answer: 56.25 percent of 80

Answer:

It would be 5:8

Step-by-step explanation:

The Correct choices are :

Answer:

isiiqywyysyu the first one the first time in a even if it well y eh I just saw your message garako thiya na na hey I k h I just got home from a ko xa ki xaina the morning to get well soon dd ko we

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

alternate interior

Answer:

its 40 degrees

Step-by-step explanation:

its said by the top person :)

Answer:

6/13

Step-by-step explanation:

because if you do 10-4=6

= kx. where k is the constant of variation. Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3.

Simply so, which graph represents an equation in the form y KX?

Slope of y = kx Theorem The graph of the direct-variation function with equation y = kx has constant slope k. Now solve this system of equations for k. So by the definition of slope, k is the slope of the line through these points. Thus, k is the slope of the line with equation y = kx.

Also, which statement is always true about the graph of an equation in the form y KX Y KX? The equation y = kx is a proportional graph. It means that you multiply x by a number and you have k. The point (0, 0) will always be on the graph, because no matter what K is, if you are multiplying by 0 for x, you will get 0 for y.

Secondly, what is Y KX called?

In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation. In this function, m (or k) is called the constant of proportionality or the constant of variation.

What is direct variation?

Direct Variation. Directly Proportional. A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).

Answer:

The will have the same amount $ 387

Step-by-step explanation:

Grayson: y = 19x + 45

Jacob: y = 16x + 90

Grayson: y = 19(18) + 45

342 + 45 = $387

Jacob: y = 16(18) + 90

288 + 90 = $378

Answer: the CORRECT answer is B

Why B?:

The CARS Checklist (Credibility, Accuracy, Reasonableness, Support), created by Dr. Robert Harris, is a system for evaluating the quality of research information.

Answer:

5/12

Step-by-step explanation:

1/4 + 1/6 = (6+4)/24 = 10/24 = 5/12

why +1/6?

because: - (-) = +

Answer:

∠ DBC = 34°

Step-by-step explanation:

∠ DBC = ∠ ABC - ∠ ABD = 64° - 30° = 34°

Answer:

no i cant

Step-by-step explanation:

i just need points uwu

baka sussy

Answer:

a negative plus positive equals a negative-

Answer:

"To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero."

Step-by-step explanation:

Simpler Explanation: If you add a positive number with a negative number, the sign (negative/positive) of the sum is the same as the integer (number) with the largest absolute value. For example;

1. 10 + -12 = -2

Here, the sum has the same sign (negative) as the largest number in the equation (-12).

2. 7 + -3 = 4

Here, the sum has the sign (positive) as the largest number in the equation (7).

Answer:

Step-by-step explanation: Exponential depreciation formula :-

y = A(1 - r)^t, where y is the value of good after t years , r is rate of depreciation and A is the initial value.

Given : A= $20800  ; r=10.75%=0.1075  

The equation models this situation:

Then, the value of car after t=13 years :-

Hence, the value of car after 13 years = $4742.10

Answer:

4m, 6m, 7m, 5m

Step-by-step explanation:

To find perimeter you just add the side lengths togeather.

Answer:

x=8

Step-by-step explanation:

Since 7-2 is 5, that means that both sides are increasing by 5.

3+5 = 8 so therefore 8 =x

Answer:

1225.50

Step-by-step explanation:

14% of 1075 =0.14 x 1075=150.5

1075 +150.5 = 1225.5

The 14% of $1075 is $150.5 thus the total cost for the hotel room overall 5 nights including tax will be $1225.50.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

The total cost before tax was $1,075.

The tax rate is 14%

14% of $1075 will be,

(14/100)1075 = $150.5

Total cost includes tax = $1075 + $150.5 = $1225.50

Hence "The 14% of $1075 is $150.5 thus the total cost for the hotel room overall 5 nights including tax will be $1225.50".

For more about the percentage,

brainly.com/question/13450942

#SPJ2

Answer:

- 16

Step-by-step explanation:

-4 - 3 = -7 (1st and 2nd)

3rd) - 7 - 3 = - 10

4th) -10 - 3 = -13

5th) -13 - 3 = -16

Answer:

a. -8

Step-by-step explanation:

Answer:

400 mph

Step-by-step explanation:

1200/3 = 400 miles per hour

Answer:

m1= 43

m2=17

m3=120

m4=m5=m6=60

m7=17

m8=120

m9=43

Step-by-step explanation:

"Given ABC is an isosceles triangle and DBE is an equilateral triangle. we have to find each missing measure.

In triangle ABC,

∠1=∠9    (∵isosceles triangle)

⇒ 4x+3=9x-47

⇒ 9x-4x=3+47 ⇒ 5x=50 ⇒ x=10

Hence, ∠9=∠1=(4x+3)°=4(10)+3=43°

Also, given ΔBDE is an equilateral triangle, and all angle of equilateral triangle are equal.

∴ ∠4+∠5+∠6=180°

⇒ ∠4+∠4+∠4=180° ⇒ 3∠4 = 180° ⇒ ∠4 = 60°

∴ ∠4=∠5=∠6=60°

By exterior angle property, ∠3=∠5+∠6=60°+60°=120°

                                            ∠8=∠5+∠4=60°+60°=120°

In ΔABD, ∠1+∠2+∠3=180°

            ⇒ 43°+120°+∠2=180°⇒ ∠2 = 17°

In ΔABD, ∠9+∠8+∠7=180°

            ⇒ 43°+120°+∠7=180°⇒ ∠7= 17°"

by SerenaBochenek

Answer:

yfyffyfyfyg

Step-by-step explanation:

xgsxfuftuxfyfjfyfyfyffyfyfygyfdtdtdhfgjhtuydxfyyxff

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Work Shown:

[tex]a^2 + b^2 = c^2\ \text{ ... pythagorean theorem}\\\\4^2 + x^2 = \left(\sqrt{65}\right)^2\\\\16 + x^2 = 65\\\\x^2 = 65-16\\\\x^2 = 49\\\\x = \sqrt{49} \ \text{ ... only consider the positive root}\\\\x = 7\\\\[/tex]

Answer:

$ 198

Step-by-step explanation:

450 + 0.06x = 3750

0.06x = 3750 - 450

x = (3300 * 0.06) = 198

x = 198

Answer:

Step-by-step explanation:

(5x +x^4) -((3x^4 )+4x), open the parenthesis and distribute the negative sign

5x+(x^4) -(3x^4) -4x, combine like terms

(-2x^4) +x

Answer:

(2,4)

X always comes before Y. So the X is 2 and the Y is 4, so (2,4).