Provide the reasons for the following proof.
The figure shows triangle W X Y with a segment X Z drawn from vertex X to point Z on side W Y.
Given: Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y
Prove: triangle W X Z is congruent to triangle Y X Z
Statements Reasons
1.Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y 1. Given.
2. angle W X Z is congruent to angle Y X Z 2. Definition of an angle bisector.
3. Segment X Z is congruent to segment X Z. 3. _____________
4. triangle W X Z is congruent to triangle Y X Z 4. _____________
A. Reflexive Property of congruent to; SSS
B. Symmetric Property of congruent to; SSS
C. Reflexive Property of congruent to; SAS
D. Symmetric Property of congruent to; SAS

SOMEONE HELP! PLEASE!

Answer:

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Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

Answer:

Step-by-step explanation:

36 percent can be written as 36/100. So now the question is 36/100 x 28.

Its easier if you simplify 100 and 28 by a common factor, which im going to use 4 for. So instead you get 36/25 x 7.

36x7=252

252/25=10.08

Answer:

46.08

Step-by-step explanation:

Remember that a percent is always a fraction out of 100, in this case 36/100, so it can also be written as a decimal number, in this case 0.36. Now all you need to do is multiply 128*0.36

The number of goodie  bags she will need to sell is 107.

Breakeven is when profit is zero. it is the point where total cost is equal to total revenue.

Breakeven: Total cost = total revenue

fixed cost + variable cost = price x quantity sold

fixed cost + (cost per unit  x quantity sold)

$250 + (1.25 x q) = 3.60 x q

$250 + 1.25q = 3.60q

In order to determine the value of q, take the following steps:

Combine and add similar terms :

$250 = 3.60q - 1.25q

$250 = 2.35q

Divide both sides o the equation by 2.35

q = 250/2.35

q =  106.3 = 107

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Answer:

8

Step-by-step explanation:

8 x 5 = 40

We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Adding up all four sides will reveal a parallelogram's perimeter.An area of a circle of radius r is known as r2 in geometry.

The circumference-to-diameter ratio, which is always the same and is roughly equivalent to 3.14159 in this context, is denoted by the Greek letter.

Let side a and the side next to it in the parallelogram be a and b, respectively.

The parallelogram's perimeter is equal to 2(a+b)=150, where a+b=75.

Since an is 25 cm taller than b, a=b+25.

By changing it in equation 1, b+25+b=75 2b=50 b=25 is obtained.

a+b=75\sa=75=25\sa=50

Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

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Answer: 844000

Step-by-step explanation:

843857 = 844000 because you round up

Answer:

a)  The product of any two odd integers is an odd integer.

b)  The sum of two negative integers is always smaller than the smallest negative integer.

Step-by-step explanation:

Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

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

Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

Answer:

Step-by-step explanation:

4(x-2)+11=3(x+3)

Use distributive property to get rid of the parentheses

4x-8+11=3x+9

Simplify the addition and subtraction

4x+3=3x+9

subtract 3 on both sides and 3x on both sides to isolate x

x=6

Answer:

(125, -312500)

C(x) = -312500

Step-by-step explanation:

use this equation into a graphing calculator and use the minimum function

The number of terms (n) in the sequence = 10.

We know that,

                      S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}

Where,

            S = Sum of A. P. series

            n = number of terms in A. P. series

            a = first term of the series

            d = common difference

According to the question,

           Sum of the series, S = 340

                         First term,  a = 7

         Common difference, d = 6

                  S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}

                  340 =  [tex]\frac{n}{2}[/tex] {2*7 + (n-1)6}

                  340 =  [tex]\frac{n}{2}[/tex] {14 + 6n - 6}

                  340*2 = n( 6n + 8)

                   680   = 6n^2 + 8n

        6n^2 + 8n - 680 = 0

        2 (3n^2 +4n - 340) = 0

            3n^2 +4n - 340 = 0

        3n^2 + 34n - 30n - 340 = 0

        n (3n+ 34) - 10 (3n + 34) = 0

        (3n + 34) (n - 10) = 0

   if we take, 3n + 34 = 0

                         3n = - 34

                           n = -34/3

which is not possible, as the number of terms can not be negative

   if we take, n- 10 = 0

                       n = 10

Hence, the number of terms in the given A. P. series is 10.

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Answer: [tex]x=0, -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}[/tex]

The solution for the expression 112 ÷ 0.16 is 700.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

112 ÷ 0.16

This can be written as,

= 112/0.16

= 700

Thus,

The solution is 700

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Answer:

Book: Library is most similar in relation to the following word pair Water: Ocean. Both pairs are closely related and are often found together.

The graph shows that the domain and range of the line segment were [-5, 1] & [-4, 7, correspondingly.

A function's domain is the set of values that it can accept. These figures represent a function like f's x-values (x). The domain of a function is the set of possible values on which it can operate. This set is the value which the return type after the x value has been entered. Y = f is a function where x is an independent variable and y is a dependent variable (x). If a value of x can be successfully utilized to produce a single value of y using a value of f, then that value is said to be within the domain of that function.

Here,

The domain denotes all conceivable possibilities for x, whereas the range denotes all possible values of y.

The graph shows that the domain and range of the line segment is [-5, 1] & [-4, 7, respectively.

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The correct answer is x² - 7x - 18 = (x - 9)(x + 2)

The integers that -3.425 lie between are -3 and -4.

The rational numbers  that -3.425 lie between to the nearest tenth are -3.4 and -3.5.

The rational numbers  that -3.425 lie between to the nearest hundredth are -3.42 and -3.43.

Integers are numbers without decimals and fractions. They are whole numbers. Integers can either be positive, negative or zero. Examples of integers are -5 and 10.

A rational number is a number that can be expressed as a fraction of two integers. Examples of rational numbers are 1/4, -2/3  

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Answer:

A is an Irregular Polygon

B is Neither a Polygon

C is an Irregular Polygon

D is a Regular Polygon

E is a Regular Polygon

ES = 10.63 units

The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places. Therefore, by measuring the length of the line segment that connects the two sites, the distance between them may be determined.

When given a straight line on a graph, you can find the length of this line by using the Distance Between Two Points Formula. This formula uses the vertices of the beginning and ending points of a straight line to find the length of the line, which is the distance between the two points.

The Distance Between Two Points Formula is:

= √(( x₂  – x₁ )² + ( y₂ – y₁) ²)

The vertices of the line ES are E ( -3, -4 ) and S ( 4, 4 ).

The distance is:

= √(( 4  – (-3) )² + ( 4 ( - 4 )) ²)

= 10. 63 units

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The total quantity of the three spices is 7/8

A recipe has three spices

1/8 teaspoon of turmeric

1/4 teaspoon of ginger

1/2 teaspoon of cumin

The total quantity of the three spices can be calculated as follows

1/8 + 1/4 + 1/2

= 7/8

Hence the total quantity of the three spices is 7/8

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Answer:

[tex]3.5\% = \frac{3.5}{100} = \frac{35}{10} (fraction) = 3 \frac{5}{10} (mixed)[/tex]

Answer:

5 people

Step-by-step explanation:

Relay race ---> 3/4 mile

Each runner runs 3/20 miles

3/4÷3/20

3/4×20/3=5

OR

3/4 --> 15/20

3/20 goes into 15/20 5 times

Answer:

5 runners

Step-by-step explanation:

Just multiply 3/20 by 3/4

The rule for the graph changes form of the function is A)The graph is reflected across the x-axis.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Function is a relation that connects members of one set in a certain way to those of another set. Formally speaking, a function from to is an object such that each is specifically linked to an object. Therefore, a function is a many-to-one (or occasionally, one-to-one) relation.

Here Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let   h(x) = f(x)-c Shifting downward c units yields this graph of h from the graph of f.

We know that if the function reflected over x-axis then

g(x) = -f(x)

Here the given function f(x) = [tex]x^2-4[/tex] then reflection over x-axis then

=> g(x) = -f(x)

=> g(x) =-( [tex]x^2-4[/tex])

=> g(x) = [tex]-x^2+4[/tex]

Hence the correct option is A)The graph is reflected across the x-axis.

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Therefore , the solution of the given problem of interest comes out to be

A = $3,130.37  is the amount after 15 years.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :  

a ) the equation that can be formed is

2500x - 1.5y = 30

b)

Using compound formula :

=> Then solve the equation for A

A = P(1 + r/n)nt

A = 2,500.00(1 + 0.015/12)(12)(15)

A = 2,500.00(1 + 0.00125)(180)

A = $3,130.37

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The total height of the building would be nh + 30.

Option (B) is correct.

What is a simplification in mathematics?

In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.

The building's total height in feet is represented by the sum of the height of each floor plus the height of the spire.

So if the height of each floor is h, and there are n floors in the building and the building's spire is 30 feet, the total height of the building is:

= n * h + 30

=nh + 30

This is because the height of each floor is h, and there are n floors, so the total height of the floors is n * h. Adding the height of the spire, 30 feet, to the total height of the floors gives nh + 30.

Hence, the total height of the building would be nh + 30.

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The graph of the given piecewise function is as attached below.

Piecewise function is a function consisted of pieces of different functions over different intervals.

From the case we have:

f(x) = 3x - 5 if x ≤ -1

f(x) = -2x + 3 if -1 < x < 4

f(x) = 2 if x ≥4

To construct the piecewise function, we can try to find the base points of each functions.

f(x) = 3x - 5; if x ≤ -1

We will take x = -1 to approximate the line position

f(-1) = 3(-1) - 5

f(-1) = -3 - 5 = -8

f(x) = -2x + 3; if -1 < x < 4

(x = -1)

f(-1) = -2 (-1) + 3

f(-1) = 2 + 3 = 5

(x = 4)

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

f(4) = -8 + 3 = -5

f(x) = 2; if x ≥ 4

(x = 4)

f(4) = 2

We can put each points on the graph and try to construct the piecewise function.

Please refer to the attached graph below for the piecewise function graph

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The acccceleration will be 1m/s² and the average speed is 47m/s.

For the acceleration problems, you must draw a tangent on curved velocity-time graphs. Since it requested acceleration at t = 10 seconds, we must create a straight line that only touches the graph once, at 10 seconds.

Now, when drawing tangents, you must be as precise as you can because they can only contact the line once.

Next, determine the gradient using the tangent. You can accomplish this by creating a triangle out of two additional lines drawn from the tangent, then dividing the rise by the run, or Y/X. The triangle that comes before the Y and the X simply denotes the Greek letter delta, which symbolizes change. Change in Y so prevails over Change in X. So 10/10 = 1. So 1m/s^2.

If we estimate the speed at 5 seconds intervals, then we have

Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7

Average speed = 331/7 = 47.29 m/s

Average speed = 47 m/s

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Answer:

Step-by-step explanation:

Let the other diagonal be d.

From the Pythagorean theorem,

d2 = 82 + 1442

d2 = 64 + 20736

d2 = 20800

d = √20800

d = 144 cm

Answer:

Step-by-step explanation:

To calculate how long it will take John to recover his investment, we need to divide the cost of the degree by the difference in income between the two options.

$10,000 / ($35,000 - $20,000) = $10,000 / $15,000 = 0.67 years or 0.67*12 = 8 months.

So, it will take John 8 months to recover his investment if he goes to school.

Please note that this is a simplified calculation as it does not take into account the cost of living, taxes, and other expenses.

The answer should be 4x(2x-3) so Renuka does not score full marks.

A number system is defined as a system of writing to express numbers.

The given expression is 8x²-12x.

To factorise this we have to find the highest common factors from both the terms.

Factors of 8 are 1, 2, 4, 8

Factors of 12 are 1, 2, 3, 4, 6,12

The highest common factor is 4.

So we have to take common 4 but Renuka has taken out 2.

So she does not got full marks.

The answer should be 4x(2x-3)

Hence, the answer should be 4x(2x-3) so Renuka does not score full marks.

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