Split the fraction using partial fraction decomposition;

Answer:

  x = 0; y = -6; z = 1

Step-by-step explanation:

You want to find the solution to the system of equations ...

This set of equations is conveniently solved using the matrix row-reduction features of a scientific or graphing calculator, spreadsheet, or any of a number of apps or on-line calculators.

The attachment shows the solution to be ...

  (x, y, z) = (0, -6, 1)

__

Additional comment

Solving a system of three or more equations "by hand" often can be done by an ad hoc process. It can be done in systematic fashion using Gauss-Jordan reduction techniques, but that often gets messy. Similarly, Cramer's Rule can be used, but that math tends to involve more arithmetic operations than are really necessary.

Adding the first equation to the other two eliminates the y-variable and reduces the system to two equations in two unknowns.

  (9x +y -3z) +(10x -y +2z) = (-9) +(8) . . . . adding [1] and [2]

  19x -z = -1 . . . . simplified

  (9x +y -3z) +(-10x -y +4z) = (-9) +(10) . . . . adding [1] and [3]

  -x +z = 1 . . . . simplified

At this point, we could graph the two equations, or we can proceed algebraically.

Adding these two equations gives ...

  (19x -z) +(-x +z) = (-1) +(1)

  18x = 0   ⇒   x = 0

Using the second of the reduced equations, we find ...

 -x +z = 1

  0 +z = 1   ⇒   z = 1

And using the second of the original equations, gives us ...

  10(0) -y +2(1) = 8

  -y = 6 . . . . . subtract 2

  y = -6 . . . . multiply by -1

Then the solution is (x, y, z) = (0, -6, 1), as above.

Answer:

The function has a minimum of -1 at x = 3

The function is increasing on the interval: (3,∞)

The function is decreasing on the interval (-∞,3)

Step-by-step explanation:

Since our parabola opens upwards on the graph, the function has a minimum.

The minimum is the lowest x-value and y-value in the function.

From left to right, the function is moving downwards (decreasing) from x = -∞ to x = 3.

From left to right, the function is moving upwards (increasing) from x = 3 to x = ∞

The amount invested in the account that paid 4% interest is $2,600

The amount invested in the account that paid 13% interest is $1,500.

a + b = 4100 equation 1

0.04a + 0.13b = 299 equation 2

Where:

a = amount invested in the account that paid 4% interest

b = amount invested in the account that paid 13% interest

The first step is to multiply equation 1 by 0,04

0.04a + 0.04b  = 164 equation 3

Subtract equation 3 from equation 2

0.09b = 135

b = 135 / 0.09

b = $1500

a = 4100 - 1500 = $2,600

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Answer:

true

Step-by-step explanation:

Answer: true

step by step explanation:

Answer:

w = -0.8

sum = 0

Step-by-step explanation:

An additive inverse is when two numbers add up to 0. 0.8+ (-0.8) = 0.

The answer will be 0. 10 >  0. 01 . Option B

Given the values as;

Turn the values into proper fractions

a. 0. 10 = 10/ 100

Reduce to simpler terms

= 10/ 100

= 1/ 10

b. 0. 01 = 1/ 100

a = 1/ 100

b = 1/ 100

This means that both decimals are not of  equal proportion and thus a is greater than (>) b

Thus, the answer will be 0. 10 >  0. 01 . Option B

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that is impossible to solve because both sides do not equal eachother

Answer:

I think 3.

Step-by-step explanation:

3*4=12 near 10

The equation that represents how many pages Shinji reads is P(n) = 25n

The given parameters are:

25 pages = 1 night

Multiply both sides by n

So, we have:

25 * n = 1 * n nights

Express as a function

25 * n = P(n)

Rewrite as

P(n) = 25n

Hence, the equation that represents how many pages Shinji reads is P(n) = 25n

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Answer:

Step-by-step explanation:

the salesperson will be paid $ 844.2 for the one pickup they sell for $ 18,760 as 4.5 % commission is theirs.

We are given that the selling price of a pick up item is given as:

Selling price = $ 18,760

Now, it is also given that, on every sale, the salesperson gain a commission of 4.5 % as their pay.

The money they get paid for one pick up that they sell will be calculated by finding the percentage. So, we get that:

Money = 4.5 % of $ 18,760

Money = 4.5 / 100 × $ 18,760

Money = 0.045 × $ 18,760

Money =  $ 844.2

Therefore, we get that, the salesperson will be paid $ 844.2 for the one pickup they sell for $ 18,760 as 4.5 % commission is theirs.

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Answer:

[tex]f'(a)=\frac{1}{2a^{3/2}+20a+50\sqrt{a}}[/tex]

Step-by-step explanation:

[tex]f'(x)=\frac{\frac{d}{dx} (\sqrt{x}+5)(1)-(\sqrt{x}+5)\frac{d}{dx}(1)}{(\sqrt{x}+5)^2} \\ \\ =\frac{\frac{1}{2\sqrt{x}}}{(\sqrt{x}+5)^2} \\ \\ =\frac{\frac{1}{2\sqrt{x}}}{x+10\sqrt{x}+25} \\ \\ =\frac{1}{2x^{3/2}+20x+50\sqrt{x}} \\ \\ \therefore f'(a)=\frac{1}{2a^{3/2}+20a+50\sqrt{a}}[/tex]

Answer:

what is the question?

()()()()()()()()()()()()()()

If one fifth times w equals negative one eight then w = -5/8

What is Rational numbers?

A rational number is any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero. In other words, a rational number can be expressed as p/q, where p and q are both integers and q ≠ 0.

given that one fifth times w equals negative one eight

we have to find the value of w

one fifth = 1/5

one fifth times w = (1/5)* w

negative one eighth = - 1/8

now according to the question

one fifth times w equals negative one eight

(1/5) *w =  -1/8

now solve the equation , we get

w= (5) * (-1/8)

  = -5/8

Hence ,if  one fifth times w equals negative one eight then w = -5/8

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From the two column proof below to prove that ABCD is a rhombus, the missing reason is reason 6; C. Opposite sides of a parallelogram are congruent.

Given: ABCD is a parallelogram.

The two column proof that ABCD is a rhombus is;

Statement 1;  ABCD is a parallelogram. AD = AB and AC bisects ∠BCD and ∠BAD

Reason 1; Given

Statement 2; ∠BCA ≅ ∠DCA

Reason 2; Definition of an angle bisector

Statement 3; AC ≅ AC

Reason 3; Reflexive property of congruence

Statement 4; ΔABC ≅ ΔADC

Reason 4; Angle Side Angle Congruence Postulate

Statement 5; AB ≅ AD, BC ≅ DC

Reason 5; Corresponding parts of congruent triangles are equal.

Statement 6; AB ≅ CD, BC ≅ AD

Reason 6; Opposite sides of the parallelogram are congruent

Statement 7; AB ≅ AD, BC ≅ CD

Reason 7; Transitive Property of Congruence

Statement 8;  ABCD is a rhombus

Reason 8: Definition of rhombus

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Not sure if I'm right, but is
it RL- lol

Step-by-step explanation:

21/2=12/3

y=10.5*4

Sana nakatulong:)

Answer:

C -

[tex]5 \frac{6}{7} [/tex]

At 17:30 the shipment arrive in Dallas (GMT -6) , if it departs Edmonton (GMT -7) at 14:45 p.m. on Thursday.

The time difference of two zone is -7-(-6) = -1

The shipment departs at 14:45 pm

flight took time = 3:45 min

adding the time = 14:45 + 3:45

                           = 18:30

So it arrived at Dallas at 18:30 according to Edmonton (GMT -7)

It arrived in Dallas according to Dallas (GMT -6) = 18:30 - 1 hour

                                                                                = 17:30

A time zone is a region where everyone adheres to the same standard time for social, business, and legal activities. Because it is simpler for regions that communicate often to maintain the same time, time zones frequently follow national borders and their subdivisions rather than strictly following longitude.

Coordinated Universal Time (UTC), which ranges from UTC12:00 to UTC+14:00, is used to determine all time zones. Most zones have full hour offsets, but some, like those in India, South Australia, and Nepal, have additional offsets of 30 or 45 minutes.

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The measurement of the fold leaflet shorter dimension stays same but the longer side becomes 99 mm.

In mathematics, dimensions are the measurements of the size or distance between an object, region, or space in one direction. In layman's terms, it refers to the measurement of something's length, width, and height.

Dimensions are commonly expressed as follows:

A leaflet is mainly folded into thirds just on long side, so the short side remains unchanged while the long dimension has become 1/3, or  297/3 = 99 mm.

The final dimensions are

210 mm × 99 mm

Therefore, the measurement of the sorter side of the fold leaflet remains same but longer side becomes 99 mm.

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The complete question is-

Another job is advertising leaflets printed on sheets of A4 paper (210 x 297 mm).

The sheets are then folded into thirds as shown.

What are the measurements in millimetres of each folded leaflet?

the percentage of the students travel over seven miles to school by train is 9 %.

Let the total number of students be represented by variable x

now, 37 % of them travel by train.

So, we get that:

By train = 37 % of x

By train = 37 / 100 (x)

By train = 0.37 x

Now, 24 % of them lives 7 miles away from the school.

So, 7 miles away = 24 % of 0.37 x

= 24 / 100 ( 0.37 x )

= 0.24 ( 0.37 x)

= 0.09 x

In percentage:

= 9 %

Therefore, we get that, the percentage of the students travel over seven miles to school by train is 9 %.

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The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.

It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Fractions simply means, numbers that are not whole.

If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.

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Answer:

When the denominator of a fraction is equal to 1 and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Step-by-step explanation:

I took a 2.12 math quiz in K12 and got it 100% Correct! Yes!

The stoplights will change color after 720 seconds. at the same time again.

Given: Stoplights A and B alternate between changing colors every 45 and 80 seconds, respectively.

One copy of each of the unique components and the common factor make up the Least Common Multiple (LCM).

The least common multiple of 45 and 80 is the amount of seconds before they change color simultaneously once more.

Since 80 = 5 x 2 x 2 x 2 and 45 = 5 x 3 x 3 respectively

A least common multiple of 45 and 80 is equal to 2x2x2x2x3x3x5 = 720.

Hence, the color of the spotlight will change after 720 seconds. at the same time again.

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The missing number in the equation is 6.

Given,

The sum of 23/6 and five times a number = 13/6 subtracted from six times the number.

We can take the number as x.

Now, the equation is:

23/6 + 5x = 6x - 13/6

Cross multiply both sides:

(23 + (5x × 6)) / 6 = ((6x × 6) - 13) / 6

We get,

(23 + 30x) / 6 = (36x - 13) / 6

Cancel 6 from both sides:

Then,

23 + 30x = 36x - 13

Add 13 to both sides:

23 + 13 + 30x = 36x - 13 + 13

We get,

36 + 30x = 36x

Add -30x to both sides:

36 + 30x - 30x = 36x - 30x

Then,

36 = 6x

x = 36/6 = 6.

That is, the missing number in the equation is 6.

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The value of the composite function (mn)(-3) is 9

The given parameters are:

m(x) = x

n(x) = -3

The composite function is given as

(mn)(x)

The above composite function is calculated as

(mn)(x) = m(x) * n(x)

Substitute -3 for x in the above function

So, the above function becomes

(mn)(-3) = m(-3) * n(-3)

So, the above function becomes

(mn)(-3) = -3 *-3

Evaluate the product in the above equation

So, we have

(mn)(-3) = 9

Hence, the value of the composite function (mn)(-3) is 9

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Complete question

If m(x) = x and n(x) = -3, calculate ( m n ) (x) for x = −3

Answer: y=-4x+7

Step-by-step explanation:

(1, 3) and (-1, 11)

m=(y2-y1)/(x2-x1) ==> Slope formula

m=(11-3)/(-1-1)

m=8/(-2)

m=-4

y=mx+b

3=-4(1)+b

3=-4+b

b=7

y=-4x+7

Thus, (x) = 3x + 18 and g(x)=x-6 are not inverses of each other.

Two function are inverse if they do undo or cancel each other, which means

f and g are inverse if

f(g(x)) = x and g(f(x)) = x

Here, f(x) = 3x + 18 and g(x)=x-6

Lets check by substituting the values in the formula

⇒ f(g(x))

⇒ f(x-6)

⇒ (3x + 18) - 6

⇒ 3x - 12

⇒ x = 4

g(f(x))

⇒ g(3x + 18)

⇒ 3(x-6) + 18

⇒ 3x - 18 + 18

⇒ 3x

⇒ x = 1/3

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

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The cost of a ride for an individual person will be $10.5

It is given that Mel and 5 friends went to ride which makes the Total number of people for the Ride will be 6. Also, Four of them rented Helmets for the rides each helmet cost $3. It is also given that the total cost of helmets and rides is $75. From this we get :

Total people = 6, Helmet cost = 4*3 = $12, and Total cost = $75

Taking the cost of a ride as 'x' we get the equation representing this statement:  

              => 4*3 + 6x = 75  =>  6x = 63

              =>  x = 10.5

We get value of x = $75.

Hence, we get the cost of an individual ride $75.

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Answer:

It traveled south for 22 kilometers.

Step-by-step explanation:

Think of it as a rectangle. Two sides are 50 kilometers (east and west), and the other two sides are 22 kilometers (north and south).