An object moving at speed s for time t travels distance st. The Brown family is taking a road trip. This morning, they drove for 2. 5 hours at a speed of 65 miles per hour. How far did the family drive this morning?
Write your answer as a whole number or decimal

The difference between the future totals of $2800 invested at 3% simple interest for 4 years and $2800 invested at 3% compound interest, compounded annually for 4 years is $15.4246 .

Suppose a sum of money is taken out on a loan for a period of n years at r% annual rate of interest at compound interest compounded annually. Then after every year, interest accrued in the last year, is not withdrawn or paid back, but it is left with the loanee. so it is considered to be loaned to the loanee. So that for the next year, the total loan amount increases by this amount. So the new principal is P + Pr = P(1+r). Continuing this idea, the total amount after n years is [tex]$A=P{(1+r)}^n$[/tex].  

In our question for the first investment P = $2800, annual rate of interest = 3%, no of periods n = 4.

So using the formula A = P(1+nr) = 2800(1 + (0.03)(4)) = 2800(1.12) = 3136

For the second investment P = $2800. annual rate of interest r = 0.03, no of

periods = 4, and it is invested at compound interest, compounded annually

So [tex]$A = P {(1 + r)}^n = 2800{(1 + 0.03)}^4 = 2800{(1.03)}^4 = 3151.4246$[/tex] .

The difference in the two total amounts = $3151.4246 - $3136 = $15.4246.

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The difference between the future total of 3% simple interest for 4 years and 3% compound interest for 4 years, compounded annually, is:

$349.40 - $336 = $13.40

Simple interest is a type of interest that is calculated only on the original amount of money borrowed or invested, called the principal. It is a linear calculation and does not take into account any interest earned on previously earned interest. The formula for simple interest is:

Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)

Compound interest is a type of interest that is calculated on the initial principal as well as on the accumulated interest from previous periods. It is a compounding calculation that allows for interest to be earned on interest. Compound interest can be compounded annually, semi-annually, quarterly, monthly, or even daily, depending on the frequency of compounding. The formula for compound interest is:

Compound Interest (CI) = [tex]p[/tex][tex](1+R)^{T}[/tex][tex]-p[/tex]

The difference between the future total of 3% simple interest for 4 years on $2800 and 3% compound interest for 4 years, compounded annually, can be calculated as follows:

For simple interest:

The formula for calculating simple interest is:

Simple Interest (SI) = P×R×T

Where:

Principal (P) = $2800

Rate (R) = 3% = 0.03 (as a decimal)

Time (T) = 4 years

Plugging in these values:

SI = $2800 x 0.03 x 4 = $336

For compound interest:

The formula for calculating compound interest is:

Compound Interest (CI) = [tex]P[/tex] [tex](1+R)^{T}[/tex]-[tex]P[/tex]

Where:

Principal (P) = $2800

Rate (R) = 3% = 0.03 (as a decimal)

Time (T) = 4 years

Plugging in these values:

CI = $2800 x (1 + 0.03)⁴ - $2800

CI = $2800 x (1.03)⁴ - $2800

CI = $2800 x 1.1255 - $2800

CI = $3149.40 - $2800

CI = $349.40

The difference between the future total of 3% simple interest for 4 years and 3% compound interest for 4 years, compounded annually, is:

$349.40 - $336 = $13.40

So, the difference is $13.40.

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The probability of the store manager selecting 2 comedies and 1 action movie out of the list of 15 movies is 0.066

The probability of the store manager selecting 2 comedies and 1 action movie out of the new list of 15 movies is 0.165

Using this formula, we can find the total number of ways in which the manager can select any 3 movies from the list of 15, which is:

¹⁵C₃ = 455

Next, we need to determine the number of ways in which the manager can select 2 comedies and 1 action movie out of the list of 15 movies. To do this, we first need to determine the total number of comedies and action movies in the list, which is 4 and 5, respectively.

⁴C₂ x ⁵C₁ = 30

Therefore, the probability of the store manager selecting 2 comedies and 1 action movie out of the list of 15 movies is:

30/455 = 0.066

Now, if two more comedy movies were added to the list in place of the 2 mystery movies, the total number of comedies in the list would increase from 4 to 6, while the total number of action movies would remain the same at 5.

Using the same formula as before, the new total number of ways in which the manager can select any 3 movies from the list of 15 movies would still be 455.

The number of ways in which the manager can select 2 comedies and 1 action movie from the new list of movies can be found using the same product rule of probability as before. We can select 2 comedies from 6 in 6C2 ways, and 1 action movie from 5 in 5C1 ways. The new total number of ways in which 2 comedies and 1 action movie can be selected is:

⁶C₂ x ⁵C₁ = 75

Therefore, the probability of the store manager selecting 2 comedies and 1 action movie out of the new list of 15 movies is:

75/455 = 0.165

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Answer:

The answer for anle X is 66°

Step-by-step explanation:

Base angles of an isosceles triangle are equal

<x=<y

<x+<y+<w=180

let<x=X

Remember <X=<Y

X+X+48=180

2X+48=180

2X=180-48

2X=132

divide both sides by 2

X=66°

<X=X

<X=66°

From the plot we deduce that

(h, k) = (1, 2)

Domain = all real numbers

Range = all real numbers

Transformations

The translation for the function

y = -(x - 1)^1/3 + 2

Shows a movement from the parent function y = x^1/3

-x^1/3 The negative sign is for reflection

-(x - 1)^1/3 represents translation right 1 unit

-(x - 1)^1/3 + 2 represents translation up 2 units

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Answer:

Gemma can type 3150 words in 3/4hr

Step-by-step explanation:

350 word------>five minutes

x words------->3/4hr

convert 3/4hr-minutes

3/4×60=45minutes

x word =350×45/5

x word=3,150 words

Answer:

The equation y = 1/(x+4) can be rewritten in slope-intercept form (y = mx + b) by isolating y:

y = 1/(x+4) can be rewritten as y = (1/x)/(1/4) = 4/x

So the equation y = 4/x is in slope-intercept form, where the slope is the coefficient of x, which is 4.

Therefore, the slope of the line y = 1/(x+4) is 4, and the correct answer is (A) 4.

The construction and the resulting triangles are interesting because they allow us to explore the properties of perpendicular lines and the angles they form.

Now, let's look at the two triangles that are formed as a result of this construction - ΔABD and ΔBCD. Since line BD is perpendicular to line AC, we know that angle ABD and angle CBD are both right angles. This is because any line that is perpendicular to another line forms a right angle with that line.

Now, let's look at the other sides of the triangles. In ΔABD, we have side AB, which is different from side BC in ΔBCD. Similarly, in ΔBCD, we have side CD, which is different from side AD in ΔABD.

So, although the two triangles share a common side (BD), they have different lengths for their other sides. This means that the two triangles are not congruent, since congruent triangles must have the same length for all their sides.

However, we can still find some similarities between the two triangles. For example, since angle ABD and angle CBD are both right angles, we know that they are congruent. Additionally, we can use the fact that angle ADB is congruent to angle CDB, since they are alternate interior angles formed by a transversal (line BD) intersecting two parallel lines (line AC and the line perpendicular to it passing through point B).

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Complete Question:

Draw a line through point B that is perpendicular to line AC Label the intersection of the line and line AC as point D. Take a screenshot of your work, save it, and insert the image in the space below.

Part B

Based on your construction, what do you know about ΔABD and ΔBCD?

The measure of the height of the building is approximately 1,154.8 feet.

We can use trigonometry to solve this problem. Let h be the height of the building. Then we have:

tan(30°) = h/2,000

We can solve for h by multiplying both sides by 2,000:

h = 2,000 tan(30°)

Using a calculator, we can evaluate tan(30°) to be approximately 0.5774. Substituting this value, we get:

h = 2,000 × 0.5774

h ≈ 1,154.8

Therefore, the height of the building is approximately 1,154.8 feet.

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Answer:

9ft

Step-by-step explanation:

I'm not sure, sorry if this didn't help you have a good day

The ordered pairs for the given equation 6x+4y=24 is (2, 3), (0, 6), (4, 0) and infinitely many other ordered pairs that satisfy the equation, depending on the values of x and y chosen.

Ordered pairs are pairs of values that are arranged in a specific order, typically written in the form (x, y), where x represents the value along the horizontal axis (often called the x-axis) and y represents the value along the vertical axis (often called the y-axis).

According to the given information:

To complete the ordered pairs so they are solutions of the equation 6x + 4y = 24, we need to find values of x and y that satisfy the equation.

Here are some possible ordered pairs that are solutions of the equation:

When x = 2, y = 3:

(2, 3)

Substituting these values into the equation:

6(2) + 4(3) = 12 + 12 = 24

So, (2, 3) is a solution of the equation.

When x = 0, y = 6:

(0, 6)

Substituting these values into the equation:

6(0) + 4(6) = 0 + 24 = 24

So, (0, 6) is also a solution of the equation.

When x = 4, y = 0:

(4, 0)

Substituting these values into the equation:

6(4) + 4(0) = 24 + 0 = 24

So, (4, 0) is another solution of the equation.

There could be infinitely many other ordered pairs that satisfy the equation, depending on the values of x and y chosen.

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If we consider grade "C" or above as a pass grade, then the number of  students who successfully passed the course are 10 students.

The Number of students who got grade "A" = 8,

The Number of students who got "B" grade is 2,

The Number of students who got grade "C" = 0,

The Number of students who got grade "D" = 0,

The Number of students who got grade "F" = 1,

Since the question asks for the number of students who successfully passed the course (i.e., grade "C" or above is considered a pass grade),

We add the number of students who got grades "A" and "B".

So, total number of students who successfully passed course are :

⇒ 8 (students who got grade "A") + 2 (students who got grade "B")

⇒ 10

Therefore, 10 students successfully passed the course.

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The given question is incomplete, the complete question is

If 8 students of the class got grade "A", 2 student got grade "B", No student got grade "C" and "D", 1 student got grade "F".

Considering grade "C" or above as a pass grade, how many students from this data successfully passed the course?

The crude death rate for all causes in Metroville is 1 per 1,000 residents if the total number of deaths from all causes is 900.

total number of residents injured from roller-skating = 1,800

total number of deaths = 90

deaths from all causes  = 900

Therefore, we can set up a proportion:

90 deaths / x residents = 1,000 deaths per 1,000 residents

x = 90,000 / 1,000

x = 90

The total population of Metroville is 90,000 residents.

The crude death rate for all causes is then:

Crude death rate = (total number of deaths / total population) * 1,000

Crude death rate = [tex](90 / 90,000) * 1,000[/tex]

Crude death rate = 1 per 1,000 residents

Therefore, we can conclude that the crude death rate for all causes in Metroville is 1 per 1,000 residents.

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It has been proved that the lines MN and PR are parallel because they have the same slope.

We are given the coordinates of the points P, Q and R as:

P(-3, -6)

Q(1, 4)

R(5, -2)

Since M is the midpoint of PQ, we have:

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

M = (-1, -1)

N is the midpoint of QR and so:

N = (1 + 5)/2, (4 - 2)/2

N = (3, 1)

Slope of MN = (1 + 1)/(3 + 1) = 1/2

Slope of PR = (-2 + 6)/(5 + 3)

Slope of QR = 4/8 = 1/2

Both slopes are equal and as such they are parallel lines

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The value of p would be could be approximately -0.391 or  0.321.

Let's start by using the quadratic formula to find the roots of the polynomial [tex]px^2 + 5x + 8p[/tex]

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

Plugging in the coefficients, we get:

[tex]x = (-5 ± √(5^2 - 4p(8p))) / 2p[/tex]

Simplifying, we get:

[tex]x = (-5 ± √(25 - 32p^2)) / 2p[/tex]

Now, we know that the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a. So:

Sum of roots = [tex](-5 + √(25 - 32p^2)) / 2p + (-5 - √(25 - 32p^2)) / 2p = -5/p[/tex]

Product of roots = [tex][(-5 + √(25 - 32p^2)) / 2p] * [(-5 - √(25 - 32p^2)) / 2p] = (25 - 32p^2) / 4p^2[/tex]

Since we're given that the sum of the roots is equal to the product of the roots, we can set these expressions equal to each other and solve for p:

[tex]-5/p = (25 - 32p^2) / 4p^2[/tex]

Multiplying both sides by 4p^2 gives:
[tex]-20p = 25 - 32p^2[/tex]

Adding [tex]32p^2[/tex] to both sides and rearranging, we get:
[tex]32p^2 + 20p - 25 = 0[/tex]

Now we can use the quadratic formula again to solve for p:

[tex]p = (-b ± √(b^2 - 4ac)) / 2a[/tex]

Plugging in the coefficients, we get:

[tex]p = (-20 ± √(20^2 - 4(32)(-25))) / 2(32)[/tex]

Simplifying, we get:

[tex]p = (-20 ± √1560) / 64[/tex]

p ≈ -0.391 or p ≈ 0.321

Therefore, the value of p could be approximately -0.391 or approximately 0.321.

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Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.

To find the time in minutes when the trough is empty, we need to solve the equation f(x) = 0, since f(x) represents the volume of water in the trough.

So, we need to solve the quadratic equation:

[tex]10x^2 - 19x + 6 = 0[/tex]

To solve this equation, we can use the quadratic formula:

[tex]x = (-b ± \sqrt(b^2 - 4ac)) / 2a[/tex]

where a = 10, b = -19, and c = 6.

Plugging in these values, we get:

[tex]x = (-(-19) ± \sqrt((-19)^2 - 4(10)(6))) / 2(10)[/tex]

[tex]x = (19 ± sqrt(241)) / 20[/tex]

So, the two solutions are:

[tex]x = (19 + \sqrt(241)) / 20 \approx1.807 minutes[/tex]

[tex]x = (19 - \sqrt(241)) / 20 \approx0.313 minutes[/tex]

However, only the second solution makes sense in this context, since the trough cannot be empty before we start draining the water. Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.

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Therefore, the correct answer is (B) No, she needs 1/2 cup more.

To determine if Patricia has enough rice cereal for her recipe, we need to calculate the total amount of rice cereal she has after all her actions and compare it to the 3 cups required for the cereal clusters.

Initially, Patricia had 5 cups of rice cereal. She used 3 cups to make granola bars, leaving her with 2 cups. She then borrowed 0.5 cup from her friend, which brings her total to 2.5 cups.

Finally, she needs 3 cups of rice cereal for the cereal clusters recipe. Since she only has 2.5 cups, she does not have enough rice cereal and needs to get more. Therefore, the correct answer is B) No, she needs 1/2 cup more.

She then borrows 0.5 cup, so she now has 2 + 0.5 = 2.5 cups.

needs 3 - 2.5 = 0.5 cups more.

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The measures represent a 7-point Likert scale.

Interval scales are numerical scales in which the difference between any two adjacent points is the same.

Examples of interval scales include temperature (in Celsius or Fahrenheit), standard IQ scores, and dates.

Ordinal scales are numerical scales in which the difference between any two adjacent points is not necessarily the same.

Examples of ordinal scales include rankings (e.g., 1st, 2nd, 3rd, etc.), letter grades (A, B, C, etc.), and Likert scales (e.g., strongly agree, agree, neutral, disagree, strongly disagree).

Ordinal scales allow for the ranking of items, but the distances between points on the scale are not necessarily equal.

Interval scales, on the other hand, measure the distance between points on the scale and the difference between any two points is the same.

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the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).

What is function?

a function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

To find the x-intercepts, we set the numerator of the function equal to zero:

[tex]2 / (x^2 + 3x - 10) = 0[/tex]

This is only true if the numerator is equal to zero, so:

2 = 0

This is not possible, so the function has no x-intercepts.

To find the vertical asymptotes, we look for values of x that make the denominator equal to zero:

[tex]x^2 + 3x - 10 = 0[/tex]

We can factor the quadratic as:

(x + 5)(x - 2) = 0

This means that the function has vertical asymptotes at x = -5 and x = 2.

Now, let's plot some points between and beyond each x-intercept and vertical asymptote:

When x = -6, f(x) = 2 / (-6)² + 3(-6) - 10 = -1/2

When x = -4, f(x) = 2 / (-4)² + 3(-4) - 10 = 1/2

When x = 0, f(x) = 2 / (0)² + 3(0) - 10 = -1/5

When x = 3, f(x) = 2 / (3)² + 3(3) - 10 = 1/2

When x = 4, f(x) = 2 / (4)² + 3(4) - 10 = -1/2

When x = 6, f(x) = 2 / (6)² + 3(6) - 10 = 1/5

Therefore, the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).

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Answer:

gcf is 'x'

Step-by-step explanation:

the common factor to the terms 'x²' and '3x' is 'x'

In light of this, the likelihood of drawing a club followed by a four from a typical 52-card deck with replacement is roughly 0.014, rounded to three decimal places.

Probability is an evaluation of an event's potential or chance of occurring. It is a number between zero and 1, where 0 denotes an impossibility and 1, a certainty, respectively, for an event. The number of favourable outcomes is divided by the total number of potential scenarios to determine the likelihood of a particular circumstance. Several disciplines, including math, statistics, science, construction, economics, and finance are heavily reliant on probability.

given

Due to the fact that there are 13 clubs in a deck of 52 cards, the likelihood of drawing a club on the initial draw is 13/52.

Given that the first card was a club, the likelihood of drawing a four on the second draw is 3/52.

We can compound the odds of the two events to determine the likelihood of drawing a club followed by a four with replacement:

P(club, then four) is equal to P(club) * P(four | club) (13/52) * (3/52), which equals 0.014.

In light of this, the likelihood of drawing a club followed by a four from a typical 52-card deck with replacement is roughly 0.014, rounded to three decimal places.

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Answer:

Step-by-step explanation:

8%

Answer:

0.08

Step-by-step explanation:

When you're looking for how to turn a fraction into a decimal, what you need to do is simply divide the numerator by the denominator.

Thus, the volume of Pyramid with the given base and height is found as:  

2342.925 sq. km.

A pyramid is just a polyhedron with a polygonal base and triangles on all of its lateral faces. In this lesson, we will only focus on pyramids with lateral faces that are congruent, or identical in size and shape.

Given data:

Volume of Pyramid:

V = base area * height

Base area = 1/2*base*height

Base area = 1/2*26.7*11.7

Base area =  156.195 sq.km.

Now,

Volume of Pyramid =  156.195 * 15

Volume of Pyramid =  2342.925 sq. km.

Thus, the volume of Pyramid with the given base and height is found as:  

2342.925 sq. km.

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Complete question:

find the Volume of Pyramid:

Base length = 26.7 km

base width = 11.7 km

Height = 15 km

Therefore, both functions have the same axis of symmetry equation, which is x = -3.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are one of the central objects of study in mathematics and have many applications in various fields such as physics, economics, engineering, and computer science. A function is typically represented using a mathematical expression or equation, and it can be analyzed and manipulated using a variety of mathematical techniques.

Here,

Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.

For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.

For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.

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The x - intercepts, when entered as ordered pairs, would be (2, 0) and (-4, 0).

The y - intercepts would be (0, -8).

The equation for the line of symmetry for the graph of f(x) would be x = -1.

The vertex of the graph of f(x) would be (-1, -9).

To find the x-intercepts, we need to set f(x) = 0 and solve for x:

x = (-2 ± √(2² - 4 x 1 x (-8))) / (2 x 1)

x = (-2 ± √(4 + 32)) / 2

x = (-2 ± √36) / 2

x = (-2 ± 6) / 2

There are two solutions:

x1 = (-2 + 6) / 2 = 4 / 2 = 2

x2 = (-2 - 6) / 2 = -8 / 2 = -4

So the x-intercepts are (2, 0) and (-4, 0).

To find the y-intercept, we need to set x = 0 and solve for f(0):

f(0) = 0² + 2 x 0 - 8 = -8

So the y-intercept is (0, -8).

To find the line of symmetry, we can use the formula:

x = -b / 2a

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

So the equation of the line of symmetry is x = -1.

To find the vertex, we need to substitute the x-coordinate of the line of symmetry into the function:

f(-1) = (-1)² + 2 * (-1) - 8 = 1 - 2 - 8 = -9

So the vertex is at the point (-1, -9).

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The value of the missing angles are:

w = 109°

x = 39°

y = 141°

z = 109°

In geometry, we know that the sum of angles on a straight line is 180 degrees. Thus:

w = 180 - 71

w = 109°

We know that alternate angles are formed when two parallel lines are cut by a transversal. Thus:

x = 39°

y = 180 - 39

y = 141°

Similarly:

z = 180 - 71

z = 109°

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Answer:√2/2

Step-by-step explanation:

Let's label the sides of the right triangle as follows:

The side adjacent to the angle θ (cosine is adjacent/hypotenuse): 6

The hypotenuse (the longest side): 6√2

The side opposite to the angle θ (sine is opposite/hypotenuse): 6√3

Using the Pythagorean theorem, we can find the length of the missing side:

a² + b² = c²

6² + (6√3)² = (6√2)²

36 + 108 = 72

144 = 72

√144 = √72

12 = 6√2

Now that we know the length of all three sides, we can use the cosine ratio to find the value of cos(θ):

cos(θ) = adjacent/hypotenuse = 6/6√2 = √2/2

Therefore, the value of cos(θ) in the right triangle with sides of 6, 6√2, and 6√3 is √2/2.

The distance the tip of the bat travels is equivalent to the length of the arc which is 205 inches

The distance the tip of the bat travels is equal to the length of the arc it sweeps through. To calculate this length, we need to use the formula:

length of arc = (angle / 360) x 2πr

where angle is the central angle in degrees, r is the radius of the circle, and π is a constant approximately equal to 3.14159.

Substituting the given values, we get:

length of arc = (255 / 360) x 2π x 46

length of arc = (0.7083) x 2 x 3.14 x 46

length of arc = 204.6 inches (rounded to two decimal places)

Therefore, the distance the tip of the bat travels is approximately 205 inches to the nearest inch.

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The shortest driving distance between the stadium and the animal shelter is given as follows:

10 blocks.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates are given as follows:

Since the spaces are filled by houses, we cannot apply the formula, hence the shortest distance is:

6 - (-3) + 3 - 2 = 9 + 1 = 10 blocks.

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If rosanne makes 112 liters of strawberry lemonade, she pours 14 of a liter of lemonade into a thermos to take to the park, rosanne's brother drink 25 liters of lemonade

To solve this problem, we can start by subtracting the 14 liters of lemonade that Rosanne poured into the thermos from the total 112 liters to get the amount of lemonade that remained:

112 - 14 = 98 liters

Next, we need to subtract the amount of lemonade that Rosanne's brother drank, which is 25 liters, from the remaining amount:

98 - 25 = 73 liters

Therefore, Rosanne's brother drank 25 liters of lemonade.

To check our answer, we can add the amount of lemonade in the thermos, the amount that Rosanne's brother drank, and the remaining amount to see if it adds up to the original 112 liters:

14 + 25 + 73 = 112

Since the sum is indeed equal to 112, we can be confident that our answer of 25 liters for the amount of lemonade that Rosanne's brother drank is correct.

In summary, to find the amount of lemonade that Rosanne's brother drank, we subtracted the amount that Rosanne poured into the thermos and the amount that her brother drank from the total amount of lemonade that Rosanne made. The answer is 25 liters.

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The proof that the table has a constant ratio is shown below

From the table of values, we have the following parameters that can be used in our computation:

f(x + 1) = ab^(x + 1)

f(x + 2) = ab^(x + 2)

f(x + 3) = ab^(x + 3)

When divided, we get the ratio r

So, we have

r = f(x + 3)/f(x + 2) = f(x + 2)/f(x + 1)

This gives

ab^(x + 3)/ab^(x + 2) = ab^(x + 2)/ab^(x + 1)

Divide through by a

b^(x + 3)/b^(x + 2) = b^(x + 2)/b^(x + 1)

Using the law of indices, we have

b^(x + 3 - x - 2) = b^(x + 2 - x - 1)

Evaluate

b^0 = b^0

This gives

1 = 1

Hence, the table has a constant ratio

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