how do exponents connect to other areas of math? Show and explain with examples.

Answer:

angle ODC=30°

Step-by-step explanation:

Parallel to the line now draw another line PQ

The other side of the fence based on the information illustrated is 6.5 feet.

It should be noted that the perimeter of a rectangle is illustrated as:

= 2(length + width)

In this case, the width is given as 7/2 = 3.5 feet.

It should be noted that the perimeter is given as 20 feet.

Therefore, the length will be:

2(length + width) = 30

2(length + 3.5) = 20

2Length + 7 = 20

2L = 20 - 7

2L = 13

L = 13/2

L = 6.5

Therefore, the length is 6.5 feet.

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The equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8) is y = - 1 / 2 x + 6(y equals negative one-half times x plus 6)

The equation of the line is perpendicular to y = 2x + 3 and passes through the point (−4, 8).

Therefore, perpendicular lines follows the rule:

m₁m₂ = -1

Hence,

2m₂= -1

m₂ = - 1 / 2

Therefore, let's find the slope of the line using (-4, 8)

8 = - 1 / 2 (-4) + b

b = 8 - 2

b = 6

Therefore, the equation of the line is y = - 1 / 2 x + 6

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Answer: The answer is D- y= -1/2x+6

We will compute the volume of each figure.

1) Figure A

We have a cone with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the cone is:

2) Figure B

We have a cylinder with:

• Ab = base area = 20 cm²,

• h = heigh = 6 cm.

The volume of the cylinder is:

3) Figure C

We have an inclined cylinder with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the inclined cylinder is:

4) Figure D

We have a parallelepiped with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the parallelepiped is:

5) Figure E

We have an inclined square pyramid with:

• Ab = base area = 20 cm²,

• h = heigh = 10 cm.

The volume of the square pyramid is:

Answer

Among these figures, figure C and figure D have the same volume.

Answer:

[tex]\sf y = \dfrac{5}{2}x +\dfrac{17}{2}[/tex]

Step-by-step explanation:

 [tex]\sf y =\dfrac{5}{2}x+1[/tex]

  m= 5/2

Parallel lines have same slope.

      Slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept

[tex]\sf y = \dfrac{5}{2}x + b[/tex]

Point (-3,1) passes through the required line. Substitute (-3,1) in the above equation and find 'b'.

        [tex]\sf 1 = \dfrac{5}{2}*(-3)+b\\\\1 =\dfrac{-15}{2}+b\\\\[/tex]

 [tex]\sf 1 +\dfrac{15}{2}=b\\\\\dfrac{2+15}{2}=b\\\\\\ \boxed{b= \dfrac{17}{2}}[/tex]

  [tex]\sf \bf y = \dfrac{5}{2}x+\dfrac{17}{2}[/tex]

The probabilities listed here, in percent form and rounded to the fourth decimal place, are 29.9474 for a 5-card poker hand.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

According to given information;

C(4,3)C(48,2)/C(52,5) - 3 of 4 aces, 2 of 48 non-aces 0.1736%

C(13,5)/C(52,5) - 5 of 13 spades 0.0495%

There are 4 face cards, ace, king, queen, jack, and 4 suits for each. 16 face cards, and 36 non-face cards - C(16,3)C(36,2)/C(52,5) 13.5747%

There are 44 cards that are not aces or kings - C(4,2)C(4,2)C(44,1)/C(52,5) 0.0609%

There is 1 jack and 48 non-jacks C(4,1)C(48,4)/C(52,5) = 29.9474%.

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The simple interest of the sum at the same rate and time is 2400

The interest that is paid on the principal and interest at regular intervals is known as compound interest.The difference between compound interest and simple interest starts to show after the first year, though.Beginning with the second year, interest is computed on both the principal amount and the interest from the prior year. As a result, interest on interest is another name for it.

Given that : Sum =8000 and time = [tex]\frac{3}{2} years[/tex] and rate is 20 %

When rate is calculate half yearly

R becomes [tex]\frac{R}{2}[/tex]

T becomes 2T

A = [tex]P(1+\frac{R}{100} )^{T}[/tex]

C.I = A-P

R = [tex]\frac{20}{2} = 10%[/tex]%

T = 2× [tex]\frac{3}{2} years[/tex] = 3years

A = [tex]P(1+\frac{R}{100} )^{T}[/tex]

A = 8000[tex]\frac{11}{10} ^{3}[/tex]

A = 8 ×1331

A = 10648

Now ,

C.I = A - P

C.I =10648 - 8000

C.I = 2468

The compound interest is 2468

Simple interest

A = P(1+rt)

A = 8000(1+0.2×1.5)

A =10400

S.I =A- P

= 10400 - 8000

=2400

The simple interest of the sum at the same rate and time is 2400

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Plug in 3 in the place of x and simplify

[tex]y=(3)^{2} \\y=3*3\\y=9[/tex]

y=9

Answer:

Step-by-step explanation:

450 * 99.40 =  44730

Answer:

10.8

Step-by-step explanation:

30% of 36

= 30/100 * 36

= 3/10 * 36

= 108/10

= 54/5

= 10.8

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Using proportions, the number of planes in each city after 8 hours is given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division, with the given ratios.

One example of application of proportions is for percentage problems, as the total amounts are multiplied by the decimal equivalent of the percentage to find the equivalent amounts.

The planes in Los Angeles after 8 hours are given as follows:

Hence the amount is:

0.7 x 30 + 0.25 x 12 + 0.125 x 8 = 25.

The planes in St. Louis after 8 hours are given as follows:

Hence the amount is:

0.2 x 30 + 0.25 x 12 + 0.5 x 8 = 13.

Initially, there were 50 planes, and 25 + 13 = 38 are in either Los Angeles or St. Louis, hence the remaining 50 - 38 = 12 are in Dallas.

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Answer: 4/5

Step-by-step explanation:

y = mx + b

m represents the slope in this line.

Answer:

4/5

Step-by-step explanation:

Equation is in slope intercept form:

[tex]y = mx + b[/tex]

where m is the slope and b us the y-intercept

so, slope is 4/5

The expression for the side length of the bulletin board is √n (option B).

A square is an object with four sides that are of equal length. The sum of angles in a square is 360 degrees. A square has two diagonals that are of equal length that bisect each other at a right angle.

The area of a square can be determined by calculating the square of a side length.

The area of a square = length x length

= length²

If the area of a square is given, to determine its side length, find the square root of the area.

Length of a side = √area

√n

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They way you can change the grouping of the addends. in $5.50+$7.83+$3.50 is;  $5.50 + ($7.83 + $3.50) =  ($5.50 + $3.50) + $7.83

There are different algebraic properties such as;

Commutative Property

Associative Property

Distributive Property

Now, the commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product. For example;

a + b + c = c + a + b or a* b = b * a

Now, the associative property states that the way in which factors are grouped in a multiplication or addition problems does not change the product. For example; x + (y + z) = (x + z) + y

Now, to our question, one way to group the addends using associative property is;

$5.50 + ($7.83 + $3.50) =  ($5.50 + $3.50) + $7.83

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The average number of viewers over the two week is D. 4.85 x 10^5.

It should be noted that the scientific notation simply has to do with writing of numbers that are either too large or too small. This will be illustrated thus:

In this case, the TV show had 5.6 x 10^5 viewers in the first week and 4.1 x 10^5 viewers in the second week.

Therefore, the average number of viewers over the two weeks will be:

= (5.6 × 10^5) + (4.1 × 10^5) / 2

= 4.85 × 10^5

Note that we had to divide by 2 since it's average.

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Answer:

Step-by-step explanation:

[tex]f(x)=x^2-12x^2+27\\f(x)=x^2-2(x)(6)+6^2-6^2+27\\f(x)=x^2-2(x)(6)+6^2-36+27\\f(x)=(x-6)^2-9[/tex]

This is the graph of the function f(x)=x² shifted right about the x-axis

by 6 units and dropped down about the y-axis by 9 units

Answer: 345.79 - The value of the digit 7 is 7 thousandths, or 0.007.

sorry if this doesn't help..

The  equation which represents the amount is p = 0.0625 t.

When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.

Sales tax rate = sales tax percent / 100.

Sales tax = list price * sales tax rate.

Total price including tax = list price + sales tax,

Total price including tax = list price + (list price * sales tax rate),

Total price including tax = list price * ( 1 + sales tax rate)

We have been given

sales tax rate = 6.25%.

The price of the item = p

The sales tax = t

We know that the amount of sales tax paid on a purchase is proportional to the price of the item.

p = 6.25% t

p = 6.25/100 t

p = 0.0625 t.

Hence , P = 0.0625 t is the equation used to represent the amount.

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To write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .

As given in the question,

Given number in decimal form is equal to 5.36

5 is the whole number and 0.36 can be written as 36 /100.

Mixed number of the given number 5.36 is equal to

= 5 ( 36 / 100)

Reduced the mixed number to get the simplest form :

5 ( 36 / 100)

= 5 ( 9 / 25)

= 134 / 25

Therefore, to write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .

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Answer:

[tex]tan(x)=\frac{44\sqrt{89}}{89}[/tex]

Step-by-step explanation:

tan is defined as: [tex]tan(x)=\frac{opposite}{adjacent}[/tex]

sin is defined as: [tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]

cos is defined as: [tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]

We can also define tan as: [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

because plugging in the definitions of sin and cos in we get: [tex]tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}[/tex]

which you'll notice is the original definition of tan(x)

So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)

[tex]sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}[/tex]

plugging in sin(x) and cos(x) we get:

[tex]tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}[/tex]

We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.

We can do this by multiplying the fraction by: [tex]\frac{\sqrt{89}}{\sqrt{89}}[/tex] which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator

[tex]tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}[/tex]

Answer:

Midpoint formula is given as [(x1+x2)÷2, (y1+y2)÷2], where x and y are coordinates of the points.

Midpoint = [(19+17)÷2, (6+(-3))÷2]

= (36÷2, 3÷2)

= (18, 1.5)

The given expressions have been evaluated to be equivalent or not equivalent as follows:

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a specific number, the same output (result) would be produced as when each addend is multiplied respectively by the number, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

Next, we would determine whether or not the given expressions are equivalent:

3x + 12 and 3(4 + x):

Opening the bracket, we have:

3(4 + x) = 3x + 12 (Equivalent).

2(3x - 30) and 6 - 30;

Opening the bracket, we have:

2(3x - 30) = 6x - 60

2(3x - 30) = 6 - 30 (Not equivalent).

4(5 - 4x) and 20x - 16;

Opening the bracket, we have:

4(5 - 4x) = 20 - 16x

4(5 - 4x) = 20x - 16 (Not equivalent).

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Answer:

25/6

Step-by-step explanation:

We determine the scale factor by comparing the lengths of corresponding sides of the square. 
The length of O’N’=15 and the length of ¯¯¯¯¯¯¯¯¯¯¯ON=9

The equation for the scale factor, k is then given by:

O’N’=kON

15=9k

K= 15/9= 5/3.

The scale factor is k= 5/3

Answer:

9.88x

Step-by-step explanation:

multiply both numbers together

Answer:

x° = 100°

Step-by-step explanation:

Straight line angles add up to be 180°

Angles opposite eachother aka "vertical angles" are the same measurements.

Answer:

<CPB

Step-by-step explanation:

Because <APE= right angle

<APC= Obtuse angle

<CPE= Obtuse Angle.

Also, <CPB because its the only angle below 90 degrees and an acute angle must be below 90 degrees.

The value of the area are;

Rectangle A = 54 square units

Triangle B = 2 square units

Rectangle C = 6 square units

Whole figure = 62 square units

The formula for determining the area of a rectangle is expressed as;

Area = lw

Where;

From the figure shown, we have two rectangles

Area of the bigger rectangle;

Length = 9

Width = 6

Now, substitute the value

Area = 9(6)

Multiply through

Area = 54 square units

Area of the smaller rectangle

Length = 9 - 7 = 2

Width = 9 - 6 = 3

Substitute the values

Area = 2(3)

Multiply through

Area = 6square units

The formula for area of a triangle is expressed as;

Area = 1/2 base× height

Base = 9 - 6 = 3

Height = 9 - 2 = 3

Substitute the value

Area = 1/ 2 ×2(3)

Area = 6/ 3

Area = 2

The total area = Rectangle A + rectangle B + Triangle

Total area = 54 + 6 + 2

Total area = 62 square units

Hence, the area is 62square units

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Answer:

A=54 B=3 Whole=73

Step-by-step explanation:

I know this because i did this aswell