How many solutions does this system have?

Answer:

The sum of the first 5 terms of the series is 77.

Step-by-step explanation:

1. Let's review the information provided to us for solving the sum of the first 5 terms of the series:

1st term = 7

2nd term = - 14

3rd term = 28

4th term = - 56

2. Let's solve the sum of the first 5 terms of the series:

Aₙ = Aₙ₋₁ * -2 ; A₁ = 7

A₁ = 7

A₂ = A₁ * -2 = 7 * - 2 = - 14

A₃ = A₂ * - 2 = -14 * - 2 = 28

A₄ = A₃ * - 2 = 28 * - 2 = - 56

A₅ = A₄ * - 2 = -56 * - 2 = 112

Sum of the first 5 terms of the series = 7 - 14 + 28 - 56 + 112

Sum of the first 5 terms of the series = 77

Answer:

[tex]\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c[/tex]

Step-by-step explanation:

[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex]

Adding and Subtracting 1 to the Numerator

[tex]\int\frac{x^{4} - 1 + 1}{x^{4} -1}dx[/tex]

Dividing Numerator seperately by [tex]x^{4} - 1[/tex]

[tex]\int 1 + \frac{1}{x^{4}-1 }\, dx[/tex]

Here integral of 1 is x +c1 (where c1 is constant of integration

[tex]x + c1 + \int\frac{1}{(x-1)(x+1)(x^{2}+1)}\, dx[/tex]----------------------------------(1)

We apply method of partial fractions to perform the integral

[tex]\frac{1}{(x-1)(x+1)(x^{2}+1)}[/tex] = [tex]\frac{A}{x-1} + \frac{B}{x+1} + \frac{C}{x^{2} + 1}[/tex]------------------------------------------(2)

[tex]\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)}{(x-1)(x+1)(x^{2} +1)}[/tex]

1 = [tex]A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)[/tex]-------------------------(3)

Substitute x= 1 , -1 , i in equation (3)

1 = A(1+1)(1+1)

A = [tex]\frac{1}{4}[/tex]

1 = B(-1-1)(1+1)

B = [tex]-\frac{1}{4}[/tex]

1 = C(i-1)(i+1)

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

Substituting A, B, C in equation (2)

[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex] = [tex]\int\frac{1}{4(x-1)} - \frac{1}{4(x+1)} -\frac{1}{2(x^{2}+1) }[/tex]

On integration

Here [tex]\int \frac{1}{x}dx = lnx and \int\frac{1}{x^{2}+1 } dx = arctanx[/tex]

[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex] = [tex]\frac{1}{4} ln(x-1)[/tex] - [tex]\frac{1}{4} ln(x+1)[/tex] - [tex]\frac{1}{2} arctanx[/tex] + c2---------------------------------------(4)

Substitute equation (4) back in equation (1) we get

[tex]x + c1 + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2[/tex]

Here c1 + c2 can be added to another and written as c

Therefore,

[tex]\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c[/tex]

Answer:

x=1

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises

so

In this problem

m∠C=(1/2)arc AB

we have

m∠C=(3x+5)°

arc AB=(16x)°

substitute the values

[tex](3x+5)\°=(1/2)(16x)\°[/tex]

solve for x

[tex]3x+5=8x\\8x-3x=5\\5x=5\\x=1[/tex]

Answer:

x = -9

Step-by-step explanation:

the equation is 2^4x = 8^x - 3.

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

since both have powers of 2

therefore

4x = 3(x-3)

4x = 3x - 9

4x -3x = -9

x = -9

Answer:

D) 2^4x=2^3x-9

Step-by-step explanation:

took quiz

Distance between the points (-3, -4)  is  5

Step-by-step explanation:

Given

points =(-3,-4) and (0,0)

To Find:

The Distance between the two given points =?

Solution:

[tex]Distance =\sqrt{(x2-x1)^2+(y2-y1)^2 }[/tex]

where

[tex](x_1, y_1)[/tex] = coordinates of the first point

[tex](x_2, y_2)[/tex] = coordinates of the second point

So here, we have  

[tex]x_1[/tex] = -3

[tex]y_1[/tex] = -4

[tex]x_2[/tex]  = 0

[tex]y_2[/tex] = 0

So, after putting the values of [tex]x_1[/tex] , [tex]y_1[/tex] , [tex]x_2[/tex] [tex]y_2[/tex]   in the above equation,  we have  

[tex]Distance=\sqrt{(0+3)^2+(0+4)^2 }[/tex]

[tex]Distance=\sqrt{(3)^2+(4)^2 }[/tex]

[tex]Distance=\sqrt{(9)+(16) }[/tex]

[tex]Distance=\sqrt{(25)}[/tex]

Distance = 5

The question is missing the figure. So, the figure is attached below.

Answer:

237.375 ft³

Step-by-step explanation:

Given:

Side length of bigger cube is, [tex]S_1=8\ ft[/tex]

Side length of smaller cube is, [tex]S_2=6.5\ ft[/tex]

Now, volume of the bigger storage unit is given as:

[tex]V_1=S_1^3\\V_1=S_1\times S_1\times S_1\\V_1=8\times 8\times 8=512\ ft^3[/tex]

Volume of the smaller storage unit is given as:

[tex]V_2=S_2^3\\V_2=S_2\times S_2\times S_2\\V_2=6.5\times 6.5\times 6.5=274.625\ ft^3[/tex]

Now, difference in the volume of the two storage units is given as:

[tex]V_1-V_2=512-274.625=237.375\ ft^3[/tex]

Therefore, the difference in their volumes is 237.375 ft³.

To find the difference in volume between two cube-shaped storage units, determine the length of one side for each cube, calculate their volumes with the formula 'Volume = side length cubed', and subtract one volume from the other.

To calculate the difference in volume between the two cube-shaped storage units, follow these steps:

For example, let's assume the side length of cube 1 is 2 meters and the side length of cube 2 is 3 meters. The volume of cube 1 will be 2^3 or 8 m³ and the volume of cube 2 will be 3^3 or 27 m³. The difference in volume between the two cubes would be 27 m³ - 8 m³ = 19 m³.

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Answer:

r=121/148 or r=0.81756

Step-by-step explanation:

-30=1/4-37r

37r=1/4-(-30)

37r=1/4+30

37r=1/4+120/4

37r=121/4

r=(121/4)/37

r=(121/4)(1/37)

r=121/148

Answer:

Step-by-step explanation:

A 40 percent

Answer: (A)

(40%)

Step-by-step explanation:

By making an equation, we can get this answer. Let's say "what percent" is wp.

20 is wp of 50

20=wp(50)

20=50wp

wp=2/5

wp=40% (A)

Answer:

B. 4

Step-by-step explanation:

The degree of the polynomial (the exponent of the highest term) is the total number of roots (including imaginary roots).

The degree of this polynomial is 4, so there are 4 roots.

Ages of Mark, Brett and Carl are 80 years, 60 years and 70 years respectively.

Solution:

Given that

Brett is 18 years younger than Mark.

Carl is 10 years younger than Mark.

The sum of the ages of Brett, Mark, and Carl is 212

Need to determine age of Brett, Mark, and Carl.

Let assume age of mark in years be represented by variable x

As it is given that Brett is 18 years younger than Mark , so if we subtract 18 from the age of Mark we will get age of Brett ,

=> Age of Brett = x – 18

Also given that Carl is 10 years younger than Mark , so if we subtract 10 from the age of Mark we will get age of Carl ,

=> Age of Carl = x – 10

Given sum of ages of Brett, Mark, and Carl is 212

=> Age of Mark + Age of Brett + Age of Carl = 212

=> x + ( x – 18 ) + ( x – 10) = 212

=> 3x – 28 = 212

=> 3x = 212 + 28

Age of Mark = x = 80 years

Age of Brett = x – 18 = 80 – 18 = 62 years

Age of Carl = x – 10 = 80 – 10 = 70 years

Hence Ages of Mark , Brett and Carl are 80 years, 60 years and 70 years respectively.

Answer:

Average rate of change= 3

Step-by-step explanation:

Recall the definition of average rate of change of a function [tex]f(x)[/tex] in an interval [tex][a,b][/tex]:

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

In your case:

[tex]f(x) = 3x+4[/tex], and the interval  [tex][a,b][/tex] i  [tex][2,6][/tex], therefore:

Average rate of change = [tex]\frac{f(6)-f(2)}{6-2}=\frac{f(6)-f(2)}{4}[/tex]

Now we evaluate the function at the two requested points:

[tex]f(x)=3x+4\\f(6)=3(6)+4=18+4=22\\f(2)=3(2)+4=6+4=10[/tex], then [tex]f(6)-f(2)=22-10=12[/tex]

So finally the Average rate of change is: [tex]\frac{f(6)-f(2)}{6-2}=\frac{12}{4} =3[/tex]

Answer:

55.19 degrees

Step-by-step explanation:

See the given diagram of the triangle attached to this question.

This is a right triangle and one of its angles other than 90° is x degrees.

Now, if we assume c is the hypotenuse and a is the perpendicular, then we can write that  

[tex]\sin x = \frac{\textrm{Perpendicular}}{\textrm {Hypotenuse}} = \frac{a}{c}[/tex]

Now, it is given that a = 7.8 cm and c = 9.5 cm.

Therefore, [tex]\sin x = \frac{7.8}{9.5} = 0.821[/tex]

⇒ [tex]x = \sin^{-1} (0.821) = 55.19[/tex] degrees. (Answer)

Answer:

22

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Answer:

$2

Step-by-step explanation:

x = daylily

y = geranium

1x + 5y = 22

13x + 1y = 30

Multiply second equation by 5 and subtract the two equations.

1x + 5y = 22

- (65x + 5y = 150)

-64x = -128

x = 2

So one daylily costs 2 dollars

Answer:

x=28

Step-by-step explanation:

-7(3+6x)=9(-5x+7)

-21-42x=-45x+63

-21-42x-(-45x)=63

-21-42x+45x=63

-21+3x=63

3x=63-(-21)

3x=63+21

3x=84

x=84/3

x=28

Answer:

x=28

Step-by-step explanation:

-7(3+6x) = 9(-5x+7)

-21-42x=-45x+63

-42x=-45x+84

3x=84

x=28

Answer:

The rate of interest paid on the principal amount is 8%.

Step-by-step explanation:

Here, Principal Amount = $2,000

Time = 3 months = (3/ 12 ) Years = 0.25 years

Rate = R

Interest Amount  = $40

Now, as we know :

Simple Interest  = [tex]\frac{P \times R \times T}{100}[/tex]

⇒[tex]40  = \frac{2,000 \times R \times 0.25}{100}\\\implies R = \frac{40 \times 100}{2000 \times 0.25}   =8[/tex]

or, R = 8%

Hence, the rate of interest paid is 8%.

All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is: P(x) = x - 0.1x P(x) = 0.9x The function that gives the price, C, if only a $150 coupon is used is: C(x) = x - 150 Choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon

The final price of the computer after both discounts is T(x) = 0.9x - 150

We have been given that all computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is:

P(x) = x - 0.1x

P(x) = 0.9x  

The function that gives the price, C, if only a $150 coupon is used is:

C(x) = x - 150  

We need to choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon.

So, we have to formulate a function to combine both the discounts.

The price after 10% discount is 0.9x and the price after $150 coupon is x-150.

So, the composite function that gives the final sale price after 10% discount followed by $150 is given as follows:

Let the final price be denoted as T(x)

Therefore,

T(x) = original price - 10% discount - $150 coupon

T(x) = x - 10% of x -150

T(x) = x - 0.1x - 150

T(x) = 0.9x -150

Hence the final price of the computer after both discounts is T(x) = 0.9x-150

Answer:

A

570

Step-by-step explanation:

got it correct

Answer:

x=-1, y=-9. (-1, -9).

Step-by-step explanation:

y=3x-6

x=2x+1

----------

x-2x=1

-x=1

x=-1

--------

y=3(-1)-6=-3-6=-9

David is 16 years old.

Alisa is 4 years old.

Answer:

7,326.64

Step-by-step explanation:

20 is 1/10 times as great as 200.

A number that satisfies this equation is 26

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32 etc.

Given here the number 6,257.11 , here the digit 2 is in the 100th place hence it is equivalent to 200 and 1/10 th of 200 is 20 . Thus any number with its tenth place with digit 2 is acceptable and 26 is one such number.

Hence, the number is  26

Learn more about decimal numbers here:

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Answewell 6 divided by 2 is great than 1 its 3 if this helps?

Step-by-step explanation:

The question presents an inequality, A/6 > 1. Solving this inequality yields A > 6, meaning any number greater than 6 will satisfy this equation.

The equation given in the question is A divided by 6 is greater than 1. This can be written in mathematical terms as A/6 > 1.

To find which numbers could represent A, you have to solve this inequality. As a first step, you can multiply both sides of the inequality by 6 to isolate A. This gives us A > 6 * 1, which simplifies to A > 6.

Therefore, any number greater than 6 should satisfy the inequality A/6 > 1.

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Answer: 20%

Step-by-step explanation: if u want it on a decimal, here :0.2

hope this helps u :)

Answer:

1. See the attached figure to this answer.

2. Lines A and B are parallel to each other.

3. Line Z is the transversal.

4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.

5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5

6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.

7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)

Step-by-step explanation:

1. See the attached figure to this answer.

2. Lines A and B are parallel to each other.

3. Line Z is the transversal.

4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.

5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5

6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.

7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)

Answer:

The answers are below:

Step-by-step explanation:

Answer 1: Attachment.

Answer 2: Line A is parallel to line B.

Answer 3: Line Z is a Traversal.

Answer 4:

[tex]\angle 3 \ and \ \angle 5\ and\\ \angle 4 \ and \ \angle 6\\[/tex] are the same side interior angles.

Answer 5:

[tex]\angle 3 \ and \ \angle 6\ and\\ \angle 4 \ and \ \angle 5\\[/tex] are the alternate interior angles.

Answer 6:

[tex]\angle 3 \ and \ \angle 7\ and\\ \angle 4 \ and \ \angle 8\\[/tex][tex]\angle 6 \ and \ \angle 1\ and\\ \angle 5 \ and \ \angle 2\\[/tex] are corresponding pair angles.

Answer 7:

[tex]\angle 8 \ and \ \angle 2\ and\\ \angle 7 \ and \ \angle 1\\[/tex]are the alternate exterior pair angles.

Answer:

Angle = 135°

Supplement of the Angle = 45°

Step-by-step explanation:

The complement of an angle, say "x", would be 90 minus that angle:

90 - x

The supplement of an angle, say "y", would be 180 minus that angle:

180 - y

Since we have 1 angle, let it be "x", and that angle is 3 TIMES the SUPPLEMENT of that angle, we can write:

x = 3(180 - x)

Now, we solve for the angle x:

[tex]x = 3(180 - x)\\x = 540 - 3x\\x + 3x = 540\\4x = 540\\x = \frac{540}{4}\\x=135[/tex]

So, the angle is 135°

The supplement of the angle is  180 - 135 = 45°

The measure of the smaller angle is 45 degrees, and the larger angle, which is three times the size of the smaller one, measures 135 degrees.

The subject of this question falls under the branch of Mathematics, specifically geometry. The question deals with supplementary angles, which are pairs of angles that add up to 180 degrees.

Let's denote the smaller angle as 'x.' According to the problem, the larger angle is three times the size of the smaller, thus it is 3x. Because these are supplementary angles, they add up to form 180 degrees. So, we can create this equation: x + 3x = 180.

By simplifying and solving for x, we get: 4x = 180, hence x = 45 degrees. Therefore, the larger angle, which is three times the smaller, is 3*45 = 135 degrees.

In conclusion, the measure of the smaller angle is 45 degrees while the larger angle measures 135 degrees.

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Answer:  The second one is not clarified give us the full clarification please....

Step-by-step explanation:

Let's evaluate the two inequalities:

1. 9g - 6 > 12g + 1

Subtracting 9g from both sides gives:

-6 > 3g + 1

Subtracting 1 from both sides gives:

-7 > 3g

Dividing both sides by -3 (and flipping the inequality sign) gives:

g < 7/3

1. 4 > + 8

This inequality is not correct, as it is missing a term on the right-hand side. It should be something like:

4 > x + 8

Subtracting 8 from both sides gives:

-4 > x

Without more information, we can't determine the value of x.

Please clarify or provide more context for the second inequality!

Answer:

The next answer is 3 hours

Step-by-step explanation:

I just did it on edge 2021 :)

Answer:

the first answer is c

Step-by-step explanation:

Answer:

h(x) = 10x

Step-by-step explanation:

given:

f(x) = 3x-1 and g(x)= 4x-2

h(x) = 2 f(x) + g(x)

= 2 (3x+1) + (4x-2)

= 6x + 2 + 4x - 2

= 10x

The question revolves around combining functions in mathematics. To solve for h(x) when h(x) is equal to 2f(x) + g(x), we substitute f(x) and g(x) values into the equation for h(x) and simplify the resulting expression. Our calculated function h(x) = 10x - 4.

This is a question about combining function operations. We have been given two functions f(x) = 3x-1 and g(x) = 4x-2, and asked to find h(x) = 2f(x) + g(x).

To solve it, we must substitute f(x) and g(x) into our equation for h(x):

So, the function h(x) when h(x) is = 2f(x) + g(x) is h(x) = 10x - 4.

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Answer:

1

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Length: a

Width: b

ab = 54

a = b + 3

=> (b + 3)b = 54

=> b^2 + 3b = 54

=> b^2 + 3b - 54= 0

=> (b - 6)(b + 9)

=> b = 6 AND b = -9

Rectangular's sides > 0 => b = 6

Hope it's helpful :)