Compare / Contrast Exponential Equations

1.) 2 (1/5)x-5

2.) y=4x

Answer: Child ticket: $8, Adult ticket: $6

Step-by-step explanation:

Let's call the price of 1 adult ticket "a" and the price of 1 child ticket "c".

On the first day, the school sold 3 adult tickets for a total of 3a dollars, and 2 child tickets for a total of 2c dollars, for a total of 34 dollars. So, we have the equations:

3a + 2c = 34

On the second day, the school sold 3 adult tickets for a total of 3a dollars and 12 child tickets for a total of 12c dollars, for a total of 114 dollars. So, we have another equation:

3a + 12c = 114

We can now use these two equations to solve for the value of "a" and "c".

We can use substitution to solve for one variable, then substitute it back into either of the equations to solve for the other variable.

Let's solve for "a" by substituting the first equation into the second:

3a + 12c = 114

3a = 114 - 12c

a = (114 - 12c) / 3

Now that we have an equation for "a", we can substitute it back into the first equation to solve for "c":

3a + 2c = 34

3[(114 - 12c) / 3] + 2c = 34

114 - 12c + 2c = 34

-10c = -80

c = $8

So, the price of 1 adult ticket is

a = (114 - 12c) / 3

a = (114 - 12 * 8) / 3

a = (114 - 96) / 3

a = 18 / 3 = $6.

Answer: 0.46.

Step-by-step explanation:

The probability that a randomly selected can of food will be corn is equal to the fraction of cans that are corn, out of the total number of cans.

Since 46 out of 100 people brought a can of corn, we can assume that there were 46 cans of corn donated. We do not know how many total cans were donated, but we can find out by using the fact that each person was required to bring one can of food. Therefore, the total number of cans donated is equal to the total number of people who attended the dance, which is 100.

So, the probability of selecting a can of corn is:

P(corn) = Number of cans of corn / Total number of cans

P(corn) = 46 / 100

Simplifying the fraction, we get:

P(corn) = 23 / 50

Therefore, the probability that a randomly selected can of food will be corn is 23/50 or approximately 0.46.

The equation of circle with center ( -6 , 3 ) is ( x + 6 )² + ( y - 3 )² = 9² , where the radius of circle r = 3 units

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be represented as r

Now , the first point is A ( -6 , 3 )

Let the second point be B ( -15 , 3 )

Let the third point be C ( 3 , 3 )

And , from the distance formula ,

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

The distance of AB = √ ( -15 + 6 )² + ( 3 - 3 )² = 9 units

The distance of AC = √ ( 3 + 6 )² + ( 3 - 3 )² = 9 units

The distance of BC = √ ( -15 - 3 )² + ( 3 - 3 )² = 18 units

So , the measure of AB = AC and the radius of the circle r = 3 units

Now , the center of the circle is A ( -6 , 3 )

where the standard form of a circle is

( x - h )² + ( y - k )² = r²,

On simplifying , we get

( x + 6 )² + ( y - 3 )² = 9²

Hence , the equation of circle is ( x + 6 )² + ( y - 3 )² = 9²

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The diameter of the pizza to the nearest inch is 11 inches.

Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:

C = πd

And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:

5.5 = (1/8)C

So we can substitute the formula for the circumference into this equation:

5.5 = (1/8)(πd)

Solving for d, we can multiply both sides by 8/π:

d = (5.5)(8/π)

Calculating the approximate value of π as 3.14, we get:

d ≈ (5.5)(8/3.14) = 11 inches

So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.

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Shawna's new score is 2 and the equation to represent Shawna’s new score would be, New score = Current score + Result of black cube + Result of red cube

What exactly are algebraic expressions?

Algebraic expressions are expressions made up of variables and constants. Additional algebraic operations include addition, subtraction, and division.

If the result of a red numbered cube represents a negative number, then we can represent the result of the red cube as -5. Similarly, if the result of a black numbered cube represents a positive number, we can represent the result of the black cube as +3.

Shawna's current score is 4, and her new score is obtained by adding the results of the two cubes to her current score. We can represent this situation with the following equation:

New score = Current score + Result of black cube + Result of red cube

Substituting the values we have for the result of the black cube, the result of the red cube, and Shawna's current score, we get:

New score = 4 + 3 + (-5)

Simplifying, we get:

New score = 2

Therefore, Shawna's new score is 2 and the equation to represent Shawna’s new score would be, New score = Current score + Result of black cube + Result of red cube.

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The solution is, Dobson have to repay B. $17,600.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

The bank grants Marcus Dobson a loan for $22,000 with an APR

of 10 percent.

He agrees to a down payment of 20 percent and will repay the loan over 24 months.

so, he paid = 22000*20%

                  = $4400

so, remained loan = $ 17600

using the formula of interest , we get,

he has to repay with interest = $ 17600* 10%* 2 + $ 17600

                                                 =$ 3520 + $ 17600

                                                  =$ 21120

Hence, The solution is, Dobson have to repay B. $17,600.

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Answer:

Your answer would be (x, y) = (0, 0)

Step-by-step explanation:

Please refer to the screenshot underneath.

The area of Gavin's bedroom is 120 square feet.

Square feet can be defined as the area of a square with sides of 1 foot.

Let B be the area of Gavin's bedroom in square feet.

According to the problem, the area of Gavin's kitchen is 10 square feet more than one-third of the area of his bedroom. So we can write:

Area of kitchen = (1/3)B + 10

We also know that the area of the kitchen is 50 square feet. So we can set up an equation:

(1/3)B + 10 = 50

Subtracting 10 from both sides, we get:

(1/3)B = 40

Multiplying both sides by 3, we get:

B = 120

Therefore, the area of Gavin's bedroom is 120 square feet.

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The radius of the cylinder is approximately 5.88 inches.

What are equivalent equations?

Equivalent equations are algebraic equations that are having identical roots or solutions.

We can solve the given equation to find the radius of the cylinder using the volume and height information

3.14 * 11 * r² = 1243.44

First, divide both sides by 3.14*11 to isolate r²:

[tex]r^2 = 1243.44 / (3.14 * 11)[/tex]

r² ≈ 34.585

Taking the square root of both sides, we get:

r ≈ 5.88

Hence, the radius of the cylinder is approximately 5.88 inches.

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Answer:

f(n) = 10 + 3n

Step-by-step explanation:

Each of the expressions has 10 + a certain number of 3's

For example for n = 3 we have
f(3) = 10 + 3 threes = 10 + 3 x 3 = 10 + 9 = 19

For n = 4, we have

f(4) = 10 + 4 threes = 10 + 4 x 3 = 10 + 12 = 22

The others follow the same pattern

So the explicit equation is

f(n) = 10 + 3n

Testing on n = 6 we get

f(6) = 10 + 6n = 10 + 6 x 3 = 10 + 18 = 28

Answer:

6 grams of sugar in 3/4 liter.

Explanation:

Recall that two 1/4 portions is equal to 1/2.  So if 1/2 liter has 4 grams, 1/4 liter will have 2 grams of sugar.

Every 1/4 liter will have 2 grams of sugar.

Therefore, 3/4 liter will have 3 times as much sugar as 1/4 liter.  The amount of sugar in 3/4 liter will be 3 times 2 grams or 6 grams of sugar in 3/4 liter

Answer:

For question 2, Ethan needs 3 cups of milk to make the batter for 3 times as many cakes.

For question 3, Isabella needs 5/4 of a gallon of the food to make 5 gallons of the mixture.

A triangle represents 1/4 of the trapezoid, a diamond represents 1/2 of the trapezoid, and a hexagon represents 1/1 of the trapezoid.

Each shape represents a different part of the overall trapezoid.

The triangle represents 1/4 of the full trapezoid. This is because the trapezoid has four triangles, all of the same size. So each triangle is 1/4 of the whole trapezoid. The diamond represents 1/2 of the full trapezoid. This is because the trapezoid has two diamonds, each of the same size. So each rhombus is 1/2 of the whole trapezoid.

The hexagon represents 1/1 of the whole trapezoid. This is because the trapezoid has only one hexagon, which is the same size as the entire trapezoid. So the hexagon is 1/1, the whole trapezoid.

In summary, a triangle represents 1/4 of a trapezoid, a diamond represents 1/2 of a trapezoid, and a hexagon represents 1/1 of a hexagon. Using these fractions, we can determine the value of each shape relative to the overall trapezoid.

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380 liters of natural oil is needed

The ratio of natural oil to synthetic oil is 4:5

Total number of petrolyn oil is 855

4x + 5x= 855

9x= 855

x= 855/9

x= 95

The number of natural oil is 4x

= 4(95)
= 380

Hence the number of liters of natural oil that is needed is 380

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Answer:

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\mathrm{3 (x - 10) = 63}[/tex]

Divide both sides by 3:-

[tex]\mathrm{x-10=\cfrac{63}{3} }[/tex]

Divide 63 by 3 = 21:-

[tex]\mathrm{x-10=21}[/tex]

Add 10 to both sides:-

[tex]\mathrm{x=21+10}[/tex]

Add 21 and 10 = 31:-

[tex]\mathrm{x=31}[/tex]

____________________

Hope this helps!

z = - 4, represents the solution of the inequality → z² + 2 < 6.

An inequality is used to compare numbers or expressions. For example -

2x + 4 > 6       4x + 6 < 8            y > 9          x < 1

All the above expressions mentioned above represent inequalities.

Given is the inequality as -

z² + 2 < 6

The given inequality is -

z² + 2 < 6

Subtract {2} from both side we get -

z² < 4

z < ± 2

Therefore, z = - 4, represents the solution of the inequality → z² + 2 < 6.

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A. (8 * t) + (8 * 8) is equivalent to 8t + 64

B. 4t + 8 + 4t is equivalent to 8t + 8

C. 4(2t + 2) is equivalent to 8t + 8

D. 8t + 64 is equivalent to 8t + 64

E. 8t + 16 is equivalent to 8t + 16

F. (8 + t) + (8 + 8) is equivalent to 16 + t.

So the expressions that are equivalent to 8(t + 8) are B and C, the expression that is equivalent to 8t + 8 is E, and the expression that is neither is F.

In the given problem, we are comparing the given expressions to see if they are equivalent to 8(t + 8), 8t + 8, or neither.

Expression A: (8 * t) + (8 * 8) = 8t + 64

This expression is equivalent to 8t + 64, which is not the same as 8(t + 8) or 8t + 8.

Expression B: 4t + 8 + 4t = 8t + 8

This expression is equivalent to 8t + 8, which means that adding up 4t and 8, and then adding 4t again to the result is the same as multiplying 8 with t and adding 8 to the result.

Expression C: 4(2t + 2) = 8t + 8

This expression is also equivalent to 8t + 8, which means that multiplying 2t + 2 with 4 is the same as multiplying 8 with t and adding 8 to the result.

Expression D: 8t + 64 = 8t + 64

This expression is the same as 8t + 64, which is not equivalent to either 8(t + 8) or 8t + 8.

Expression E: 8t + 16 = 8t + 16

This expression is the same as 8t + 16, which is not equivalent to either 8(t + 8) or 8(t + 8).

Expression F: (8 + t) + (8 + 8) = 16 + t

This expression is not equivalent to either 8(t + 8), 8t + 8, or neither.

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--The question is incomplete, answering to the question below--

"Drag each expression to show whether it is equivalent to 8(t + 8), 8t + 8, or neither.

A. (8 * t) + (8 * 8)

B. 4t + 8 + 4t

C. 4(2t + 2)

D. 8t + 64

E. 8t + 16

F. (8 + t) + (8 + 8)"

59 is a prime number.

This means that it cannot be divided evenly by any other number except for 1 and itself. A composite number, on the other hand, can be divided evenly by at least one other number besides 1 and itself.

To determine if a number is prime or composite, you can use a simple test. Start by dividing the number by 2. If the result is a whole number, then the number is composite.

If the result is not a whole number, try dividing by 3, 4, 5, and so on until you find a whole number result or until you reach the square root of the original number. If you reach the square root without finding a whole number result, then the number is prime.

For example, with the number 59:

59 / 2 = 29.5 (not a whole number)
59 / 3 = 19.67 (not a whole number)
59 / 4 = 14.75 (not a whole number)
59 / 5 = 11.8 (not a whole number)
59 / 6 = 9.83 (not a whole number)
59 / 7 = 8.43 (not a whole number)
59 / 8 = 7.38 (not a whole number)

Since we have reached the square root of 59 without finding a whole number result, we can conclude that 59 is a prime number.

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Answer:

Below

Step-by-step explanation:

There are 5280 ft in a mile...how many 5280's are there in 30 000 ?

30 000 ft  / 5280 ft/mile  = 5.68 miles

The height of 30,000 feet above sea level corresponds to 5.68 miles.

To convert feet to miles,

we can use the conversion factor 1 mile = 5280 feet.

Therefore, to find how many miles 30,000 feet corresponds to, we can divide 30,000 by 5280:

=30,000 feet / 5280 feet/mile

≈ 5.68 miles

So, 30,000 feet above sea level corresponds to 5.68 miles.

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The number of rectangular table is equal to 5 rectangular tables.

The number of circular table is equal to 5 circular tables.

In order to write a linear system of equations to describe this situation, we would a assign variable to the number of circular table and the number of rectangular table respectively, and then translate the word problem into a linear equation as follows:

Since there are 9 tables and 80 chairs set up with 8 chairs each for the circular table and 10 chairs each for the rectangular table, a linear equation to model this situation is given by:

8x + 10y = 80    .......equation 1.

x + y = 9            .......equation 2.

In this scenario, we would use an online graphing calculator to plot the linear system of equations in order to determine the solution (point of intersection) as shown in the image attached below, which is at the ordered pair (5, 4).

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Seraphina's speed has increased by a factor of around 23% compared to the first hour.

What Is a Change in Percentage?

The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.

How can you determine the percentage to the closest tenth?

Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.

Percent Change Formula = [tex]\frac{ (Final value -Initial value)}{ (Initial value)}[/tex]× 100

Percent Change               = [tex]\frac{(74-60)}{60}[/tex]× 100

…                                     = [tex]\frac{14}{60}[/tex] × 100

...                                     ≈ 0.23333 × 100

Percent Change             ≈ 23.33%

The pace of Seraphina increased by around 23% in the second hour compared to the first.

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19 has an infinite number of multiples since we can multiply 19 by any positive integer to get a new multiple.

A multiple of number is product of that number and  other integer.

To find the multiples of 19, we need to multiply 19 by every positive integer. So, the multiples of 19 are:

19 × 1 = 19

19 × 2 = 38

19 × 3 = 57

19 × 4 = 76

19 × 5 = 95

19 × 6 = 114

19 × 7 = 133

19 × 8 = 152

19 × 9 = 171

19 × 10 = 190

and so on.

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Answer:

scalene, right triangle

Step-by-step explanation:

Determine whether it is a triangle and the triangle's type:

Answer: scalene, right triangle

The magnitude of the horizontal and vertical components are 21.33 m/s and 38.48 m/s

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

Velocity = 44 meters per second

Direction = S 61° E

This means that

V = 44 and angle = 61°

The direction angle is 61° from the positive x-axis (E), so we can use the following trigonometric relationships to find H and V:

H = 44 * cos(61°) --- horizontal

V = 44 * sin(61°) --- vertical

Using a calculator, we can find that:

H = 21.33 m/s

V = 38.48 m/s

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Both clusters are relevant to her career.

Cluster is derived from the old english word clyster, which means a group. Cluster is now used as both a noun and a verb.

The army sergeant who works as a trauma surgeon is probably in the Health Services and Government and Public Administration clusters.

Health Services occupations include diagnosing, treating, and preventing illnesses and injuries, while Government and Public Administration occupations include planning, managing, and providing government functions and services. The individual is a member of the military, which is a government organisation, and a trauma surgeon, which is a part of the healthcare industry. As a result, both clusters are pertinent to her career.

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Amongst the options circle shape from the Clade Race would be considered plesiomorphic.

A primitive or ancestral character state is called plesiomorphy or known as a plesiomorphic character), and a shared plesiomorphy is called a symplesiomorphy. For example, let us take an example of hair. It is a unique mammalian character that evolved with the evolution of mammals.

The term apomorphy means a specialized or derived character state which is plesiomorphy. It refers to a primitive or ancestral trait. An same as autapomorphy, it is a derived trait that is unique to one group, while a same as synapomorphy is a derived trait shared by two or more groups.

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