Jerome wants to buy grass seed to cover his whole lawn, except for the pool. the pool is 4 5/6 m by 2 1/3 m. find the area the grass seed needs to cover.

The roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex]also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

To find the roots of equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3,[/tex] we can substitute [tex]y = 2^(^x^-^2^)[/tex]to get:

[tex]y + 2^(^5^-^x^)^/^y = 3[/tex]

Multiplying both sides by y, we get:

[tex]y^2 + 2^(^5^-^x^) = 3y[/tex]

Substituting y = 2^(x-2), we get:

[tex]2^(^2^x^-^8^) + 2^(^5^-^x^) = 3 * 2^(^x^-^2^)[/tex]

Multiplying both sides by 2^8, we get:

[tex]4(2^x) + 32 = 768(2^(^2^-^x^))[/tex]

Simplifying, we get:

[tex]4(2^x) - 768(2^-^x) + 32 = 0[/tex]

Dividing both sides by 4, we get:

[tex]2^x - 192(2^-^x) + 8 = 0[/tex]

Multiplying both sides by [tex]2^x[/tex], we get:

[tex]4^x - 192 + 2^x = 0[/tex]

Adding 192 to both sides, we get:

[tex]4^x + 2^x - 192 = 0[/tex]

This is the same as the given equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

Therefore, we have shown that the roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex] also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

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Answer:

9th term is

[tex]a_9 = \dfrac{1280}{2187}\\[/tex]

Step-by-step explanation:

This sequence is clearly a geometric progression where the ratio of any term to the previous term is constant and known as common ratio

The 3 terms given are:
15, 10 and 20/3

10 ÷ 15 = 2/3

20/3 ÷ 10 = 2/3

So the common ratio is 2/3

For a geometric sequence with common ratio r and first term a₁, the nth term is given by the equation

aₙ = a₁ · rⁿ⁻¹

Here a₁  = first term = 15

r = 2/3

So the general equation for the nth term of this equation is
aₙ = 15 · (2/3)ⁿ⁻¹

The 9th term would be

[tex]a_9 = 15 \cdot \left(\dfrac{2}{3}\right)^{9-1}\\\\a_9 = 15 \cdot \left(\dfrac{2}{3}\right)^{8}\\\\a_9 = 15 \cdot \left(\dfrac{256}{6561}\right)\\\\a_9 = 15 \cdot \left(\dfrac{256}{6561}\right)\\[/tex]
15 is divisible by 3 giving 5
6561 is divisible by 3 giving 2187

So the above expression simplifies to
[tex]a_9 = 5 \cdot \dfrac{256}{2187}\\\\a_9 = \dfrac{1280}{2187}\\[/tex]

Answer:

It the distance from mid line to top of wave.

Step-by-step explanation:

Answer:

Height of a wave (from mid line to max.

Step-by-step explanation:

The ages of the​ teacher's three children whose product is 72 will be 3,3,8.

Let the age of three children be x, y, z

x × y × z = 72

x + y + z = No. of rooms

Now possible answers can be three numbers whose product is 72

There are two possible answers in which the product of the number is 72 and the sum of the number is also same

1) 2 × 6 × 6 = 72  and 2 + 6 + 6 = 14

2) 3 × 3 × 8 = 72  and 3 + 3 + 8 = 14

Now teacher gave a hint that his oldest child is good at math

Oldest means one of the three child is oldest so the only possible answer could be 3,3,8

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The value of the function at that point is equal to the z-coordinate of the point on the plane.

A horizontal tangent plane is a plane that is parallel to the x-y plane and tangent to a surface at a point where the slope in the horizontal direction is zero.

To use the tangent plane equation to find a horizontal tangent plane, we need to find the partial derivatives of the function with respect to x and y, evaluate them at the point of interest, and check if they are both zero.

If they are both zero, then the tangent plane is horizontal and the equation simplifies to f(a,b) = z.

The tangent plane equation is given by:

f(a,b) + f(1)(x-a) + f(2)(y-b) = z

where (a,b) is the point where the tangent plane intersects the surface, and f(1) and f(2) are the partial derivatives of the function with respect to x and y, evaluated at (a,b).

To use this equation to find the horizontal tangent plane, we first find the partial derivatives f(1) and f(2), and evaluate them at the point where we want to find the tangent plane. If f(1) and f(2) are both zero at that point, then the tangent plane is horizontal and the equation simplifies to:

f(a,b) = z

This means that the value of the function at that point is equal to the z-coordinate of the point on the plane.

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To multiply -1(x^2-4x+8), we need to distribute the -1 to each term inside the parentheses:

-1(x^2-4x+8) = -x^2 + 4x - 8

So, the product of -1 and the expression (x^2-4x+8) is -x^2 + 4x - 8.

Using the combine clues method:

[tex]R_1=7\\\\R_2=9\\\\R_3=8\\\\S_1=2\\\\S_2=4\\\\S_3=5\\\\T_1=10\\\\T_2=14[/tex]

Certain items that must be worn, used, or accessed in order to access particular clues. The maximum skill level needed to solve each master clue is shown.

Clue 1: [tex]R_1 + R_2 + R_3 = 24[/tex]

Clue 2: [tex]R_1 + R_2 =16[/tex]

Since, [tex]R_1 + R_2 + R_3 = 24[/tex] (from clue 1)

[tex]R_1 + R_2 + R_3 = 24\\\\16 + R_3 = 24[/tex]

Subtract both the sides by 16,

[tex]R_3=8[/tex]

Clue 3:

We need to find the blank [tex]R_1 +[/tex] __ [tex]+S_2=20[/tex] and [tex]S_2=4[/tex]

Since, [tex]R_1 + R_2 = 16[/tex] (from clue 2)

So,

[tex]R_1 + R_2 + S_2 = 20\\\\16 + S_2 = 20[/tex]

Subtract 16 from both sides.

[tex]16 + S_2 - 16 = 20 -16\\\\S_2 = 4[/tex]

So,

[tex]R_1 + R_2 + S_2 = 20[/tex]

Clue 4:

We need to find the blank [tex]R_2[/tex] = __

[tex]S_2 + R_2 = 13[/tex]

Since, [tex]S_2 = 4[/tex]

[tex]S_2 + R_2 = 13\\\\4 + R_2 = 13[/tex]

Subtract 4 from both sides.

[tex]R_2 = 9[/tex]

So, [tex]R_2 = 9[/tex]

Clue 5:

We need to find the blank ___ [tex]+ T_2 = 22[/tex] and [tex]T_2=[/tex] ___

[tex]R_3 + T_2 = 22[/tex]

Since, [tex]R_3 =8[/tex] (from the Clue 2)

[tex]R_3 + T_2 = 22[/tex]

[tex]8 + T_2 = 22[/tex]

Subtract both the sides by 8,

[tex]T_2 = 14[/tex]

So, [tex]R_3 + T_2 = 22[/tex]

Clue 6:

We need to find the blank [tex]T_1 +[/tex] ___ = 24 and ___ = 10

Since, [tex]T_1 + T_2 = 24[/tex] (from the Clue 5)

[tex]T_1 + 14 = 24[/tex]

Subtract both the sides by 14,

[tex]T_1 = 10[/tex]

Clue 7:

We need to find the value of [tex]S_1[/tex],

Given [tex]T_1 + R_3 + S_1 =20[/tex]

Since, [tex]T_1=10[/tex] and [tex]R_3=8[/tex]

[tex]10+ 8 + S_1 = 20\\\\18 + S_1 = 20[/tex]

Subtract both the sides by 18,

so, [tex]S_1=2[/tex]

Combining this with what we learned from Clue 2 and Clue 6, we know

[tex]S_1=2[/tex]

Now, we need to find the blank, [tex]S_1 + S_2 +[/tex] ___ = 11

Combining this with what we learned from Clue 3 and Clue 7, we know:

___ = 5

[tex]S_1 + S_2 + S_3 = 11\\\\2 + 4 + S_3 = 11\\\\6 + S_3 = 11[/tex]

Subtract both the sides by 6,

[tex]S_3 = 5[/tex]

For [tex]R_1[/tex]

Since,

[tex]R_1 + R_2 + R_3 = 24\\\\R_1 + 9 + 8 = 24\\\\R_1 + 17 = 24[/tex]

Subtract both the sides by 17,

[tex]R_1 = 17[/tex]

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Answer: 5 1/4

Step-by-step explanation: 3/4 times 7/1 equals 5.25

Turn the decimal to a fraction and get 5 1/4

System of equation Sam can use is 13b + 4t = 327.50 and 6b + 2t = 142.47 where "b" represents bushes and "t" represents trees.

Let the cost of bushes represented by b

cost of trees represented by t

First order is 13 buses and 4 trees and total is $327.50

By using the data equation form will be

13b + 4t = 327.50

Second order is 6 bushes and 2 trees and total is $142. 96

By using data the equation form will be

6b + 2t = 142.96

These set of equation will for and can be used.

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There would be of 11.3 times rs. 1300 is the value including 13% vat on rs. 13000

To find out how many times Rs. 1300 is contained in the value including 13% VAT on Rs. 13000, we need to first calculate the total value including VAT.

VAT is a tax that is added to the net price of a product or service. In this case, the net price is Rs. 13000 and the VAT is 13% of the net price, which is:

VAT = 13% of Rs. 13000

= 0.13 x 13000

= Rs. 1690

So, the total value including VAT is:

Total value = Net price + VAT

= Rs. 13000 + Rs. 1690

= Rs. 14690

Now, to find out how many times Rs. 1300 is contained in this value, we divide the total value by Rs. 1300:

Number of times = Total value / Rs. 1300

= Rs. 14690 / Rs. 1300

= 11.3 (approx)

Therefore, the value including 13% VAT on Rs. 13000 is about 11.3 times the value of Rs. 1300.

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Answer: x=4/3

Step-by-step explanation:

3x-2=2

3x=2+2

3x=4

x=4/3

The value or n(C) based on the information will be 6.

In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. More formally, if a is a factor of b, then b can be expressed as a product of a and some other number or expression.

For example, in the expression 12 = 2 x 2 x 3, the numbers 2 and 3 are factors of 12. Similarly, in the expression x² - 4, (x - 2) and (x + 2) are factors because if we multiply them together we get x² - 4.

The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the set C contains six elements. Hence, n(C) = 6.

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As per the given geometric sequence, the sum of the greater and lesser consequents is 51.

We are given that the antecedents (which are just the first three terms) of a geometric sequence are 2, 3, and 5. Let's call the common ratio of this sequence r. Using the definition of a geometric sequence, we can write the terms of this sequence as 2, 2r, 2r² (since the first term is 2 and the common ratio is r), 3, 3r, 3r², 5, 5r, 5r².

Next, we are told that the product of the consequents (which are just the terms after the first three) is 810. To find the product of the consequents, we just multiply all the terms after the first three together. So we have:

(2r³) * (3r²) * (5r) = 30r⁶

We know that this product is equal to 810, so we can set up the equation:

30*r⁶ = 810

Solving for r, we get:

r⁶ = 27

r = 3 (since 3⁶ = 729)

Now that we know the common ratio is 3, we can find the terms of the sequence by multiplying each antecedent by 3. So the terms of the sequence are:

2, 6, 18, 3, 9, 27, 5, 15, 45

The greater and lesser consequents are 45 and 6, respectively. So the sum of the greater and lesser consequents is:

45 + 6 = 51

Therefore, the answer to the problem is 51.

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Complete Question:

In a series of equal geometric ratios, the antecedents are 2, 3, and 5. If the product of the consequents is 810, find the sum of the greater and lesser consequents.

To create a dot plot that represents the given data, we need to place each data point on a number line and then represent it with a dot above its corresponding value. The number line should range from 0 to the maximum number of pets owned by any student, which in this case is 4.

First, we place a dot above the value 0, which occurs twice in the data set. Then, we place three dots above the value 1, which occurs five times in the data set. Next, we place two dots above the value 2, which occurs twice in the data set. Finally, we place one dot above the value 3 and one dot above the value 4.

In summary, the dot plot will have one dot above 3 and one dot above 4 for the number of pets axis, and for the number of students axis, we will have two dots above 0, five dots above 1, two dots above 2, and no dots above 3 or 4. This represents the distribution of the data in a visual way.

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The radius of the circle is 2mm

It is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.

The equation is written as;

C = 2πr

Such that the parameters are;

From the information given, we have thatt;

The radius of the circle = r

The circumference = 12.56mm

Substitute the values, we have;

12. 56 = 2×3.14r

Multiply the values

r = 12. 56/6. 28

divide the values

r = 2mm

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In triangle ABC with angle B as a right angle, if the measure of angle A is greater than 75 degrees (e.g., 80 degrees), side BC can be approximately 9.848 units, and the hypotenuse AC can be 10 units.

In triangle ABC with angle B as a right angle, to find measures of side BC and hypotenuse AC such that the measure of angle A is greater than 75 degrees, we can use the sine function.

Determine the sine of angle A. Since angle A needs to be greater than 75 degrees, let's choose 80 degrees as an example.
sin(80°) = opposite side (BC) / hypotenuse (AC)

Choose a convenient value for the hypotenuse (AC). Let's choose AC = 10 units.

Solve for the opposite side (BC).
sin(80°) = BC / 10
BC = 10 * sin(80°)
BC ≈ 9.848

If the measure of angle A is more than 75 degrees (for example, 80 degrees), side BC and the hypotenuse AC in the triangle ABC with a right angle can both be 10 units.

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Answer:

w

Step-by-step explanation:

w

The required values on the graph, the solution is approximate x = -0.33.

We can begin by combining like terms on the left-hand side:

3x² - 6x - 4 - 2/x + 3 + 1 = 0

3x² - 6x - 2/x = -3

Next, we can factor out the x term:

x(3x - 2) - 2(3x - 2) = -3

(x - 2)(3x - 2) = -3

Since the equation is equal to -3, we can add 3 to both sides to get:

(x - 2)(3x - 2) + 3 = 0

We can then factor the left-hand side to get:

(x - 2)(3x - 2 + 3) = 0

(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0

This equation has two solutions: x = 2 and x = -1/3.

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

1. The growth factor for the number of customers over a year is approximately 1.4266.

2. the growth factor in customers over a decade period is approximately 5.927.

Factors that affect how many consumers there are in a year are

c(12)/c(0) = (400 x (1.03)¹²) / (400 x (1.03)⁰)

= (1.03)¹²

= 1.4266....

Therefore, the growth factor for the number of customers over a year is approximately 1.4266.

2. To write an equation for the number of customers c as a function of the number of years y, we can substitute m = 12y into the original equation

[tex]c(y) = 400 x (1.03)^{12y}[/tex]

one decade = 10 years

= 120 months

We must calculate the value of the equation at m=120 and divide it by the equation's value at m=0.

c(120) / c(0) = [400 x (1.03)¹²⁰] / [400 x (1.03)⁰]

= (1.03)¹²⁰

= 5.927...

Therefore, the growth factor in customers over a ten-year period is approximately 5.927.

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Given Question is incomplete, complete question is given below:

A small printing company launched an online ordering system to expand its business. The equation [tex]c=400(1. 03)^m[/tex] represents the number of customers c it has in terms of the number of months m since it launched the ordering system.

1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value

2. If y is time in years, write an equation for the number of customers c as a function of the number of years y after the introduction of the ordering system. If this model continues to apply for a decade, by what factor will the number of customers grow in one decade?

Stem plots (also known as stem-and-leaf plots) have several advantages over frequency distributions, including:

1. Stem plots show individual data points: Unlike frequency distributions, which group data into intervals, stem plots show each individual data point. This makes it easier to see the distribution of the data, including the shape, the range, and any outliers or gaps. Stem plots can also reveal patterns and trends in the data that may not be apparent from a frequency distribution.

2. Stem plots are easy to construct: Constructing a stem plot requires minimal computation and is relatively simple to create by hand. It involves only sorting the data and then splitting each data point into a stem (the leading digits) and a leaf (the trailing digit). This makes stem plots a convenient tool for quick exploratory data analysis, especially when dealing with small to moderate-sized datasets. In contrast, constructing a frequency distribution can be more time-consuming, as it requires choosing appropriate intervals and counting the number of data points in each interval.

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If Tamekia and Marsha work for 22 hours, Marsha will earn $27.50 more than Tamekia.

To determine the amount of money each person can earn, we need to know the hourly rate and the number of hours worked. Tamekia estimates that she can earn between $6.00 and $6.25 per hour. Let's assume that she can earn $6.25 per hour. If Tamekia works for 22 hours, her total earnings will be:

Total earnings for Tamekia = Hourly rate x Number of hours worked = $6.25 x 22 = $137.50

Now let's look at Marsha's earnings. Marsha estimates that she can earn between $7.50 and $8.00 per hour. Let's assume that she can earn $7.50 per hour. If Marsha works for 22 hours, her total earnings will be:

Total earnings for Marsha = Hourly rate x Number of hours worked = $7.50 x 22 = $165.00

To determine how much more money Marsha will earn than Tamekia, we need to subtract Tamekia's total earnings from Marsha's total earnings:

Difference in earnings = Total earnings for Marsha - Total earnings for Tamekia = $165.00 - $137.50 = $27.50

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question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.

Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.

Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!

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A restaurant meal cost $90 and there was a 6% meals tax on the price of the meal. The meal tax was $5.40 and the total price of the meal with the meal tax was $95.40.

Find the meal tax, you need to calculate 6% of the $90 meal cost.
Convert the percentage to a decimal by dividing by 100, so 6% = 0.06.
Multiply the meal cost by the decimal. In this case, $90 × 0.06 = $5.40.
So, the meal tax was $5.40.
Find the total price of the meal with the meal tax, you need to add the meal tax to the original cost of the meal.
Add the meal tax to the original cost, so $90 + $5.40 = $95.40.
The total price of the meal with the meal tax was $95.40.

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The equation of the perpendicular line to y = -3x + 4 and passing through (-6, 2) is y = (1/3)x + 4.

There are a lot of perpendicular lines that we may see in reality. The corners of a chalkboard, a window, the sides of a set square, and the Red Cross symbol are a few examples.

Knowing that the slopes of perpendicular lines are the negative reciprocals of one another is necessary to determine the equation of a line perpendicular to a given line.

The given line has a slope of -3, so the slope of a line perpendicular to it would be the negative reciprocal of -3, which is 1/3.

We also know that the line passes through the point (-6, 2).

The equation of the line passing through (-6, 2) and perpendicular to y = -3x + 4 can be found using the point-slope form of a line:

y - 2 = (1/3)(x + 6)

Simplifying this equation, we get:

y = (1/3)x + 4

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The surface area and volume of the triangular prism are:

S = [tex]204 in^2[/tex]

V = [tex]144 in^3[/tex]

The area= 12 inches

The volume = 144 cubic inches

The area of each triangular face is already calculated (A = 12 square inches). The three rectangular faces have dimensions 5 x 12, 6 x 12, and 4 x 12.

Calculate the area of each rectangular face:

5 * 12 = 60 square inches

6 * 12 = 72 square inches

4 * 12 = 48 square inches

Now, sum the areas of all faces to get the surface area (S):

S = (2 * 12) + 60 + 72 + 48 = 204 square inches.

So, the surface area and volume of the triangular prism are:

S = [tex]204 in^2[/tex]

V = [tex]144 in^3[/tex]

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Answer: 141

Step-by-step explanation: 188 x 75% = 141

Answer:

141

Step-by-step explanation:

I looked it up.

To find the median of the data, we first need to arrange the numbers in order from smallest to largest:

3, 14, 624

Since we have an odd number of data points, the median is the middle number. In this case, the median is 14.

Therefore, the median of the data collected is 14 meters.

To find the local rate of change on a curve at a specific point, we need to find the slope of the tangent line at that point. The tangent line represents the instantaneous rate of change or the rate of change at that particular point.

To find the slope of the tangent line at (-6,8) on the parabola, we need to take the derivative of the function at that point.

Assuming that the parabola is defined by the equation [tex]y = ax^2 + bx + c,[/tex]

where a, b, and c are constants, we can find the derivative of the function as follows:

[tex]dy/dx = 2ax + b[/tex]

Substituting [tex]x = -6,[/tex] we get:

[tex]dy/dx = 2a(-6) + b[/tex]

To find the values of a and b, we need more information about the parabola.

If we have the equation of the parabola or another point on the curve, we can use it to find the values of a and b.

Once we have the values of a and b, we can substitute them into the derivative equation and evaluate it at [tex]x = -6[/tex] to find the slope of the tangent line at (-[tex]6,8[/tex]), which is the local rate of change at that point.

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