Find the area of the shape.
Either enter an exact answer in terms of iT or use 3.14 for
and enter your answer
as a decimal.
units?

Answer:

j=19

Step-by-step explanation:

In the image, it shows that the weight of 5 + j is equal to the weight 24. Using this information, let's create a equation and solve for j:

5 + j = 24   [Subtract 5 from both sides]

j = 19

So, j must equal 19 for both sides of the hanger to be equal.

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In a case whereby formula for the area of a triangle is A=1/2bh. Kevins answer for the area of this triangle is 40 inches2, then Kevins solution is not correct because the correct solution is 20inches.

The concep[t that will be used is the area of triangle, The area of the triangle can be calculated using

A=1/2bh

where  A = area

b = base=5

h= height =8

then A=1/2*8*5= 20 inches

Therefore, the correct area of triangle from the fiqure is 20 inches

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$2360 was invested at 7% and $1910 was invested at 8% to get a total interest of $318

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 7% and y represent the amount of money invested at 8%.

The total interest is $318, hence:

0.07x + 0.08y = 318   (1)

she has $450 more in the 8% account, hence:

y = x + 450    (2)

Solving both equations simultaneously:

x = 2360, y = 1910

$2360 was invested at 7% and $1910 was invested at 8%.

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Answer:

Tthe length of the A4 sheet of paper is √(1/6m² * √2) and the breadth is √(1/6m² * √2) / √2

Step-by-step explanation:

To calculate the length and breadth of an A4 sheet of paper, we can use the information provided in the problem.

First, we know that the ratio of the length to the breadth is √2:1. This means that for every √2 units of length, there is 1 unit of breadth.

Next, we know that the area of the sheet is 1/6m². To find the length and breadth, we can use the formula for the area of a rectangle, which is length x breadth.

So, we can set up the equation:

(length) x (breadth) = 1/6m²

We can then use the information about the ratio of length to breadth to set up a proportion:

length/breadth = √2/1

Now we can cross-multiply and substitute this proportion into our area equation:

length x breadth = 1/6m²

length x (length/√2) = 1/6m²

length^2 = 1/6m² * √2

length = √(1/6m² * √2)

To find the breadth we can use proportionality again

breadth = length/√2

So, the length of the A4 sheet of paper is √(1/6m² * √2) and the breadth is √(1/6m² * √2) / √2

TOYS is a rectangle with diagonals TY and OS intersecting at point J. If angle TYO = 43°, then angle YJS = 68.5°.

Given that TOYS is a rectangle, we know that:

The diagonals TY and OS bisect each other.

The diagonals TY and OS are congruent (equal in length).

Using the information above, we can draw the following interpretation s:

We can see that:

Triangle TYJ is isosceles (because TY = OJ).

Angle TYJ = (1/2) * Angle TYO = (1/2) * 43° = 21.5°

Angle YJS = 90° - 21.5° = 68.5°

So, angle YJS = 68.5°.

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The measure of angle AOB is 180°.

Since COE and BOD are right angles, the measure of both angles is 90°.

The measure of COD is 1/4th of the measure of BOC, which is 90°. Therefore, the measure of COD is 90/4 = 22.5°.

Adding the measures of all three angles gives us 180°.

Therefore, the measure of AOB = 180 - (90 + 22.5) = 67.5°

Answer:

=-16

Step-by-step explanation:

Step 2, divided first within first parentheses

Step 4, subtract first within the parentheses.

（³√27-14÷2) (6-8)²

 =(3-14÷2) (6-8)²

 =(3-7) (6-8)²

 =(-4) (-2)²

 =(-4) 4

 =-16

The limit of the function [tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] is 12 and from the graph, we can say that for x = 2, g (x) is continuous while f (x) is not.

The function is [tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex].

We firstly simplify the expression.

We can write the function as:

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [tex]\lim_{x\rightarrow 2}\frac{(x)^3-(2)^3}{x-2}[/tex]

Using the formula, [tex](a)^3-(b)^3 = (a-b)(a^2+ab+b^2)[/tex]

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [tex]\lim_{x\rightarrow 2}\frac{(x-2)(x^2+2x+4)}{x-2}[/tex]

Simplify

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [tex]\lim_{x\rightarrow 2}[/tex](x^2 + 2x + 4)

Using, [tex]\lim_{x\rightarrow c}[/tex] f(x) = f(c)

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [(2)^2 + 2×2 + 4]

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = (4 + 4 + 4)

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = 12

We have [tex]\frac{x^3-8}{x-2}[/tex] = (x^2 + 2x + 4)

So the simpler function is

g(x) = (x^2 + 2x + 4)

that agrees with the function f(x) = [tex]\frac{x^3-8}{x-2}[/tex] except x = 2.

Now we graph the function f(x) and g(x).

We can see that for x = 2, g (x) is continuous while f (x) is not.

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The complete question is:

Write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result.

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex]

Answer:

To solve for x, you can use the equation 6x = 5. This gives x = 5/6.

According to the information, it can be inferred that the words that complete the sentences are: Radius, 3.14, radius, circumference, and both.

To complete the sentences we must read each of them several times and identify its main theme; this will help us identify the missing term by context.

Additionally, we must read the text on the left side where we will find related information that will help us find the correct terms.

According to the above, the complete sentences would look like this:

In Rachel's method, 4 represents the radius of the rug, and the fraction 11/7 3.14 a good approximation for

In Erik's method, the height of the parallelogram is approximately equal to radius and the length is approximately equal to circumference.

Therefore, both suggested a reasonable method for approximating the area of the rug.

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The best course grade your friend can earn is 92%.

To earn a 75% for the course, your friend would need to score a minimum of 18.75% on the final exam.

This is calculated by:

(0.75 - 0.82) / 0.25

= (0.18) / 0.25

= 0.1875 or 18.75%.

As a result, the best course grade your friend can earn is 92% and the your friend would need to score a minimum of 18.75% on the final exam.

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Answer:

The function 8(x) is a parabola that opens downward and is centered at (0,0). The domain of 8(x) is x∈R and the range of 8(x) is y∈[0,∞).

To arrive at the new function g(x), follow these steps:

Base Graph: The base graph of 8(x) is shown below.

Vertical Reflection: To reflect the parabola about the x-axis, multiply the function by -1. The new function is g(x) = -8(x).

Horizontal Reflection: To reflect the parabola about the y-axis, multiply the function by -1. The new function is now g(x) = 8(-x).

Horizontal and Vertical Translations: To translate the parabola 4 units to the left and 2 units up, add 4 to the x-coordinates and subtract 2 from the y-coordinates. The new function is g(x) = 8(x-4)-2.

The resulting graph is shown below. The domain of g(x) is x∈R and the range of g(x) is y∈[-2,∞).

The correct answer is option B.

The entire length of hose

Since the early 17th century, primrose and cowslip have been cultivated as Hose in Hose mutants, which exhibit strong homeotic sepal to petal conversion. The S locus, which regulates floral heteromorphy in Primula species, is linked to the phenotypic, which exhibits varying penetrance and expressivity. Here, we show that the primrose B-function MADS box genes PvDef and PvGlo are upregulated in the first floral whorl in association with the homeotic conversion of sepals to petals in Hose in Hose. We have found and characterized a retrotransposon insertion in the PvGlo promoter that is connected to the up-regulated expression of PvGlo, as well as a restriction fragment length polymorphism linked with PvGlo that cosegregates with the Hose in Hose phenotype.

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The manager is mistaken in believing that the set of integers is the best domain for this model. The domain in this case represents the times of day when shoes were sold.

Hours are continuous values that can be any real number between 0 and 24. As a result, a set of real numbers such as 0 = t = 14, where t represents the hour of the day, would be a better domain for this model.

The manager wants to achieve by analyzing the data. This could be to gain insights into customer behavior, identify areas for improvement, measure the success of marketing efforts, etc.

The domain of integers would be appropriate only if the number of pairs of shoes sold could only be an integer value, which is not the case for online shoe sales.

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To solve the previous exercise step by step, we first need to break down the equation into its components:

z^6−16z^3 +128 = 0

Now, we can use the quadratic formula to solve this equation:

x = (-b ± √(b² - 4ac)) / 2a

In this case, we have:

a = 1 b = -16 c = 128

So, the quadratic formula reduces to:

x = (-(-16) ± √((-16)² - 4(1)(128))) / 2(1)

Simplifying, we get:

x = (16 ± √(256 - 512)) / 2

And finally we get the solutions:

x = (16 ± √(-256)) / 2

Which simplifies to:

x = (16 ± 4i) / 2

And the solutions are:

z = 2, 4i, -2, -4i

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Answer: I'm sorry, but I'm unable to answer your question as you haven't provided any information about the minimum payment that he must make to CreditFirst and Sun Money. Please provide more details and I'll do my best to help you.

Step-by-step explanation:

An arithmetic progression is a set of numbers with a fixed difference between any two succeeding numbers (A.P.). Examples of A.P. include 3, 6, 9, 12, 15, 18, and 21.

A.P. and G.P. application: A series of terms known as an arithmetic progression (AP) have identical differences. In a geometric progression (GP), the common ratio is multiplied by the previous term to produce each succeeding term.

Given,

a₁ = x

a₂ = 2x + 1

a₃ = 11

a₂ - a₁ = a₃- a₂

(2x + 1) - (x) = 11 - (2x + 1)

2x - x + 1 = 11 - 2x - 1

x + 1 = -2x + 10

2x + x = 10 - 1

3x/3 = 9/3

x = 3  

The arithmetic sequence:  3, 7, 11

Common difference: 4

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The correct answer is option 1. 13.33 cm. In a rectangle ABCD, The length of PC is 13.33 cms.

In a right triangle BPC, we have two sides: BP = AP = 6 cm and PD = 10 cm. Using the Pythagorean theorem, we can find the length of PC:

[tex]PC^2 = BP^2 + PD^2\\= > PC^2 = 6^2 + 10^2\\= > PC^2 = 36 + 100\\= > PC^2 = 136\\= > PC = \sqrt{136} \\= > PC = 13.33 cm[/tex]

In the rectangle ABCD, we have a right triangle BPC. Point P is on side AB and is such that ∠BPC = ∠ADP. Therefore, BP and PD are the corresponding sides of the two right triangles. Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (PC) is equal to the sum of the squares of the lengths of the other two sides (BP and PD), we can find the length of PC.

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The line with slope -2 through the point (-13, 21) is y = -2x + b where b= y intercept, found by plugging in the values x=-13 and y=21.

21 =-2(-13) + b

b = 21 -26 = -5

y =-2x -5 is the equation in slope intercept form

or

2x +y =-5 in standard form the graph is a downward sloping straight line

y intercept is (0,-5), x intercept is (-5/2, 0) = (-2 1/2, 0)

plot those two points,  connect them with a straight line

add arrows on both ends of the line to indicate the line goes forever in both directions

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Answer:

191 i guess

Step-by-step explanation:

πr^2=3.14*4.5^2=63.585

63.585*3(three pieces only)=191 approximately

Answer:

approximately 87,178,291,200

Step-by-step explanation:

The number of ways to arrange the letters of the word 'jvuyojzrxccome' is 14! (14 factorial), since there are 14 distinct letters in the word. This is a very large number, approximately 87,178,291,200.

Given that, 3x -2 < 2x+1

⇒3x-2x < 1+2

⇒ x< 3 or x∈ (-∞,3)

Both the lines y=3x -2 and y=2x+1 will meet at x=3.

The black line clearly reveals the solution of 3x -2<2x + 1.

An inequality is formed by two real numbers or two algebraic expressions linked by the symbol ", V, ", or '>'.

As an example: Three, five, and seven are numerical inequalities. Literal inequalities are x 5, y > 2, and x > 3. axe + b 0 and axe + b > 0 are simple inequalities in a single variable.

Slack inequalities in one variable are axe + b 0 and axe + b > 0.

axe + by c, axe + by > c are two-variable strict inequalities.

Slack inequalities in two variables are axe + by c and axe + by > c.

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The total bill with 6 percent of tax is $36.87, for which the server must be paid one $20 bill, one $10 bill, one $5 bill, one $1 bill and 0.87 pennies.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The amount for total bill is $34.78.

The sales tax percentage added is 6%.

The total bill including tax will be -

Final Bill = Total Bill + (Total Bill × tax)

Substitute the values into the equation -

Final Bill = 34.78 + (34.78 × 6%)

Final Bill = 34.78 + (34.78 × 0.06)

Final Bill = 34.78 + 2.0868

Final Bill = 36.8668 ≈ 36.87

Therefore, the final bill is $36.87.

The amount of $20 bill = 1

The amount of $10 bills = 2

The amount of $5 bills = 1

The amount of $1 bills = 5

The amount of pennies = x

So, the amount of bill given to server to make a total of $36.87 is -

1 × ($20) + 1 × ($10) + 1 × ($5) + 1 × ($1) + x = $36.87

20 + 10 + 5 + 1 + x = 36.87

36 + x = 36.87

x = 36.87 - 36

x = 0.87

Therefore, along with 1 bill each 0.87 pennies should be given to the server.

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Answer: The area of the rectangular region is 27 m².

Step by step explanation:

Data :

We calculate the area taking into account the formula that I will give you:

[tex] \bold{A = b * h }[/tex]

We simplify according to the given formula:

[tex]\bf A = 9(3)[/tex]

[tex]\boxed{ \bf A = 27 \: {m}^{2} }[/tex]

Rpt: The area of the rectangular region is 27 m².

Answer:

the answer is diet coke divided by the square root times the 10/4

Step-by-step explanation:

Answer: C) x=2 or x=-4/7

The number of sausage rolls is 8 and the chicken pie is 12.

How many of each item did she buy?

The first step is to form a system of equations using the information in the question:

c + s= 20 equation 1

2.50c - 1.50s = 18 equation 2

Where:

c = number of chicken pies bought

s = number of sausage rolls bought

The elimination method would be used to determine the required values.

Multiply equation 1 by 2.50

2.5c + 2.5s = 50 equation 3

Subtract equation 2 from equation 3:

4s = 32

Divide both sides of the equation by 4

s = 32 / 4

s = 8

Substitute for s in equation 1:

c + 8= 20

c = 20 - 8

c = 12

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The given triangles OML and ONP are similar triangles by SAS postulate.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Consider triangle OML and ONP
OL / OP = OM/ON
13.5/3 = 9/2
4.5 = 4.5

And
∠O = ∠O  [common angle]

Thus, both triangles are similar triangle by the SA postulate of similarities.

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Answer:

83 and 84

Step-by-step explanation:

Let's call the two integers x and (x + 1), respectively.

x + (x + 1) = 167

2x + 1 = 16

2x = 166

x = 83

The two integers are 83 and 84

The answers are,

A) The median is 18.

B) The mean is 2.25.

C) The data set is not symmetrical because it is skewed left.

What is median and mean of data set?

The measure of central tendency that is most frequently used is the mean. The average of the specified set of data is what it actually reflects. Both continuous and discrete data types can use it. It is determined by dividing the total number of values in the data collection by the total sum of all the values.

In most cases, the median shows the midpoint of the supplied set of data when it is presented in a specific order.

Here the given data set is 48,16,8,6,37,20.

To find median , we need  rearrange then into ascending order then,

=> 6,8,16,20,37,48.

Here mid point of the data set is 16 and 20. Then,

=> [tex]\frac{16+20}{2}[/tex]

=> [tex]\frac{36}{2}[/tex]

=> 18.

Now to find mean of the data set we need to add all data and divide them by number of data, Then

=> [tex]\frac{48+16+8+6+37+20}{6}[/tex]

=> [tex]\frac{135}{6}[/tex]

=> 2.25

Now the data set is not symmetrical because it is skewed left.

Hence the answers are,

A) The median is 18.

B) The mean is 2.25.

C) The data set is not symmetrical because it is skewed left.

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