5.
What is the width of a rectangle if the area is 2x²-x-6 and the length is 2x + 3?
O-x-1--
x-2
3
2x+3
O-x+ 2
MacBook Air
2x²-1
2
Onone of the answer choices

the first term of the geometric series is approximately 105.294.

How to solve the problem?

The formula for the sum of a geometric series is given by:

Sn = a1(1 - rⁿ)/(1 - r)

where a1 is the first term, r is the common ratio, n is the number of terms, and Sn is the sum of the series.

We are given that Sn = 3045, r = 2/5, and An = 120, where An is the nth term of the series. We can use these values to solve for a1.

First, we can use the formula for the nth term of a geometric series:

An = a1 * rⁿ⁻¹

Substituting An = 120 and r = 2/5, we get:

120 = a1 * (2/5)ⁿ⁻¹

We also know that the sum of the series is Sn = 3045. Substituting the formula for Sn and solving for n, we get:

3045 = a1(1 - (2/5)ⁿ)/(1 - 2/5)

12180 - 4(2/5)ⁿ = 5a1

a1 = (12180 - 4(2/5)ⁿ)/5

Now we can substitute this expression for a1 into the equation we obtained for An:

120 = [(12180 - 4(2/5)ⁿ)/5] * (2/5)ⁿ⁻¹

Simplifying and solving for n, we get:

n = log(12/5) / log(2/5)

Substituting this value of n back into the expression for a1, we get:

a1 = (12180 - 4(2/5) power (log(12//log(2/5))) / 5

Using a calculator, we can evaluate this expression to get:

a1 ≈ 105.294

Therefore, the first term of the geometric series is approximately 105.294.

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Answer: [tex]-6x^3+23x^2+59x-120[/tex]

Step-by-step explanation:

(2x – 3)(8 + 3x)( 5 - x)

To multiply this polynomial we can break it down into two steps.

First, lets multiply (2x – 3)(8 + 3x) from the polynomial (2x – 3)(8 + 3x)(5 - x).

Its best to rearrange the x in the parenthesis, so it can look and be much easier: (2x – 3)(8 + 3x)  ->  (2x – 3)(3x + 8)

Now lets multiply it out: (2x – 3)(3x + 8)

[tex]6x^2+16x-9x-24[/tex]

After multiplying it out, combine like terms:

[tex]6x^2+7x-24[/tex]

Now take this polynomial and multiply the remaining factor, (5 - x)

[tex](-x + 5)(6x^2+7x-24)\\\\-6x^3+-7x^2+24x+30x^2+35x-120[/tex]

Now lets combine like terms!

[tex]-6x^3+23x^2+59x-120[/tex]

So the answer is: [tex]-6x^3+23x^2+59x-120[/tex]

The length of the ramp is approximately 4.95 meters and the angle the ladder makes with the ground is approximately 58.21 degrees.

To solve x^2 + 8x - 20 = 0 using the Zero Product Property, we first need to factor the quadratic equation into two linear factors:

So, we have

(x + 2)(x - 10) = 0

This gives

x = -2 and x = 10

To find the length of the ramp, we can use the trigonometric ratio of tangent.

We know that the vertical height (opposite side) of the ramp is 1.8 meters and the angle between the ramp and the ground (angle of elevation) is 20

So, we have

tan(20) = opposite / adjacent

tan(20) = 1.8 / adjacent

This gives

adjacent = 1.8/tan(20)

Evaluate

adjacent = 4.95

Therefore, the length of the ramp is approximately 4.95 meters.

We know that the ladder is 20 feet long and reaches a point 17 feet up the wall.

Let the angle the ladder makes with the ground be θ.

Using the trigonometric ratio of sine, we have:

sin(θ) = opposite / hypotenuse

sin(θ) = 17 / 20

Taking the arc sine of both sides, we get:

θ = sin^(-1)(17/20)

Using a calculator, we get:

θ ≈ 58.21 degrees

Therefore, the angle the ladder makes with the ground is approximately 58.21 degrees.

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The equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, x, can be represented as y = 2x + 125, where 2x represents the total amount she saves from her allowance and 125 represents the initial amount she saved.

This is a linear equation in slope-intercept form, where the slope of the line is 2, indicating that she saves $2 per day, and the y-intercept is 125, indicating that she had already saved $125 before starting to save from her allowance. To graph this equation, we can plot the y-intercept at (0, 125) and use the slope to find other points on the line. For example, after 5 days, she would have saved y = 2(5) + 125 = 135 dollars, giving us the point (5, 135). Plotting this point and connecting it with the y-intercept will give us a straight-line graph.

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Answer:

50.23

Step-by-step explanation:

To calculate the difference between the offensive and defensive values, we simply subtract the defensive value from the offensive value:

81.8 - 31.57 = 50.23

The difference between the offensive and defensive values is 50.23.

The distance between point A (6,3) and A' (2,1) is half of the original distance between A and B (6,3) and (15,3). Therefore, the scale factor is one half.

To determine the scale factor used to create the image of the second polygon A'B'C'D' from the original polygon ABCD, we can compare the side lengths of the two polygons.

The scale factor used to create the image is one half. This is because the distance between each vertex in the original polygon and the corresponding vertex in the image polygon is half of the original distance. For example,
Let's take the horizontal sides:
Side AB in polygon ABCD has length 15 - 6 = 9 units.
Side A'B' in polygon A'B'C'D' has length 5 - 2 = 3 units.

Now, we can find the scale factor by dividing the side length of A'B' by the side length of AB:
Scale factor = (A'B') / (AB) = 3 / 9 = 1/3

So, the scale factor used to create the image is one third.

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Answer: -4x(x-1)

Step-by-step explanation:

Since both are perfect squares just factor.

Value of side x in equilateral triangle is 6units.

An equilateral triangle is a type of triangle in which all three sides are of equal length. Equilateral triangles are also equiangular, meaning all three angles are of equal measure and are each 60 degrees. Because all three sides and angles are equal, equilateral triangles are symmetric about their center point, and their three medians, altitudes, and angle bisectors are all the same line.

Area of equilateral triangle = √3/4×a²

Given side length=12

So, area of equilateral triangle =√3/4×12²=62.35383

We know that

Area of triangle= ½×base×height

Given

Base=12

let height of triangle be=y

Area=½×12×y

62.35383=½×12×y

y=10.39

Using pythagoras' theorem,

c²=a²+b²

122=x²+10.392

x=√144-107.95

x=6

Hence, value of side x in equilateral triangle is 6units.

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The net profit can be calculated by subtracting the production costs from the total revenue generated by selling tickets. Since each ticket was sold for a fixed price, we can assume that the relationship between the net profit and the number of tickets sold is linear.

We know that when 200 tickets were sold, the net profit was $12,000, which means that the slope of the linear function is:

[tex]\text{slope = (net profit at 200 tickets - net profit at 0 tickets)} \div (200 - 0)[/tex]

[tex]\text{slope} = (\$12,000 - \$1,200) \div 200[/tex]

[tex]\text{slope} = \$55[/tex]

The y-intercept of the linear function represents the net profit when no tickets have been sold, which is equal to the negative of the production costs:

[tex]\text{y-intercept} = -\$1,200[/tex]

Therefore, the equation of the linear function is:

[tex]\text{y} = \$55x - \$1,200[/tex]

where x is the number of tickets sold and y is the net profit in dollars.

The graph of this function is an increasing linear function in quadrant 1 with a positive y-intercept, which is choice A. Therefore, the answer is choice A: graph of an increasing linear function in quadrant 1 with a positive y-intercept.

0.2342 is the probability that the number of women that would prefer to drink tea over coffee is within 1 standard deviation of the mean

Let's start by finding the mean and standard deviation of the number of women who prefer to drink tea over coffee in a sample of 7 women.

The mean is given by:

μ = np

where n is the sample size and p is the probability of success (the proportion of women who prefer tea over coffee).

So, for this problem, μ = 7 * 0.31 = 2.17

The standard deviation is given by:

σ = sqrt(np(1-p))

where sqrt denotes the square root.

So, for this problem, σ = sqrt(7 * 0.31 * (1 - 0.31)) = 1.22

2.17 - 1.22, 2.17 + 1.22

= 0.95, 3.39

using binomial probability

p^x * 1 - p

= 0.31 * 7 x 0.108

= 0.2342

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Answer:

(D) 8 units to the left

Step-by-step explanation:

Took the test, got it right. FLVS

In a perfectly competitive market, firms are price takers, meaning they have no market power and must accept the market price for their output.

A market price is the price at which a good or service is sold in a specific market. The forces of supply and demand determine market price in a competitive market.

Firms in a perfectly competitive market are price takers, which means they lack market power and must accept market prices for their output.

As a result, in a perfectly competitive market, the demand for multiple variable inputs is derived from the marginal product of each input.

The marginal product is the extra output generated by adding one more unit of an input while holding all other inputs constant.

Thus, the value of the marginal product, which is the marginal product multiplied by the market price of the output, is the demand for an input.

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Answer:

a = 3√2;

b = 3

Step-by-step explanation:

Use trigonometry:

[tex] \tan(45°) = \frac{b}{3} [/tex]

Cross-multiply to find b:

[tex]b = 3 \times \tan(45°) = 3 \times 1 = 3[/tex]

Use the Pythagorean theorem to find a:

[tex] {a}^{2} = {3}^{2} + {b}^{2} [/tex]

[tex] {a}^{2} = {3}^{2} + {3}^{2} = 9 + 9 = 18[/tex]

[tex]a > 0[/tex]

[tex]a = \sqrt{18} = \sqrt{9 \times 2} = 3 \sqrt{2} [/tex]

Answer: it makes 74 degree

Step-by-step explanation: This forms a right triangle. The 25-ft ladder is the hypotenuse of the right triangle. and the 7ft bottom of the ladder is the base of a triangle

For the angle where the ladder meets the ground, the

ground is the adjacent leg. The ladder is the hypotenuse.

Call the angle between the ladder and the ground angle A.

The trig ratio that relates the adjacent leg and the hypotenuse is cosine.

Choose Download as ePub or Download as PDF from the Personal Books screen's export icon. The Apple Ibooks icon will say Transfer to Books when you select Open in.

A book is a device for storing data in the form either writing or images. Books are often made up of several pages that are bound together and covered in reeds, parchment, vellum, or paper.

Books are important in life, especially for young people. Reading books helps pupils learn more, improves their intelligence, and raises their awareness of the diverse nations and civilizations throughout the world.

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The correct order of the steps is:

1. Create a new document using a book template.
2. Add text to the book, then tap the More button in the upper-right corner.
3. Enter EPUB information, then tap Export.
4. Tap Export, then choose EPUB.
5. Choose Copy to Books to open the EPUB book in the Books app

.Your answer: To create an EPUB book and open it in the Books app, follow these steps in the correct order: 1. Create a new document using a book template. 2. Add text to the book, then tap the More button in the upper-right corner. 3. Tap Export, then choose EPUB. 4. Enter EPUB information, then tap Export. 5. Choose Copy to Books.

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A) Let X be the amount of time it takes Capt. Rigg to land a plane from announcement to touch down. We know that X has a uniform distribution from 0 to 25 minutes. The probability that it takes at least 5 minutes to land the plane is equal to the probability that X is greater than or equal to 5:

P(X ≥ 5) = (25-5)/(25-0) = 20/25 = 0.8

So the probability that, for a randomly selected flight, it takes Capt. Rigg at least 5 minutes to land the plane after the announcement is 0.8.

b) Since X has a continuous uniform distribution, the probability that it takes exactly 15 minutes to land a plane is 0.

Since the two equations represent the same line, there are infinitely many solutions to the system.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, each containing one or more terms, separated by an equal sign. The terms may contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. Equations are used to represent relationships between variables and to solve problems in mathematics, science, engineering, and many other fields. They can be classified based on their degree, number of variables, and the types of functions they involve. Linear equations, for example, involve only first-degree terms and are used to represent straight lines; quadratic equations involve second-degree terms and are used to represent parabolas.

Here,

To determine whether the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point, we can first put the equations in slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.

10y + 8x = 10

10y = -8x + 10

y = (-4/5)x + 1

5y - 5 = -4x

5y = -4x + 5

y = (-4/5)x + 1

Notice that the two equations have the same slope of -4/5 and the same y-intercept of 1. Therefore, the two lines are identical and intersect at every point on the line.

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After answering the presented question, we can conclude that inequality therefore, the solution for z is z < -7.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

[tex]15 - 3(2 - z) < -12\\15 - 6 + 3z < -12 \\9 + 3z < -12 \\3z < -21 \\z < -7 \\[/tex]

Therefore, the solution for z is z < -7.

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Answer:

54 degrees

Step-by-step explanation:

Any angle subtended by the angle is twice the angle subtended by the same angle.

Or m<LMP =2m<LNM.

So m<LNM = 108/2 = 54 degrees.

Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.

The answer to this problem: 7

Answer: 20

Step-by-step explanation:

The answer of the given question based on the relation is R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}.

Set listing notation is a way to represent a set by listing all of its elements between curly braces { }. If a set has a large or infinite number of elements, it may not be practical to list all the elements. In such cases, we can use set-builder notation to describe the set using a condition or a rule.

The "has the same parity as" relation on set A means that any two elements in A are related if they have the same parity (either both even or both odd).

So, we can write the relation R as a set of ordered pairs where each pair consists of two elements that have the same parity.

R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}

In this set, the ordered pair (x, y) indicates that x and y have the same parity. For example, (1, 3) is in R because 1 and 3 are both odd. Similarly, (2, 4) is in R because 2 and 4 are both even.

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The limit of (2n)! as n goes to 0 does not exist.

Limits are a fundamental concept in mathematics that describe the behavior of a function as the input variable approaches a certain value, either from one or both sides. They are used to determine values that a function can get arbitrarily close to but not necessarily equal to.

The limit of (2n)! as n goes to 0 does not exist, as the factorial function is not defined for non-negative integers less than 1. The factorial function is defined as the product of all positive integers up to and including the argument. Therefore, for non-negative integers less than 1, the factorial function is undefined. The limit does not exist because the function is undefined for the given value of n.

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Prove that Limit (2n)! as n goes to 0 does not exist.

Answer:

[tex]x {}^{ \frac{5}{8} } [/tex]

Step-by-step explanation:

[tex]1. \: \sqrt{x {}^{ \frac{5}{4} } } \\ 2. \: x {}^{ \frac{5 \times 1}{4 \times 2} } \\ 3. \: x {}^{ \frac{5}{4 \times 2} } \\ 4. \: x {}^{ \frac{5}{8} } [/tex]

The premise is that both of my next-door neighbors and I have brick homes. So, all of the homes in our area are brick construction. A good illustration of inductive reasoning is this.

2. Given that the pattern appears to be multiplying by 3, then 6, then 9, then 12, and so on, the next multiplication fact is probably 37 x 15 = 555.

3.

(A) The number 101 comes next in the list.

(b) The following digit in the series is -10.

4. According to the formula n(n+1)/2, the first n positive integers are added together. Hence, 48(48+1)/2 = 1176 is the sum of the first 48 positive integers.

5.

(A) The formula n(3n-1)/2 yields the nth pentagonal number. Thus, 6(3x6-1)/2 = 91 is the sixth pentagonal number.

(b) The expression n(n+1)/2 yields the nth triangular number. Hence, 8(8+1)/2 = 36 is the eighth triangular number.

6. There are ten ways to use the four nickels, three dimes, and two quarters to make a 30-cent purchase from the vending machine.

7. The first week, Ronnie had $12 to his name.

8.a.The ones digit in the number 24000 is 6.

(b) 341's units digit is 3.

9. 19 rungs make up the ladder.

10. Catwoman owns 42 felines.

11. 58 nests would require 8 birdhouses, plus 2 additional nests.

12. A total of 60 pupils received an A or a B.

13.

(a) 550 cups are anticipated to be consumed in 2004.

(b) The year 2003 exhibits the biggest decline in cups.

14. Since 2001, the typical class size has risen.

15. During 2001 and 2002, as well as between 2004 and 2005, the average class size increased. From 2001 to 2003, the average class size grew by two pupils.

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The relation between time and depth is not prοpοrtiοnal as 2/100 ≠ 4/180 ≠ 6/260 ≠ 8/340.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality"

To solve questions that involve a table showing the relationship between two variables, such as depth and time in this case, you may want to consider the following steps:

A quick check οf table values shοws the relatiοnship is nοt prοpοrtiοnal:

100/2 = 50 ≠ 45 = 180/4

That is, the ratiοs οf table values are nοt cοnstant.

2/100 ≠ 4/180 ≠ 6/260 ≠ 8/340

Therefore, the relation between time and depth is not prοpοrtiοnal.

When the values are graphed, the line thrοugh the pοints dοes nοt intersect the οrigin. This is further indicatiοn the relatiοnship is nοt prοpοrtiοnal.

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Complete question:

Answer:

S ========================= 9

because 9+ 1= 10

simple

Answer:

s=3

Step-by-step explanation:

3s+1 = 10

To solve for s in this two step equation, we must first subtract 1 from each side.

3s+1-1 = 10-1

3s = 9

Then divide by 3 on each side.

3s/3 = 9/3

s=3

Colby spends 29 minutes making her collage.

50 is the total amount of minutes and 21 minutes is a part of that total.

This means we have to subtract.

50 - 21 = 29.

Answer: I thank it is 200 point in 2 hour

Step-by-step explanation: