How do you find the base and value of an exponent?

A mile is 5,280 feet long and an hour is 3,600 seconds long, thus 60 miles per hour is 60 x 5,280 / 3,600 = 88 feet per second.

How Do I Determine the Unit Rate? The denominator of a unit rate is always 1. To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.

Miles per hour is a relatively typical example of a unit rate that we face on a daily basis. This rate is a unit rate since it describes the number of miles in one hour.

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Answer:

3 inches

Step-by-step explanation:

The perimeter is the sum of all the sides of a shape. A rectangle has 4 sides.

2 * 2 = 4

One side is 2 in., so the parallel side is also 2 in.

10 - 4 = 6

Subtract the sum from the perimeter.

6 / 2 = 3

Since there are two sides left, divide by 2.

An exponential function is a function in which the variable appears in an exponent.

The most common form of an exponential function is f(x) = aˣ, where a is a positive constant, known as the base of the function, and x is the variable. The variable x is called the exponent of the function.

The base, a, determines the growth rate of the function. If the base is greater than 1, the function will increase rapidly as x increases. If the base is between 0 and 1, the function will decrease rapidly as x increases.

Exponential functions can also be written in the form y = a×bˣ, where a and b are constants, b is the base and x is the exponent. In this form, a represents the y-intercept of the function, which is the point where the function crosses the y-axis.

An exponential function can be recognize by the presence of the variable in an exponent and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.

In conclusion, an exponential function is a function in which the variable appears in an exponent and is defined as f(x) = aˣ or y = a×bˣ, where a is the base of the function and x is the exponent.

The base determines the growth rate of the function and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.

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HI is 7 because all sides are equal. K is 100 because J is 40 and L is also 40 because they are equal. All triangles are equal to 180. 40+40+100=180

If the equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books. The number of books is 4.

Given data:

Equation: 3.95m + 8.95b = 47.65

Where:
Magazine, m = 3

Now let find the number of book by using the equation to solve for b

3.95(3) + 8.95b = 47.65

11.85 + 8.95b = 47.65

Collect like terms

8.95b = 35.8

Divide both side by 8.95b

b = 35.8/8.95

b = 4 books

Therefore we can conclude that the number of books is 4.

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The complete question is;

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.

It is possible that Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct

The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example the little "2" says to use 8 two times in a multiplication: 82 = 8 × 8 = 64.

What are powers?

A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

Since 2376÷10

It will give us

237.6

So to convert to standard form it will be

2376×10^-1

How

Since the point has been shifted to the right side

And it will definitely give us 2376.0

But the point zero is not necessary

10^1 also means 0.1

So it is possible

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Answer:

2:10 or 1:5

Step-by-step explanation:

Answer: 4 squares to 1 triangle

Step-by-step explanation: both can be divided by two and that is the largest number they can be divided into

3/4 and 9/10 using the least common denominator is 15/20 and 18/20.

LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.

Given, are two fractions 3/4 and 7/10 we know the LCM of 4 and 10 is 20.

∴ (3×5)/(4×5) and (7×2)/(10×2).    

(we have to multiply same constant to the fraction to retain it's original value).

So,  3/4 and 4/10 using the least common denominator is 15/20 and 14/20.

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Answer:

B) Alternate Interior Angles Theorem

Step-by-step explanation:

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. In the above diagram, m∠3 ≅ m∠6

Answer:

The correct answer is A

I hope that helped.

Step-by-step explanation:

The inequalities given are 9) "And inequality, 10) "Or" inequality.

Compound inequalities are inequalities which consist of two or more simple inequalities.

"And" compound inequality has both the inequalities true.

"Or" compound inequalities have any one of them as true.

9. |5 + m| < 13

This can be written as,

-13 < 5 + m < 13

-13 - 5 < m < 13 - 5

-18 < m < 8

This is an "and" inequality. Because m can lie between -18 and 8.

10. 4 |y + 6| ≥ 3

|y + 6| ≥ 3/4

-3/4 ≥ y + 6 ≥ 3/4

-3/4 - 6 ≥ y ≥ 3/4 - 6

-6.75 ≥ y ≥ -5.25

The value of y can be either ≤ -6.75 or y ≥ -5.25. y cannot be both.

So this is an "or" inequality.

Hence the first one is and inequality and the second one is or inequality.

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Answer: D

Step-by-step explanation:

Answer:

D) 320 pi

Step-by-step explanation:

pi*r^2*h is the equation for the volume of a cylinder.

If you plug in the given values, then you get 320pi.

The answer is D) 320 pi.

Hope this helped! :)

We cannot construct a triangle with side lengths 3.5 cm, 9.2 cm and 5.3 cm. So it is not possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm. This is because these lengths does not follow triangle inequality theorem.

It is not possible to construct a triangle using the given side lengths of 3.5 cm, 9.2 cm, and 5.3 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if we take 3.5 cm and 5.3 cm as two sides, the sum of their lengths is 8.8 cm. But the length of the third side (9.2 cm) is greater than 8.8 cm, so these three side lengths cannot form a triangle.

It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle.

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The finance charge on the average daily balance for the one month is $2.07.

The finance charge is the interest and other fees charged on a credit facility.

To compute the finance charge, we apply the annual percentage rate (APR) on the Average Daily Balance, multiplied by the number of days in the billing cycle, and divided by 365.

Days 1-3: $200 (initial balance)            $600 ($200 x 3)

Days 4-20: $300 ($100 purchase)    $5,100 ($300 x 17)

Days 21-30: $150 ($150 payment)    $1,500 ($150 x 10)

Total = $7,200

Average Daily Balance = $240 ($7,200/30)

APR interest rate = 10.5%

MPR interest rate = 0.875% (10.5%/12)

Finance Charge = $2.07 ($240 x 10.5% x 30/365)

Or $ ($240 x 0.875%)

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Therefore , equation problem answer is there will be six 5 mark problem and twenty two 3 mark problem.

Remove parentheses from each side of the equation and combine similar terms to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.

Here,

Given :

Since the total number of points is 28, we can create the Let Statements:

Let x= one type of question

Let 28-x= the other type of questions

Create an equation to relate the number of questions to the price

100=5x+3(28-x) Distribute

100=5x+82-3x Subtract 76 from both sides of the equation

100-82=5x-3x Combine like terms

18=3x Divide both sides by 3

x=6

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The reason why these triangles are similar is A. AA.

A similar triangle is a triangle in which the corresponding angles are congruent (equal in measure) and the corresponding sides are in proportion. This means that the corresponding sides of two similar triangles are in the same ratio, but the triangles may be different sizes.

A triangle is a three-sided polygon. It is defined by three points in a plane, called its vertices, and the straight lines connecting each pair of these points, called its sides. The three angles of a triangle always add up to 180 degrees.

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So on solving the provided question we can say that -  all angles of triangle - 180; x = 60

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

all angles of 180

x +90+30 = 180

x = 60

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Answer:

A. $189.

B. $130.

C. Stephanie's.

D. The Mean.

E. The mean is the average of the data. The Median is just the middle number which doesn't reveal all that much about the data.

Answer:

A.) $189

B.) $145✔️ | *(not $130❌)*

C.) Stephanie's

D.) Median✔️ | *(not "mean"❌)

E.) Because there is an outlier, the median is better representative than the mean.

Answer:

4^2 or 16

Step by step explanation:

4^5 = 4x4x4x4x4

4^3 = 4x4x4

4^5 ÷ 4^3 = 4x4x4x4x4 ÷ 4x4x4 = 4x4

4x4 = 4^2 = 16

A graph which represents the inequality y is less than negative one-third times x plus 1 is shown in the image below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In order to determine and plot the graph which represents the inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than or equal to one-third times x plus 1 ⇒ y < x/3 + 1.

Next, we would use an online graphing calculator to graphically solve the given inequality.

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Answer:

B

Step-by-step explanation:

The graph shows the answer accurately

A description which best compares the graphs of the two functions above include the following: B. The line for function A is steeper.

In order to compare the two functions, we would have to find the slope of function B based on the data points contained in the table by using the slope formula.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m = (-1 - (-2))/(3 - 0)

Slope, m = (-1 + 2)/3

Slope, m =1/3

From function A y = 3x - 2, the slope is equal to 3. Consequently, we can logically deduce that the line representing function A is steeper than the line representing function B because its slope is bigger i.e 3 > 1/3.

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Answer:It is not possible to answer this question without knowing the rate at which the other person was running.

Step-by-step explanation:

Answer:

1) can 2) can’t 3) can’t 4) can

Step-by-step explanation:

There are 66 golf balls in total 1 and 4 are the only equations that equal 66

The length of the side indicated in the similar figure can be found using the concept of similarity.

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Answer:

the first and the third

Step-by-step explanation:

The solution of system of equations are (4, 2). Therefore, option A is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y=-x+6 ---------(I)

On a coordinate plane, a line goes through (0, 0) and (4, 2).

Here, slope m=(2-0)/(4-0)

= 1/2

Substitute m=1/2 and (4, 2) in y=mx+c, we get

2=1/2 (4)+c

c=0

y=1/2 x ---------(II)

Substitute equation (II) in equation (I), we get

1/2 x=-x+6

x=-2x+12

x+2x=12

3x=12

x=4

Substitute x=4 in equation (II), we get

y=2

Then, solution of system of equations is (4, 2)

Therefore, option A is the correct answer.

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To convert from base 10 to base e, we need to split down a number in base e into the powers of e.

When we convert from base 10 to base e, the pattern will be exactly the same. It will be just with e instead of 10.

For example, to see how many digits (before the decimal point) of ln(12) = 2.4849...

It means that the first digit will be on the e^2 position. Now lets find:

12 / e^2 = 1.624…

So, there will only be a 1 in the e^2 position. The remaining is 12 – e^2. The next position is e^1 position. To find out what’s on this position, we need to do the following calculation:

(12 – e^2) / e = 1.696…

The next digit will also be a 1.

Now we do the 1’s position:

(12 – e^2 – e) / 1 = 1.892…

Next digit’s a 1.

We can continue for a few more decimal places:

(12 – e^2 – e – 1) / e – 1 = 2.426…

Next digit’s a 2.

(12 – e^2 – e – 1 – 2 * e – 1) / e – 2 = 1.159…

Next’s digit a 1.

So, 12 in base e is 111.21…

Since e is irrational and 12 is not, this will be never ending. But there will only can be 0’s, 1’s, and 2’s, since e is less than 3.

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The expression 30m × 2.01m will be 60.3m²

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression will be:

= 30m × 2.01m

= 60.3m²

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The quadrilateral MNPQ is trapezoid but not an isosceles trapezoid .

A trapezoid, as well known as a trapezium, is a closed, flat shape with four straight sides and one pair of parallel sides.

Here given points,

M(-2,0), N(0,4), P(5,4), and Q(8,0) are given.

We are familiar with the slope formula,

Slope = y2 - y1 / x2 - x1

So here,

Slope of MN = 4 - 0 / 0 - (-2)

                     = 4/2

                     = 2

Slope of NP = 4 - 4 / 5 - 0

                     = 0/5        

                     = 0

Slope of PQ = 0 - 4 / 8 - 5

                     = -4/3

Slope of QM = 0 - 0 / -2 -(-8)

                     = 0/10

                     = 0

Therefore we can see, NP||QM and MN∦PQ.

Therefore MNPQ is a trapezoid because it has two parallel sides.

By using distance formula,

MN = [tex]\sqrt{0-(-2)^{2} +(4-0)^{2} }[/tex]

      = √20

      = 2√5 units

PQ = [tex]\sqrt{(8-5)^{2} +(0-4)^{2} }[/tex]

      = √25

      = 5 units

Here MN ≠ PQ , MN and PQ are not congruent to each other.

Therefore MNPQ not is a isosceles trapezoid.

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A quadrilateral shape called a trapezoid that has exactly one set of parallel sides. Isosceles Trapezoid: A trapezoid with congruent non-parallel sides.

A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed by two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle.

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. A quadrilateral's internal angles add up to 360 degrees in all cases. The four angles found at each vertex of a four-sided form are referred to as the interior angles of a quadrilateral and are the only angles in a quadrilateral. Every quadrilateral's internal angles add up to 360 degrees.

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