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The right triangles are congruent by HL theorem.

The triangles having congruent corresponding parts are called congruent triangles.

Given are two right triangles, with equal hypotenuse and one of the bases.

The question is by which theorem do they are congruent,

HL theorem :-

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Since, we know that, when two right triangles have congruent hypotenuse and one of their legs are also congruent, then both are congruent by HL theorem of congruence.

Here, both the right triangles are following the condition of the HL theorem.

Hence, the correct option is HL.

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Answer:

i think it 20 if im wrong im sorry

The height of the prism is 9 inches if the area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

Please refer to the attached picture for the figure:

We have:

The area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.

As we know the area of the rectangular face = lengthxwidth

From the figure:

The area of the rectangular face = hx5

h is the height of the rectangular prism.

45 = hx5

h = 45/5

h = 9 inches

Thus, the height of the prism is 9 inches if the area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.

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Answer:

[tex]4i \sqrt{6} [/tex]

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.

given

Table 1:  

x 0 -4 3 -2 9 3

y 5 8 7 8 5 -2

No, Table 1 is not a function.

Since there are two images of element '3'.

i.e. 3 is mapped to 7 and -2.

Table 2:

x 2 -7 5 1 -6 3

y 5 8 -6 8 5 7

Yes, this relation is a function.

Because corresponding to each x there is a single image.

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

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Answer:Y, R, B, G

Step-by-step explanation:

Order matters since the ball is being replaced each time. This is all the possible combinations to take 2 balls with replacement, so you can look at the list and see that RR, RB, and RG are listed. The only other combination when choosing a red first would be to pick a yellow, so RY. This is the same pattern for the others also. Look at the list and see what combinations are already listed.

This is the correct answer;

Please leave a Thanks!

It helps!

Answer:

8×5= 40 is the answer .......

One pitcher serves 8 people, so to figure out how many 5 pitchers would serve you would do 8×5 which is 40. 5 pitchers would serve 40 people. I hope this helps!

Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.

Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.

And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.

I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

m + n = - 2

4(m + n) = - 2(4) (multiplying both sides by 4)

4m + 4n = - 8

4m + 4n - 3 = - 8 - 3 (Subtracting 3 from both sides)

4m + 4n - 3 = - 11

Candles should burn one hour for every 1 inch in diameter of the actual candle size. For example, a candle that is 2 inches across should burn for 2 hours.

At what rate does then candle burn, in inches per hour?

Smaller candles with smaller wicks will burn at a rate of 7 to 9 hours per 28 g of wax used. Larger candles with larger wicks consume wax at a faster rate. The larger wicks can be expected to yield 5 to 7 hours per 28 g of wax used.

Estimate the total number of burns by dividing the total wax weight used in the candle (not the weight of the candle with container) by the amount of wax used from burning the candle. Finally, multiply the estimated total burns by the burn time hours. This will provide an estimate of the candle's burn time.

The two main factors for burning candles is wick size and type of wax. Wider or thicker wicks will burn much faster than thin ones, and the material the wick is made with can also make an impact. Different types of candle wax burn at different temperatures.

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Answer:

60cm

Step-by-step explanation:

given:

focal length (f) = 20cm

image height (v) = ½u

object height (u) = ?

(1÷v) + (1÷u) = (1÷20)

(1÷(½u)) + (1÷u) = (1÷20)

(2÷u) + (1÷u) = (1÷20)

(3÷u) = (1÷20)

u = 20 × 3

u = 60cm

Answer:

where is the circle graph

Answer:

A. 103 degrees

B. 77 degrees

C. 60 Degrees

Step-by-step explanation:

A. Triangles' interior angles add up to 180, so if you already have 2 angles you just need to put them together, and subtract them from 180.

47+30=77

180-77=103

B. Lines also are 180, so 103-180=77

C. Interior angles of a triangle add up to 180, so 180/3 is how you get your answer.

Answer:

Step-by-step explanation:

$4.50 + $4.50(0.15) = $5.18

$2.25 + $2.25(0.15) = $2.59

$3.00 + $3.00(0.15) = $3.45

Answer:

a. x^4 - 12x^3 + 2x^2 - 2x + 4

Degree: 4

b. x^4 - 2x^2 - 2x - 4

Degree: 4

Step-by-step explanation:

For part a, all you are doing is adding the polynomials together. They already set up the boxes in standard form, so all you need to do is add each like term as I wrote out in the answer. The degree is then going to be the first exponent that you see once the polynomial is in standard form, which is 4.

For part b, you are now subtracting the polynomials. Again, it is set up for you in standard form. There is no x^3 terms because they cancel out, but you basically subtract each like term from another, and remember to distribute the subtraction sign (it acts as a -1) across the parenthesis. The degree is the first exponent you see, and that is 4.

By DeMoivre's theorem,

(3 (cos(5π/6) + i sin(5π/6)))⁴ = 3⁴ (cos(4×5π/6) + i sin(4×5π/6))

… = 81 (cos(20π/6) + i sin(20π/6))

… = 81 (cos(10π/3) + i sin(10π/3))

… = 81 (cos(-2π/3) + i sin(-2π/3))

… = 81 (cos(2π/3) - i sin(2π/3))

… = 81 (-1/2 + √3/2 i )

… = -81/2 + 81√3/2 i

The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;

[tex]\bar {x}[/tex] ≈ 13.05

Median = 13.60

The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.

The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.

The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;

The number of data points = 28

The sum of the data is;  (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5

The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05

The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;

2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2

The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;

Median = (12.6 + 14.6)/2 = 13.60

The median is 13.60

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Answer:

[tex]\frac{27}{8}[/tex]

Step-by-step explanation:

using the rules of  exponents/ radicals

• [tex](\frac{a}{b}) ^{-m}[/tex] = [tex](\frac{b}{a}) ^{m}[/tex]

• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{n}[/tex]

then

[tex](\frac{16}{81}) ^{-\frac{3}{4} }[/tex]

= [tex](\frac{81}{16}) ^{\frac{3}{4} }[/tex]

= [tex]\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }[/tex]

= [tex]\frac{3^3}{2^3}[/tex]

= [tex]\frac{27}{8}[/tex]

Answer:

Step-by-step explanation:

w≥-2

or -2 ≤w≤5

Answer:

C. 2^8p=2^5p+15

:D

Answer:

1,440 inches^3

Step-by-step explanation:

First, remember the formula for volume is v = l x w x h

Next, sub in your values for your prism 6 x 15 x 16 = 1,440in^3

So, the final answer is 1,440 inches^3

Answer:

Option (1)

Step-by-step explanation:

Given : m(arc BCD) = 148°

By the property,

Inscribed angle formed by an arc measures half the measure of the arc.

m(arc BCD) = 2(m∠BCD)

148° == 2(m∠BCD)

m(∠BCD) = 74°

Therefore, Option (1) will be the correct option.

Answer:

57 dollars and 66 cents will be subtracted from the depositeand get the answer of 157.66

Step-by-step explanation:

Answer:

8835.73ft^3

Step-by-step explanation:

First:

Find area of the base circle.

Diameter is 15, so radius is 7.5

Area of the base circle is 56.25pi (use formula: A=pi(r)^2 ) (also ill convert pi into decimals only later)

next find the volume of the cylinder

height is 40 so volume = 56.25pi*40 = 2250pi

next find the volume of the dome at the top.

you know the radius is 7.5

Use volume of sphere formula below :

4 /3πr^3

=1767.15

alright now add the two bolded values

1767.15+2250pi

= 8835.73

hope this helps

The correct factorization of 33³ × 39 × 4¹¹ = 2²² × 3⁴ × 11³ × 13

Factorization is the collecting together of the common terms of an expression so as to have it in simpler form.

To find  the correct factorization of 33³ × 39 × 4¹¹, we write out each term in terms of its common factors.

so, we have that the factorization of the first term is 33³ = (3 × 11)³ = 3³ × 11³

Also, we have that the factorization of the second term is 39 = 3 × 13

Finally, we have that the factorization of the last term is 4¹¹ = (2²)¹¹ = 2²²

So, we have that 33³ × 39 × 4¹¹ = 3³ × 11³ × 3 × 13 × 2²²

= 3³ × 3 × 13 × 11³  × 2²²

= 2²² × 3⁴ × 11³ × 13  

So, the correct factorization is 2²² × 3⁴ × 11³ × 13

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Answer:

the answer is 0 you're welcome bye

Step-by-step explanation:

lcm = hcf × remaining expressions

7xy= 7 × x × y

6y² = 6 × y × y

here only y is common in both. so y is the hcf. now, without hcf, the remaining expressions are : 7x and 6y.

so LCM = hcf × remaining expressions

= y × 7x × 6y

= 42xy²