Given the following information about two triangles, triangle CAT and triangle DOG:



Which postulate can be used to prove triangle CAT and triangle DOG are congruent?



SSS Postulate


SAS Postulate


SSA Postulate


ASA Postulate


AAS Postulate



Choose all that apply

Answer:

1. 4

2. 10

3. 14

Step-by-step explanation:

A = -6

B = 0

C = 4

D = 8

1. BC = |0 - 4| = 4

2. AC = |-6 - 4| = |-10| = 10

3. AD = |-6 - 8| = |-14| = 14

Answer:

1.  BC = 4

2.  AC = 10

3.  AD = 14

Step-by-step explanation:

Ruler Postulate

The distance between any two points on a number line is their difference.

Question 1

Given:

Therefore, using the Ruler Postulate:

⇒ BC = |b - c|

⇒ BC = |0 - 4|

⇒ BC = |-4|

⇒ BC = 4

Question 2

Given:

Therefore, using the Ruler Postulate:

⇒ AC = |a - c|

⇒ AC = |-6 - 4|

⇒ AC = |-10|

⇒ AC = 10

Question 3

Given:

Therefore, using the Ruler Postulate:

⇒ AD = |a - d|

⇒ AD = |-6 - 8|

⇒ AD = |-14|

⇒ AD = 14

The expression is option B and the solutions of the equation 2x² - x - 15 = 0 are x = 3 and x = -5/2.

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

The solutions of a general quadratic equation ax² + b x + c = 0 can be found using the formula,

x = [-b ± \(\sqrt{b^2-4ac}\) ] / 2a

Given quadratic equation is 2x² - x - 15 = 0.

a = 2, b = -1 and c = -15

Solutions of the equation can be found using the formula.

x = [-(-1) ± \(\sqrt{(-1)^2-4(2)(-15)}\) ] / 2(2)

  =  [1 ± \(\sqrt{1-4(2)(-15)}\) ] / 2(2), which is the expression given in option B.

Solving this,

x = 1 ± \(\sqrt{1+120}\) ] / 4

x = (1 ± 11) / 4

x = 3 and x = -10/4 = -5/2

Hence the required expression is option B.

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Your question is incomplete. The complete question with the missing part is given below.

Which expression can be simplified to find the solution(s) of the equation 2x²-x-15 = 0?

A.  [1 ± \(\sqrt{1-4(2)(15)}\)] / 2(2)

B. [1 ± \(\sqrt{1-4(2)(-15)}\)] / 2(2)

C. [1 ± \(\sqrt{1+4(2)(15)}\)] / 2(2)

D. [1 ± \(\sqrt{-1-4(2)(-15)}\)] / 2(2)

E. [-1 ± \(\sqrt{1-4(2)(-15)}\)] / 2(2)

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Tom will pay a total of $13,424.20 in interest over the term of the loan.

The formula to calculate the monthly payment for an amortized loan is given by:  `P = r(PV) / [1 - (1 + r)^(-n)]`Where P is the monthly payment, r is the interest rate per month, PV is the present value of the loan, and n is the number of payments or the total number of months.

Substituting the given values, we get:P = 0.0052083333 × 44,000 / [1 - (1 + 0.0052083333)^(-7×12)]P = 632.32Therefore, Tom's monthly payment is $632.32 (rounded to the nearest cent).b. Since Tom pays the monthly payment each month for the full term, his total amount to repay the loan is equal to the present value of the loan.

Therefore, the total amount to repay the loan is $44,000 (rounded to the nearest cent).c. The total amount of interest paid over the term of the loan can be calculated as the difference between the total amount repaid and the principal amount of the loan.

Therefore, the total interest paid is: Total interest paid = Total amount repaid - Principal amount of the loan Total interest paid = $57,424.20 - $44,000Total interest paid = $13,424.20

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If E(X) = 6 and E(Y) = 10, and the random variables are independent variables, the value of E(X | Y) is 6

Given, E(X) = 6 and  E(Y) = 10.

It is also given that X and Y are independent variables.

So, if two random variables X and Y are independent, which means that if knowing the value of one of them does not change the probability of occurring of the other one. In other words, if X and Y are independent, we can write:

                           P(Y | X) = P(Y)

So, in the question, we are asked to determine the value of E(Y | X).

                        ∴ E(X | Y) = E(X)

                        ∴ E(X | Y) = 6

Hence, the value of E(X | Y) is 6

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To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

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The value of h variable in the missing angle is; h = 22.4°

There are three interior angles in a triangle, when these three interior angles are added together, they give a sum of 180 degrees according to the triangles sum theorem.

Triangle UVW is sketched in the diagram attached attached, where:

m∠WUV = 36°

m∠UVW = (5h − 64)°

m∠AWB = (5h − 16)°.

m∠AWB = m∠VWU = (5h − 16)° [congruent angles]

m∠WUV + m∠UVW + m∠VWU = 180° [triangle sum theorem]

Substitute the relevant values to get;

36 + 5h − 64 + 5h − 16 = 180

Combine like terms to get;

10h - 44 = 180

10h = 180 + 44

10h = 224

10h/10 = 224/10

h = 22.4

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Answer:

The answer is 22.4

Step-by-step explanation: I got it right on my test.

Answer:

#14) B) 7 cars

#15) C) 37

Step-by-step explanation:

Hope this helps

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Hi my lil bunny!

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If an octagon is 24, how many is a pentagon?

Ans : Pentagon has 5 sides.

( A five-sided shape is called a pentagon. A six-sided shape is a hexagon, a seven-sided shape a heptagon, while an octagon has eight sides. The names of polygons are derived from the prefixes of ancient Greek numbers. )

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Have a great day/night!

❀*May*❀

The pentagon is 15, when octagon is 24.

What is Polygon?

A polygon is a figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides).

Polygon with 8 sides known as Octagon and polygon with 5 sides known as Pentagon.

Here, given that, Octagon = 8 sides = 24

So, 1 side= 3

Then, we get, pentagon = 5 sides = (5×3) = 15

Hence, the pentagon is 15.

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300 x 0.4 = 120

120 x 3 = 360

a. $360

300+360= 660

b. $660

2000 x 3.5 = 7000

7000 x 4 = 28000

a. $28,000

2000 + 28000 = 30000

b. $30,000

Answer:

D: 2/3x - 13/12 = -5/12x

Step-by-step explanation:

2/3x - 5/6 = -5/12x + 1/4

To simplify, the denominator must be the same. So,

5/6 = 10/12

and 1/4 = 3/12

Then, you move the values to the same side via addition or subtraction.

2/3x (- 10/12 - 3/12) = -5/12x

2/3x - 13/12 = -5/12x

1) adjacent

2) linear pair

3) complementary

4) vertical

5) linear pair

6) linear pair

7) complementary

8) vertical

9) adjacent

10) adjacent

11) vertical

12) adjacent

13) adjacent

14) vertical

Answer:

y = -8

Step-by-step explanation:

When y = -2/5, the slope is 0.

Seeing this, we can make the equation the same as the y-value of the point given.

Hence,

y = -8

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Answer:

Probability (Roulette ball not landing on red) = 10 / 19

Step-by-step explanation:

Given:

Number of total slots = 38

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Find:

Probability (Roulette ball not landing on red)

Computation:

Probability (Roulette ball not landing on red) = 1 - Probability (Roulette ball landing on red)

Probability (Roulette ball not landing on red) = 1 - (18 / 38)

Probability (Roulette ball not landing on red) = 20 / 38

Probability (Roulette ball not landing on red) = 10 / 19

The equation of the line parallel to the given line is 3x - 2y + 5 = 0.

What is the equation of a line?

The set of points that make up a line in a coordinate system is represented algebraically by a line's equation.

A straight line's equation is y=mx+c, where m denotes the gradient and c, commonly known as the y-intercept, is the height at which the line crosses the y-axis.

The given line is -3x+2y = 4

Then,  \(y = \frac{3}{2}x + 2\)

Slope \((m_1) = \frac{3}{2}\) and \(c_1\) = 2

Now, the slope of the parallel line \(m_2\) = \(m_1\) = 3/2

and passes through a point (-1,1)

Then,

the equation of the parallel line is

\(or, y-y_1=m(x-x_1) \\\\or, y-1=\frac{3}{2}(x+1) \\\\ or, 2y-2=3x+3\\\\or, 3x-2y+5=0\)

Hence, the required equation of the line is 3x - 2y + 5 = 0.

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The rate 880 yards in 2 minutes to feet per minute is  1320 feet per minute

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

Rate = 880 yards in 2 minutes

This means that

Rate = 440 yards in 1 minute

The general rule of conversion is that

1 yard = 3 feet

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

Rate = 440 * 3 feet in 1 minute

Evaluate

Rate = 1320 feet in 1 minute

So, we have

Rate = 1320 feet per minute

Hence, 880 yards in 2 minutes to feet per minute is  1320 feet per minute

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Answer:

El número es el 47

Step-by-step explanation: Con los dígitos de los siguientes números se obtiene que su suma es 11

47        4  +  7  =  11

38         3  +  8 =  11

29         2   + 9  = 11

Si se cambia el orden de los dígitos:

47       se convierte en    74        74 - 47  =  27

38                  "    "             83        83 - 38 =  45

29                  "    "             92        92 - 29 = 63

Entonces el número solicitado es el 47

Answer: Answer #1

Step-by-step explanation: −3.3m+9.2n−4.2  Brainliest please?

−3.3m+9.2n−4.2 Is the correct answer for the Diagnostic Test B

I took the quiz and got 100% on it

May I be the Brainliest

I hope you guys do good!

Answer:10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

took the test

Answer:

By simplifying the expression we get

4/3

\(a(n) = p(1 + i) ^{n - 1} \)

where n is a positive Integer.

Here,

P= Principal

I= interest

N= Duration (positive integer)

Hope this helps ..

Good luck on your assignment...

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

Describe a formula. To create the expression known as an equation, two sides are connected by the equals symbol (=). The variables in the equation 2x+1 = 9 are 2x+1 on the left and 9 on the right (RHS).

To simplify the equation 2/3x + 5 = 1/5 - 2x, we can start by getting rid of the fractions. To do this, we can multiply every term in the equation by the least common multiple (LCM) of the denominators of the fractions, which is 15.

So, we have:

15 * (2/3x + 5) = 15 * (1/5 - 2x)

Expanding the left-hand side, we get:

10x + 75 = 3 - 30x

Bringing all the x terms to one side and all the constant terms to the other, we get:

10x + 30x = 3 - 75

Combining like terms, we get:

40x = -72

Dividing both sides by 40, we get:

x = -72/40 = -9/5

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

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The answer is:

Work/explanation:

The difference is the result of subtracting one number from another one.

So the difference of twice a number and 9 means we subtract twice a number (let n be that number) and 9: 2n - 9

Next, 5 times that difference is 5(2n - 9)

Finally, this equals 7 : 5(2n - 9) = 7

__________________________________________________________

Use the distributive property

\(\sf{5(2n-9)=7}\)

\(\sf{10n-45=7}\)

Add 45 on each side

\(\sf{10n=7+45}\)

\(\sf{10n=52}\)

Divide each side by 10

\(\sf{n=\dfrac{52}{10}}\\\\\\\sf{n=\dfrac{26}{5}}\)

25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

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Therefore, the probability that someone who brings a laptop on vacation also uses a cell phone is 3.52 or 352%.

To find the probability that someone who brings a laptop on vacation also uses a cell phone, we need to use conditional probability.

Let's denote the events:

A: Bringing a laptop

B: Using a cell phone

We are given the following information:

P(A) = 25% = 0.25 (Probability of bringing a laptop)

P(B) = 30% = 0.30 (Probability of using a cell phone)

P(A ∩ B) = 88 out of 100 who bring a laptop also check work email (88/100 = 0.88)

P(B | A) = ? (Probability of using a cell phone given that someone brings a laptop)

We can use the conditional probability formula:

P(B | A) = P(A ∩ B) / P(A)

Substituting the given values:

P(B | A) = 0.88 / 0.25

Calculating the probability:

P(B | A) = 3.52

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Answer:

c

Step-by-step explanation:

edge

Answer:

x =20.8

Step-by-step explanation:

We can find the value of 1/2 of x using the Pythagorean theorem

a^2 + b^2 = c^2

a^2 + 6^2 = 12^2

a^2 = 36+144

a^2 = 108

Take the square root

sqrt(a^2) = sqrt( 108)

a =sqrt(36*3)

a = sqrt(36) sqrt(3)

a = 6sqrt(3)

Now x = 2 times the length of a

x = 2 * 6 sqrt(3)

x = 12 sqrt(3)

x =20.78460969

x =20.8

The family-sized box requires 130 more square inches of cardboard than the regular-sized box, has an additional 228 cubic inches of cereal capacity, and costs less per cubic inch of cereal.

To calculate the additional square inches of cardboard needed for the family-sized box, we need to find the difference in surface area between the regular-sized box and the family-sized box.

The regular-sized box has a surface area of 2 x 6 + 2 x 11 + 6 x 11 = 104 square inches.

The family-sized box has a surface area of 2 x 8 + 2 x 15 + 3 x 15 + 3 x 8 + 3 x 15 = 234 square inches.

Therefore, the additional square inches of cardboard needed for the family-sized box is 234 - 104 = 130 square inches.

B. To find how many more cubic inches of cereal fit in the family-sized box than the regular-sized box, we need to calculate the difference in volume between the two boxes.

The regular-sized box has a volume of 2 x 6 x 11 = 132 cubic inches.

The family-sized box has a volume of 3 x 8 x 15 = 360 cubic inches.

Therefore, the additional cubic inches of cereal that fit in the family-sized box is 360 - 132 = 228 cubic inches.

C. To determine which cereal costs less per cubic inch of cereal, we need to divide the cost of each box by its respective volume.

The regular-sized box costs $3.99 for 132 cubic inches of cereal, which gives us a cost of $0.03 per cubic inch.

The family-sized box costs $5.69 for 360 cubic inches of cereal, which gives us a cost of $0.02 per cubic inch.

Therefore, the family-sized box costs less per cubic inch of cereal.

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The statement is false. A smaller margin of error will result in a smaller confidence interval, not a larger one, as we become more confident.

In statistics, a confidence interval is a range of values within which we estimate the true population parameter to lie. It provides a measure of uncertainty or variability around the point estimate. The margin of error is the maximum amount by which the estimate might differ from the true population parameter.

When constructing a confidence interval, we typically choose a level of confidence, such as 95% or 99%. This level of confidence represents the probability that the interval will contain the true parameter value in repeated sampling. A higher level of confidence corresponds to a narrower interval because we want to be more confident that the true parameter value falls within that range.

The margin of error is influenced by various factors, such as the sample size, standard deviation, and the desired level of confidence. When the sample size increases or the standard deviation decreases, the margin of error decreases. This means that with more data or less variability, we can estimate the population parameter more precisely, resulting in a smaller margin of error.

The confidence interval is calculated by taking the point estimate and adding or subtracting the margin of error. Therefore, a smaller margin of error will lead to a narrower interval. This narrower interval indicates a higher level of confidence as we are more certain about the location of the true population parameter.

For example, if we have a sample mean of 50 with a margin of error of 5 at a 95% confidence level, the confidence interval would be [45, 55]. If we have a smaller margin of error, say 2, the confidence interval would be [48, 52]. The smaller margin of error in the second case reflects a higher level of confidence and a narrower range.

In conclusion, a smaller margin of error will result in a smaller confidence interval, not a larger one. As we become more confident in our estimate, the interval becomes narrower, indicating a higher level of precision.

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