For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Use the image below for Part A, Part B, and Part C.

Two triangles: GHI and JKL
Both have one similar angle but different side lengths

Part A: Sharon says the triangles above are similar using the AA Postulate. Is she correct?

Part B: Explain the answer from Part A.

Part C: If HI=7, find KL. Show your work.



Please Help!

This formula describes how the amount of Francium-223 (N(t)) decays over time (t). The initial amount of Francium-223 is 15 grams, and each 22 minutes the amount is halved.

Step 1: Start with the formula

N(t) = 15 * (1/2)^(t/22).

Step 2: Substitute the value for N(t). For example, if you want to find the amount of Francium-223 after 44 minutes,

N(44) = 15 * (1/2)^(44/22).

Step 3: Calculate the fraction (1/2)^(44/22). This is equal to (1/2)^2, or 1/4.

Step 4: Multiply the initial amount of Francium-223 (15) by the fraction (1/4). The result is

15 * (1/4) = 3.75 grams.

The formula N(t) = 15 * (1/2)^(t/22) describes how the amount of Francium-223 (N(t)) decays over time (t). The initial amount of Francium-223 is 15 grams, and each 22 minutes the amount is halved. To calculate the amount of Francium-223 after a certain time, substitute the value for N(t). Then calculate the fraction (1/2)^(t/22) and multiply it by the initial amount of Francium-223 (15). The result is the amount of Francium-223 after the specified time. For example, after 44 minutes, the amount of Francium-223 is 15 * (1/4) = 3.75 grams.

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A line segment is merely a portion of a line, one with definite ends and a finite length.

A line segment is merely a portion of a line, one with definite ends and a finite length. An object with only one dimension, a line has length but no width. A line is made up of several points that are endlessly stretched in the opposing directions. In a two-dimensional plane, it is specified by two points. Collinear points are described as two points that are on the same line.

An endlessly long, two-directional line is referred to as a line. It just has one, and that is length. Collinear points are those that are situated along the same path. Two points make up a line, which is written as follows with an arrowhead: AB.

O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.

Given the following details as:

N is between M and O.

O is between N and P .

NO=6 and NP = 8.

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Answer:

Step by step explanation:

To find the average temperature, you take the three different temperatures you had throughout the day and divide them by how many different kinds there are. (3).

This means that the average is 1°F. This is because you have to add -3 + 12 + (-6) = 3.

Then you have to divide 3 by the amount of numbers you need to average between. In this case, you have to divide 3 by 3.

So, your final answer is:

The average temperature for the day was 1°F

The equation of the function in the form y=mx+b is y = 110x-2020

Adaptation of function speed

A line's equation is written as mx + b = y, where m denotes the rate of change or slope.

The intercept is B.

utilizing the coordinates

Calculate the slope.

m = 550/5

m = 110

The intercept for

280 + 110(20) + b

280 = 2200 + b

b = 180 - 2200

b = -2020

The equation for the function of the type y=mx+b is hence y = 110x-2020.

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The complete question would be:

The table shows the distance Penelope is from the park as she walks to soccer practice. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and initial value. Then write the equation of the function in the form y=mx+b

Answer:

--------------------------

Distributive Property is:

Apply it to the given expression:

The matching choice is C.

Answer:

[tex] \sf \: c) \: 30 - 6q[/tex]

Step-by-step explanation:

Given expression,

→ 6(5 - q)

Let's simplify the expression,

→ 6(5 - q)

→ 6(5) - 6(q)

→ (6 × 5) - (6 × q)

→ (30) - (6q)

→ 30 - 6q

Hence, option (c) is correct.

Answer:

The cost of 1 child is £ 3.40 and the cost of 1 parent is £ 4.10. To determine this, we can use the following equation:

Cost of 1 child = (13.20 - 5.10) / (5 parents + 3 children)

Cost of 1 parent = (13.20 - 5.10) / (2 parents + 1 child)

Hope this helps!

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

By the Pythagorean Theorem, the sum of the squares of the leg lengths is equal to the square of the hypotenuse:

[tex]a^2+b^2=c^2\\20^2+15^2=c^2\\400+225=c^2\\625=c^2\\25=c[/tex]

Hence, the hypotenuse has a length of 25

Two tiny parallel horizontal lines serve as the "equality sign" connecting 1 kilogramme of NaCl to 27 ml of a solvent.

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Answer:

2nd

Step-by-step explanation:

Answer: They are not proportional.

Step-by-step explanation: The numerator is multiplied my 0.5 but the denominator is not.

Answer:

perimeter= 9+9π cm

area= 40.5-10.125π cm²

Step-by-step explanation:

area of the square =9x9=81cm²

area of the two semicircles which have the same diameter =area of one circle

= (9÷2)²π =(81÷4)π

area of the whole shaded part = 81- (81÷4)π cm²

the area of each shaded part= (81-(81÷4)π)÷2

= 40.5-10.125π cm²

circumference of 2 semicircles= circumference of 1 circle = 2πr = 2x9xπ= 18π cm

then are perimeter of the whole shaded part = 18π+9+9= 18+18π cm

perimeter of each shaded part = (18+18π)÷2=

9+9π cm

Answer:

Game 1

Equal chance

Game 2

Step-by-step explanation:

A BETTER CHANCE OF WINNING

Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning.

Game I

a.Picking a prime number from the integers between 1 and  20

b.Picking a multiple of 5 from the integers between 1 and  20

c.Picking a multiple of 7 from the integers between 1 and 40  

Hint:

Find the percent chance that each event will occur and compare the results.

a.Picking a prime number from the integers between 21 and  40

b.Picking a multiple of 5 from the integers between 1 and  40

c.Picking a multiple of 6 from the integers between 1 and  25

Answer:

Game 1

Equal chance

game 2

Answer:

66

Step-by-step explanation:

22 per minute

?   Per 3 minutes

22 x 3 = 66

Answer: The position of the whale relative to the surface of the water can be determined by multiplying the rate at which it descends (22 feet per minute) by the amount of time it has been descending (3 minutes).

Position = Rate x Time

Position = 22 feet/minute x 3 minutes = 66 feet

So, after diving for 3 minutes, the position of the whale relative to the surface of the water is 66 feet.

It means the whale descended for 66 feet from the surface level of the water.

Please keep in mind that this information is assuming a linear motion, without taking into account any other factors that could affect the whale's descent such as currents or obstacles in the water.

Step-by-step explanation:

In the given arithmetic progression Common difference is 14.

An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).

Given, the n term of ap is Sₙ = 3n² + 5n

Where n is the number of terms

S₁ = 3* 1 + 5*1

S₁ = 8

S₂ = 3 * 4 + 5*2

S₂ = 22

common difference = 22-8

Common difference = 14

therefore, the Common difference in the given AP is 14.

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The distance that Nick has to drive to reach Kansas will be at least 250 miles.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Nick is driving from Brookville to Kansas City, a distance of more than 325 miles and after driving 75 miles, Nick stops for gas.

An inequality to determine how much farther Nick has to drive to reach Kansas City will be:

x > 325 -75

x > 250

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The side of the cube, the faces will be 13 cm.

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

Sarah has a cube with a volume of 2,197 cubic cm.

side is ∛(2197) =13 cm

So the side of the cube will be 13 cm.

Hence, the side of the cube, the faces will be 13 cm.

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The inequalities that have the same graph as x<4 are:

Hence, option(B) , (C) and (D) are correct.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

x +6 < 10 ⇒ x < 10-6 ⇒ x < 4

5x < 20 ⇒ x< 20/5 ⇒ x < 4.

x-2 > 2 ⇒ x < 2 + 2 ⇒ x < 4.

Hence, option(B) , (C) and (D) are correct.

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Your question is incomplete but most probably the question was:

Select all the inequalities that have the same graph as x <4.

A. x < 2.

B. x+6 < 10

C. 5x < 20

D.  x-2 > 2

E. x <8

The value of x is 14.7224.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Sin 60° = x/17 ____(1)

Sin 60° = √3/2 _____(2)

From (1) and (2) we get,

√3/2 = x/17

x = 17√3/2

x = 17 x 1.73205 / 2

x = 14.7224

Thus,

The value of x is 14.7224.

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The shape of a decagon will remain the same when it is rotated through

its angle of rotational symmetry.

The rotation about the center will carry a regular decagon back to itself is 36°.

Note the following

The angle of rotational symmetry of a decagon is the smallest angle that a decagon can be rotated by such that the image formed by the rotation coincide with the preimage;

A decagon has 10 sides, the interior angle of a regular decagon is given as follows;

Each interior angle =  (n-2)*180/10 = 144⁰

A decagon has a reflective symmetry, therefore, the lines of symmetry joining opposite vertices are straight lines.

The number of diagonals in a decagon = 5

Rotating through the vertex and opposite vertex of the diagonals gives the number of image of the rotation that is similar to the preimage of a decagon as ten.

Therefore, a rotation of  (360/10) = 36⁰, about the center will carry a regular decagon back to itself.

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Therefore the cost of each pair of incense is 2.4 in terms of x.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Let x be the cost of one pair of incense.

We know that the total amount spent on apples and oranges is the same as the total cost of 12 pairs of incense. Therefore:

(cost of apples + cost of oranges) = 12x

We also know that the cost of the apples is 3x the cost of the incense, and the cost of the oranges is 2x the cost of the incense. Therefore, we can substitute these values into the equation:

(3x + 2x) = 12x

5x = 12x

x = 12/5 or 2.4

So the cost of each pair of incense is 2.4 in terms of x.

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The first number is 11 and second number is 12.We can find by solving two consective numbers.

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed and it follows a pattern. For example 1, 2, 3 are the first three consecutive natural numbers.

An odd number of consecutive numbers has a whole number as an average. This average is always the middle number. So that means that the sum of the numbers will be Sum = average \times number of consecutive numbers.

Now we find

Let x be a first number and x+1 be a second number.So

x+x+1=23

2x+1=23

2x    =23-1

2x    =22

  x   = 11

x+1= 11+1=12

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The length of f = 66 centimeters

It is a law that express a relationship between side length of triangle and their opposite angles.

If ABC is triangle, then sine rule can be expressed as

BC/ sin A = AB /sin C = AC /sin B

Given, a triangle fgh where angle ∠ f = 131° and ∠g = 47°

also, side length, g = 64 cm

the remaining angle ∠ h = 180° - (131°+47°)

∠h = 2°

this is because angle sum of three angle for a triangle is 180 degrees.

what is the length of f?

we know that Δf g h has three side f g, g h and f h.

we denote the side f g = h, side g h = f and side f h = g

according to the sine rule for a triangle

h/ sin h = f /sin f = g /sin g

f/ sin f = g/ sin g

f / sin 131° = 64 / sin 47°

f = (64 × sin 131°) / sin 47°

f = 66 cm

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3.) x = 15.25 or 15 1/4 ( not sure if you'll need to round your answer )

4.) x =6

5.) x = 10

6.) x = 9

Explanation:

1.) write your equation down 8x + 9 = 131

2.) Subtract +9 from 131. you'll get 122

3.) divide 8x and 122.

4.) Then there's your answer 15.25

you'll do the same thing throughout each equation. write down your equation but with the 22x and 23x you're going to subtract 22x from 23x. and you'll get 1x then continue on the same way as with the last equation.

Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.

Noah would need more cubes to fill the 1 1/2 inch cube because the cubes he is using have a smaller edge length than the cubes Lin is using. The larger the edge length of the cubes being used, the fewer number of cubes needed to fill a given space.

To see this, you can calculate the volume of the cube being filled by both Lin and Noah. The cube that Lin is filling has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Lin is using have a volume of (0.5)^3 = 0.125 cubic inches. So, Lin needs 3.375/0.125 = 27 cubes to fill the 1.5 inch cube.

The cube that Noah is filling also has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Noah is using have a volume of (0.25)^3 = 0.03125 cubic inches. So, Noah needs 3.375/0.03125 = 108 cubes to fill the 1.5 inch cube.

As we can see, Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.

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Answer:-√2 sin (45° - A)

Step-by-step explanation:

Answer:

y = x - 2

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

Choose any two points on the line.            

 (2,0)  ; (0,-2)

Now, find the slope.

        [tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                   [tex]= \dfrac{-2 - 0}{0 - 2}\\\\=\dfrac{-2}{-2}\\\\= +1[/tex]

m = 1.

Now, y = 1x +  b

The (2 , 0) passes through the line. Substitute x = 2 and y = 0 in the above equation and find the value of 'b'.

       0 = 1*2 + b

       0 =  2 + b

        -2 = b

Equation of line:

              y = x - 2

The correct statement based on the data is,

⇒ The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

Option 2 is true.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

The given table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.

       Mangos Used    Smoothie Size

Kim         1                         8 oz

Bri           3                        24 oz

Angela    4                        32 oz

Now, By definition of ratio, we get;

The ratio of smoothie size to mangos used for Bri is,

⇒ 24 : 3

⇒ 8 : 1

And, The ratio of smoothie size to mangos used for Angela is,

⇒ 32 : 4

⇒ 8 : 1

Thus, The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

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An expression that describes the given situation is; Total yards = -6 - 5 and the solution is -11

In mathematics, a positive number means we have a plus sign before the number which means if we have +2, it means that there has been a gain of 2 units. In a similar manner, a negative number represents a loss which means that if we have -3, it simply means there is a loss or reduction of 3.

Now, we are told that during a football game, the hawks lost 5 yards due to a penalty and lost 6 yards from a quarterback sack. Thus, using the concept of positive and negative numbers above, we can develop the total number of yards as;

Total yards = -6 - 5

Total yards = - 11 yards

This represents a loss.

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The scale factor of segment AB was 1.94.

Scale factor is a number by which a given set of measurements is multiplied in order to increase or decrease the size of the measurements. It can be used to enlarge or reduce the size of an object, image, or diagram. It is a useful tool in many areas of mathematics, including geometry, engineering, and computer graphics.

The scale factor for segment AB can be found by taking the ratio of the lengths of the two segments. To calculate this, use the distance formula to find the length of segment AB and A'B' and set them equal to each other.

The distance formula is: d = √[(x2-x1)^2 + (y2-y1)^2]

The coordinates of A and B are (0, 0) and (6, 9), respectively. The coordinates of A' and B' are (0, 6) and (6, 9), respectively.

For segment AB, the distance formula becomes: d = √[(6-0)^2 + (9-0)^2], which simplifies to d = √[36 + 81], which simplifies to d = √117.

For segment A'B', the distance formula becomes: d = √[(6-0)^2 + (9-6)^2], which simplifies to d = √[36 + 9], which simplifies to d = √45.

The scale factor is then found by taking the ratio of the two distances, √117/√45, which simplifies to √117/3, or approximately 1.94. Therefore, the scale factor of segment AB was 1.94.

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Answer:

6 and -13

Step-by-step explanation:

Absolute Values are magnitudes (only positive values) of any values (be it positive or negative.)

Example: |4.5| = 4.5, |-6.7| = 6.7

1. |2x + z| + 2y

= |2(2.1) + (-4.2)| + 2(3)

= |4.2 - 4.2| + 6

= 0 + 6

= 6

2. 4a - |3b + 2c|

= 4(-2) - |3(-3) + 2(2)|

= -8 - |-9 + 4|

= -8 - |-5|

= -8 - 5

= -13

Answer:

A) Angle 2, Angle M

B) Angle M

C) Angle NM (or MN), Angle QM (or MQ)

Step-by-step explanation:

A) So M is the vertex of angle QMP, and the picture tells you that it's angle 2

B) M is the middle angle

C) The diagram shows you the answer