Which is NOT a method that can be used to prove that lines i and k are parallel?
Responses
A Show congruence of a pair of alternate interior angles.Show congruence of a pair of alternate interior angles.
B Show that both lines are perpendicular to a third line.Show that both lines are perpendicular to a third line.
C Show that a pair of interior angles on opposite sides are supplementary.Show that a pair of interior angles on opposite sides are supplementary.
D Show congruence of a pair of corresponding angles.Show congruence of a pair of corresponding angles.
Question 2
Lines l and k intersect forming two pairs of vertical angle. If one of these angles measure 120°, what are the measures of the other three angles?
Responses
A 60°, 60°, 60°60°, 60°, 60°
B 120°, 120°, 120°120°, 120°, 120°
C 60°, 90°, 90°60°, 90°, 90°
D 60°, 60°, 120°60°, 60°, 120°

Answer:

c. x > 2.

Step-by-step explanation:

4x + 1/2 (2x+4) > 12

4x + x + 2 > 12

5x > 10

x > 2.

Answer:

16t+55t+6t=77. 55-6=49

The difference between 2/5(d-10)-2/3(d+6) is -56.

Firstly simplifying the terms to find the difference. Simplifying the first part -

Rewriting the expression

Expression 1 = 2/5(d - 10)

Multiplying the terms with the bracket

Expression 1 = 2d/5 - ((2×10)/5)

Multiplying the terms on Right Hand Side

Expression 1 = 2d/5 - 2×2

Performing multiplication

Expression 1 = 2d/5 - 4

Simplifying the second part -

Rewriting the expression

Expression 2 = 2/5(d + 6)

Multiplying the terms with the bracket

Expression 2 = 2d/5 + ((2×6)/5)

Multiplying the terms on Right Hand Side

Expression 2 = 2d/5 - 12×5

Performing multiplication

Expression 2 = 2d/5 - 60

Subtracting expression 2 from expression 1

Difference = 2d/5 - 60 - (2d/5 - 4)

2d/5 will be subtracted to give 0

Difference = - 60 + 4

Performing subtraction

Difference = - 56

Therefore, the difference between mentioned expressions is -56.

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Answer: D

Step-by-step explanation:

The x-intercepts are where the graph meets the y-axis.

The y-intercepts are where the graph meets the x-axis.

Answer: D x-intercepts: (-10,0) and (2,0)

y-intercept (0,-5)

Answer:

y = - x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x + 9 ← is in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c substitute (7, - 13 ) into the partial equation

- 13 = - 7 + c ⇒ c = - 13 + 7 = - 6

y = - x + 6 ← equation of parallel line

Answer:

Step-by-step explanation:

Parallel lines have the same slope. So the slope of the line that's parallel to

Now, plug that into the Point-slope formula:

Where:

Plug in the values:

I hope this helps!!

(C) "Eukaryotic cells must be smaller than prokaryotic cells due to the increased number of organelles" is not the reason for the small size of the cells.

The reasons for the small size of cells are as follows:

Option (C) is not mentioned the reasons for the small size of the cell, so (C) is the answer.

Therefore, (C) "Eukaryotic cells must be smaller than prokaryotic cells due to the increased number of organelles" is not the reason for the small size of the cells.

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The complete question is given below:

Which is NOT a reason for the small size of cells?

A) nutrients and wastes must enter and leave the cell through the plasma membrane

B) the nucleus can only control a certain amount of cytoplasm

C) the increased number of organelles requires that eukaryotic cells be smaller than prokaryotes cells

D)materials must be able to move quickly and efficiently through the cytoplasm

E) as the linear dimensions of a cell increase, the volume increases twice as fast as the surface area

The value of the x, when y = 10 by the direct proportional is found as x = -5.

As per the given question;

y is in the direct variation with x.

This can be written as; y ∝ x.

Or, y = kx

Where, k is proportionality constant.

put the values;  y = 6 when x = -3

6 = -3 k

k = -2

Now, the value of x when y = 10.

y = kx ; put the value of y and k

10 = (-2)x

x = -5

Thus, the value of x in direct variation with y = 10 is found as x = -5.

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Answer:

  14

Step-by-step explanation:

You want to know how old Mark is if he is 6 years younger than twice his brother's age, and their combined age is 24.

Let m and b represent Mark's age and his brother's age, respectively.

The given relations are ...

Solving the second equation for b, we have ...

  b = 24 -m

Using that in the first equation gives ...

  m = 2(24 -m) -6

  m = 48 -2m -6

  3m = 42 . . . . . . . . . add 2m, combine like terms

  m = 14

Mark is 14 years old.

__

Check

Mark's brother is 24 -14 = 10. Twice that less 6 is 2×10 -6 = 14, which is Mark's age, as it should be.

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Answer:

Step-by-step explanation:

Answer:

x=37

Step-by-step explanation:

3x + 3 + 2x - 8 = 180

solve for x and x = 37

hope this helped

have a good day sir ^^

Answer:

x=37

Step-by-step explanation:

180=5x+3-8

180=5x-5

+5      +5

185=5x

/5     /5

37=x

x=37

Answer:

[tex]\frac{x}{3}\sqrt{\frac{x}{3}}[/tex]

Step-by-step explanation:

[tex]g(h(x))=g(x/3)=\sqrt{x/3} \\ \\ f(g(h(x)))=f(\sqrt{x/3}) \\ \\ =(\sqrt{x/3})^3 \\ \\ =\frac{x}{3}\sqrt{\frac{x}{3}}[/tex]

The measure of angle AXY based on the information will be A. 70°.

It should be noted that the value of a right angle is equal to 90°.

In this case, we will add the angles that are given and equate them to 90°. This will be:

6x + 40 + 10 + 2x = 90°

8x + 50 = 90°

Collect like terms

8x = 90° - 50°

8x = 40°

Divide

x = 40° / 8

x = 5°

Therefore, the value of angle AXY will be:

= 6x + 40

where x = 5.

= 6(5) + 40

= 30 + 40

= 70°

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Answer:

there's no ratio, or maybe u can help me out

The dilated picture of the point D dilation that is necessary is -6.

Given that,

To determine thee dilated image of point D (-2, 0), on the graph.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

The scale factor is defined as the ratio of modified change in length to the original length.

Here,Formerly point D is located at (-2, 0).

Now multiplying with the scale factor 3 the point goes

(-2 * 3, 0*3) => (-6, 0).

Thus, The required dilated image of the dilation of point D is -6.

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The linear graph of y = 2x + 3 is shown below.

To graph the linear equation, plot each points from the table of values on a coordinate plane then connect the points to each other as a straight line.

Given the table, to fill it, substitute each value of x into y = 2x + 3:

For x = -2:

y = 2(-2) + 3

y = -4 + 3

y = -1

For x = -1:

y = 2(-1) + 3

y = -2 + 3

y = 1

For x = 0:

y = 2(0) + 3

y = 3

Thus, plot the points, (-2, -1), (-1, 1), (0, 3), (1, 5), and (2, 7) on a graph. The graph is shown below.

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Sam's score percentage for the whole year was  15 %

This  is a simple question of average,

Sam improved his score by 20% in the 1st semester, and in the 2nd semester, his score improved by 10%.

let 20  in out of 100 and 10 out of 100.

then, the total percentage score is equal to 20+10=30.

and, the total percentage in which out of getting is 100+100 =200

we have to find sam's score percentage for the whole year

which is equal to the total percentage score by sam's divided by percentage which is out of getting and whole multiplied by 100 Because we are finding the percentage.

=>30*100/200=>15 percentage.

So, Sam's score percentage for the whole year= is 15 %

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Answer:

2, 3

Step-by-step explanation:

[tex]g(x)=\frac{1}{2}(4x+6) \\ \\ =2x+3[/tex]

Answer:[tex]96cm^2\\[/tex]

Step-by-step explanation:

64= [tex]x^3\\[/tex]

[tex]\sqrt[3]{64} =4[/tex]

So a side is 4, and surface area of one side is 4x4 = [tex]16cm^2[/tex]

cude has 6 faces, 16*6 = [tex]96cm^2\\[/tex]

Answer:

96 cm²

Step-by-step explanation:

If the side of a cube is a, then volume = a³

There are six surfaces for a cube and each surface has an area of a²
So total surface area = 6a²

Since we are given volume = 64 cm³, each side must be ∛64 = 4 cm

So total surface area = 6 x 4² = 6 x 16 = 96 cm²

If Lucy earns $15.75 per hour. Last week she worked 25 hours her gross pay is $393.75 . If Lance has a yearly salary of $52,300 and pays 21% in taxes her  taxed amount  is $10,983, net pay is  $41,317 and paycheck is $2,179.

1. Gross pay

Using this formula to determine the gross pay

Gross pay = Amount earn per hour × Number of hours worked

Let  plug in the formula

Gross pay =  $15.75 per hour × 25 hours

Gross pay = $393.75

2a. Taxed amount

Amount in Tax = Salary × Tax percentage

Amount in taxes = $52,300 × 21%

Amount in taxes = $10,983

2b. Net pay

Net pay = Gross  - Deduction

Net pay =  $52,300 - $10,983

Net pay = $41,317

2c. Paycheck

Paycheck = $52,300 / 24 months

Paycheck = $2,179 per paycheck

Therefore we can conclude that the her gross pay is $393.75

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After solving with help of the formula to find the volume of the sphere we find that the volume of the sphere is 3053.63

The radius of the sphere = 9 units

Height of sphere  =7 units

 the value of π is given in the question =3.14

The volume of the sphere = 4/3 × π × r^3

                                             = (4/3) × 3.14×9^3

                                             = (4/3) × 3.14 × 27

                                             = 4 × 3.14 × 9

                                             = 36 × 3.14

                                             = 3053.63

The volume of the sphere is 3053.63

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The Equation of line -

The slope intercept form of a line is given by -

y = mx + c

m is the slope of line

c is the y - intercept

Given is a line that passes through the point (3, 10) and in case [1] is parallel to line y = x - 1 and in case [2] is  perpendicular to y = x - 1.

Case 1 -  Line is parallel to the line y = x - 1

Assume that the equation of line is -

y = mx + c

Since, the line is parallel, both lines will have same slope and is given by -

m = 1

Since, the line passes through the point (3, 10) we can write -

10 = 1 x 3 + c

c = 7

We can write the equation of line parallel to line y = x - 1 as -

y = x + 7

Case 2-  Line is perpendicular to the line y = x - 1 -

Assume that the equation of line is -

y = mx + c

Since, the line is perpendicular, the product of slopes of both lines will be equal to 1. The slope (m) of the line will be -

m x 1 = -1

m = -1

Since, the line passes through the point (3, 10) we can write -

10 = -3 + c

c = 13

We can write the equation of line perpendicular to line y = x - 1 as -

y = - x + 13

Therefore, the equation of line -

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If the rows are  perpendicular to the footpath, then the gardener ensure that that the rows are parallel.

Parallel:

Any two lines are said to be parallel if the Corresponding angles so formed are equal.

Given,

The head gardener at a botanical garden wants to plant rosebushes in parallel rows on either side of an existing footpath.

Here we need to find how can the gardener ensure that that the rows are parallel.

To know the answer, we have to consider the following,

Let us consider,

If the gardener digs every row at a 90° angle to the footpath, then each row will be exactly perpendicular to the foot path of the garden.

Which means,

If the rows are  perpendicular to the footpath, then the rows are parallel.

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Option A 2X+y=1, the perpendicular graph, is correct.

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The three more solutions to the given linear equation are (2,-9/2), (6,-3/2), and (5,-9/4).

Given equation:-

y = (3/4)x - 6

We have to create a table of values to obtain ordered pairs.

Also, we have to plot these ordered pairs to create a linear graph and based on the  graph we have created, we have to find three more solutions to the equation.

Let x = 0

y = 0 - 6 = -6

Ordered pair = (0,-6)

Let y = 0

0 = (3/4)x - 6

6 = (3/4)x

x = 8

Ordered pair = (8,0)

Let x = 4

y = 3 - 6 = -3

Ordered pair = (4,-3)

The graph of these three ordered pairs is attached below.

Based on the graph the other 3 ordered pairs that we can find are (2,-9/2), (6,-3/2), and (5,-9/4).

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Answer:

r=-4

Step-by-step explanation:

use the slope formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Then plug in x and y values and set that equal to m=1

1=[tex]\frac{-2-8}{r-6}[/tex]

multiply r-6 over

r-6=-10

r=-4

The number of books Henry read each number is 3 or 6/2 in a fraction.

A fraction is used to denote a portion or component of a whole. 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, and the denominator is the number at the bottom.

As given in the question,

The number of books read in 2 months is 4.

Henry read books at a constant rate.

The Number of books read by Henry in 1 month is ( 6/2 ) = 3 books.

Therefore, the number of books read by Henry as per the given condition of reading 6 books in 2 months at a constant rate is equal to 6/2.

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The postulate that can be used to prove that the triangles are congruent is: AAS.

The AAS congruence postulate states that if two angles and one non-included side of one triangle are congruent to corresponding two angles and one non-included side of another triangle, it can be proven that both triangles are congruent triangles.

From the image, we know that triangles RST and UVT have:

Two pairs of congruent angles, which are angle RST ≅ angle UVT and angle RTS ≅ UTV (vertical angles)

One pair of non-included congruent sides, which are RT ≅ UT.

Thus, we can conclude that they are congruent triangles based on the AAS congruence postulate.

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The set of possible values for "p" is ((4-√7)/9, (4+√7)/9).

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