Which theorem or postulate could be used to prove the congruence of the triangles?

Answer:

y = 2x + 5

Step-by-step explanation:

The slope of 2 parallel line are always the same. This means that we can easily tell that the slope of the equation that we are trying to solve has a slope of 2. To find the "b" in the slope-intercept form, plug in the coordinates given and that's how you get the answer above.

The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3), and the minima of the given function at the point (-3, -12), and maxima at point (3,2).

A graph can be defined as a pictorial representation or a diagram of any function that represents data or values.

According to the given graph,

We can see that the function is decreasing at the interval (-∞, -3), then the function is increasing at the interval (-3, -1), then the function is decreasing at the interval (-1, 1), the function is increasing at the interval (1, 3), and the function is decreasing at the interval (3, ∞).

The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3).

Thus, the minima of the given function at the point (-3, -12), and maxima at point (3,2).

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Answer:

4.32 s (if you were asked to use 32.17 for g)

4.33 s (if you were asked to use 32 for g)

4.318 s (if you were asked to use 32.174 for g)

Step-by-step explanation:

This is an example of free fall! The free fall equation in terms of distance is as follows:

[tex]s=\frac{1}{2}gt^2[/tex]

Let's rearrange the equation so it's in terms of time.

[tex]t=\sqrt{\frac{2s}{g} }[/tex]

Plugging in [tex]300ft[/tex] for the distance and [tex]32.17\frac{ft}{s^2}[/tex] for the acceleration due to gravity,

[tex]t=\sqrt{\frac{2(300)}{32.17} }\\t=\sqrt{18.65}\\ t=4.32s[/tex]

The answer will vary based on what value you use for acceleration due to gravity. If you were asked to use 32, the answer will be 4.33s, if you were given a more specific value, like 32.174, the answer will be 4.318.

Answer:

[tex]x=-\frac{y^{2} }{4}[/tex]

Step-by-step explanation:

This graph is in terms of x.

let thee present age be x.

(x-15)^2=x+15

=>x^2–31*x+210=0

=>(x-21)(x-10)=0

x=10 or x=21

present age can not be 10 as it would result at absurd negative age( -5) 15 years ago.

so present age is 21.

Answer: 64/225 is already in simplest form

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator GCD (greatest common denominator) of 64 and 225 

Divide both the numerator and denominator by the GCD

64÷1/225÷1

fraction: 64/225

Therefore, 64/225 simplified to lowest terms is 64/225.

(-2 - 2(-1/2))^3

= (-2 + 1)^3

= (-1)^3

= -1

Answer:

So, she should add 13 trees per acre for maximum harvesting

Step-by-step explanation:

a farmer finds that if she plants 80 trees per acre, each tree will yield 55 bushels of fruit. she estimates that for each additional tree planted per acre, the yield of each tree will decrease by 2 bushels. how many trees should she plant per acre to maximize her harvest? trees

Let x be the number of trees per acre she adds

Total trees per acre = 80+x

Yield per tree = 55-2x

F(x) = 4400−105x−2x2

Applying differentiation,

F1 (x) = -105 – 4x

Putting F1 (x) =0, gives x = -270/4

X= -67.5

F11 (x) = -4 < 0, hence maximum at x =-67.5

Trees

80-67.5 = 13

So, she should add 13 trees per acre for maximum harvesting

Answer:

The answer is 0.05556

0.5/9 gives you that

Binomial probability distribution = 0.0231

The following is the probability using the binomial distribution:

P(X = 24) = 0.0231.

In terms of the normal approximation to the binomial, it is discovered that:

Part 2: C. Yes, because np(1-p)≥10, the normal distribution can be used.

Part 3: The likelihood is: 0.0227.

Part 4: The distinction is: 0.0004.

Binomial probability distribution

The following is the mass function for the probability of exactly x successes:

P(X = x) = [tex]C_{n,x}[/tex].[tex]P^{x}[/tex].[tex](1-P)^{n-x}[/tex]

[tex]C_{n,x}[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]

In which the following parameters are defined:

The number of trials in the experiment is n.

The probability of success on a single trial of the experiment is given by p.

The values of these parameters are given in the context of this problem as follows:

n = 59, p = 0.3, X = 24.

Hence the probability is:

P(X = x) = [tex]C_{n,x}[/tex].[tex]P^{x}[/tex].[tex](1-P)^{n-x}[/tex]

P(X=24) = [tex]C_{59,24}[/tex].[tex](0.3)^{24}[/tex].[tex](0.7)^{35}[/tex] = 0.0231

In the context of this problem, the condition for the approximation is verified as follows:

np = 59 x 0.3 = 17.7 ≥ 10.

n(1 - p) = 59 x 0.7 = 41.3 ≥ 10.

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Answer:

Combine like terms.

Step-by-step explanation:

Subtract 0.02x from 0.05x

Then your equation should look like:

0.03x + 3 = 4

In the expression 8ab + 3b + 16 - 4a ,

(a) the number of terms are four .

(b) the factors of 8ab are  1 , 8 , a , b , 8a , 8b , ab , 2ab .

(c) the third term "16"is a constant .

In the question ,

the expression is given as 8ab + 3b + 16 - 4a .

Part(a)

the number of terms that are there in the expression is 4 ,

the terms are 8ab , 3b , 16 , 4a .

Part(b)

the first term is 8ab ,

the factors of 8ab is 1 , 8 , a , b , 8a , 8b , ab , 2ab .

Part(c)

the constant term is 16 , because there is no variable .

Therefore , In the expression 8ab + 3b + 16 - 4a ,

(a) the number of terms are four .

(b) the factors of 8ab are  1 , 8 , a , b , 8a , 8b , ab , 2ab .

(c) the third term "16"is a constant .

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Answer:

  C.  6 times as many as c is 72

Step-by-step explanation:

You want to know if c = 12, which statement is true.

We can substitute 12 for c in each expression and write it as a math equation. That makes it easier to see if it is true.

  12 = 5×4

  12 = 20 . . . . . false

  27 = 12×3

  27 = 36 . . . . . false

  6×12 = 72 . . . . . TRUE

  8 + 12 = 15

  20 = 15 . . . . . false

Answer: 13x^6+3x^4+9x^3+2x^2+13

Step-by-step explanation:

The required solution is Option D.

sin 21 = x / 22

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sinθ

sec θ = 1/cosθ

cot θ = 1/tanθ

Given data ,

Let the triangle be ΔABC and ∠B = 90°

The angle ∠A = 21°

θ = 21°

The value of the hypotenuse = 22

The value adjacent to the right angle is BC = x

From the trigonometric functions , we know that

sin θ = opposite / hypotenuse

So ,

sin θ = x / 22

Hence , the required solution is sin 21 = x / 22

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Answer:

Please refer photo for answer

According to the combination method, the number of elements in the sample space for this experiment is 3060

Combination method:

Basically, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter

Given,

A person eating at a cafeteria must choose 4 of the 18 vegetables on offer.

Here we have to calculate the number of elements in the sample space for this experiment.

While we looking into the given question, we have identified the following things,

They are

Total number of available vegetables = 18

Number of choices we have made = 4

Therefore, here the value of n = 18 and the value of x = 4,

Therefore, according to the ncx formula, it can be written as,

=> ¹⁸n₄ = 18! / 4! (18 - 4)!

=> ¹⁸n₄ = 18! / 4! (14)!

=> ¹⁸n₄ = 3060.

Therefore, there are 3060 number of elements in the sample space for this experiment.

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For the given graph, the gradient of the given blue line in the graph is equal to 2.

As given in the question,

For the given graph,

Consider two pairs of coordinates on the blue line of the given graph,

( x₁ , y₁ ) = ( 2, 2 )

( x₂ , y₂ ) = ( 3, 4 )

Gradient is nothing but slope of the line

Formula to calculate the gradient of the given blue line of the graph is given by:

Gradient = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value in the formula we get,

Gradient = ( 4 - 2 ) / ( 3 - 2 )

              = 2 / 1

              = 2

Therefore, for the given graph, the gradient of the given blue line in the graph is equal to 2.

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The speed is 20/9 miles per hour.

From the question, we have

In 1/4 hour walked = 5/9 mile

In 1 hour walked = 5/9 *4 mile

=20/9 miles per hour

The speed is 20/9 miles per hour (MPH)

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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aₙ = aₙ₋₁ - 9 is the recursive formula of Arithmetic progression.

Arithmetic progression is a sequence of number in order with same difference .

A fixed number is added to any term of a AP to get next term . That Fixed number is known as common difference.

In the question,

16 , 7 , -2 , -11 . . . .

First term of AP : a₁ = 16

Second term : a₂ = 7

Common difference : d = a₂ - a₁

=> d = 7 - 16

=> d = -9

The recursive formula of AP : aₙ = aₙ₋₁ + d

Here d = -9 , substituting d

The recursive formula of given AP : aₙ = aₙ₋₁ - 9

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Cone A Has same height Twice radius of cone b what is ratio of volume of cone A to volume B therefore The ratio is 4:1

We know that,

[tex]volume of cone = \frac{1}{3}\pi (r)^{2}h[/tex]

From the question, we have

Cone A has same height of cone B

Cone A has twice radius of cone B

Ratio,

[tex]\frac{volume of cone A}{volume of cone B} = \frac{\frac{1}{3}\pi (2r)^{2}h }{\frac{1}{3}\pi (r)^{2}h} \\=\frac{4}{1}[/tex]

Divide:

Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.

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Answer:

a) y=4

b) x=8

Step-by-step explanation:

a) y will always be equal to 4 for this equation, so y=4

b) y will always be equal to 8 for this equation, so x=8

Each board must be within how many inches of 15 is l' actual = (15±0.03) inch, l" actual = (15±0.03) inch.

size is the quantification of attributes of an item or occasion, which can be used to evaluate other objects or occasions. In other words, measurement is a system of figuring out how massive or small a bodily amount is compared to a primary reference quantity of the identical kind.

size is the simple idea inside the have a look at of arithmetic and technology. measurement quantifies the traits of an object or occasion, which we can compare with other things or activities. measurement is the most commonly used word, on every occasion we address the department of an amount. dimension gear makes our lives higher and more secure, and they enhance the best and quantity of lifestyles. measurement is a contrast of an unknown quantity with a known fixed amount of the equal kind. The cost received on measuring a quantity is referred to as its value. The value of a quantity is expressed as numbers in its unit.

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The value of x is 51°

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.

Given a right triangle with hypotenuse = 9 and perpendicular = 7

Using sine of angle, we get,

sinx = perpendicular/hypotenuse

sinx = 7/9

x = [tex]sin^{-1}[/tex]7/9

x = 51°

Hence, The value of x is 51°

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∠E is 74° because it is alternate to the given angle of 74°.

∠E is and the 74° angle are alternate interior angles. Alternate interior angles are a pair of angles on the inner side of two parallel lines. But the angles should be on the opposite sides of the transversal. A transversal line is a straight line that intersects two or more parallel lines.

So here, ∠E and 74° lie on the inner sides of two parallel lines on the opposite sides of the transversal.

Therefore <E = 74°

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Answer:

3 with 1 left over

Step-by-step explanation:

3 * 5 + 1 = 16

Answer:

3 with 1 left over.

Step-by-step explanation:

16÷5=3remainder1

HOPE IT HELPED

Answer:

b=17/4

x=-3/5

Step-by-step explanation:

This is what i put for the hw and i got 100% on it. If you want you can just write a bunch of random equations that look like they relate to the question and then just write and circle the answer, which is exactly what i did

Answer:

Step-by-step explanation:

1) 3b + 9 - 5b + 3 = -14 + 6b - 8, for b?

→ 3b + 9 - 5b + 3 = -14 + 6b - 8

→ -2b + 12 = 6b - 22

→ -2b - 6b = -22 - 12

→ -8b = -34

→ b = -34/-8

→ [ b = 17/4 ]

Hence, the value of b is 17/4.

2) 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x, for x?

→ 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x

→ -2x + 13 = 25 + 30x - 12x

→ -2x - 18x = 25 - 13

→ -20x = 12

→ x = 12/-20

→ [ x = -3/5 ]

Hence, the value of x is -3/5.