What is the inverse?

 In 14x¹³ ,  x¹³ is exponent with base x , power 13 and 14 as coefficient

Exponent is a method of expressing large numbers in terms of powers.

It means when a number is multiplied by itself many times we can express expressed it in exponent form .

The symbol used for representing the exponent is "^" .This symbol is known as carrot

Base is that number that is being multiplied.

tells how many times that number is multiplied.

In the given question,

14x¹³

Base = x

because x is multiplied 13 times

so, Power = 13

Exponent = x¹³

Coefficient = 14

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a) The lower bound of the length of the line is 12.12

b) The upper bound of the length of the line is 12.25

What is a lower bound?

The least value that would round up to the predicted value is the lower bound. The smallest value that would round up to the following anticipated value is the upper bound.

What is an upper bound?

A value that is greater than or equal to every element of a set of data.

What is the difference between the lower and upper bound?

An element of K that is greater than or equal to each element of S is known in mathematics as an upper bound or majorant of the subset S of some preordered set (K, ), especially in order theory. In addition, each element of K that is less than or equal to each element of S is characterized as a lower bound or minorant of S.

Here,

We have to find the lower bound and upper bound of 12.2

We get a lower bound = 12.12

and upper bound = 12.25

Hence, a) The lower bound of the length of the line is 12.12

b) The upper bound of the length of the line is 12.25

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A statement of the equation could be as; "John bought y oranges which are 5 times the apples more than 3".

An equation is an expression that shows the relationship between two or more numbers and variables.

The information provided is that the real-world situation in which opposite quantities combine to make zero.

We have been given an equation as y = 5x + 3

A statement of equation could be as; "John bought y oranges which are 5 times the apples more than 3".

If the number of apple x is 6 then;

y = 5x + 3

y = 5(6) + 3

y = 33

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The solution for the -

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

is (1, 1)

AND

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

is (0, 1)

The general equation of a straight line is -

[y] = [m]x + [c]

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 following set of equations

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graphs that the solution is given for first set is of simultaneous equations as (1, 1) and the second set of simultaneous equations as (0, 1)

Refer to the two graphs attached.

Therefore, the solution for the -

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

is

(1, 1)

AND

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

is

(0, 1)

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Answer:

n = 49

Step-by-step explanation:

49 has a factor of -7 which can also add up to -14

Eg : -7(-7) = 49, -7 + (-7) = -14

49

x²-14x+49=(x-7)²

An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial.

It is of the form (ax2 + bx + c).

Real numbers a, b, and c are present here, and a ≠0.

The given equation is x2 + 14x + c

To find the value of c

We can take half of the linear coefficient and square it

14/2 = 7

72 = 49

Therefore, the value of c is 49.

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Answer:

last one: 20

Step-by-step explanation:

4 divided by 5 is 0.8

so is 20 divided by 25

The coordinates of X’ is (4,12)

Dilation means changing the size of an object without changing its shape.

Given that, Line segment XY is located at X(2, 6) and Y(4,8). If the line segments are dilated by a scale factor of 2 with a centre of dilation of

T(0,0).

The rule for a figure dilated by a scale factor k with a centre of dilation (a, b) is;

(x, y) → (k(x-a) + a, k(y-b) + b)

The line segment is dilated by a scale factor of 2 with a centre of dilation of T(0,0)

According to the rule,

(x, y) → (2(x-0) + 0, 2(y-0) + 0)

(x, y) → 2x + 2y

The coordinates of X' are (2, 6)

X(2, 6) → (2*2, 2*6)

X(2, 6) → (4, 12)

Hence, The coordinates of X’ is (4,12)

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If the given quadrilateral is a parallelogram, then the value of x = 8  and the value of y = 9

The given quadrilateral is a parallelogram.

Then the opposite side of of the parallelogram will be equal

Then the equation will be

4x - 17 = 2x - 1

4x - 2x = -1 + 17

2x = 16

x = 16/2

Divide the terms

x = 8

Similarly given angles will be equal

3y + 5 = 5y - 13

5y - 3y = 5 + 13

2y = 18

y = 18 / 2

Divide the terms

y = 9

Hence, the if the given quadrilateral is a parallelogram, then the value of x = 8  and the value of y = 9

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The critical t-distribution values converge to the critical z-distribution values as a particular family of t-distributions that t2 has 2 degrees of freedom (df) and t9 has 9 degrees of freedom.

The maximum number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the total number of items in the data sample. Degrees of freedom, also known as numerical freedom of variance, are the maximum number of logically independent values that can be present in sample data. Degrees of freedom are frequently brought up when discussing various mathematical hypothesis testing techniques, like the chi-square.

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Answer:draw a vertical line on the 4th line on the x axis(the horizontal one)

Step-by-step explanation:

If the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol. The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages.

It is given that, the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue.

If blue, then 60%. 2/5 are red and 1/3 are blue. Two redfish and three bluefish are present.

Thus, if the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

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First derivative of the given function √2-3x  using first principle method is equal to -3.

As given in the question,

Given function is equal to :

f(x) = √2-3x

First derivative of the given function √2-3x  using first principle method is given by:

    f'(x) = [tex]\lim_{h \to \ 0}[/tex] [ (f(x +h) -f(x) ) / h]

Substitute the value of the function we get,

⇒f'(x) =  [tex]\lim_{h \to \ 0}[/tex] [ √2 -3(x +h ) - (√2 -3x) ] /h

⇒f'(x) =  [tex]\lim_{h \to \ 0}[/tex] [ √2 -3x -3h -√2 +3 x]/ h

⇒f'(x) =  [tex]\lim_{h \to \ 0}[/tex] (-3)

⇒f'(x) = -3

Therefore, first derivative of the given function √2-3x  using first principle method is equal to -3.

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25 g of  5% ointment and the pure ingredient are needed to compound the prescription.

A ratio is a comparison of two or more numbers that indicates their relative sizes. When two or more ratios are multiplied termwise, the resulting ratio is known as a compound ratio. The first quantity in the ratio is known as the antecedent, and the second quantity is known as the consequent.

For example, the compound ratio of two ratios, a:b and m:n, is am: bn.

Given,

Prescription requirement 50g for 10% ointment

but pharmacist has 5% ointment and pure ingredient

then to compound the prescription pharmacist needs x g

calculation:-

[tex]50 : 10 :: x : 5\\\\\frac{50}{10}=\frac{x}{5}\\\\5=\frac{x}{5}\\\\x=25[/tex]

Thus, required quantity of ointment and pure ingredient is 25 g.

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Answer:

  7.8

Step-by-step explanation:

You want the distance between P(8, 2) and Q(3, 8).

The distance between points is given by the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((3 -8)² +(8 -2)²) = √((-5)² +6²) = √61

  d ≈ 7.8

The distance between points P and Q is about 7.8 units.

__

Additional comment

You will notice that the desired distance is the length of the hypotenuse of a right triangle with legs that are 5 and 6. The Pythagorean theorem tells you that length is √(5² +6²) = √61, as above. The distance formula is based on the Pythagorean theorem.

You can find the relevant triangle leg lengths by counting grid squares on the graph. Of course, the distance formula does the same thing by subtracting coordinate values.

a) the acceleration = 0.028 m/s²

b) constant speed = 10m/s

d) Distance travelled during first 10 sec = 50m

e) Distance travelled during last 10 sec = 75m

f) the total distance travelled = 350 m

Total distance travelled during first 10 sec = area of triangle

= 1/2 * 10 * 10

= 50m

Total distance travelled during next 15 sec = area of square

= 15 * 15

= 225

Total distance travelled during last 10 sec = area of triangle

= 1/2 * 10 * 15

= 75m

Total distance travelled = 50 + 225 + 75

= 350m

Velocity = Total distance / Time taken

= 350/ 35

= 10m/s

Acceleration = Velocity / time taken

= 10 / 35

= 0.028 m/s²

c)

= -0.028 m/s²

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The equation y = -2x +12 in slope - intercept form.

Find the slope of the line that is parallel to y = -2x +3

Slope (m) = -2

Substitute and calculate ;

m = -2, x = 8 ,y = -4 into y = mx + b

-4 = -2 x 8 + b

Calculate the product :

-4 = -16 + b

Calculate the sum or difference:

-b = -12

b = 12

Again, Substitute m = -2 , b = 12 into y = mx +b :

y = -2x + 12

Rewrite the equation y = -2x + 12 in slope - intercept form:

y = -2x + 12

Hence, The equation y = -2x +12 in slope - intercept form.

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The length, l, of Olive’s picture frame is 18 - 1.25d, if Olive and Ryan have picture frames with the same perimeter.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

The perimeter of the rectangle = 2(length + width)

Let a by b the dimensions for Olive's picture

Let c by d the dimensions for Ryan's picture

b = 1.25d

The perimeter of the picture = 2(9 + 9) = 36

2(a + b) = 36

a + b = 18

a = 18 - b = 18 - 1.25d

Thus, the length, l, of Olive’s picture frame is 18 - 1.25d, if Olive and Ryan have picture frames with the same perimeter.

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Answer:

x = 12

Step-by-step explanation:

Given equation,

→ 6 + 12(x + 3) = 7x + 30 + 6x

Now the value of x will be,

→ 6 + 12(x + 3) = 7x + 30 + 6x

→ 6 + 12x + 36 = 7x + 30 + 6x

→ 12x + 42 = 13x + 30

→ 13x + 30 = 12x + 42

→ 13x - 12x = 42 - 30

→ [ x = 12 ]

Hence, the value of x is 12.

The correct answer to reflection of hexagon  is Option B

y=x, x-axis, y=x, y-axis

What is hexagon?

6-sided polygon is called hexagon , it is type of polygon( a plane figure made up of lines).

Main body:

using point B(−3,1)

Across the line y=x(x,y)→(y,x)

so we get (1,−3)

Across the x-axis (x,y)→(x,−y)

we get (1,3)

Across the line y=x(x,y)→(y,x)

we get (3,1)

Across the y-axis (x,y)→(−x,y)

we get (−3,1)

Hence the option B is correct.

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The suitable equation and solution is given by (D) g=48 gifts.

Given that max organized a community toy drive for the holidays.

He asked each family to donate a total of 4 gifts.

12 families participated in the toy drive.

If the total number of gifts is g, then the equation is given by,

g = 12*4 = 48 gifts.

Hence the correct option is (D) g=48 gifts.

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Answer:

Part a) consecutive interior angles

Part b) 

Part c) m∠5=

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

Part a) Angles 3 and 5 are consecutive interior angles

therefore

m∠3+m∠5=

Part b) we have

m∠3=

m∠5=

substitute

Part c) solve for x

Find the value of m∠5

m∠5=

m∠5=

Answer:

Step-by-step explanation ma is 9 because p + i=o K/x 798 g ćxΨ / ʥ and 78 / 2 +e =9 then oi x l = j j also = 6 and that's how you do it

The value of the quantity after 99 months is 5228.58.

Given that,  an initial value = 5900, rate of decay = 0.85% and time period = 7 years.

The quantity decreases slowly after which the rate of change and the rate of growth decreases over a period of time rapidly. This decrease in growth is calculated by using the exponential decay formula.

The exponential decay formula formula is [tex]Amount=Initial\ value(1-\frac{r}{100} )^{\frac{t}{n} }[/tex]

Here, the value [tex]=5900(1-\frac{0.85}{100} )^{\frac{99}{7} }[/tex]

= 5900×[tex](0.9915)^{14.14}[/tex]

= 5900×0.8862

= 5228.58

Therefore, the value of the quantity after 99 months is 5228.58.

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The "average" of the "positive distances" of each point from the mean is the mean absolute deviation. There is more variability in the data the higher the MAD (the data is more spread out). The MAD aids in determining if the mean of the set serves as a reliable predictor of the values included therein.

Find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data. Divide the total number of data values by the sum of the individual data values. By using the formula |data value - mean|, determine the absolute value of each data value's variance from the mean.

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is. The mean absolute deviation may be calculated as shown below.

Step 1: First, determine the mean.

Step 2: Determine the positive distances between each data point and the mean. Absolute deviations are those.

Step 3: Combine those deviations.

Step 4. Multiply the total by the number of data points.

The simplest approach to learn about mean absolute deviation is probably to follow these steps in the example below, however here is a more formal method to express the stages in a formula:

GAD (Greatest Absolute Deviation) = ( ∑ | [tex]x_{i}[/tex] - [tex]x_{mean}[/tex] | ) / n

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​

Answer:

Connie - [tex]x^{2} + 10[/tex]

Step-by-step explanation:

10 more means that you are adding ten to the square of x

For the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that, Rasheed has two and three-fourths cups of berries. He uses four-sixths of a cup of berries to make a milkshake. He then uses one-half of a cup of berries.

The number of cups of berries will Rasheed has left is found by subtracting the total used amount from the total amount,

=2 3/4-(4/6+1/2)

=11/4-(4/6+1/2)

=11/4 - 7/6

=19/12

=1 7/12

1.58

Thus, for the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.

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The answer of this 70/cos 20° round to 1 decimal place  is 74.5

To solve the equation 70/cos 20° , firstly we need to find out the value of the cos 20°.

From the simple calculator we can find the value of cos 20° which is 0.9397.

Now we use this value to solve the above equation.

70/cos 20°;

70/0.9397;

74.491.

written that we  have to round of the value to first decimal place, so the answer will become 74.5

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