for the following right triangle. find the side length x. round your answer to the nearest hundreth.

Answer:

a)  Area of inner square = 58 cm²

b)  Area of inner square = (2x² - 2xy + y²) cm²

Step-by-step explanation:

To calculate the area of a square, multiply the length of one of its sides by itself. This can be expressed as A = s², where A is the area and s is the side length of the square.

To calculate the area of a triangle, halve the product of its base and height. This can be expressed as A = (1/2)bh, where A is the area, b is the base and h is the height of the triangle.

The easiest way to calculate the area of the inner square is to subtract the areas of the 4 congruent triangles from the area of the outer square.

[tex]\hrulefill[/tex]

The outer square has a side length of 10 cm. Therefore its area is:

[tex]\implies \sf A_{outer\;square} = 10^2 = 100 \; cm^2[/tex]

Each corner triangle has a height of 3 cm and a length of (10 - 3) cm.

Therefore, the area of one triangle is:

[tex]\implies \sf A_{triangle}=\dfrac{1}{2} \cdot 7 \cdot 3=10.5\;cm^2[/tex]

Therefore, the area of the inner square is:

[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=\sf 100-(4 \cdot 10.5)\\&=\sf 100-42\\&=\sf 58\; cm^2\end{aligned}[/tex]

[tex]\hrulefill[/tex]

The outer square has a side length of y cm. Therefore its area is:

[tex]\implies \textsf{A$_{\sf outer\;square}$} = y^2 \; \sf cm^2[/tex]

Each corner triangle has a height of x cm and a length of (y - x) cm.

Therefore, the area of one triangle is:

[tex]\begin{aligned}\implies \sf A_{triangle}&=\dfrac{1}{2} \cdot (y-x) \cdot x\\\\&=\dfrac{1}{2}x(y-x)\;\sf cm^2\end{aligned}[/tex]

Therefore, the area of the inner square is:

[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=y^2-4\left(\dfrac{1}{2}x(y-x)\right)\\\\&=y^2-2x(y-x)\\\\&=y^2-2xy+2x^2\\\\&=(2x^2-2xy+y^2)\; \sf cm^2\end{aligned}[/tex]

Answer:

Step-by-step explanation:

To find the maximum height of the ball, we need to find the vertex of the parabolic function h(t) = -t^2 + 8t + 32. The vertex represents the highest point of the parabolic curve.

The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = -1 and b = 8, so we have:

x = -b/2a = -8/(2(-1)) = 4

Therefore, the vertex occurs at time t = 4.

To find the y-coordinate of the vertex, we evaluate the function at t = 4:

h(4) = -4^2 + 8(4) + 32 = 16 + 32 = 48

Therefore, the ball reaches a maximum height of 48 feet above the ground.

After answering the presented question, we can conclude that The answer for the following expression will be as follows  [tex]4.4 X 10^3 = 4400[/tex]

In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.

The answer for the following expression will be as follows

[tex]4.4 X 10^3 = 4400[/tex]

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The amount that she needs to pay on her debt to reach a 25% debt-to-credit ratio is given as follows:

$2,535.

The amount that she needs to pay on her debt reach a 25% debt-to-credit ratio is obtained applying the proportions in the context of the problem.

She has a credit limit of $7,950.00, hence 25% of her credit limit is obtained as follows:

0.25 x 7950 = $1987.5.

She current has $4,522.50 on debts, hence the amount that she needs to pay for the debts to be reduced to $1987.5 is given as follows:

4522.5 - 1987.5 = $2,535.

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The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.

Answer:

Step-by-step explanation:

The discriminant value (denoted by Δ) of a quadratic equation in the form of ax² + bx + c = 0 is given by the expression b² - 4ac.

For the quadratic equation m² + 18m + 17 = 0, a = 1, b = 18, and c = 17. Substituting these values into the expression for the discriminant, we get:

Δ = b² - 4ac

Δ = (18)² - 4(1)(17)

Δ = 324 - 68

Δ = 256

Therefore, the discriminant value of the quadratic equation m² + 18m + 17 = 0 is 256.

Answer:

The probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98%

Step-by-step explanation:

We want to find the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed, which can be written as P(A|U). Using Bayes' theorem, we have:

P(A|U) = P(U|A) * P(A) / P(U)

We are given P(A) = 0.06 (6% of the labor force is Asian), P(U|A) = 0.05 (among Asians in the labor force, 5% are unemployed), and P(U|not A) = 0.06 (among non-Asians in the labor force, 6% are unemployed).

To find P(U), we can use the law of total probability:

P(U) = P(U|A) * P(A) + P(U|not A) * P(not A)

We know P(A) = 0.06, so P(not A) = 1 - P(A) = 0.94.

Therefore,

P(U) = 0.05 * 0.06 + 0.06 * 0.94 = 0.0602

Now we can substitute all the values into Bayes' theorem:

P(A|U) = 0.05 * 0.06 / 0.0602 = 0.0498

So the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98% (rounded to the nearest percentage with no decimal places).

Answer:

Step-by-step explanation:

Me personally, I think buffets are the best because you can take as music food as you much, without being charged for much! But thats only for some buffets. If you go to a chinese buffet, they might lower the price allowing you to get as much food as you please!

The slope of the function is -29 and the y-intercept is the point (0, 2).

What is function ?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range).

To find the slope and y-intercept of the function p(x) = 2 - 29x, we can write it in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

So, by comparing p(x) = 2 - 29x with y = mx + b, we can see that:

m = -29 (the coefficient of x)

b = 2 (the constant term)

Therefore, the slope of the function is -29 and the y-intercept is the point (0, 2).

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The linear equation on the graph can be written as:

y = (3/4)*x - 1

Here we have the graph of a linear equation, these are written as:

y = mx + c

Where m is the slope and c is the y-intercept.

On the graph we can see that the line intercepts the y-axis at y = -1, then we can write:

c = -1

So the linear equation is:

y = mx - 1

Looking at the graph we can see that the line also passes through the point (4, 2).

Replacing that in the linear equation we will get:

2 = m*4 - 1

2 + 1 = m*4

3 = m*4

3/4 = m

Then the linear equation on the graph is:

y = (3/4)*x - 1

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Given:-

Solution:-

p³+10+m-m

put the value of p nd m in eqⁿ :

━━━━━━━━━━━

hope it helps⸙

The value of expression at m = 8 and p = 3 is,

⇒ 37

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ p³ + 10 + m - m

Now,

Put m = 8 and p = 3 in above expression, we get;

⇒ p³ + 10 + m - m

⇒ 3³ + 10 + 8 - 8

⇒ 27 + 10

⇒ 37

Thus, The value of expression at m = 8 and p = 3 is,

⇒ 37

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The length of line JC is 20 miles.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of sides of triangle.

To find the length of line JC, which is the hypotenuse of the right triangle JSC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

In this case, we have:

JS² + SC² = JC²

Substituting the given values, we get:

12² + 16² = JC²

144 + 256 = JC²

400 = JC²

Taking square root both sides, we get:

JC = √400

JC = 20

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Answer:

Step-by-step explanation:

b

Callie will need a total of 112 feet of fence for the triangle DFG.

We can find the amount of fence needed by finding the relationship between both triangles and find the missing side.

The sum of all the sides of the triangle will be known as the perimeter of the triangle. we can use this knowledge to find the amount of fence needed.

Both triangles are similar and are in the ratio of 1:7To find the missing side of triangle DFG, we multiply the corresponding side of triangle BAC by 7 to find the missing side.

This will give us 7 x 7 = 49ft

To find the amount of fence needed for triangle DFG we add all the sides of triangle DFG which will be 49 + 35 + 28.

The total will be 112ft.

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Answer:

a. aₙ=(aₙ₋₁ x 0.98) + 1150

Answer:

72 cm^2

Step-by-step explanation:

2(3 x 2) + 2(6 x 3) + 2(6 x 2) = 2(6) + 2(18) + 2(12)

= 12 + 36 + 24 = 72 cm^2

Answer:

We can use the simple interest formula to find the rate of interest that the town savings bank pays:

Simple Interest = Principal x Rate x Time

where Principal is the initial deposit, Rate is the interest rate, and Time is the time period.

We know that the Principal is $5000, the Simple Interest earned over the first 10 years is $2950, and the Time is 10 years. Substituting these values into the formula, we get:

$2950 = $5000 x Rate x 10

Simplifying the equation, we get:

Rate = $2950 / ($5000 x 10)

Rate = 0.059 or 5.9%

Therefore, the town savings bank pays an interest rate of 5.9% on its savings accounts.

The x- and y-intercepts as required to be determined in the task content are; (-4/3, 0) and (0, -4).

As evident in the task content; the given function is; f(x) = - 3x - 4.

The x-intercept represents the value of x when f(x) = 0.

0 = -3x - 4

3x = -4

x = -4 / 3.

The y-intercept represents the value of f(0); hence, we have that;

f (x) = -3(0) - 4

f(0) = -4.

Ultimately, the points which correctly represents the x- and y-intercepts are; (-4/3, 0) and (0, -4).

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The height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.

area of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel bases.

we shall represent the height of the trapezoid with the letter h so that:

21 cm² = 1/2 × (5 + 9) cm × h

21 cm² = 1/2 × 14 cm × h

21 cm² = 7 cm × h

divide through by 7 cm

h = 21 cm²/7 cm

h = 3 cm

Therefore, the height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.

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H o: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] = 0 This is the null hypothesis, which states that there is no difference in the mean depression symptoms before and after therapy.

A hypothesis is a proposed explanation for a phenomenon. It is a testable statement about the relationship between two or more variables that can be used to generate further investigation and research. Hypotheses are developed from research questions and provide a basis for predicting outcomes and testing theories. Hypotheses are not guesses or hunches; rather, they are educated statements that are backed up by evidence.

Ha: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] ≠ 0 This is the alternative hypothesis, which states that there is a difference in the mean depression symptoms before and after therapy.

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The upper and lower interval estimate are often describe as associated with a specific level of confidence.

In statistics, interval estimate is the process of determining the interval, or range of values, within which a parameter—such as the mean (average) of a population—is most likely to fall.

The interval encompassing a population parameter is determined by computing the statistic from values obtained from a random sample chosen from the population and by using the understanding (derived from probability theory) of how accurately sample properties reflect those of the full population.

The possibility that the estimated confidence interval estimate will include the genuine population parameter is frequently referred to as the confidence level.

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The value of the fraction x/y is 3/25 and option b is the correct answer.

An expression for a portion of a whole is a fraction. In general, the whole can be any particular object or value, and the fraction might be a piece of any quantity out of it.

The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.

The given equation is:

5x + y / y = 8/5

Divide the terms individually at the left side of the equation:

5x/y + y/y = 8/5

5 (x/y) + 1 = 8/5

5 (x/y) = 8/5 - 1

5 (x/y) = 3/5

x/y = 3/25

Hence, the value of the fraction x/y is 3/25 and option b is the correct answer.

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The area of the shaded region of the composite shape is: 21.03  cm²

The formula for the area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Area of given triangle = ¹/₂ * 14 * 14 = 98 cm²

Area of sector is given by the formula:

θ/360 * πr²

Area of sector = 45/360 * π * 14 * 14

= 76.97 cm²

Thus:

Area of shaded portion = 98 cm² - 76.97 cm² = 21.03  cm²

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Answer: The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:

Debit Allowance for Doubtful Accounts account: $500

Credit Bad Debt Expense account: $500

The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.

Step-by-step explanation:

Yes, the previous balance in the Allowance for Doubtful Accounts account does come into play when you add $500 to the account. The Allowance for Doubtful Accounts account is a contra asset account that is used to offset the Accounts Receivable account. It represents an estimate of the amount of accounts receivable that are expected to be uncollectible.

The balance in the Allowance for Doubtful Accounts account is based on the estimated amount of uncollectible accounts, which is typically a percentage of the total accounts receivable balance. When you add $500 to the account, you are increasing the estimated amount of uncollectible accounts.

To record this journal entry, you would debit the Allowance for Doubtful Accounts account for $500 and credit an expense account (such as Bad Debt Expense) for the same amount. The previous balance of $2,000 would also be included in the account balance and would be reflected in the new balance of $2,500.

The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:

Debit Allowance for Doubtful Accounts account: $500

Credit Bad Debt Expense account: $500

The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.