Which is a correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” when n = 4?
The correct expression is StartFraction n cubed Over 16 EndFraction minus 2 + 8.
The correct expression is 2 minus StartFraction n cubed Over 16 EndFraction + 8.
One of the steps to determining the value when n = 4 is 1 minus 2 + 8.
One of the steps to determining the value when n = 4 is 2 minus 1 + 8.
The value when n = 4 is 6.
The value when n = 4 is 7.
The value when n = 4 is 9.
The value when n = 4 is 10.

Area of the shape formed by joining triangle , trapezium and rectangle with height 3.5cm is equal to 6.25cm².

As given in the question,

Height of the shape = 3.5cm

length of the rectangle =3cm

Base of a triangle= 8mm

                           = 0.8cm

Parallel sides of the trapezium

side1 = 0.8cm

side 2= 3cm

Let x represents the height

Ratio of the height of rectangle ,trapezium and triangle =2:3:2

2x +3x+2x =3.5

⇒7x =3.5

⇒x =0.5

Height of rectangle =2×0.5

                             = 1cm

Height of trapezium =3×0.5

                               = 1.5cm

Height of the triangle =2×0.5

                                 = 1cm

Area of triangle = (1/2)× 0.8 ×1

                        = 0.4cm²

Area of trapezium = (1/2) ×(0.8+3)×1.5

                            = 2.85cm²

Area of rectangle = 3 ×1

                            =3cm²

Area of the shape =0.4 +2.85 +3

                            = 6.25cm²

Therefore, area of the shape formed by joining triangle , trapezium and rectangle with height 3.5cm is equal to 6.25cm².

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Answer:2x+ 24

Step-by-step explanation:

6x-4x=2x+ 24

Answer:

✨hello mark as branlist pls x=3

Step-by-step explanation:

6x+24−4x=30

6x+24−4x=30

6x+24+−4x=30

(6x+−4x)+(24)=30

2x+24=30

2x+24=30

2x+24−24=30−242x=6

2x

2

=

6

2

x=3

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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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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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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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!!

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

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1. Yes. There is a proportional relationship between the cost of items before tax and the price after tax because they share a constant of proportionality.

2. The constant of proportionality refers to the relative ratio that establishes the proportional relationship between two values.

Other descriptions of the constant of proportionality include:

Two variables possess a proportional relationship when their ratio or product produces a constant.

We can use the equation, k = y ÷ x, to find the constant of proportionality.

For instance, let the cost of items before tax be $100 with a 7% sales tax. The cost of the articles after tax is $107.

Therefore, the constant of proportionality is 1.07 ($107/$100).

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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

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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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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Answer:

1. e

2. c

3. f

4. b

5. a

6. d

Step-by-step explanation:

Addition - Subtraction

Subtraction - Addition

Multiplication - Division

Division - Multiplication

x^2 = square root X

square root x = x^2

Answer:

A to 5. B to 3. C to 1. D to 6. E to 2. F to 4.

Step-by-step explanation:

It makes sense.

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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(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 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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Answer:

Step-by-step explanation:

The function which contains non-negative real number is y = (x - 1)² and the domain is [0, ∝).

What is real number?

In mathematics, real number are those numbers which contain negative numbers, whole numbers as well as natural numbers. And all the positive real number lies in the first quadrant in the graph. The set of real numbers (denoted by R) includes both rational numbers (positive, negative and zero) and irrational numbers.

According to the question, the given functions whose domain consists of all non-negative real numbers.

Non-negative real numbers lie in the first quadrant. Therefore, the function(d) contains all non-negative real numbers.

Given function: y = (x - 1)²

The domain for this function is: [0, ∝)

Hence, the function which contains non-negative real number is y=(x - 1)² and the domain is [0, ∝).

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Answer:

$60.20

Step-by-step explanation:

7.5 percent of 56 can be found by multiplying 56 times .075, which equals 4.2. Add that to 56 and you get the total cost, which is $60.20

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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Answer:

The correct answer is B) Option B has a higher present value at time zero.

Step-by-step explanation:

We use spreadsheets to compare both options.

We have to calculate

future value

present value

Option A

Net Present Value (NPV) 10534,87

Future value  12.547

Option B

Net Present Value (NPV) 10692,05  is higher than option A

Future value  12.734 is higher than option A

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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]

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)

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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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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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

Answer:

2, 3

Step-by-step explanation:

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