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The given statement "when a transversal crosses two parallel lines, Corresponding angles are created, which are congruent to one another" is TRUE.

The angles created when a transversal intersects two parallel lines are known as corresponding angles.

Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.

Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Therefore, the given statement "when a transversal crosses two parallel lines, Corresponding angles are created, which are congruent to one another" is TRUE.

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The value of y is 2/3, and RS = 9 and ST = 9.

What is the value of​ y?

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Answer:

461.814 is part A

103.67 is part

Answer:HEYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY TOMATOE TOMATOE TOMATOE BOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Step-by-step explanation:

The expression that shows how much the individual earns everyday if they sell n items would be = $5 × n = $5n.

A salesperson is an individual that helps in the marketing and selling of goods and products for a company and who is equally rewarded with bonus after each sale that is made.

The amount of money that the salesperson makes = $10/day

The amount of money given as bonus for each item sold = $5

Therefore when the number of items sold = n, the amount made = $5 × n = $5n

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Answer: ±1.4

Step-by-step explanation:

f(x)=ax^2+c

The graph passes through (2,2) and (-2,2)

Vertex:(0,-2)

f(x)=ax^2-2

4a-2=2

4a=4

a=1

f(x)=x^2-2

if f(x)=0

x^2-2=0

x^2=2

x=±[tex]\sqrt{2}[/tex]=±1.414

x=±1.4

There is no number that satisfies this criteria

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: let the two numbers be x and y then

we have x+y=1 and xy=7

Solving these two equations we get x²-x+7=0

∴x=1±√1-28 /2 but this is not a real number

Hence, such a number doesnt exist.

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Answer:

To divide using long division, we first divide the leading term of the dividend (3r³) by the leading term of the divisor (r) to get the first term of the quotient (3r²). Then, we multiply the divisor (r + 4) by the quotient term (3r²) and subtract it from the dividend. We then bring down the next term of the dividend (11r²) and repeat the process. This will give us the quotient and the remainder.

The long division process is as follows:

(r + 4) | (3r³ +11r²-6r-18)

| 3r² (3r²)

|__

| -9r² +11r²-6r-18

|____

| -2r-18

|____

| +12r + 72

|____

| -36

|____

So the quotient is 3r² - 2r + 12 and the remainder is -36

And we can write the division as (3r³ +11r²-6r-18)÷(r + 4) = 3r² - 2r + 12 +(-36)/(r + 4)

Answer:Answer Choice C

Step-by-step explanation:To solve this problem, we need to find the area of the rectangle by doing 9X5, which is 45. Next we have to find the area of the triangle, and then subtract it by the area of the rectangle to find the area of the figure. To find the area of a triangle, we do BaseXHeight divided by 2, and in this problem, we do 9X2 (which is 18) and 18 divided by 2 which gets us 9. Now we subtract 9 from 45, which gets us 36 which means 36m2 is the answer to this problem.

To determine the probability that the sample mean for French is greater than that of the Americans, we need to use the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means will become more and more normal, regardless of the distribution of the population from which the samples are drawn.

So, we can assume that the sample means of both American and French adults will be normally distributed with a mean of 43.5 hours/week and 36 hours/week respectively and a standard deviation of 4.6/sqrt(110) and 5.1/sqrt(135) respectively.

We can use these assumptions and the Z-score formula to find the probability that the sample mean for French is greater than that of Americans.

Z = (36 - 43.5) / (sqrt((4.6/sqrt(110))^2 + (5.1/sqrt(135))^2))

The resulting Z-score will be negative, meaning that the probability that French sample mean is greater than American sample mean is low and it's a rare event.

Therefore , as a result, the answer to the provided linear equation is 5/23 pounds of cashews and 13/46 pounds of peanuts.

A linear equation is characterized as having a max of just one degree. A Any equation with a maximum degree of 2 or above is considered to be nonlinear. A graph with a linear equation has a straight line. A curve is created on the graph by a nonlinear equation.

Here,

Half of x is equal to the weight of peanuts,

so if x is the weight in pounds of cashews.

Ours has

=>5.75 x + 2.30 (1/2 x)

=>575x+115−230x =190

=> 1.90 x=75/345 = 5/23 pounds of cashews

Pounds of peanuts:

=> 1/2−x=23/46 −10/46= 13/46

As a result, the answer to the provided linear equation is 5/23 pounds of cashews and 13/46 pounds of peanuts.

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Answer:

[tex]\displaystyle \frac{\sqrt{5}-1}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{1+\sqrt{5}}\\\\=\frac{2}{1+\sqrt{5}}*\frac{1-\sqrt{5}}{1-\sqrt{5}}\\ \\=\frac{2(1-\sqrt{5})}{1-5}\\ \\=\frac{2(1-\sqrt{5})}{-4}\\\\=\frac{\sqrt{5}-1}{2}[/tex]

The approximate area of the shaded sector is 97 cm^2

What is area of circle ?

area of circle can be defined as the product of pi and square of radius ,the value of pi is 22/7 or 3.14 .

Given , diameter = 12

We need to convert diameter to r

d =2r

d/2 =r

12/2=r

6 =r

The radius is 6

A= pi *6^2

A = 36 *(3.14)

A = 113.04 cm^2

Now the fraction of the circle that is shaded is 301degrees out of 360

(A circle is 360 degrees)

=310/360 * area of a circle

=310/360 * 113.04

= 97.34

Hence , The approximate area of the shaded sector is 97 cm^2 .

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False, Shapes can be both 2 dimensional (L*W) and 3 dimensional (L*W*H) whereas Form gives us the typical significance of the shape

Points, line segments, circles, and curves are used to build closed geometric objects. We can see these forms all around us. Examples of geometric shapes include circles, rectangles, triangles, and others. Pizza is a cylinder with triangle pieces.

3.1 Euclidean geometry.

3.2 Differential geometry. 3.2.1 Non-Euclidean geometry.

3.3 Topology.

3.4 Algebraic geometry.

3.5 Complex geometry.

Hence from the given arguments we see

Shapes can be both 2 dimensional (L*W) and 3 dimensional (L*W*H) whereas Form gives us the typical significance of the shape

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Answer:

Step-by-step explanation:

$126-$70 =

Answer:

x = 120

Step-by-step explanation:

the sum of the exterior angles of a triangle is 360°

x is an exterior angle of the triangle , then

x + x + x = 360

3x = 360 ( divide both sides by 3 )

x = 120

The 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is given as follows:

($629, $727).

The bounds of the confidence interval are given as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The parameters for this problem are of:

[tex]\overline{x} = 678, \sigma = 560, n = 500[/tex]

Hence the lower bound of the interval is of:

[tex]678 - 1.96\frac{560}{\sqrt{500}} = 629[/tex]

The upper bound of the interval is of:

[tex]678 + 1.96\frac{560}{\sqrt{500}} = 727[/tex]

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The slope is (2/3 - 2/(3+h))/ h and as h is made closer and closer to 0, the slopes of the lines tend toward the derivative of the function f(x) at x = 3.

a) To find the slope of the line between the points (3, f(3)) and (3.1, f(3.1)), we use the formula m = (f(3.1) - f(3)) / (3.1 - 3) = (f(3.1) - f(3)) / 0.1

b) To find the slope of the line between the points (3, f(3)) and (3.01, f(3.01)), we use the formula m = (f(3.01) - f(3)) / (3.01 - 3) = (f(3.01) - f(3)) / 0.01

c) To find the slope of the line between the points (3, f(3)) and (3.001, f(3.001)), we use the formula m = (f(3.001) - f(3)) / (3.001 - 3) = (f(3.001) - f(3)) / 0.001

As h is made closer and closer to 0, the slopes of the lines tend toward the derivative of the function f(x) at x = 3.

Now to find a simplified rational expression for the slope of the line between (3, f(3)) and (3 + h, f(3 +h)), (h 0) :

The slope is equal to (f(3+h) - f(3)) / h

With f(x) = 2/x, we substitute it into the equation above and we get (2/(3+h) - 2/3) / h

The simplified rational expression for the slope is (2/3 - 2/(3+h))/ h

The graph of y = f(x) = 2/x between x = 1/2 and x = 4 :

This is the graph of a hyperbola that is symmetric about the y-axis and passes through the origin (0,0) and as x increases from 1/2 to 4, y decreases from 4 to 1/2.

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The figure shows intersecting lines k and m, the measure of angle a is 94 degrees.

What are parallel lines ?

parallel lines can be defined as the lines which are equi distant from each other and which never meet or intersect each other.

Given,

In the figure the lines k and m are intersecting.

so,

by adding 86 degrees with a it should result into 180 degrees.

86+a  = 180

a = 180 - 86

a = 94

Hence, The figure shows intersecting lines k and m,  the measure of angle a is 94 degrees.

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Based on the table, the equation of the function h(x) is h(x) = f(x) - 1

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

The functions f(x) and h(x)

When the x values of both functions are compared, we can see that they have the same x values

However, for the y values

The function h(x) is 1 lesser than the function f(x)

This means that

h(x) = f(x) - 1

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Sally put in 36 hours, Harold put in 30 hours, and Nora put in 15 hours.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let x be the work hours of Sally, y be the work hours of Harold and z be the work hours of Nora.

x+y+z=81

x=y+6

y=2z

x=2z+6

2z+6+2z+z=81

6+5z=81

5z=75

z=15

y=2z

=30

x=y+6

=30+6

=36

Sally worked for 36 hours while Harold worked for 30 hours and Nora worked for 15 hours.

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The degree of the function is 3, and the end behavior is that as x gets very large or very small the function increases or decreases without bound respectively.

Generally, The degree of a polynomial function is the highest power of the variable in the function. In this case, the highest power of x is 3, so the degree of the function is 3.

The end behavior of a polynomial function refers to how the function behaves as the value of x gets very large or very small (i.e., as x approaches positive or negative infinity).

To find the end behavior, we look at the leading term, which is the term with the highest degree. In this case, the leading term is 3x³. Since the coefficient of x³ is positive, the end behavior of the function as x approaches positive infinity is positive infinity, and as x approaches negative infinity, the end behavior of the function is negative infinity.

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a. At the end of the 3 1/2 years, the amount of interest Damian has paid is $4,288.73.

b) When Damian pays off his credit card, the total amount (principal and interest) he has paid will be $14,488.73.

The interest is computed using an online finance calculator, setting the following parameters, based on the compounding interest system.

The calculator also shows the total payments made for the duration of the credit balance.

N (# of periods) = 42 months (3.5 years x 12)

I/Y (Interest per year) = 21%

PV (Present Value) = $10,200

FV (Future Value) = $0

Results:

PMT = $344.97

Sum of all periodic payments = $14,488.73

Total Interest = $4,288.73

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If there were 50 workers, they would set 2,500 stones each day.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

Assuming each worker set the same number of stones each day, the total number of stones set each day would be 50 times the number of workers. For example, if there were 20 workers, they would set 1,000 stones each day.
The number of stones set each day could also vary depending on the number of workers and the number of days they worked in a week. For example, if the workers worked a six day week and worked 50 out of the 52 weeks each year, the total number of stones set each day would be 50 times the number of workers multiplied by six. For example, if there were 20 workers, they would set 12,000 stones each day. If there were 50 workers, they would set 30,000 stones each day.

The number of stones set each day can also be affected by the production rate of the workers, the quality of the stones, and the amount of time required to set each stone. If the production rate was low, the number of stones set each day would also be lower. Similarly, if the quality of the stones was poor, the workers would likely take longer to set each stone, thus reducing the number of stones set each day.

Overall, the exact number of stones set each day depends on the number of workers, the number of days they work each week, their production rate, and the quality of the stones.

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Answer:

4.2571428571 (but you should probably round for 4.3 or 4.26)

Step-by-step explanation:

if he spent $7.45 and each pound costs $1.75 then just divide 7.45 by 1.75.

Anthony bought exactly 4.2571428571 pounds of trail mix. However, it can be rounded off to 4.3 pounds.

The total amount spent on trail mix= $7.45

1 pound of trail mix costs $1.75

Therefore, the amount of trail mix bought= total amount spent on it / the cost of 1 pound of the product

= 7.45 / 1.75

= 4.2571428571 pounds

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The required order of buttons to press on a scientific calculator to enter 2.8 x 10⁷ is  [2] [.] [8] [EE] [7] . Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
While using the calculator, for the expression 2.8 × 10⁷,
We have to tap on tabs as,  [2] [.] [8] [EE] [7] where [.]  is the multiplication operator and {EE} is the exponential operator.

Thus, the required order of buttons to press on a scientific calculator to enter 2.8 x 10⁷ is  [2] [.] [8] [EE] [7] . Option A is correct.

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The required probability is 7/18 that an eighth grader chosen at random will play the keyboard.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The total number of eighth-grade students in the School of Rock is 12 + 6 + 4 + 14 = 36 students.

The number of eighth-grade students playing the keyboard is 14 students.

So, the probability that an eighth grader chosen at random will play the keyboard is :

⇒ 14/36

In the simplest form, 14/36 can be reduced to 7/18.

Thus, the required probability is 7/18.

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Answer:

The area of a circle is given by the formula A = πr^2, where A is the area, r is the radius, and π is approximately equal to 3.14. Since the diameter of the dartboard is 30 millimeters, the radius is half of that, or 15 millimeters. Therefore, the area of the dartboard is A = π(15^2) = 225π square millimeters.

Step-by-step explanation: