Find the product with the exponent in simplest
form. Then, identify the values of x and y.
6^1/3x6^1/4=6^x/y
X= ,y=

60% of Julio's number was Bill"s number

percentage, a relative value indicating hundredth parts of any quantity.

Given,

bill and julio each thought of a whole number between 1 and 20.

Bill"s number was 15

Julio's number was 6

We need to find what percent of Julio's number was Bill"s number

Original number minus new number by original number

(15-61)/15

9/15

0.6

Now we have multiply with 100 as it is a hundredth part.

0.6×100=60

Hence, 60% of Julio's number was Bill"s number

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1. The Millers pay $675 monthly to repay their mortgage loan.

2. The average monthly expenditure for the telephone for Millers is $41.00.

3. The Millers' average monthly expenditure for transportation costs is $592.46.

4. The information is not available for determining the amount the Millers' monthly savings.

The average cost is the mean, which represents the quotient of the total costs and the number of months.

We compute the average cost using the division operation.

July $37.85

August $47.29

September $37.85

Total costs = $122.99

Average cost = $41.00 ($122.99 ÷ 3)

                         July           August       September

Gasoline        $118.60       $123.36        $96.74          $338.70

Car loan         278.50         278.50        278.50           835.50

Car repair       126.36         278.50         198.31            603.17

Total costs  $523.46      $680.36      $573.55       $1,777.37

Average monthly transportation cost = $592.46 ($1,777.37 ÷ 3)

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Answer:

7 Years

Step-by-step explanation:

1 Year: 6,18

2 Years: 7,17

3 Years: 8,16

4 Years: 9,15

5 Years: 10,14

6 Years: 11,13

7 Years: 12,12

Answer:

  C = (5, 4)

Step-by-step explanation:

You want the coordinates of point C, located 3/4 of the way from A(-4, -2) to B(8, 6).

That point is ...

  C = A +3/4(B -A)

  C = (-4, -2) + (3/4)((8, 6) -(-4, -2))

  C = (-4, -2) + (3/4)(8+4, 6+2) = (-4, -2) + (3/4)(12, 8) = (-4, -2) +(9, 6)

  C = (-4 +9, -2 +6)

  C = (5, 4)

__

Additional comment

Equivalently,

  C = (3B +A)/4 = (3(8, 6) +(-4, -2))/4 = (24 -4, 18 -2)/4 = (5, 4)

The method shown above may be more intuitive. The formula shown here is a result of simplifying the one used above.

When computing the weighted average of the coordinates, the nearest point (B) gets the higher weight (3/4).

The required lines are parallel to x-axis and they are horizontal lines.So option (B) is correct.

Given two points  on a line, we can compose a condition for that line by finding the slant between those places, then, at that point, settling for the y-intercept in the slope-intercept equation y=mx+b.

a) y =9

It is equation of line parallel to x-axis.

b) A line passing through the points (0, 1) and (1, 1).

Using two point formula,

(y - 1) = [tex]\frac{1-1}{1-0}[/tex](x - 0)

y = 1

So, it is also a line parallel to x-axis.

Thus, both the lines are parallel to x- axis or can say horizontal lines.

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The solution to the equation in surd form is x = 5 ± √41/2

From the question, we have the following parameters that can be used in our computation:

2/x + 5/(x+2) = 1

Take the LCM

So, we have the following equation

(2(x + 2) + 5x)/x(x + 2) = 1

So, we have

(2(x + 2) + 5x) = x(x + 2)

Open the brackets

2x + 4 + 5x = x² + 2x

Evaluate the like terms

x² - 5x - 4 = 0

Using a quadratic formula, we have

x = 5 ± √[(-5)² - 4 * 1 * -4]/2 * 1

So, we have

x = 5 ± √41/2

Hence, the solution is x = 5 ± √41/2

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Answer: $552

Step-by-step explanation:

Let x be the number of year and y is the total amount

We have the equation

y= 6.5x + 500

Then put 8 in for the x

y= 6.5(8) + 500

y= $552

(-∞, ∞) is the domain of y=-0.25x² and (−∞,0] is range.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is y=-0.25x²

y equal to minus zero point two five times of x square.

We need to find the domain and range of the function.

Let us find few points of x and y.

x    0    1            2           3              4

y    0    -0.25    -1        -0.5625     -4

In the given attachment the graph is given.

The domain is:

{x∣x is R} or (-∞, ∞)

The range is {x∣x≤0} or (−∞,0]

Hence, the domain of y=-0.25x² is (-∞, ∞) and range is (−∞,0].

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Answer:

(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab)

Which of the following shows the sum of the polynomials rewritten with like terms grouped together?

[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)

[3a2 + (–3a2)] + (–5ab + 2b2) + (b2 + 8ab)

[3a2 + 3a2] + (5ab + 8ab) + (b2 + 2b2)

[3a2 + 3a2] + (5ab + 2b2) + (b2 + 8ab)

The answer is A.

Step-by-step explanation:

The solution for the system of equations would be x = 2 and y = 3.

The general equation of a straight line is -

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the graph of y = 5 - x.

Refer to the image of the graph attached. It shows the graph of -

and

The common point of intersection will be the solution for the system :

Therefore, the solution is x = 2 and y = 3.

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The ordered pair that represents the point (- 6, - 10) after a reflection over the y-axis will be;

⇒ (6, - 10)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The point is,

⇒ (- 6, - 10)

Now,

Since, The point is,

⇒ (- 6, - 10)

We know that;

The rule for the reflection over the y-axis is;

⇒ (x, y) → (- x, y)

So, The ordered pair that represents the point (- 6, - 10) after a reflection over the y-axis will be;

⇒ (- (- 6), - 10)

⇒ (6, - 10)

Thus, The ordered pair that represents the point (- 6, - 10) after a reflection over the y-axis will be;

⇒ (6, - 10)

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The value of the angle x in the triangle is; x = 70°

Looking at the given image, it is clear that both triangles are similar triangles. This is because we see that after the duplicate, 2 sides apiece are equal.

Thus, the third angle bordering the center of the triangle with one angle as 15° is;

y = 180 - (15 + 20)

Since sum of angles in a triangle equals 180 degrees.

y = 180 - 35

y = 145°

Similarly,

z = 180 - (20 + 15)

z = 180 - 35

z = 145°

Now, sum of angles at a point is 360 degrees. Thus;

x = 360 - (145 - 145)

x = 70°

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The number of words he still need to write in one of his writing sessions would be = 95 minutes.

A graduate is an individual that has completed studies in an institution for a number of years and is being issued a certificate afterwards.

The number of words committed for a day by Nick = 500 words.

He writes 120 words = 30 mins

The total number of words remaining = 500 - 120 = 380 words.

Therefore the time it will take to finish the remaining 380 words in the day = X mins.

If 30 mins= 120 words

X mins = 380 words.

Make X mins the subject of formula;

X mins = 380× 30/120

X mins = 11,400/120

X mins= 95 minutes.

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The Taylor series of the function is the sum of derivatives of the function up to infinite.

The Taylor series for a function f(x) centered at a is given by:

f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

To find the Taylor series for f(x) = In(x) centered at a = In(9), we can plug in the values into the formula above:

In(x) = In(9) + In'(9)(x-In(9)) + In''(9)(x-In(9))^2/2! + In'''(9)(x-In(9))^3/3! + ...

= In(9) + (1/9)(x-In(9)) - (1/81)(x-In(9))^2 + (1/729)(x-In(9))^3 + ...

This is the Taylor series for f(x) = In(x) centered at a = In(9).

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The solutions of system of equation are x = 1 and y =-4.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given that the system of equation;

-5x-4y = -17 , (equation 1)

-3x-y =  1, (equation 2)

First step is to write both equation in the standard form, both of these above equations are in standard form.

Now we will make the coefficients of variable y opposite, for that we multiply -4 to the equation 2.

12x+4y = -4

Now, in equation 2 coefficients of variable y are opposite.

Next step is combining the both of the equation;

-5x + 12x = -17 -4

7x = -21

x = -3

Substitute the value of x into equation 2,

-3x-y = 1

-3 (-3) -y = 1

-y = 1-9

y = 8

Therefore, the solutions of system of equation, x = -3 and y = 8.

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Answer: 37, 15, 12, 0, -6, -8, -23

Step-by-step explanation:

So, the higher the negative number, the lower the value is. Hope this helps!

The number of days required to complete his task is 9 days.

What is a graph?

The graph of a relation R is the set of all points (x, y) in a coordinate plane such that x is related to y through the relation R.

Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day.

So he will complete 4 assignments each day and he has to complete the 36 overdue assignments.

The number of days required to do this = 36/4

                                                                  = 9 days.

Hence, the number of days required to complete his task is 9 days. and this relation can be expressed on the graph as

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Answer:

There is around 30 meter in 100 feet

Step-by-step explantion I did it mentally.

The value of [tex]f_{x}[/tex](3,2)≈12.2, [tex]f_{x}[/tex](3,2.2)≈16.8, [tex]f_{x}[/tex](3,2)≈23.25

This problem aims to find the values of a function having alternate independent variables.

A-

[tex]f_{x}(3,2) f_{x} (x,y)=lim_{h-0} \frac{(3+0.5,2)-f(3,2)}{0.5}[/tex]    considering h =±0.5

Solving for h=0.5

⇒[tex]\frac{f(3.5,2)-f(3,2)}{0.5}[/tex]

Using the table to plug in the values of the function: 22.4-17.5/0.5=9.8

Now, solving for h=-0.5

⇒[tex]\frac{f(3.5,2)-f(3,2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 22.4-17.5/(-0.5)=14.6

Taking the average of both ±0.5 answers for the final answer of f(3,2)

[tex]f_{x}(3,2)=\frac{9.8+14.6}{2} \\or, f_{x}(3,2)=12.2[/tex]

B-

[tex]f_{x}(3,2.2)=lim_{h-0} \frac{(3+0.5,2.2)-f(3,2.2)}{0.5}[/tex]    considering h =±0.5

Solving for h=0.5

⇒[tex]\frac{f(3.5,2.2)-f(3,2.2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 26.1-15.9/0.5=20.4

Now, solving for h=-0.5

⇒[tex]\frac{f(2.5,2.2)-f(3,2.2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 9.3-15.9/(-0.5)=13.2

Taking the average of both ±0.5 answers for the final answer of f(3,2.2)

[tex]f_{x}(3,2.2)=\frac{20.4+13.2}{2} \\or, f_{x}(3,2.2)=16.8[/tex]

C-

[tex]f_{xy} (3,2)=lim_{h-0} \frac{f_{x}(3,2+h)-f_{x} (3,2) }{h} \\[/tex]     considering h =±0.2

Solving for h=0.2

⇒[tex]\frac{f_{x} (3,2.2)-f_{x} (3,2)}{0.2}[/tex]

Plugging in the answers from A and B: 16.8-12.2/0.2= 23

Now solving for h= -0.2

⇒[tex]\frac{f_{x} (3,1.8)-f_{x} (3,2)}{-0.2}[/tex]

Plugging in the values: 7.5-12.2/-0.2= 23.5

Taking an average of h=±0.2 answers to find the final answer:

[tex]f_{x}(3,2)=\frac{23+23.5}{2} \\or, f_{x}(3,2)=23.25[/tex]

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The result in the form of a mixed number if we multiply the numerator of the complex fraction in part D by the reciprocal that you found in part E is  8[tex]\frac{1}{4}[/tex].

A whole number and a legal fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it. An integer (whole number) plus a correct fraction together make up a mixed number, also known as a mixed fraction (a fraction whose numerator is less than its denominator).

Pretzels, peanuts, Cheerios, and of course rice and corn Chex are all included in this mix, which is why it is called a mix. It is possible for a number to contain both an integer and a fraction. As a result of combining these two sorts of numbers, they are known as "mixed numbers."

PART D:

(33/8)/(11/4)

Reciprocal of PART E is:

11/4

Therefore, multiplying it with PART D, we get:

=((33/8)/(11/4))×(11/4)

=(33/8)×(4/11)×(11/4)

=33/8

=8[tex]\frac{1}{4}[/tex]

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The true statement about exponential smoothing forecasting model is option (d) The exponential smoothing technique is most useful when short-term forecasts are needed.

Exponent:

In math, exponent tells a number says how many times to use that number in a multiplication.

Given,

Here we need to find the statements about exponential smoothing forecasting model is true.

In order to find the true statement we have to know the definition of exponential smoothing forecasting model.

Exponential smoothing forecasting model also known as ETS model is a family of forecasting models.

And it is used as weighted averages of past observations to forecast new values.

And the idea is to give more importance to recent values in the series. Therefore, as observations get older in time, the importance of these values get exponentially smaller.

Based on these explanation we have identified that option (d) is correct.

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1. [tex]\overline{AD}[/tex] bisects [tex]\angle A[/tex] (given)

2. [tex]\angle CAD \cong \angle DAB[/tex] (definition of angle bisector)

3. [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

4. [tex] \angle ADC[/tex] is a right angle (given)

5. [tex]\angle ADC[/tex] and [tex]\angle ADB[/tex] are supplementary (angles that form a linear pair are supplementary)

6. [tex]\angle ADB[/tex] is a right angle (an angle supplementary to a right angle is a right angle)

7. [tex]\angle ADC \cong \angle ADB[/tex] (all right angles are congruent)

8. [tex]\triangle ADB \cong \triangle ADC[/tex] (ASA)

ΔADB ≅ ΔADC by ASA congruence rule as they have angle- side- angle ratio are same.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved. "≅" is the congruence symbol.

When two figures resemble one another in terms of size and shape, this is what mathematics refers to as congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent.

Given: AD bisect Angle A          

That means ∠BAD = ∠CAD

Proof:   In ΔADB and ΔADC              

∠ADB = ∠ADC (each right angle)

AD = AD (Common)

∠BAD = ∠CAD (Given)              

By ASA Congruence Rule  

ΔADB and ΔADC are Congruent  

Hence Proved.

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Answer:

x(x-2)

Step-by-step explanation:

The simplified form of the expression 2/5 + 5/20 is 13/20

The expression is

2/5 + 5/20

The expression is the mathematical statement that consist of different variables, numbers and mathematical operator. The mathematical operators are addition, subtraction, division and multiplication

The expression is

2/5 + 5/20

Cross multiply the terms in the expression

2/5 + 5/20 = (2×20) + (5×5) / (5 × 20)

Multiply the terms in the numerator and denominator

= (40 + 25) / 100

Add the terms in the numerator

= 65 /100

Simplify the terms by dividing 5 on the both numerator and denominator

= 13/20

Therefore, the simplified form is 13/20

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Answer:

Not 100% sure but I believe the answer is 110592.

Step-by-step explanation:

48^3= 110592

Answer:

12 and 24 gcf = 4

so the only choice left is

(H) 4x²y

(I) 4xy

12x²y³ + 20x³y = lowest of x is x² and y is y

then its

(H) 4x²y

Answer:

See below

Step-by-step explanation:

1).  A = k / (B^3)   <==== this becomes   A = 512/(B^3)  when you use the                                                                               answer from 2).      (below)

2).     When A = 64  and B = 2 :

           64 = k / (2^3)

              64 = k / 8

                   k = 64*8 = 512

Answer:

x = 1 1/2

Step-by-step explanation:

1/3 x + 1/4 = 3/4

Solving for x

Subtract 1/4 from each side

1/3 x + 1/4 -1/4 = 3/4-1/4

1/3 x = 2/4

Simplify

1/3x = 1/2

Multiply each side by 3

1/3 x * 3 = 1/2 * 3

x = 3/2

Changing to a mixed number

x = 1 1/2

Answer:

[tex]\sf \frac{3}{2} = 1 \frac{1}{2} \\ [/tex]

Step-by-step explanation:

[tex] \sf \frac{1x}{3} + \frac{1}{4} = \frac{3}{4} \\ [/tex]

To solve easily, multiply the whole equation by it's LCM ( LCM of 3 & 4 is 12 ).

[tex] \sf12 \times ( \sf \frac{1x}{3} + \frac{1}{4} = \frac{3}{4} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \\ \\ \sf \frac{1x}{3} \times 12 + \frac{1}{4} \times 12= \frac{3}{4} \times 12\\ \\ \sf \sf \frac{12x}{3} + \frac{12}{4} = \frac{36}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf4x + 3 = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

And now solve for x.

First, subtract 3 from both sides.

[tex] \sf4x = 9 - 3 \\ \sf4x = 6[/tex]

Divide both sides by 4.

[tex] \sf \: x = \frac{6}{4} \\ [/tex]

To write the fraction in its simplest form, divide both the numerator and denominator by 2.

[tex] \sf \frac{3}{2} = 1 \frac{1}{2} \\ [/tex]

Equation which represents the m(x) and n(x) are inverse functions given by Option B.

3[7x/(3 - x)] / [ ( 7x / 3 - x ) + 7 ] =7[3x/(x + 7)] / [ 3 - ( 3x / x + 7 )  ] =x.

As given in the question,

Given functions are

m(x) = 3x /(x+7) and n(x) = 7x/ (3 - x)

Let y = m(x)

y = 3x /(x+7)

Now replace x by y and vice versa:

x = 3y / (y + 7) __(1)

Now substitute (1) in n(x)

n(x) = 7x/ (3 - x)

      = 7[3y / (y + 7)] / [ 3 - 3y / (y + 7) ]  __(3)

      = y

Now n(x) = y

y = 7x/ (3 - x)

Replace x by y and vice versa

x = 7y /( 3 - y )  __(2)

Now , substitute (2) in m(x)

m(x) = 3x /(x+7)

       = 3[7y /( 3 - y ) ] / [ 7y /( 3 - y )  + 7 ]  __(4)

       = y

Replace y by x in (3) and (4)

Equation representing m(x) and n(x)  as inverse functions:

3[7x/(3 - x)] / [ ( 7x / 3 - x ) + 7 ] =7[3x/(x + 7)] / [ 3 - ( 3x / x + 7 )  ] =x.

Therefore, equation representing m(x) and n(x) as inverse function is given by :

Option B. 3[7x/(3 - x)] / [( 7x / 3 - x ) + 7] =7[3x/(x + 7)] /[3 - ( 3x / x + 7 )] =x.

The complete question is :

Marin write the functions m(x) = 3x /(x+7) and n(x) = 7x/ (3 - x).

Which equation must be true for m(x) and n(x) to be inverse functions?.

Options are shown in attachment.

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