12. Sam's garden is 12.3 square meters. His neighbors have a garden plot that is 100 times the size al Sam's garden. How big is the neighbors' garden? SHOW WORK.

The required two-column proof that the triangles are congruent is explained below.

A triangle is a three sided plane shape whose the sum of internal angles is 180^o. Thus two or more triangles are said to be congruent when their corresponding sides and measure of internal angles are equal.

When two triangles are congruent, it can be proven in all respect that they are thus equal (considering their corresponding length of sides and measure of internal angles).

The two column proof required in the question is given below:

        STATEMENT                                     JUSTIFICATION

1. <WXZ ≅ <YXZ                                  Property of an angle bisector.

2. <XZW  ≅ <XZY                                Definition of a perpendicular bisector.

3. WX ≅ YX                                          Congruent sides of a triangle.

4. WZ ≅ YZ                                           Definition of a midpoint.

Therefore,

ΔWXZ ≅  ΔYXZ                                    Angle-Angle-Side theorem

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Marco practiced 1.13 hours more on Tuesday than on Monday.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. 

Given that,

Marco practiced for only 7/10 hours on Monday (less than the expected  [tex]1\frac{1}{4}[/tex]hours)

He practiced for [tex]1\frac{5}{6}[/tex] hours on Tuesdays.

He is supposed to practice [tex]1\frac{1}{4}[/tex] hours each day.

Finding the difference between the hours he practiced each day:

[tex]1\frac{5}{6} - 7/10 = 11/6-7/10= (110-42)/60 = 68/60 = 1.13 hours[/tex]

Thus,  Marco practiced 1.13 hours more on Tuesday than on Monday.

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Answer:

y = -4/1x + 28

Step-by-step explanation:

y=Mx +b

slope (m): -4/1

Y intercept (b): 28

Answer:

46.28

Step-by-step explanation:

i did pemdas

When an image is enlarged using a scale factor between 1 and 1, the image does not change in size.

A scale factor of 1 means that the image is not being enlarged or reduced in size; it is remaining the same size. Therefore, the image will appear the same as it did before the enlargement.

A scale factor of less than 1 means that the image is being reduced in size, and a scale factor greater than 1 means that the image is being enlarged in size. But when it comes to scale factor between 1 and 1, the image will not change in size, it will appear the same as it was before.

It's important to note that when you're enlarging an image using a scale factor that's less than 1, the image becomes smaller but when you're using a scale factor greater than 1 the image becomes larger.

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It costs $4 for 2 visits, $8 for 4 visits, $10 for 5 visits, and $16 for 8 visits.

2 visits: c = 2v = 2(2) = $4,

4 visits: c = 2v = 2(4) = $8,

5 visits: c = 2v = 2(5) = $10,

8 visits: c = 2v = 2(8) = $16.

2 visits: c = $30, cost per visit = $15

4 visits: c = $60, cost per visit = $15

5 visits: c = $75, cost per visit = $15

8 visits: c = $120, cost per visit = $15

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Answer: The ratios do form a proportion. The cross products are equal (16 * 22 = 26 * 12)

Step-by-step explanation:

a. The simple interest for 4 years would be $960.

b. The amount at the end of the 4 years would be $2160.$

A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.

a. For calculating simple interest for the 4 years

We have been given data as:

Principal (P) = $1200

Rate of Interest (R) = 20%

Time (T) = 4 years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

The simple interest for 4 years would be:

⇒ 1200 x 20% x 4 = 960

b. For calculating the amount at the end of the 4 years

The amount at the end of the 4 years would be:

1200 + 960 = 2160

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As a result, according to Pythagoras' Theorem, the third side, or hypotenuse, has a value of 8 units, whereas the other two sides are 6 and 7.

The Pythagorean Theorem, often known as the Pythagorean Theorem, is the fundamental Euclidean geometry relationship between the three sides of a right triangle. The area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the right angle equals the sum of the squares that span its sides. It is sometimes written as the generic algebraic notation a2 + b2 = c2.

given

x2 = a2 + b2

x2 = 6*6 + 28

x2 = 36 + 28

x2 = 64

x = 8

As a result, according to Pythagoras' Theorem, the third side, or hypotenuse, has a value of 8 units, whereas the other two sides are 6 and 7.

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No, 6 is not considered as a prime number, it is a composite number.

As given in the question,

Given number is equal to :

6

Prime numbers are those numbers which has only two factors one and the number itself.

Example of prime numbers are :

2, 3, 5, 7, 11, 13,... so on.

Here six has more than two factors .

Factors of 6 are equal to :

1, 2, 3, 6

There are four factors of six.

When a number has more than two factors then it is considered as composite number.

Example of composite factors are :

4, 6, 8, 9, 10, ... so on.

6 is a composite number.

Therefore, 6 is not a prime number it is a composite number.

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It's the last one

Because its one fourth of the original ones minus the original giving you the answers -3, 4.5, -1.5, 1.5, 3, -1.5, 3 and 3 again.

The value of x is given as follows:

x = 13.7.

The value of x is obtained using similar triangles, which share these two following features:

The proportional side lengths are given as follows:

Hence the proportional relationship of these lengths is given as follows:

x/16 = 6/7.

Meaning that the value of x is obtained as follows:

7x = 16 x 6

x = 16 x 6/7

x = 13.7.

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if we plug in different values for the input, we get corresponding values of output. There is always a pattern in the way input values x and the output values y are related which is given by the function rule.

What are the Slope and intercepts ?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction of function

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

On the x-axis, negative numbers are below the origin, and on the y-axis, they are to the left of the origin. If the x-value is negative, begin at the origin and go to the left; if the y-coordinate is negative, move downward.

Line graphs, also known as XY graphs, are used to visually represent data (the outcomes of an experiment) in order to demonstrate the link between various factors, such as the severity of the disease and time.

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On solving the provided question we can say that based on the provided graph obtaining a doctorate after earning a master's degree.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things.

so here,

based on the provided graph  obtaining a doctorate after earning a master's degree.

High education is generally highly valued by employers. People with greater education tend to be seen as candidates with a larger variety of skill sets than other candidates with lower level of education, which would positively affect their income level (although this may not always be the case).

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The correct question is -

Based on the information provided in the graph, for which of the following situations could you expect to have the greatest increase in salary? a. Having a high school diploma and going to college for a year. b. Having an associate’s degree and getting a bachelor’s degree. c. Having a bachelors degree and getting a master’s degree. d. Having a master’s degree and getting a doctorate degree.

Answer:

Triangle: 15 cm

Rectangle: w = 2.5 cm

Step-by-step explanation:

Rectangle: A = w · l

2.5 · 6 = 15cm

Triangle: A = hᵇb/2 = 6 · 5/2 = 15 cm

I hope this helps!

The equation that models the situation is 33 / 4 = h + 13 / 4.

Jamal measured the height of a flower growing in his garden at the beginning of the month. The flower was 3 1 / 4 inches tall . The flower grew h inches during the month.

At the end of the month it was 4 1 / 8 inches tall.

Hence, the equation to model the situation can be represented as follows:

Let's convert the mixed fractions to improper fractions.

3 1 / 4  inches = 13 / 4 inches

4 1 / 8 inches = 33 / 4 inches

Hence, the equation is as follows:

33 / 4 = h + 13 / 4

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Answer:c

Step-by-step explanation:

c

Answer:

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

Solve the following equation:

The Function given as [tex]y=3^{x}[/tex] is an Exponential function and the base is 3 and the exponent in the function is x .

What are Exponential function ?

The exponential Functions are defined as a function written as [tex]f (x) = a^{x}[/tex], where the "variable x" is called exponent and the "number a" is a constant called the base of the function and base should be greater than 0.

the given function is [tex]y=3^{x}[/tex] ,

So , according to the definition of Exponential Function ,

we can see that the base of the function is 3 and is greater than 0 ,

the exponent is x .

Therefore , the function [tex]y=3^{x}[/tex] is an Exponential Function .

The given question is incomplete , the complete question is

Is [tex]y=3^{x}[/tex] an exponential function ?

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A reflective pronoun is a pronoun  formed with -self or -selves that refers to the subject. Hence, option B is correct.

When a pronoun is used to refer to the same noun as both the subject and the object of a verb, it is known as a reflexive pronoun. The pronouns that in English finish in "self" or "selves" are things like "himself," "myself," "ourselves," etc.

Words like myself, you, him, her, it, ourselves, ourselves, and yourselves are examples of reflexive pronouns. They make a reference to someone or something. When the subject and the object of a verb are the same, reflexive pronouns are frequently used. I cut myself yesterday night while preparing dinner.

Thus, option B is correct.

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Using the equation we know that the required value of x is (B) 30 cm.

Basically, an equation is when you have two expressions with the same value on either side of an "equal to" sign.

For example, 3x + 5 = 15.

There are lots of different types of equations, like linear, quadratic, and cubic, among others.

So, looking at the diagram, the equation is true.

x/75 = 12/30

Solve as follows:

30x = 12 * 75

30x = 900

30x/30 = 900/30

x = 30

Therefore, using the equation we know that the required value of x is (B) 30 cm.

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Correct question:

What is the value of x?

(A) X= 4.8 cm

(B) X= 30 cm

(C) X= 93 cm

(D) X= 187.5 cm

Answer:

the answer is in the images

Complete transformations and then enter the final coordinates of the figure will be: A(2,2) B(1,-2) C (4,-4)

If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,

(x, y) → (x + 4. y + 1)

Therefore, vertices of the image triangle ABC will be,

A(2, 2) → A'(2+4, 2+1)

         → A'(6, 3)

B(5, -1) → B'(5+4, -1+1)

         → B'(9, 0)

C(1, -2) → C'(1+4, -2+1)

Then reflected across y-axis.

Rule for the reflection across y-axis will be,

(x, y) → (-x, y)

A'(6, 3) → A"(-6, 3)

B'(9, 0) → B"(-9, 0)

C'(5, -1) → C"(-5, -1)           → C'(5, -1)

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The 5 coordinate systems are Cartesian Coordinate System, Polar Coordinate System, Cylindrical Coordinate System, Spherical Coordinate System, Elliptic Coordinate System.

1. Cartesian Coordinate System: This system uses two perpendicular axes (X and Y) to determine the location of a point. The point's coordinates are the distances from the origin point (0, 0). The axes divide the plane into four quadrants and the coordinates can be positive or negative. The axes are also referred to as the x-axis and y-axis.

2. Polar Coordinate System: This system uses an angle and a distance from a fixed origin point to specify a point. The angle is measured in radians and the distance is measured from the origin. The coordinates of the point are usually written as (r, θ).

3. Cylindrical Coordinate System: This system combines the two-dimensional polar system and the one-dimensional Cartesian system. It uses three coordinates, (r, θ, z) to determine a point's location in three-dimensional space. The r coordinate is the distance from the origin, θ is the angle measured from the z-axis, and z is the height.

4. Spherical Coordinate System: This system uses three coordinates, (r, θ, φ), to determine a point's location in three-dimensional space. The r coordinate is the distance from the origin, θ is the angle measured from the z-axis, and φ is the angle measured from the x-axis.

5. Elliptic Coordinate System: This system uses two coordinates, (a, b), to specify a point on an ellipse. The a coordinate is the distance from one of the ellipse's foci, and the b coordinate is the distance from the other. This system is useful for describing orbits, such as those of planets.

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The nearest whole number to which the new height of the image is enlarged is 9cm.

What is meant by height?

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12) The new height is 9cm it was originally 4cm wide and 3cm tall, scale factor is 3.

14) The new width is 12cm it was originally 2cm tall  and 4cm wide, scale factor is 3.

In mathematics, a scale factor is the proportion between corresponding measurements of an object and a representation of that object. The copy will be bigger if the scale factor is a whole number. A fraction scale factor means that the copy will be smaller.

To increase an object by a scale factor, measure each side of the object and multiply the result by the scale factor. A 2x2 cm square is presented to you.

Increase the square by a scale factor of 2.

To do this, multiply each side by 2.

The result is a 4x4cm square.

12) scale factor = 12/4

scale factor = 3

14) scale factor = 6/2

scale factor = 3

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Answer:

-11/12

Step-by-step explanation:

Answer:

Photo 1:

             Question 4:

                   If the angles are the same (two 45° and one 90°) the vertical  side is equal to side C. the Pythagorean theorem states that A²+B²=C².

if Side C is equivalent to 4, both sides of the right angle are 4 (Because they are equivalent to each other.) so 4²+4²= 4 x [tex]\sqrt{2}[/tex] (5.8) so D=5.8, C=4

D is roughly 1.45 C

Step-by-step explanation:

Answer:

Step-by-step explanation: 7 x + 9 = 23. 7x+9=23. Subtract 9 from both sides. Subtract 9 from both sides.

7x=23-9. 7x=23−9. Subtract 9 from 23 to get 14. Subtract 9 from 23 to get 14.

7x=14. 7x=14. Divide both sides by 7. Divide both sides by 7.

x=\frac{14}{7} x=714​ Divide 14 by 7 to get 2. Divide 14 by 7 to get 2.