What additional information would you need to prove that angle ABC is congruent to DEF by SAS?

A. AC = EF

B. BC = FE

C. AC = FE

D. BC = EF

The shaded area is approximately 113.04 mm² (to 3 significant figures).

To calculate the shaded area, we need to determine the area of the semicircle and subtract the area of the circle.

The radius of the semicircle is half the diameter, so it is 24 mm / 2 = 12 mm.

The area of a semicircle is given by (π × r²) / 2, where r is the radius.

Substituting the values, the area of the semicircle is (π × 12²) / 2 = (π × 144) / 2 = 72π mm².

Now let's calculate the area of the circle.

The radius of the circle is half the diameter of the semicircle, which is 12 mm / 2 = 6 mm.

The area of a circle is given by π × r², where r is the radius.

Substituting the values, the area of the circle is π × 6² = π × 36 = 36π mm².

Finally, we can calculate the shaded area by subtracting the area of the circle from the area of the semicircle:

Shaded area = Area of the semicircle - Area of the circle

= 72π - 36π

= 36π mm²

To find the answer to 3 significant figures, we can approximate π as 3.14:

Shaded area ≈ 36 × 3.14 mm²

≈ 113.04 mm²

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The store at which the apple will cost the cheapest is: Store A

The formula for the slope between two coordinates is:

Slope = (y₂ - y₁)/(x₂ - x₁)

Now, all the lines in the attached graph pass the origin and so they will all have the coordinate (0, 0)

The slope for each line will give us the cost for each apple in the store.

Thus:

Slope for store A = (3 - 0)/(4 - 0)

Cost for store A apple = $0.75

Slope for Store B = (5 - 0)/(5 - 0)

Cost for store B apple = $1

Slope for Store C = (5 - 0)/(4 - 0)

Cost for store C apple = $1.25

Slope for Store D = (6 - 0)/(3 - 0)

Cost for store C apple = $2

Thus, store A has the cheapest Apple

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The expression for the nth term is [tex]f(n) = 6 * (-1/5)^{n-1[/tex] and the 12th term is -6/48828125

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

a = 6

r = -1/5

The nth term of the geometric sequence is represented as

[tex]f(n) = ar^{n-1[/tex]

using the above as a guide, we have the following:

[tex]f(n) = 6 * (-1/5)^{n-1[/tex]

For the 12th term, we have

[tex]f(12) = 6 * (-1/5)^{11[/tex]

Evaluate

f(12) = -6/48828125

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(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By applying a reflection over the x-axis to the parent absolute value function g(x) = |x + 2| - 4, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

x and y represent the data points.

m represent the slope.

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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f(x) = -215 and [tex]g(x) = -98x^2[/tex] satisfy the given conditions, and h(x) = (f o g)(x) is equal to [tex]-215 - 98x^2.[/tex]

To find the functions f(x) and g(x) such that h(x) = (f o g)(x) and g(x) = 1-7x, we need to substitute the expression for g(x) into the equation for h(x).

Given: g(x) = 1 - 7x

Substituting g(x) into h(x), we have:

[tex]h(x) = (1 - 7)^3 - 2(1 - 7x)^2 + 4(1 - 7x) - 1[/tex]

Simplifying the expression further:

[tex]h(x) = (-6)^3 - 2(1 - 7x)^2 + 4(1 - 7x) - 1[/tex]

[tex]= -216 - 2(1 - 14x + 49x^2) + 4(1 - 7x) - 1[/tex]

[tex]= -216 - 2 + 28x - 98x^2 + 4 - 28x - 1[/tex]

[tex]= -215 - 98x^2[/tex]

Therefore, f(x) = -215 and [tex]g(x) = -98x^2.[/tex]

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Answer: 645

Step-by-step explanation:

Answer:

Step-by-step explanation:

75x86=6450.

Answer:

To translate the argument into symbolic form, we can assign variables:

P: He drives fast

Q: He will not crash

The argument can then be expressed as:

If P, then ~Q

To determine if the argument is valid or invalid, we need additional information or premises. An argument is considered valid if the conclusion follows logically from the premises.

If there are additional premises provided, please provide them so that we can evaluate the validity of the argument.

Step-by-step explanation:

The area of the region in the curves is 9 square units

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

f(x) = 4 - 2x² and g(x) = 2x.

In the region that lies inside the curves, we have

x = -2 and 1

So, we have

[-2, 1]

This represents the interval

For the surface generated around the region bounded by the curves, we have

A = ∫[a, b] [f(x) - g(x)] dx

This gives

A = ∫[-2,1] [4 - 2x² - 2x] dx

Integrate

A = 4x - x² - 2x³/3 [-2,1]

Expand

A = |4(-2) - (-2)² - 2(-2)³/3 - (4(1) - (1)² - 2(1)³/3)|

Evaluate

A = 9

Hence, the area of the region in the curves is 9 square units

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Question

If R is the region bounded above by the graph of the function f(x) = 4 - 2x² and below by the graph of the function g(x) = 2x, find the area of the region . This question requires you show your ability to us apply Calculus. Show all working.​

To determine the minimum number of visits Wyatt needs to earn his first free movie ticket, we can set up an inequality using the information provided. So,  the inequality that represents this is: 25 + 11.5x ≥ 230

Let x be the number of visits Wyatt needs.
We know that Wyatt receives 25 reward points just for signing up and earns 11.5 points for each visit. So, the total number of points he earns can be represented by the equation: 25 + 11.5x

To earn his first free movie ticket, Wyatt needs at least 230 points.

Therefore, the inequality that represents this is: 25 + 11.5x ≥ 230

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Answer:

[tex]\displaystyle{x^2+y^2=5}[/tex]

Step-by-step explanation:

Given the polar equation of:

[tex]\displaystyle{r^2 =5}[/tex]

We know that 'r' represents the radius which equals to:

[tex]\displaystyle{r = \sqrt{x^2+y^2}}[/tex]

Therefore, by substitution, we have:

[tex]\displaystyle{\left(\sqrt{x^2+y^2} \right)^2=5}[/tex]

Cancel the square root:

[tex]\displaystyle{x^2+y^2=5}[/tex]

Therefore, the cartesian equation is:

[tex]\displaystyle{x^2+y^2=5}[/tex]

The function c(n) = (4)^(n-1) does not represent the number of likes each day based on the given information.

The given function c(n) = (4)^(n-1) represents the number of likes on the video on each day, where n is the number of days since the video was posted.

We are told that on the first day, there were 100 likes. Therefore, we can substitute n = 1 into the function and solve for the constant factor:

c(1) = (4)^(1-1) = 4^0 = 1

Since c(1) represents the number of likes on the first day and it is given as 100, we can equate it with the value obtained from the function:

1 = 100

However, this equation is not true. Therefore, the function c(n) = (4)^(n-1) does not represent the number of likes each day based on the given information.

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The manager needs 50 pounds of Earl Grey Tea and 150 pounds of Orange Pekoe Tea.

Let the amount of Earl Grey Tea (which sells for $4 per pound) be represented by x, then the amount of Orange Pekoe Tea (which sells for $2 per pound) is 200-x. We want to determine how much of each type of tea should be mixed so that the new blend will sell for $2.50 per pound.

Step-by-step explanation:The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey Tea that sells for $4 per pound with some Orange Pekoe Tea that sells for $2 per pound to get 200 pounds of the new blend.

We are to determine how many pounds of Earl Grey Tea and Pekoe Tea are required if the selling price of the new blend is to be $2.50 per pound. Let x be the amount of Earl Grey Tea (which sells for $4 per pound). Then the amount of Orange Pekoe Tea (which sells for $2 per pound) is 200-x.

We want to determine how much of each type of tea should be mixed so that the new blend will sell for $2.50 per pound. We can start the problem by setting up an equation that relates the price of the new blend with the prices of the two types of tea:4x + 2(200-x) = 2.5(200).

Simplify and solve for x:4x + 400 - 2x = 5002x + 400 = 5002x = 100x = 50.

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       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

Answer:

increase by 87.5%

Step-by-step explanation:

150 ÷ 80 - 100 = 87.5

new value ÷ original value - 100= percentage change

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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The sets of values that can be the measures of the exterior angles of a triangle include the following:

A. 120°, 110°, 130°

D. 120°, 120°, 120°.

In order to determine an obtuse triangle, we would apply Pythagorean theorem:

c² = a² + b²

Where:

For any obtuse triangle, the square of the hypotenuse is greater than the sum of the square of both the adjacent and opposite side:

c² > a² + b²

For any obtuse triangle, the set of angle measures that are required with respect to the exterior angles of a triangle must fall within the following range;

90° < θ < 180°

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Step-by-step explanation:

To solve x^2+10x=15, we can complete the square by adding (10/2)^2=25 to both sides, resulting in (x+5)^2=40. Then, we can take the square root of both sides and solve for x, giving us x=-5±2√10. Alternatively, we can factor the quadratic as (x+5-2√10)(x+5+2√10)=0 and solve for x.

Answer:

You should reverse the inequality sign when you multiply or divide both sides of an inequality by a negative number. Addition and subtraction never change the direction of the inequality sign. Multiplication and division do change the direction of the inequality, but only if the number you’re multiplying or dividing by is a negative number.

Step-by-step explanation:

Step-by-step explanation:

negative  three   PLUS   negative three   equals  negative six  

The length of each piece of a rope which is 6 m long and that has to be cut into 24 pieces will be equal to 25 cm.

We have given a rope whose length is 6m and that has to be cut into 24 pieces.

Length (L) = 6m

Now, as we need the answer in cm we have to convert m into cm

1m = 100 cm

Multiplying both sides by 6 we get,

1m * 6 = 100cm * 6

6m = 600cm

Given that, we have to cut the rope into 24 pieces, the length of each piece will be:

Length of each piece = Length of rope(in cm)/ Number of cuts

Putting values in the above equation we get,

Length of each piece = 600÷24

Solving the above equation,

Length of each piece of a rope = 25 cm

Therefore, we obtain the length of each piece to be 25 cm

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The domain of the graph are All real numbers

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

The graph

The graph is an exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

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Based on your annual review score of 3.4, you would receive a merit increase of 2.5%.

To determine the merit increase based on your annual review score of 3.4, we need to calculate the increase increment based on the given scale.

First, we need to determine the number of 0.4-point increments between your score of 3.4 and the baseline score of 2.6, which is the starting point for merit increases. The difference is 3.4 - 2.6 = 0.8.

Since the merit increases go up by 1% for every 0.4 points, we divide the difference of 0.8 by 0.4 to find the number of 0.4-point increments:

0.8 / 0.4 = 2

So, there are 2 increments of 0.4 points.

Next, we calculate the merit increase percentage. The baseline increase is 0.5%, and it increases by 1% for each 0.4-point increment. Since we have 2 increments, the increase percentage would be:

0.5% + 2 * 1% = 0.5% + 2% = 2.5%

Therefore, based on your annual review score of 3.4, you would receive a merit increase of 2.5%.

It's important to note that this calculation assumes a linear progression of merit increases based on the given criteria. The actual merit increase policy may vary depending on company practices and policies.

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The new balance is$1,912.40 (rounded to two decimal places).To calculate the new balance after one month, we can multiply the current balance by (1 + Periodic Rate):

To find the monthly periodic rate, we can use the formula:Periodic Rate = (1 + Annual Percentage Rate)^(1/Number of Periods) - 1.

In this case, the Annual Percentage Rate (APR) is 12.5%, and since the interest is compounded monthly, the Number of Periods is 12.

Substituting the values into the formula, we have:

Periodic Rate = (1 + 0.125)^(1/12) - 1.

Calculating this expression, we find:

Periodic Rate ≈ 0.0103.

Therefore, the monthly periodic rate is approximately 0.0103, or 1.03%.

This means that every month, the balance on Owen's credit card will increase by 1.03% due to the compounded interest.

New Balance = $1,892.32 * (1 + 0.0103).

New Balance ≈ $1,912.40 (rounded to two decimal places).

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Answer: 76kg

Step-by-step explanation:

If the mass of sugar in one jar is 19kg, then the mass of 4 such jars of sugar can be found by multiplying the mass of one jar by 4:

Therefore, the total mass of 4 jars of sugar is 76kg.

__________________________________________________________

The mass of sugar is 19 kg. What is the total mass of 4 such jar of a sugar?

The total mass of four jars of sugar is 76 kg.

The total mass of four jars of sugar can be found by multiplying the mass of one jar by 4:

[tex]\large\rm{Total\: mass = 19\: kg \times 4 = \boxed{\rm{\:76\: kg\:}}}[/tex]

[tex]\therefore[/tex] The total mass of four jars of sugar is 76 kg.

- Mass is a measure of the amount of matter an object contains. It is a fundamental property of an object and is typically measured in units such as kilograms or grams. Mass is different from weight, which is the force of gravity acting on an object's mass. Mass is an intrinsic property of an object and remains constant regardless of its location, while weight can vary depending on the gravitational field it is in. Essentially, mass determines an object's resistance to acceleration or change in motion.

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Answer:

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

Let the distance we are looking for be d.

If cat runs d meters, then mouse runs 160 m less because of the head, and the ratio of the distance they cover is 9/7.

Set up an equation to reflect it:

Solve it for d:

So, the cat must run 720 m to catch the mouse.

The inequality showing that the total number of eggs laid by the first hen was greater than the total number of eggs laid by the second hen can be represented as:

7 * › > 8 * y

In this inequality, "7 * ›" represents the total number of eggs laid by the first hen, and "8 * y" represents the total number of eggs laid by the second hen. The inequality states that the product of 7 and the number of weeks for which the first hen laid eggs is greater than the product of 8 and the number of weeks for which the second hen laid eggs.

Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

Answer:

positive correlation

Step-by-step explanation: