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The proof of congruence by SAS, then 2 corresponding sides and the corresponding included angles of both triangles are equal.

Angles who are of same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of same measure, then

\(m\angle A = m\angle B\)is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

The SAS postulate , Two sides and the included angle of one triangle are identical to the corresponding two sides and the included angle of another triangle.

In the triangle, the angles mCAD and mACB are congruent.

m∠CAD ≅ m∠ACB

Since m∠CAD and m∠ACB are congruent, AD and BC must also be congruent.

As a result, the SAS Congruence postulate is proven.

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The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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The angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.

The angle of elevation is the angle θ between the horizontal line given as 2000 feet and the line of sight which is above the horizontal line.

The angle θ in degree is calculated, and then converted to radian as follows:

since the camera and the rocket is 4255 feet apart, then;

θ = tan⁻¹(4255/2000)

θ = 64.82482°

To convert 64.82482° to radian, we multiply by π/180

θ' = 64.82482° × π/180

θ' = 1.13186 approximately to 5 decimal place.

Therefore, the angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.

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Given:

An annual pass to a park costs $120.

To find:

The 200% of the full price using percent model.

Solution:

In the percent model,

100% = 1 box

It means 1 box represents park costs $120.

200% = 2 box

\(120+120=240\)

It means 2 box represents park costs $240.

Therefore, 200% of the full price is $240.

The number of lines of symmetry that the symbol for a state capital has is 4.

The square symbol is often used in maps to represent the capital of a state.  The square symbol has 4 lines of symmetry. A line of symmetry is a line that runs through a shape and thus divides it. Four lines of symmetry can be drawn across a square.

A  rectangle only has two lines of symmetry. A rhombus shape will also have 2 lines of symmetry. So, for the representation of the state capital, the lines of symmetry are 4 in number.

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Answer:

225 feet

Step-by-step explanation:

if you multiply 15 x 15 you get 225

if this is wrong i am so sorry

To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

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Answer:

2.00 and 3.00

Step-by-step explanation:

2.49=2.00

why 4 is less than 5 so it turns to zero

and

2.98=3.00 because 9 is greater than 5 so it transfer to 1

Standard deviation does not mean independent events.

No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.

Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.

Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.

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Answer:

The answer is x=57

Step-by-step explanation:

First, we would set the number to x.

Then, we turn the words into an equation.

x+75 = 3x-39

Isolate the x.

-2x = -114

So...

x = 57

The large jar has better value for money than the smaller one.

To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.

For the first jar we have:

q = £4.10/540 = 0.0075

For the second jar we have:

q' = £2.81/360 = 0.0078

Then we can see that the large jar has the best value for money.

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Answer:

Es el acronimo de la (Contraloría General de la República

Step-by-step explanation:

Espero ayudarte suerte

Significado de SGR. El significado de la sigla SGR es el acrónimo de Sociedades de Garantía Recíproca. El significado de la sigla SGR es el acrónimo de sociedad de garantía recíproca y pertenece a la categoría Europa. El significado de la sigla SGR es el acrónimo de Sociedad de Garantías Recíprocas.

Answer:

  1/3 to 1/2 teaspoons of lemon extract

Step-by-step explanation:

The proportions you say are ...

  1 tsp lemon extract : 2 tbsp lemon juice

  extract : juice = 1 tsp : 6 tsp = 1 : 6

If you have 2-3 teaspoons of lemon juice, you have the equivalent of 2/6 to 3/6 = 1/3 to 1/2 teaspoons of lemon extract.

Answer:

Step-by-step explanation:

here is a step-by-step explanation:

Convert half a gallon of milk to liters. There are 3.785 liters in a gallon, so half a gallon is 1.892 liters.

Convert 5 ounces to liters. There are 0.147868 liters in 5 ounces.

Divide the total volume of milk (1.892 liters) by the volume of each bottle (0.147868 liters) to find out how many bottles can be filled completely:

1.892 liters / 0.147868 liters per bottle = 12.8 bottles

Note that the answer is not a whole number, which means there will be some leftover milk after 12 bottles are filled.

To find out how many milliliters are in each bottle, we can convert 5 fluid ounces to milliliters:

5 fluid ounces x 29.5735 milliliters per fluid ounce = 147.868 milliliters

Therefore, each bottle will contain approximately 147.868 milliliters of milk.

So, in summary, with half a gallon of milk, you can fill 12 bottles completely and each bottle will contain about 147.868 milliliters of milk.

From the information available, we have Traci's monthly budget as follows;

If her net annual income is $16752, then her monthly income would be;

To determine if the monthly budget is balanced, surplus or deficit, we shall find the difference between budgeted amount and actual income.

If both figures are equal, we have a balance

If the income is higher than the budget, we have a surplus

If the income is lesser than the budget, we have a deficit.

The income here is $1,396 and this is higher than the budget which is, $1,300. Therefore we would have;

ANSWER:

Her budget is not balanced.

It shows a surplus of $96

Step-by-step explanation:

heres the formula A=12b(base)h(hight)

Answer:

Step-by-step explanation:

It has (1/2) included in the formula to find area

Answer:

options a is correct

4/7 likely

Probability = Favourable outcomes/ Total outcomes

All outcomes that we have are = 1,2,3,4,5,6,7,8

→ Total outcomes are 8 .

Favourable outcomes are = 1,3,5,7

→ Favourable outcomes are 4.

P(odd) = 4 divided by 8

→ P( odd) is 1/2 , 50% , equally likely.

So option 2nd is correct .

Answer: The 24th customer.

Step-by-step explanation:

8th customer: Free Coffee       12th customer: Free Bagel

16th customer: Free Coffee      24th customer: Free Bagel

24th customer: Free Coffee

You're welcome!

Answer:

person above me is correct

Step-by-step explanation:

449.86

To compute the moment of the second sample, we need to compute the sum of the squares of the sample values.

This formula is:

Sum = ∑(x_i^2)

After inserting the example values:

Sum = 6.2^2 + 7.4^2 + 9.6^2 + 11.5^2 + 13.5^2

Simplifying this formula to:

Total = 38.44 + 54.76 + 92.16 + 132.25 + 181.25

Adding these terms gives us the following final result:

Total = 449.86

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Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

Answer:

x = 18 degrees

Step-by-step explanation:

We are given 72 degrees. The box on the bottom left of the ramp is at a 90 degree angle. Given that this triangle will add up to 180 degrees no matter what we add the two given degrees; 72 + 90 = 162. Now we subtract; 180 - 162 = 18 degrees.

Answer:

The general term is

Sn = -(-2)ⁿ.3¹⁻ⁿ

step by step Explanation:

we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....

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If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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Answer:

Step-by-step explanation: