Special Right Triangles 1
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A TUV is a 30°-60°-90° triangle where m/T-90. The length of the hypotenuse is 16√3 units. The length of the long side of the triangle is x
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From the graph, Jerimiah walks along 44 city blocks.

Hence the correct option is (D).

It is given that each unit on the grid represents 1 city block.

From the given graph we can see that

Number of city block between Restaurant and Museum = 7

Number of city blocks between Museum and Hotel = 4

Number of city blocks between Hotel and Arena = 7

Number of city blocks between Arena and Restaurant = 4

Total number of city blocks along the rectangular path = (7 + 4 + 7 + 4) = 22 city blocks.

Jerimiah walks twice around the rectangular path.

So Jerimiah walks through = 2*22 = 44 city blocks.

Hence the correct option will be (D).

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The question is incomplete. The complete question will be -

The value of the median number of eggs laid in a year is,

⇒ 231

We have to given that;

The data table shows the numbers of eggs laid by individual chickens in a year.

Now, We can arrange it into ascending order as;

⇒ 222, 229, 229, 231, 234, 235, 262

Since, There are 7 terms

Hence, Median is,

= (7 + 1)/2

= 4th term

= 231

Thus, The value of the median number of eggs laid in a year is,

⇒ 231

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Answer:

A. 229 is correct

answer D.231 is wrong

The area of a regular hexagon with side length 14 inches is 509.22 square inches.

Given that, a regular hexagon with side length 14 inches.

We know that, area of a regular hexagon can be calculated using A=3√3/2 a².

Here, area of a regular hexagon = 3√3/2 ×14²

= 3√3 ×98

= 509.22 square inches

Therefore, the area of a regular hexagon with side length 14 inches is 509.22 square inches.

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The number of mugs that Maggie made with the left over clay that she had would be = 23 mugs

The total quantity of clay that Maggie bought = 50lbs

The quantity she used for sculpture = 15.6lbs

The quantity of clay she used for mug = 0.84 lbs

The quantity of clay left = 19.28 lbs

If 0.84 = 1 mug

19.28 = X

make X the subject of formula:

X = 19.28/0.84

= 23 mugs

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Answer: 2, 2, 135, 9, 5, 35, 15, 10, 15, 15

Step-by-step explanation:

The maximum value of the data = 64

We know that in the box and whisker plot with the left end of the whisker represents the minimum value of the data and the right end of the whisker represents the maximum value.

From the attached box and whisker plot, we can observe that between two numbers on the number line there are 5 equal units.

So, the value of each unit length = 4 unit

Here, the left end of the whisker has value 8 and the right end of the whisker has value 64

This means that the meaximum value = 64

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Answer:

larger angle = 63°

Step-by-step explanation:

complementary angles sum to 90°

let x be the smaller angle then larger angle is x + 36 , then

x + x + 36 = 90

2x + 36 = 90 ( subtract 36 from both sides )

2x = 54 ( divide both sides by 2 )

x = 27

Then

larger angle = x + 36 = 27 + 36 = 63°

The value of distance between two points on graph is,

⇒ d = √32 units

We have to given that;

The coordinates of two points are,

⇒ (9, - 4) and (5, -8)

We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, The value of distance between two points on graph is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (5 - 9)² + (- 8 - (-4))²

⇒ d = √ 16 + 16

⇒ d = √32

Thus, The value of distance between two points on graph is,

⇒ d = √32 units

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The speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min

The total area or region that is covered by a rectangular prism's six faces is known as its surface area.

Solids called prisms have identical polygon bases and flat parallelogram sides. Prisms come in a variety of shapes, including triangles, squares, rectangles, pentagons, hexagons, and more.

Thus, it can be seen that the speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min

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The two animals are at different stages in their life cycle.  Hence option C: Different stages. The panther is an embryo and the pelican is an infant.

The two creatures are at distinct points of their developmental process. The panther, denoted as Animal 1, is characterized as a cluster of cells undergoing division within its maternal host. This is one that then shows that the panther is at a very early stage of growth, and that it is in embryonic phase.

The pelican, is one that is also known as Animal 2, that has successfully hatched from its egg, telling us the conclusion of its embryonic phase and the start of the post-embryonic phase.

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Answer:

Step-by-step explanation:

Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.

The 8th term of the sequence is 781, 250.

We have geometric sequence 10, 50, 250,...

First term= 10

Common ratio = 50/10 = 5

So, the 8th term of sequence is

= 10 x [tex]r^{8-1[/tex]

= 10 x [tex]r^7[/tex]

= 10 x [tex](5)^7[/tex]

= 10 x 5 x 5 x 5 x 5 x5 x 5 x 5

= 10 x 78125

= 781, 250

Thus, the 8th term of the sequence is 781, 250.

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The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the  option (A).

(A) Angles ∠B and ∠C are complementary, not congruent

Complementary angles are angles that when added together are equivalent to 90°

The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;

Statement [tex]{}[/tex]                   Reason

1 m∠B = θ [tex]{}[/tex]                   The acute angles in a right triangle are congruent

2 sin(θ) = AB/BC    [tex]{}[/tex]     Definition of sine

3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine

4 cos(θ) = AB/BC [tex]{}[/tex]       Substitution

5 cos(θ) = sin(θ) [tex]{}[/tex]         Substitution

Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)

The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.

The acute angles in the right triangle are ∠B and ∠C

The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°

Therefore the acute angles in a right triangle are always complementary, and not always congruent.

The correct option is therefore the option (A)

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The probability that a statistics teachers do not know the true meaning of life is 46.8%

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

53.2% of Americans say they believe that statistics teachers know the true meaning of life.

This means that

P(Believe) = 53.2%

For the required probability, we have

P(Not believe) = 1 - P(Believe)

So, we have

P(Not believe) = 1 - 53.2%

Evaluate

P(Not believe) = 46.8%

Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%

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The plan would be to send 2 group members back to base camp with enough food to sustain them for 5 days, while the remaining 3 members continue to receive 5,600 calories per day from the remaining food supply to complete the journey to the South Pole.

To create a plan for the rest of the trip, we need to consider the total number of days it will take for the group to return to base camp from their current location, and the number of group members who can be taken to the South Pole given the remaining food supply.

Given that the group is missing 28,000 calories, we can calculate the number of days of food that are missing by dividing 28,000 by the daily requirement of 5,600 calories per person. This gives us 5 days of missing food. Therefore, the group has enough food for 5 people to continue to receive 5,600 calories per day for 5 days, but not for all 5 members to continue for the entire trip.

To maximize the number of group members who can continue to the South Pole, we can send two members back to base camp immediately with enough food to sustain them for 5 days (2 people x 5 days x 5,600 calories/day = 56,000 calories). This will leave us with 3 group members who can continue to receive 5,600 calories per day for the remaining journey.

Assuming the trip back to base camp takes the same amount of time as the trip to the current location, we can estimate that the total trip duration will be around 20 days. Therefore, the remaining 3 group members will need a total of 20 days x 3 people x 5,600 calories per day = 336,000 calories.

Given the remaining food supply of 28,000 calories, we have a total of 364,000 calories available (28,000 missing calories + 336,000 required calories). Therefore, the 3 remaining group members can continue to receive their required daily calorie intake and complete the journey to the South Pole.

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The image point of (-7, -8) after the sequence of transformations is given as follows:

(-4.5, -4).

The original coordinates are given as follows:

(-7, -8)

The first transformation is a dilation with a scale factor of 1/2, meaning that each coordinate is multiplied by 1/2, hence:

(-3.5, -4).

The second transformation is a translation of one unit left, meaning that one is subtracted from the y-coordinate, thus the image point after the sequence of transformations is given as follows:

(-4.5, -4).

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Answer:

Step-by-step explanation:

tan theta=5/6

theta=tan-1(5/6)

        =39.8º

The explicit formula for the sequence defined by the recursive formula a₁ = 150 and aₙ = -1/5 aₙ₋₁ is aₙ = 150 [tex](-1/5)^{(n-1)[/tex].

To find the explicit formula that represents the sequence defined by the given recursive formula, we need to find a pattern in the sequence and express it using a formula.

The first term in the sequence is a₁ = 150. To find the second term, we use the recursive formula: a₂ = -1/5 a₁ = -1/5(150) = -30. To find the third term, we use the recursive formula again: a₃ = -1/5 a₂ = -1/5(-30) = 6.

We can continue this process to find the fourth term: a₄ = -1/5 a₃ = -1/5(6) = -6/5, and so on.

By observing the pattern, we notice that each term is obtained by multiplying the previous term by -1/5. Therefore, the explicit formula for the sequence can be written as:

aₙ = 150 [tex](-1/5)^{(n-1)[/tex]

This formula gives the value of any term in the sequence based on its position n. It can be used to find any term in the sequence without having to recursively calculate all the previous terms.

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Answer:

78.947%

Step-by-step explanation:

It says A OR B, so:

5/19 + 6/19 + 4/19

11/19 + 4/19

15/19 = approx. 0.78947 = 78.947%

The estimated number of the 160 ducks that have blue marks would be 5 ducks.

Assuming none of the 50 people have received a considerable reward, it is probable that winning a small prize bears higher odds than claiming a more substantial one. Estimating, the probability of achieving a large prize may be considered half as likely to succeed as obtaining a smaller sum:

P ( large prize ) :

= 0.5 x P(small prize)

= 0.5 x 0.06 = 0.03

Number of ducks with blue marks (large prize):

= ( total number of ducks ) x P( large prize )

= 160 x 0.03

= 4.8

= 5 ducks

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Answer:

The answer is Area: 25.5

Step-by-step explanation:

Answer:

LCM of 4 and 5 is 20.

a/b = 3/4 = 15/20

b/c = 5/6 = 20/24

a:b:c = 15:20:24

The perimeter of rectangle W'X'Y'Z is 16 units

he rectangle has four sides. There are two lengths and two widths in a rectangle. Therefore, the perimeter of the rectangle is twice the sum of two adjacent sides that are length and width. The formula is given by:

Perimeter of rectangle = 2(l + b)

We have :

Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'

So, By the image:

The analysis will be the:

Rectangle of WXYZ = 2 × 4

and, The rectangle of W'X'Y'Z' = 2 × WXYZ

                                                   = 16

W'X' = 4

W'Z' = 4

Hence, The perimeter of rectangle is = 4 + 4 + 4 + 4 = 16

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The given question is incomplete, So i take the similar question :

Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'. What is the perimeter of rectangle W'X'Y'Z?

And also to see the attachment.

Answer:

Step-by-step explanation:

sum of angles in a triangle=180º

90+60x+30x=180

90+90x=180

90(1+x)=180

1+x=2

x=1

angle A=30º

Answer:

Answer is A

Step-by-step explanation:

A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.

B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.

Answer:

Step-by-step explanation:

the median would be 9.

Answer:She is not correct The graph of g grows at a faster rate

than the graph of because 8 greater than 2

Step-by-step explanation:

Using PEMDAS, the exponents are done first.

8^3 = 512

4*2^3 = 32

This works for every number that X can be, 3 was just an example.

The proportional relationship used to find B, the area of the base with a volume of V, is given as follows:

B = V/6.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table given in the image at the end of the answer, we have that the base area is a sixth of the volume, hence the equation is:

B = V/6.

The table is given by the image presented at the end of the answer.

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i Got u Bro! Answer:X=8x/15+77/15

:D

The requried, $1000 is invested at 6%, and $7000 is invested at 10%

Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.

We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.

So we have the system of equations:

x + y = 8000 (1)

0.06x + 0.1y = 760 (2)

We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:

0.06x + 0.06y = 480 (3)

0.1y - 0.06y = 0.04y = 280

y = $7000.

Substituting y = $7000 into equation 1, we get:

x + $7000 = $8000

So x = $1000.

Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.

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