A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?

Answer:

To find the value of "c" for which the number "a" (-5 in this case) is a solution of the equation, we can substitute "a" into the equation and solve for "c".

Given equation: 4x + 1 + 7c = 8c - 3x + 6

Substituting x with "a": 4(-5) + 1 + 7c = 8c - 3(-5) + 6

Simplifying the equation: -20 + 1 + 7c = 8c + 15 + 6

Combining like terms: -19 + 7c = 8c + 21

Moving all "c" terms to one side: 7c - 8c = 21 + 19

Simplifying: -c = 40

Dividing both sides by -1 to isolate "c": -c/-1 = 40/-1

Flipping the sign when dividing by a negative number: c = -40

So, the value of "c" for which the number "a" (-5) is a solution of the equation is c = -40.

Answer:

[tex]c=-40[/tex]

Step-by-step explanation:

Since a is a Solution to the Equation , then it satisfies the Equation

Substitute by [tex]x=a=-5[/tex] into the Equation [tex]4x+1+7c=8c-3x+6[/tex]

Then [tex]4(-5)+1+7c=8c-3(-5)+6[/tex]

Then [tex]-20+1+7c=8c+15+6[/tex]

By adding like-terms

Then [tex]-19+7c=8c+21[/tex]

Then [tex]8c-7c=-19-21[/tex]

Then [tex]c=-40[/tex]

The volume of the cone is 288π m³. Hence, the answer is option C, 288π m³.

A cone is a shape created by connecting all the points of a circular base (which does not contain the apex) to a common point known as the apex or vertex using a series of line segments or lines. The height of the cone is determined by measuring the distance between its vertex and base.

The formula for the volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.

Substituting the given values, we get:

V = (1/3)π(6²)(24)

V = (1/3)π(36)(24)

V = (1/3)(864π)

V = 288π

Therefore, the volume of the cone is 288π m³.

Hence, the answer is option C, 288π m³.

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Every six months, you will receive $21.50 back from your bond.

The 4.3% coupon is the annual interest rate, which is paid semi-annually (twice a year).

To find the amount earned every 6 months, we need to divide the annual interest rate by 2:

(4.3% / 2) = 2.15%

Next, we need to calculate the dollar amount earned every 6 months. To do this, we need to find 2.15% of the bond's face value:

2.15% of $1000 = $21.50

Therefore, you will earn $21.50 off your bond every 6 months.

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The correct answer is not listed among the options. The correct answer is E. 1/x.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find f'(x), we need to differentiate the function f(x) with respect to x. Since we are given k(x) = 3x, we can use the chain rule to differentiate f(x) = ln(k(x)) = ln(3x) as follows:

f'(x) = d/dx [ln(3x)]

= 1/(3x) * d/dx [3x] (applying the chain rule)

= 1/(3x) * 3

= 1/x

Therefore, the correct answer is not listed among the options. The correct answer is E. 1/x.

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Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.

The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

where  (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.

To answer this we need to know the equation of a circle.

Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:

(x - a)² + (y - b)² = r²

We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.

We can now substitute these information in the circle equation,

(x - -3)² + (y - 6)² = 2²

(x+3)² + (y - 6)² = 4

That is the equation of the given circle is (x+3)² + (y - 6)² = 4.

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Answer:

As the number of sides of the bases of a prism increases, the shape of the prism becomes more complex and closer in form to a cylinder. For example, a prism with two identical polygonal bases, such as a rectangular prism or a triangular prism, will have a more blocky or pyramidal shape. However, as the number of sides of the base increases, the shape of the prism becomes more cylindrical and less pyramidal in appearance. This is because the more sides a polygon has, the more closely it approximates a circle, and the cross-section of the prism becomes more circular in shape.

When the number of sides of the base of a prism increases, the prism becomes more like a cylinder.

The expression that is equivalent to 6x2y + 2xy^5 include:

2(3x²y + xy^5).

2xy(3x + y⁴)

xy(6x + 2y⁴)

An expression can refer to a variety of things depending on the context in which it is used.

In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"

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The area of the rectangular picture frame with twenty inches in length, and a width of fifteen inches is 180inches.

Given length of the rectangular picture frame = 20inches

Given width of the rectangular picture frame = 15inches

The formula for finding the area of a rectangular frame is the multiplication of both length and width = Length x Width

So, the area of the given rectangular picture frame = 20 x 15 = 180 inches

From the above explanation, we can conclude that the area of the given rectangular frame with length of 20 inches and the width of 15 inches is 180 inches.

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Answer:

B

Step-by-step explanation:

All of the lines of best fit are close to the points in the scatter plot except B.

The line of best fit in B does not even touch any of the points in the scatter plot, so it is not a good example of a line of best fit.

Therefore, you are three times more likely to be on time than be late if you take Route C to school.

Relative frequency is a statistical term that refers to the proportion or percentage of times an event or a particular value occurs within a larger set of data. It is calculated by dividing the number of times the event or value occurs by the total number of observations in the data set.

Here,

To determine how many times more likely you are to be on time than late if you take Route C, we need to compare the heights of the green and red bars for Route C. From the graph, we can see that the green bar (representing on-time arrivals) is approximately three times taller than the red bar (representing late arrivals) for Route C.

To calculate how many times more likely you are to be on time than late if you take Route C, we need to find the ratio of the heights of the green and red bars:

Ratio = height of green bar / height of red bar

Looking at the segmented bar graph, we can see that the height of the green bar for Route C is approximately 0.45, and the height of the red bar is approximately 0.15.

Ratio = 0.45 / 0.15

= 3

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Answer:

24.6 degrees.

Step-by-step explanation:

To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.

sin(θ) = opposite/hypotenuse

sin(θ) = 3/7

Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.

θ = sin^-1(3/7)

θ ≈ 0.429 radians

To find the degree measure, we must convert radians to degrees by multiplying by 180/π.

θ ≈ 0.429 x 180/π

θ ≈ 24.6 degrees

Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.

The mean low temperature in Ketchikan from Monday to Friday is given as follows:

b. -5.4 ºF.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The five observations in the data-set are given as follows:

-10, -20, 5, 3 and -5.

Hence the mean of the data-set is given as follows:

(-10 - 20 + 5 + 3 - 5)/5 = -5.4 ºF.

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Answer:

it would be 3 or 2

Step-by-step explanation:

the cost of day old donuts after the discount is $4.95.

         A discount is a decrease in the cost of a good or service. Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price.

       Discounts are offers or rebates made to customers on the marked-down prices of goods. We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Let's examine the connections between these concepts.

       The formula to calculate the discount is:

Discount = List Price - Selling Price

Discount (%) = (Discount/List Price) × 100

the discount is 40% ⇒0.4

customer buys 3 donuts.

price of 1 donut = $2.75

total cost for 3 donuts= $2.75 x 3 = $8.25

discount for 1 donut= [tex]\frac{0.4}{100}* 2.75[/tex]=$1.1

so, for 3 donuts discount = $1.1 x 3 = $3.3

therefore the final price to be paid by customer is

                    =$8.25-$3.3

                    =$4.95

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Answer:

g to the power of 2

Step-by-step explanation:

Me=smart

The scatter plots that do not show a linear relationship are B and C

The distribution of points on a scatter plot's graph can show a linear relationship between two variables. A linear relationship exists between two variables when there is a consistent change in one variable for every change in the other.

The horizontal axis and the vertical axis of a scatter plot each indicate a separate variable. Each data point is plotted on the graph based on its values for the two variables. If the variables are related to one another linearly, the points will often fall in a straight line.

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Answer:

(a) The total ratio is 1 + 3 = 4, so Jill's share is (3/4) of £60:

Jill's share = (3/4) × £60 = £45.

(b) The ratio of their ages remains the same, so if Jack is one year older, Jill is also one year older. Therefore, Jill's age is 4 and Jack's age is 2, and Jack's share is (2/4) of £60:

Jack's share = (1/2) × £60 = £30.

(c) Let x be the age of Jack when he receives £25 from Uncle Fred. According to the problem, Jill is always two years older than Jack. Therefore, when Jack is x years old, Jill is x + 2 years old. The ratio of their ages is x : (x + 2), and this ratio is equal to 5/7 (25 pounds is 5/7 of 35 pounds, which is the total amount that they will receive). We can write an equation to solve for x:

x/(x+2) = 5/7

7x = 5(x + 2)

7x = 5x + 10

2x = 10

x = 5

Therefore, Jack will be 5 years old when he receives £25 from Uncle Fred at Christmas.

A) £45 because Jill will get 3/4 and Jack will get 1/4. To check our work, 60 divided by 4 is 15. 15 times 3 is 45 and 15 times one is 15.

B) £30 because it is a new year, both nephews will increase by one year. Now Jill is 4 and Jack is 2. So each kid will get half the share. 2 divided by 4 is 0.5 which is half of one. Half of 60 is 30.

C) 5 years Jill will always be 2 years older than Jack; this shows us that if some more years pass, Jill will be 7 and Jack will be 5 —> 1/4 x £60 = £25 Multiplying both sides by 4/60, we get:x = 5/4. This means Jack will be 5.

—————

Please remember to revise this and make it in your own words if you want! I am unsure about question C so comment!! I hope this helps you. -Doodle

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Answer:

s^2+2s-8

Step-by-step explanation:

(s-2)(s+4)

=s^2+4s-2s-8

simplified= s^2+2s-8

Answer:

s^2+2s-8

Step-by-step explanation:

(s-2)(s+4)

=s^2+4s-2s-8

simplified= s^2+2s-8

The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).

Looking at the graph, we can see that:

Thus, the correct piecewise function that represents g(x) is:

g(x) = {-2 if x ≤ -1

{ (x-1)^2 if -1 < x ≤ 0

{ -x+1 if x > 0

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Answer:

C. y = 3/2x + 4

Step-by-step explanation:

C. y = 3/2x + 4

Answer: cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

All numbers are positive because it is first quadrant.  Draw a line out.

sin = opp/hypotenuse.  the opposite line of the angle (y) =3

and hypotenuse=4

use pythagorean theorem to find x

4²=3²+x²

[tex]x=\sqrt{7}[/tex]

now use cos=adjacent/hypotenuse

cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]

Using the magnitude formula we know the amount of energy released by an earthquake with a magnitude of 5.5 is 4.5 * 10¹².

The magnitude or size of a mathematical item defines whether it is larger or smaller than other objects of the same kind in mathematics.

Formally speaking, the size of an object is the visible outcome of an ordering—of the class of objects to which it belongs.

The most frequent way to gauge an earthquake's size is through its magnitude.

It is a gauge for the magnitude of an earthquake's sole source.

As a result, it is the same regardless of how or where you view it, and the following computation can be made:

So, in the given situation we will be using the formula:

M = 2/3 log E/E₀

Where E is the power released in Joules and x, the minimal measure released by such an earthquake shall be allotted to.

Assuming 5.5, the same magnitude is given when the above equation is used:

M = 2/3 log E/E₀

5.5 = 2/3 log (E/10⁴°⁴)

8.5 = log (E/10⁴°⁴)

10⁸°⁵ = E/10⁴°⁴

E = 10⁴°⁴ * 10⁸°⁵

E = 4.5 * 10¹²

Therefore, using the magnitude formula we know the amount of energy released by an earthquake with a magnitude of 5.5 is 4.5 * 10¹².

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Correct question:

The magnitude, M, of an earthquake, is represented by the equation M=23logEE0 where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. In scientific notation rounded to the nearest tenth, what is the amount of energy released by an earthquake with a magnitude of 5.5?

Answer:

Step-by-step explanation:

b

Answer:

47 + 9f [tex]\leq[/tex] 120

Step-by-step explanation:

B is the correct answer.

The difference between 6 5/6 and 5 1/2 is 4/3 .

To subtract these mixed numbers, we need to first convert them into improper fractions:

6 5/6 = (6 x 6 + 5)/6 = 41/6

5 1/2 = (5 x 2 + 1)/2 = 11/2

Now we can subtract:

41/6 - 11/2

To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:

11/2 = (11 x 3)/(2 x 3) = 33/6

Now we can subtract the fractions with the same denominator:

41/6 - 33/6 = 8/6

Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:

8/6 = 4/3

As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..

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The complete question is:

What is the rule for the sequence

5/6, 1 1/2, 2 1/6, 2 5/6.....

Answer:

If (x-1) is a factor of the polynomial f(x) = 4x² - 4x² - x - K, then we know that (x-1) divides evenly into the polynomial, which means that the polynomial can be written as:

f(x) = (x-1)(ax + b)

where a and b are constants that we need to determine. We can use the distributive property to expand this expression and equate it with the original polynomial:

f(x) = (x-1)(ax + b) = 4x² - 4x - K

Expanding the left side of the equation, we get:

ax² + bx - ax - b = ax² - (a-b)x - b = 4x² - 4x - K

Now we can equate the coefficients of the like terms on both sides of the equation.

The coefficient of x^2 on the left side is a, and on the right side it is 4. Therefore, we have:

a = 4

The coefficient of x on the left side is b - a, and on the right side it is -4. Therefore, we have:

b - a = -4

Substituting a=4, we get:

b - 4 = -4

Solving for b, we get:

b = 0

So the polynomial can be written as:

f(x) = (x-1)(4x + 0) = 4x² - 4x

Therefore, K = 0.

To find the roots of the equation, we need to set f(x) = 0 and solve for x:

4x² - 4x = 0

Factor out 4x:

4x(x - 1) = 0

So the roots of the equation are x = 0 and x = 1.

Approximately 1.18 hours the concentration is highest.

The given function is c(t)=100t/t² +85.

When the concentration is highest, the function becomes

100t/t² +85 =0

100/t +85=0

100+85t=0

85t=100

t=100/85

t=1.18 hours

Therefore, approximately 1.18 hours the concentration is highest.

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The line plot representing the values on the number line can be presented as follows;

[tex]{}[/tex]         ×

[tex]{}[/tex]         ×                             ×

[tex]{}[/tex]         ×      ×                     ×      ×

<-|------|------|------|------|------|------|------|------|->

 [tex]{}[/tex]0     1/8    1/4          1/2   5/8  3/4           1

A line plot is a graph displaying data as points above a number, which indicates the frequency of the data.

The values in the fraction can be expressed as follows;

5/8, 5/8, 1/4, 1/8, 1/8, 3/4, 1/8

The values that are repeated can be excluded to get;

Values to be represented are; 5/8, 1/4, 1/8, 3/4

The above fractions can be expressed as fractions with a denominator of 8 as follows;

5/8, 1/4, 1/8, 3/4 = 5/8, 2/8, 1/8, 6/8

The fractions can be arranged in increasing order as follows;

5/8, 2/8, 1/8, 6/8; 1/8, 2/8, 5/8, 6/8

The fractions 1/8, 2/8, 5/8, 6/8, can therefore, be entered into the number line as follows;

<-|------|------|------|------|------|------|------|------|->

 0[tex]{}[/tex]    1/8   2/8          1/2    5/8  6/8           1

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The formula and the differences are shown below

The formula to calculate weighted average is:

weighted average = (w1x1 + w2x2 + ... + wnxn) / (w1 + w2 + ... + wn)

Where x1, x2, ..., xn are the values being averaged, and w1, w2, ..., wn are their corresponding weights.

The weighted average gives more importance or weight to certain values than others.

The weights can represent the relative importance, significance, or contribution of each value to the final average.

The main difference between ROR and weighted return is that ROR measures the return of a single investment, while weighted return measures the return of a portfolio or investment that is composed of multiple assets with different weights.

Weighted return takes into account the relative importance of each asset or security in the portfolio, while ROR does not consider the impact of other investments.

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Where the conditions above are given with regard to the above triangle, the ratio AD:DB is 1:1.

Since D is the midpoint of AB, we have:

AD = DB

Let M and N be the midpoints of OA and OB, respectively. Then we have:

AM = MO = x/2

BN = NO = y/2

Also, from the given information, we have:

OD = 3/7x + 4/7y

Since D is the midpoint of AB, we have:

AD + DB = AB

Substituting AD = DB, we get:

2AD = AB

Therefore:

AD = AB/2

We can express AB in terms of x and y using the law of cosines:

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos(BOA)

Since M and N are midpoints, we have:

OM = OA/2 and ON = OB/2

Therefore, using the law of cosines, we have:

MN^2 = OM^2 + ON^2 - 2(OM)(ON)cos(MON)

Substituting OM = OA/2 and ON = OB/2, we get:

MN^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

But MN = OD, so we can also express this as:

OD^2 = (3/7x + 4/7y)^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

Substituting OD^2 = (3/7x + 4/7y)^2 and simplifying, we get:

9x^2 + 16y^2 = 49(OA^2 + OB^2) - 42(OA)(OB) cos(BOA)

Substituting AB^2 = OA^2 + OB^2 - 2(OA)(OB) cos(BOA) and simplifying, we get:

9x^2 + 16y^2 = 49AB^2

Substituting AD = AB/2, we get:

9x^2 + 16y^2 = 49(2AD)^2

Simplifying, we get:

x^2 + 4y^2 = 28AD^2

We want to find the ratio AD:DB, which is the same as the ratio AD:(AB - AD). Substituting AB = 2AD, we get:

AD:(AB - AD) = AD:AD = 1:1

Therefore, the ratio AD:DB is 1:1.

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