100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

The solution is: the value of x in this triangle is x = 83°.

Here, we have,

given that,

the angles of a triangle are:

44, 53 and x

now, we have to find the value of x in this triangle.

we know that,

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

so, we have,

44 +  53 + x = 180°

or, x=  83

Hence, The solution is: the value of x in this triangle is x = 83°.

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a. Natural numbers: 0, 4.2, √9

b. Whole numbers: -8, 0, 4.2, √9

c. Integers: -8, 0, 4.2, √9

d. Rational numbers: -8, 5/6, 0, 4.2, √9

e. Irrational numbers: √2, π

f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9

We have,

a. Natural numbers:

5/6, 0, 4.2, √9 (The natural numbers are positive integers excluding zero)

b. Whole numbers:

-8, 0, 4.2, √9 (Whole numbers include zero and all positive integers)

c. Integers:

-8, 0, 4.2, √9 (Integers include positive and negative whole numbers, including zero)

d. Rational numbers:

-8, 5/6, 0, 4.2, √9 (Rational numbers can be expressed as a fraction of two integers)

e. Irrational numbers:

√2, π (Irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal expansions)

f. Real numbers:

-8, 5/6, 0, 0.1, √2, π, 4.2, √9 (Real numbers include all rational and irrational numbers)

Thus,

a. Natural numbers: 0, 4.2, √9

b. Whole numbers: -8, 0, 4.2, √9

c. Integers: -8, 0, 4.2, √9

d. Rational numbers: -8, 5/6, 0, 4.2, √9

e. Irrational numbers: √2, π

f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9

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The complete question.

-8, 5/6, 0, 0.1, √2, π, 4.2, √9

List all numbers from the given set that are a. natural​ numbers, b. whole​ numbers, c.​ integers, d. rational​ numbers, e. irrational​ numbers, and f. real numbers.

The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²

A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.

Surface area of a pyramid is expressed as;

area of 4 lateral face + area of base

area of base = 440²

= 193600 units²

area of a lateral = 1/2 bh

= 1/2 × 440 × 356

= 78320

For four surfaces = 4 × 78320 = 313280

Total surface area = 313280+78320

= 391600 units ²

Volume of a pyramid is expressed as;

V = 1/3base area × height

V = 1/3 × 440² × 280

V = 18069333.33 units³

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The solution is: the dimensions of the flag in inches is:

40 inches by 55 inches.

The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;

L is the length of the flag

W is the width of the flag

From the diagram, L = y and W = 11y/8

Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.

190 = 2(y+11y/8)

190 = 2y + 11y/4

multiply through by 4

760 = 8y+11y

760 = 19y

y = 760/19

y = 40

The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.

Hence, the dimensions of the flag in inches is 40 inches by 55 inches.

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complete question:

Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.

Answer:

Step-by-step explanation:

Answer:

653.3 bacteria

Step-by-step explanation:

A continuously growing population of bacteria is modeled by the function:

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

where:

In this problem, we are given the following values:

We can plug these into the function to solve for [tex]P(2)[/tex].

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]

[tex]P(2) = 484 \cdot e^{0.3}[/tex]

Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.

[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]

In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.

Diagram of how a function relates two relations.

We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.

We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write

(

0

,

100

]

. We will discuss interval notation in greater detail later.

Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.

Before we begin, let us review the conventions of interval notation:

The smallest term from the interval is written first.

The largest term in the interval is written second, following a comma.

Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.

Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.

Carter would need to invest approximately $76,869.06 to reach a value of $174,000 in 19 years with a 4.3% annual interest rate compounded daily.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

Accrued amount A = $174,000

Compounded daily n = 365

Time t = 19 years

Interest rate r = 4.3%

Principal P = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 4.3/100

r = 0.043

Plug these values into the above formula and solve for principal P.

[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\A = 174,000( 1 + \frac{0.043}{365})^{(365\ *\ 19)}\\\\A = \$ 76,869.06[/tex]

Therefore, the principal that needs to invested is $76,869.06.

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The equation of the given sine function is y = 4 × sin((π/5)x) + 2.

The equation of the given sine function can be determined based on the given information. We know that the general form of a sine function is:

y = A × sin(Bx - C) + D,

where A represents the amplitude, B represents the frequency, C represents the phase shift, and D represents the vertical shift.

In this case, we are given the following information:

Amplitude (A) = 4: The amplitude is the distance between the maximum and minimum values of the function. Since the function is reflected over the x-axis, the amplitude is positive 4.

Midline (D) = 2: The midline is the horizontal line around which the graph oscillates. In this case, it is y = 2, indicating a vertical shift of 2 units upwards.

Period = 10: The period is the distance between two consecutive peaks (or troughs) of the function.

Given that there is no phase shift, the phase shift (C) is 0.

From the given information, we can deduce the values of A, B, C, and D to construct the equation.

A = 4 (amplitude)

D = 2 (vertical shift)

C = 0 (no phase shift)

To determine B, we use the formula:

B = 2π / Period

Plugging in the value for Period (10), we can calculate B:

B = 2π / 10 = π / 5

Therefore, the equation of the given sine function is:

y = 4 × sin((π/5)x) + 2.

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Eight fourths is proportional to the value of 2/1

Proportionality of values means the relationship that exists between two variables where their ratios are equivalent to each other.

A ratio that is made up of two variables is said to be proportional to another ratio when after being simplified one arrives at the same ratio.

Using the 8:4 or 8/4. This is equivalent to 2/1 and also equivalent to 16/8 as the simplification leads to 2/1

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Answer:

Step-by-step explanation:

use gauth math it helps with maths

The value of the home after 5 years would be $194,415.

How to calculate the value of the home after 5 years

First, let's calculate the increase in value for each 3-year period:

After the first 3 years:

Increase = 9% of $150,000 = 0.09 * $150,000 = $13,500

After the second 3 years:

Increase = 9% of ($150,000 + $13,500) = 0.09 * ($150,000 + $13,500) = $14,850

After the third 3 years:

Increase = 9% of ($150,000 + $13,500 + $14,850) = 0.09 * ($150,000 + $13,500 + $14,850) = $16,065

Now, let's add these increases to the initial value of the home to find the value after 5 years:

Value after 5 years = $150,000 + $13,500 + $14,850 + $16,065 = $194,415

Therefore, the value of the home after 5 years would be $194,415.

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Fifty-four and eight tenths" can be expressed in expanded form as the sum of 54 (representing 50 + 4) and 0.8, which represents the decimal part.

To write the number "fifty-four and eight tenths" in expanded form, we can break it down into its individual place values and numerical components.

The number "fifty-four" can be broken down as follows:

The digit 5 represents the value of 50, which is 5 tens.

The digit 4 represents the value of 4, which is 4 ones.

So, "fifty-four" can be expressed as 50 + 4.

Next, we have "eight tenths". This can be expressed as 8/10 or simply 0.8 since each tenth is equal to 0.1.

Putting it all together, the number "fifty-four and eight tenths" can be written in expanded form as:

50 + 4 + 0.8

Simplifying further, we can combine the integer and decimal parts:

54 + 0.8

Therefore, the expanded form of "fifty-four and eight tenths" is 54 + 0.8.

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The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A

The formula for calculating the surface area of a cone is expressed as;

SA = πr² + πrl

Such that the parameters are;

Substitute the values, we have;

Surface area= 3.14 × 16 = 3.14 × 4 × 8

Multiply the values

Surface area = 50.24 + 100.48

Add the values

Surface area = 150.8 in²

Volume of the cone is;

Volume = 3.14 × 4² × 6.9/3

Volume = 3.14 × 16 × 6.9/3

Volume =116. 1in³

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When it comes to long-term investment goals like early retirement, it is generally recommended to focus on investments that offer potential growth over an extended period of time. Here are some investment options and advice that could be beneficial for your friend:

Stock market investments: Investing in a diversified portfolio of stocks can provide the potential for long-term growth. Your friend can consider investing in individual stocks or exchange-traded funds (ETFs) that represent a basket of stocks.

Mutual funds: Mutual funds offer diversification by pooling money from multiple investors to invest in a variety of assets. They are managed by professionals who make investment decisions on behalf of the investors.

Index funds: Index funds are a type of mutual fund that aims to replicate the performance of a specific market index, such as the S&P 500. They offer broad market exposure and generally have lower expense ratios compared to actively managed funds.

Retirement accounts: Encourage your friend to take advantage of tax-advantaged retirement accounts like a 401(k) or an individual retirement account (IRA). These accounts provide tax benefits and can help grow savings faster.

Dollar-cost averaging: Advising your friend to invest regularly, regardless of market conditions, through a strategy called dollar-cost averaging can help mitigate the impact of market volatility. By investing a fixed amount at regular intervals, your friend will buy more shares when prices are low and fewer shares when prices are high.

Rebalancing: As time goes on, it's important to periodically review and rebalance the investment portfolio. This involves adjusting the asset allocation to maintain the desired level of risk and return. Regularly rebalancing ensures that the investments stay aligned with the financial goals and risk tolerance.

Emergency fund: Remind your friend about the importance of building an emergency fund with three to six months' worth of living expenses. This will provide a safety net and help prevent the need to tap into long-term investments during unforeseen circumstances.

Seek professional advice: Depending on your friend's knowledge and comfort level with investing, it may be helpful to recommend consulting with a financial advisor who can provide personalized advice based on their specific financial situation and goals.

Remember, investing involves risks, and it's crucial for your friend to carefully evaluate investment options, consider their risk tolerance, and have a long-term perspective. Regularly monitoring and adjusting the investment strategy over time will help ensure progress towards achieving their financial goals.

Answer:

[1;1;1]

Step-by-step explanation:

try this option; all the details are in the attachment.

Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

Now, the distance Donald traveled on each of his trips to the amusement park.

If he drove a total of 399 kilometers over the course of four trips, we can find the average distance he traveled per trip by dividing the total distance by the number of trips.

So, We get;

= 399 divided by 4

= 399 / 4

= 99.75 kilometers per trip

≈ 100 kilometers per trip.

Therefore, Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

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Answer:

  B, C, D

Step-by-step explanation:

You want to identify the shapes that are similar to polygon K.

Polygon K is a right triangle that has leg lengths in the ratio 4:2 = 2:1.

Polygons B, C, and D are right triangles similar to polygon K:

Polygons A and E are also right triangles, but have different ratios of leg lengths. In A they are 1/1, and in E they are 4/3. These triangles are not similar to triangle K.

__

Additional comment

Polygons similar to the same polygon are similar to each other. Rigid transformations such as reflection and rotation result in figures congruent to the original. Congruent figures are also similar.

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The values of  x and y is x=8 and y=12.

We are given that;

The dimensions=7 and 24

Now,

(x+y)^2= 7^2 + 24^2

x^2+y^2+2ab=49+416

x^2+y^2+2xy=465

Also, 7^2=x2+h2

49=x2+15

x2=49+15

x2=64

x=8

Substituting the values of x

8+y=20

y=12

Therefore, by Pythagoras theorem the answer will be x=8 and y=12.

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The value of the equation 6 sinθ=5 for θ is 56.4 degrees

From the question, we have the following parameters that can be used in our computation:

6 sinθ=5

Express the equation properly

So, we have the following representation

6 sin(θ) = 5

Divide both sides of the equation by 6

This gives

sin(θ) = 5/6

Evaluate the quotient

sin(θ) = 0.833

Take the arc sin of both sides

θ = sin⁻¹(0.833)

Evaluate

θ = 56.4

Hence, the value of the equation for θ is 56.4 degrees

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Complete question

Approximate θ in the equation, to the nearest 0.1 degrees

6 sin(θ) = 5

a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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The circle graph percentage is solved and the measure of ∠KL = 54° and the measure of ∠LMJ = 198°

Given data ,

Let the circle graph gives the percentage of students who favor the different lunch menus offered by the school cafeteria

Now , the measures of the angles are given by

The measure of ∠KL = 15 %

15 % ( 360 ) = 54°

Therefore , the measure of ∠KL = 54°

And , the measure of ∠LMJ = ( 24 % + 21 % ) of 360

The measure of ∠LMJ = 198°

Hence , the circle graph percentage is solved

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Answer:  The jar contains a total of 18 coins (8 pennies + 3 nickels + 5 dimes + 2 quarters). To get more than 4 cents, we need to choose a nickel, dime, or quarter. There are 3 nickels, 5 dimes, and 2 quarters, for a total of 10 coins that satisfy this condition. Therefore, there are 10 ways to choose a coin from the jar that is more than 4 cents.

Answer:

Step-by-step explanation:

The function you provided, f(x) = -2.5 + 7, represents a linear function rather than a radical function. A linear function has a constant slope and a constant y-intercept.

The end behavior of a linear function is determined by its slope. In this case, the slope of the function is 0 since there is no term involving x. When the slope is 0, it means the function is a horizontal line.

The function f(x) = -2.5 + 7 represents a horizontal line at y = 4.5. As x approaches positive infinity (∞) or negative infinity (-∞), the value of y remains constant at 4.5. Therefore, the end behavior of this linear function is that y approaches 4.5 as x approaches both positive and negative infinity.

In conclusion, the end behavior of the function f(x) = -2.5 + 7 is that y approaches 4.5 as x approaches positive and negative infinity.

In a case whereby A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position the degrees north of west it turned is 72°

From trigonometry, the law of cosines states  the side c of a triangle can be found as

c² = a² + b² - 2abcos(C)

where

C = angle opposite to side c.

a and = lengths of the other sides.

a = 94, b = 119, c = 173.

c² = a² + b² - 2abcos(C)

173² = 94² + 119² - 2 x 94 x 119cos(C)

22327cos(C) = -6932

cos(C) = -6932/22327

C = arccos(-6932/22327)

C = 108º.

Then,

T = 180 - C

= 180 - 108 = 72º.

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The sample data suggest that the population proportion is not significantly greater than 0.59 at the significant level of 0.01.

In this case, the test statistic is calculated as follows:

z = (106/150 - 0.59) / sqrt(0.59(1-0.59)/150)

= 1.55

The p-value is calculated as the area under the standard normal curve to the right of the test statistic. In this case, the p-value is calculated as follows:

p-value = p(Z > 1.55)

= 0.123

Since the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis. Therefore, we cannot conclude that the population proportion is significantly greater than 0.59 at the significant level of 0.01.

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The solution to the inequality expression is -8/9 ≤ x ≥ 4/9

From the question, we have the following parameters that can be used in our computation:

|3x + 6/9| ≥ 2

Expand the inequality expression

So, we have

-2 ≤ 3x + 6/9 ≥ 2

Subtract 6/9 from both sides

So, we have

-24/9 ≤ 3x ≥ 12/9

Divide through the equation by 3

-8/9 ≤ x ≥ 4/9

Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9

The graph is attached

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The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer: 19

Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).

Hope this helps!

The points (1,0) (8,0). and. (3,0) are not the solution of system of inqualities

From the question, we have the following parameters that can be used in our computation:

The graph

Also, we have the following ordered pairs

(1,0) (8,0). (0,4). (3,0)

From the graph, we have the following ordered pairs in the shaded region

(0, 4)

Other points (1,0) (8,0). and. (3,0) are not in the shaded region

This means that (1,0) (8,0). and. (3,0) are not the solution of system of inqualities

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