I NEED ANSWERS RN PLS ASAP!

Based on the diagram, determine whether each statement below can be used to justify the claim that “Triangles ABC and ADC are congruent”. Select yes or no for each statement.

(The statements are there in the pic sorry they’re too long and i don’t have that much time)

A domain restriction placed on a non-invertible function affect its inverse.

Using inverse function concepts, it is found that:

The inverse of the function is \(y = \sqrt{x+3}-1\), and the domain of the inverse function is \(\left[-3,\infty ]\)

   A function will have an inverse if for each output, there is only one respective input.

   The domain of the inverse is the range of the original function.

The function given is:

\(f(x) = (x+1)^{2} -3\)

   It's range is \(\left[-3, \infty]\), which will be the domain of the inverse.

To find the inverse, we exchange x and y, and isolate y, then:

\(y = (x+1)^{2} - 3\\ \\x = (y+1)^{2} - 3\\\\(y+1)^{2} = x+3\\ \\\sqrt{((y+1)^{2}} = \sqrt{x+3} \\\\y+1 = \sqrt{x+3}\\\\y = \sqrt{x+3} -1\)

The inverse of the function is \(y = \sqrt{x+3} -1\), and the domain of the inverse function is \(\left[-3, \infty]\).

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The number of students who will not be able to ride on the bus for the school trip is given by the equation A = 15 students

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of students for the trip = 235 students

The number of buses = 5 buses

The number of students in a bus be = B

Now , each seat on the bus can occupy = 2 students

So , 22 seats can occupy = 22 x 2 students

22 seats in the bus can occupy = 44 students

So , the number of students in a bus B = 44 students

And , the total number of students in 5 buses = 5 x number of students in a bus B

Substituting the values in the equation , we get

The total number of students in 5 buses = 5 x 44

The total number of students in 5 buses = 220 students

So , the remaining number of students A = total number of students for the trip - total number of students in 5 buses

Substituting the values in the equation , we get

The remaining number of students A = 235 - 220

The remaining number of students A = 15 students

Therefore , the value of A is 15 students

Hence , the number of students is 15 students

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Let x represent the original cost of one shirt. The equation is 5x - 47.50 = 0, which can be solved to find that x = $9.50.

Gina was shopping and saw a t-shirt she liked, but couldn't decide which color to buy. The clerk offered to reduce the price by $2.50 per shirt if Gina bought more than one. She decided to purchase 5 shirts in different colors and the total cost of all 5 shirts was $47.50. To find the original cost of one shirt before the discount, we can set up an equation. Let x represent the original cost of one shirt. The equation would be 5x - 47.50 = 0, since the total cost of the 5 shirts was $47.50. When this equation is solved, x = $9.50, which is the original cost of one shirt before the discount. Therefore, the total cost of all 5 shirts was reduced by $2.50 for each shirt, from $9.50 to $7.00.

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For the transformation at -78 °C, appropriate reagents include lithium aluminum hydride (LiAlH4) and diethyl ether.

At -78 °C, certain chemical reactions require the use of specific reagents to achieve the desired transformation. One commonly used reagent is lithium aluminum hydride (LiAlH4), which acts as a strong reducing agent. It is capable of reducing various functional groups, such as carbonyl compounds, to their corresponding alcohols.

Diethyl ether is typically employed as a solvent to facilitate the reaction and ensure efficient mixing of the reactants. Researchers often utilize this low temperature for reactions involving sensitive or reactive intermediates, as it helps control the reaction and prevent unwanted side reactions.

The use of LiAlH4 and diethyl ether provides a reliable combination for achieving the desired transformation at this temperature, enabling chemists to manipulate and modify compounds in a controlled manner.

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Answer:

y = \(\frac{3}{2}\)x + \(\frac{7}{2}\)

Step-by-step explanation:

The base form of the slope-intercept form is y = mx + b. We need to think of this as a system of linear equations problem, where we are solving for m and x using 2 equations. Substituting the x and y coordinates of the 2 points, we have 5 = m + b and -1 = -3m + b.

Let's now solve the system by elimination. We first subtract to eliminate the variable b and we get 6 = 4m, so m = \(\frac{3}{2}\). Then we substitute \(\frac{3}{2}\) for m in any of the equations and we get b = \(\frac{7}{2}\). Thus, the equation of the line that goes through (1, 5) and (-3, -1) is y = \(\frac{3}{2}\)x + \(\frac{7}{2}\).

The equivalent fraction for \(\(0.6\overline{8}\)\) is:

\(\(\frac{68.2}{99}\)\)(in simplest form)

To find the 5th term in the expansion of \(\((2x - y)^9\),\) we can use the binomial theorem. The general term in the expansion of \(\((a + b)^n\)\) is given by the binomial coefficient \(\binom{n}{k}\) multiplied by\(\(a^{n-k}\)\) and \(\(b^k\)\), where \(k\) represents the term number.

In this case, we have \(\(a = 2x\)\) and\(\(b = -y\),\)and we want to find the 5th term \((\(k = 4\))\)in the expansion of\(\((2x - y)^9\).\) Using the binomial coefficient, we have:

\(\(\binom{9}{4}(2x)^{9-4}(-y)^4\)\)

Simplifying this expression, we get:

\(\(\binom{9}{4}(2x)^5(-y)^4\)\)

The binomial coefficient \(\binom{9}{4}\) can be calculated as:

\(\(\binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9 \cdot 8 \cdot 7 \cdot 6}{4 \cdot 3 \cdot 2 \cdot 1} = 126\)\)

So, the 5th term in the expansion of \((2x - y)^9\) is:

\(\(126 \cdot (2x)^5 \cdot (-y)^4 = -126 \cdot 32x^5y^4 = -4032x^5y^4\)\)

Therefore, the 5th term is\(\(-4032x^5y^4\).\)

Now, let's find an equivalent fraction for \(0.6\overline{8}\).

Let's represent \(\(0.6\overline{8}\) as \(x\):\)

\(\(x = 0.6\overline{8}\)\)

Now, we multiply both sides of the equation by 100 to shift the decimal point:

\(\(100x = 68.\overline{8}\)\)

Subtracting the original equation from the new equation, we eliminate the repeating part:

\(\(100x - x = 68.\overline{8} - 0.6\overline{8}\)\)

Simplifying, we get:

\(\(99x = 68.\overline{8} - 0.6\overline{8}\)\)

\(\(99x = 68.2\)\)

Dividing both sides by 99, we find:

\(\(x = \frac{68.2}{99}\)\)

To express this fraction in simplest form, we can divide the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 68.2 and 99 is 1. So, the equivalent fraction for \(\(0.6\overline{8}\)\) is:

\(\(\frac{68.2}{99}\)\)(in simplest form)

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It takes Bill approximately 6.5 hours to clean the house alone. Since it takes Billy one hour longer, it takes him approximately 7.5 hours to clean alone.

Let's denote the time it takes Bill to clean the house alone as "x" hours. According to the given information, it takes Billy (the son) one hour longer to clean alone than it takes his dad. Therefore, it takes Billy "x + 1" hours to clean alone. When they work together, they can clean the house in 4 hours. We can set up the following equation based on their combined work rate:

1/x + 1/(x + 1) = 1/4

[(x + 1) + x] / (x * (x + 1)) = 1/4

(2x + 1) / (x * (x + 1)) = 1/4

Cross-multiplying, we have:

4(2x + 1) = x * (x + 1)

\(8x + 4 = x^2 + x\\x^2 - 7x - 4 = 0\)

Now we can solve this quadratic equation. Using the quadratic formula, we get:

x = (-(-7) ± √((-7)² - 4 * 1 * (-4))) / (2 * 1)

x = (7 ± √(49 + 16)) / 2

x = (7 ± √65) / 2

Since the time taken cannot be negative, we consider the positive root:

x = (7 + √65) / 2

≈ 6.5

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Step-by-step explanation:

\( {7}^{2} - 7 = 49 - 7 = 42 \\ so \: required \: answer \: is \: 42\)

The travel times for Bus 14 are more tightly clustered around the median compared to Bus 47.

In mathematics and statistics, range is a measure of the spread or dispersion of a set of data, and it represents the difference between the largest and smallest values in a dataset.

To calculate the range of a dataset, you simply subtract the minimum value from the maximum value. For example, if you have a dataset of test scores: 65, 72, 80, 85, 92, 98. The highest score is 98, and the lowest score is 65. Therefore, the range of the test scores is 98 - 65 = 33.

While range is a simple and easy-to-calculate measure of dispersion, it can be sensitive to outliers or extreme values in the dataset, which may not be representative of the overall data. Other measures of dispersion, such as variance or standard deviation, may be more appropriate in some cases.

To determine which bus is the most consistent, we need to use a measure of variability. The most appropriate measure of variability to use in this case is the interquartile range (IQR), which is the difference between the first and third quartiles.

For Bus 47, the first quartile is 10, and the third quartile is 18. So the IQR is 18 - 10 = 8.

For Bus 14, the first quartile is 12, and the third quartile is 18. So the IQR is 18 - 12 = 6.

Since the IQR for Bus 47 is larger than the IQR for Bus 14, we can conclude that Bus 14 is more consistent in terms of travel times to school. This means that the travel times for Bus 14 are more tightly clustered around the median compared to Bus 47.

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Adding 16 to the given equation we get:

Simplifying the above result we get:

Dividing the above equation by 7 we get:

Simplifying the above result we get:

Answer:

Answer:

Step-by-step explanation:

7x-16=-2how do i find the solution of x

7x - 16 = -2

7x = - 2 + 16

7x = 14

x = 14 : 7

x = 2

-------------------------------

check

7 × 2 - 16 = -2               (remember PEMDAS)

14 - 16 = -2

-2 = -2

the answer is good

Answer:

x and y

Step-by-step explanation:

In algebraic expressions, letters represent variables. These letters are actually numbers in disguise. In this expression, the variables are x and y. We call these letters "variables" because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression.

Please mark me the brainliest!?!

Answer:

Donkey Kong

Step-by-step explanation:

One notable observation about the direction in which the United States expanded is that it predominantly expanded in a westward direction.

The grand narrative of the United States' expansion reveals a prevailing inclination towards a westerly trajectory. Throughout its storied history, the United States embarked on a gradual voyage of territorial growth, beginning from the original 13 colonies nestled along the eastern seaboard and unfurling steadfastly towards the resplendent horizons of the western expanse.

This westward expansion, driven by a tapestry of motivations encompassing territorial acquisitions, pioneering expeditions, ambitious settlements, and the lure of economic prosperity, forged an indelible path that spanned the entire breadth of the continent, from the Atlantic Ocean to the Pacific Ocean.

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Answer:

it is not a fair game since omar has 1/2 chance to win, kaitlyn has a 1/3 chance, and tynessa has a 1/6 chance

Step-by-step explanation:

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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The value of x in the proportion 2.3/4 = x/3.7 is approximately 2.152.

To solve the proportion 2.3/4 = x/3.7, we can use cross multiplication. Cross multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction and vice versa.

In this case, we have (2.3 * 3.7) = (4 * x), which simplifies to 8.51 = 4x. To isolate x, we divide both sides of the equation by 4, resulting in x ≈ 2.152.

Therefore, the value of x in the given proportion is approximately 2.152.

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer:

-2 is the correct answer

Answer:

x = -2

Step-by-step explanation:

x + 9 = 7

=> x = 7 - 9

=> x = -2

Answer:

p + (m × 1) = t

If a plant is already ___cm tall and it will grow one cm every month, an equation to find out how much the plant grew in __ months is this:

(Let t = total number of centimeters, m = number of months, and p = the length of the plant already.)

Therefore, the equation you can use is p + (m × 1) = t.

Given:

Total number of hours = 70 hours

Amount he charges (base fee) = $75

Amount he charges per hour =

In the standard economic model of exponential discounting, you would choose to drive the Ferrari on the last day (fourth day) since it maximizes your discounted utility. However, if you derive b from anticipation alone with α=2, you would choose to drive the Ferrari on the first day. If you derive utility from both anticipation and consumption with α=2, you would still choose to drive the Ferrari on the last day.

In the standard economic model of exponential discounting, the discounted utility of driving the Ferrari for c days can be calculated as \(u(c) / (1 + r)^t, where u(c)\) is the utility function, r is the daily discount rate, and t is the time period.

a. With a daily discount rate of 0.5, you would choose to drive the Ferrari on the last day (day 4) since it maximizes your discounted utility. The utility function \(u(c) = (10c)^2\) does not affect the timing of your choice.

b. If you derive utility from anticipation alone, not consumption, with α=2, the timing of your choice changes. In this case, you only consider the utility derived from anticipating driving the Ferrari. The utility function becomes \(u(c) = α^t\), where α=2. As α increases with time, you would choose to drive the Ferrari on the first day (day 0) to maximize your utility from anticipation.

c. If you derive utility from both anticipation and consumption with α=2, the timing of your choice reverts to the standard model. The utility function remains \(u(c) = (10c)^2\), and with a value of α=2, the highest discounted utility is still achieved by driving the Ferrari on the last day (day 4).

Therefore, depending on the consideration of anticipation alone or anticipation and consumption together, your choice of when to drive the Ferrari may differ.

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Answer:

Step-by-step explanation:

we have perimeter 16

for perimeter 4+4+4+4 we add together it's 16

for area we have 4 times 16

Answer:

x=56

Step-by-step explanation:

okay so

x=180- (64+60)

x= 180-124

x= 56

Answer:

Surface area = 96 square units

Step-by-step explanation:

The surface area of a rectangular prism is simply the sum of all the areas of the 2-D that make up the rectangular prism.  In this prism, there are:

Thus, we can find the area of the individual shapes, and the sum of these areas is the surface area of the triangular units in square units:

Area of the triangles:

Because the two triangles have the same dimensions, we can find the area of one triangle and multiply it by two to find the total area of both triangles.

The formula for the area of a triangle is given by:

A = 1/2bh, where

Since the base of both triangles is 6 units and the height is 2 units, we can plug in 6 for b and 2 for h to find A, the area of one triangle in square units:

A = 1/2(6)(2)

A = 3(2)

A = 6

Now we can multiply this area by 2 to find the total area of both triangles:

2A = 2(6)

2A = 12

Thus, the total area of both triangles is 12 square units:

Area of the left and right rectangles:

Similar to the triangles, the congruence of the two rectangles on the left and right allows us to find the area of one rectangle and later double it to find the total area of these two rectangles.

The formula for the area of a rectangle is given by:

A = lw, where

Since the length of both rectangles (on the left and right) is 7 units and the width is 3 units, we can plug in 7 for l and 3 for w to find A, the area of one of the two rectangles (on the left and right):

A = 7 * 3

A = 21

Now we can double this area to find the total area of the two rectangles on the left and right:

2A = 2(21)

2A = 42

Thus, the total area of the two rectangles (on the left and right) is 42 square units:

Area of the middle rectangle:

Now we can find the area of the middle rectangle by first identifying the length and width and then by plugging into the rectangle area formula.  Since the length is 7 units and the width is 6 units, we can plug in 7 for l and 6 for w to find A, the area of the middle rectangle in square units:

A = 7 * 6

A = 42

Thus, the area of the middle rectangle is 42 square units:

Surface area of the triangular prism:

Since we now know the area of all five shapes that compose the triangular prism, finding the sum of these areas will give us SA, the surface area of the triangular prism in square units:

SA = 12 + 42 + 42

SA = 54 + 42

SA = 96

Thus, the surface area of the triangular prism is 96 square units.

    There are 14 girls and 19 boys in the chess club.

    Let x be girls and y be boys in the chess club. First, we need to write the system.

    We know there are 33 students in total.

x + y = 33

    We also know there are five more boys than girls in the club.

x + 5 = y

x + y = 33

x + 5 = y

    First, we will solve for y with substitution:

x + y = 33

x + (x + 5) = 33

2x = 28

x = 14

    Now, we will plug in this x-value:

x + y = 33

(14) + y = 33

y = 19

           There are 14 girls and 19 boys in the chess club.