2. Use what you know about equivalent expressions to write an expression equivalent to the
one given.
a. 5n
b. 2n+2
c. 4n-4
d. 3n+2n + n

Answer:

-0.5

-1/2

Let's do... 8/16

First, divide 8 by 16

8/16 = -0.5

so the answer should be: -0.5

Well, let's see how to do it:

Remove the decimal point and put -5 over 10→ -5/10 (add as many zeros as necessary after the 1)

Now simplify to the lowest terms: -5/10 simplifies to -1/2

To remove any confusion, 1/2 is the same as 8/16, 8 is half of 16, and 1 is half of 2.

Hope this helped!

Ratio of selling price to the cost price =17/20

Cost price is the amount paid while purchasing an assets or manufacturing product. On the other hand, selling price is the amount that is earned by the seller when products or assets are sold.

What is the ratio of the selling price to the cost price?

given, a trader made a loss of 15% when an article was sold.

let, the purchasing price of article = $ Y

as he made a loss of 15%

so the amount of loss = Y 15/ 100

Now, the selling price will be Y - Y15/100

selling price = (100Y -15Y) /100 = 85Y/100

selling price = 17Y/20

ratio of the selling price to the cost price = 17Y/100/Y = 17/20

ratio = 17/20

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Answer: To write the equation of the line that is parallel to the graph of y = x – 4 and passes through the point (-2, 3), we can use the fact that parallel lines have the same slope.

The slope of y = x – 4 is 1, since the coefficient of x is 1.

So, we can write the equation of the line in the slope-intercept form y = mx + b, where m = 1 and b is the y-intercept. To find the y-intercept, we can substitute the point (-2, 3) into the equation:

y = 1x + b

3 = 1(-2) + b

3 = -2 + b

b = 5

so the equation of the line in slope-intercept form is y = 1x + 5

To write the equation of the line that is parallel to the graph of y + 2x = 4 and passes through the point (-1, 2), we can use the fact that parallel lines have the same slope.

The slope of the equation y + 2x = 4 is -1/2, since the coefficient of x is -1/2.

So, we can write the equation of the line in the slope-intercept form y = mx + b, where m = -1/2 and b is the y-intercept. To find the y-intercept, we can substitute the point (-1, 2) into the equation:

y = -1/2 x + b

2 = -1/2(-1) + b

2 = -1/2 + b

b = 5/2

so the equation of the line in slope-intercept form is y = -1/2x + 5/2

It's important to note that the slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

The linear function that models the amount left is a = 84 - 16d where 16 is the slope of the equation. At the fourth day, there isn't enough money left for the shirt.

A linear function is a type of mathematical function in which the output is directly proportional to the input. A linear function can be expressed by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

To solve this problem, we have to write a linear function that shows how much is spent in d number of days.

a)

The linear function is

a = 84 - 16d

a = Total amount left

d = number of days.

b)

The cost of the shirt is $38, at the end of the fourth day, we would have

a = 84 - 16(4)

a = 84 - 64

a = 20

The money left isn't enough

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The equation for a homogeneous differential in its general solution.

= (x² + 4y²)³x² = c.

When both f(x,y) and g(x,y) have the same degree, a differential equation of the form f(x,y)dy = g(x,y)dx is referred to as a homogeneous differential equation. For k 0, a function of the type F(x,y) that can be expressed in the form kn F(x,y) is referred to as a homogeneous function with degree n.

If M(x,y) and N(x,y) are both homogeneous functions that have the same degree, then a first-order differential equation is said to be homogeneous. is homogeneous since it contains homogeneous functions that have the same degree, M(x,y) = x 2 - y 2, and N(x,y) = xy (namely, 2).

[tex]$\mathrm{v}+\mathrm{x} \frac{\mathrm{dv}}{\mathrm{dx}}=-\left(\frac{\mathrm{x}^2+\mathrm{v}^2 \mathrm{x}^2}{3 \mathrm{xv} \mathrm{x}}\right)=-\left(\frac{\mathrm{x}^2\left(1+\mathrm{v}^2\right)}{3 \mathrm{x}^2 \mathrm{v}}\right)$[/tex]

[tex]$v+x \frac{d v}{d x}=-\left(\frac{1+v^2}{3 v}\right)$[/tex]

[tex]$x \frac{d v}{d x}=\frac{-1-v^2}{3 v}-v=\frac{-1-v^2-3 v^2}{3 v}=\frac{-1-4 v^2}{3 v}$[/tex]

[tex]$\frac{3}{8} \int \frac{8 v}{1+4 v^2} d v=-\int \frac{d x}{x}$[/tex]

Integrating we have [tex]$\frac{3}{8} \log \left(1+4 v^2\right)=-\log x+\log c$[/tex]

= 3log(1 + 4v²) + 8 log x = log c

= (1 + 4v²)³.x⁸ = c

= [tex]$\left(1+4 \frac{y^2}{x^2}\right)^3 \cdot x^8=c$[/tex]

= (x² + 4y²)³x² = c.

the general solution of the homogeneous differential equation.

=  (x² + 4y²)³x² = c.

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50 is not a solution of the inequality -3x > -36

a relationship between two expressions or values that are not equal to each other is called 'inequality.

-3x > -36

Now let us check which are all the solutions of the inequality

0>-36 is possible.

Hence 0 is a solution

-3(-22)>-36

66>-36

Hence -22 is a solution

-3(50)>-36

-150<-36

50 is not solution of the inequality.

-33>-36

11 is also solution of the inequality

Hence, 50 is not a solution of the inequality -3x > -36

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The Area Of Regular hexagon that has the radius of 5 units is 65 square units .

The formula to calculate the area of regular hexagon is = [tex]\frac{1}{2} \times a\times P[/tex] ;

where "a" is apothem and "P" is Perimeter .

the number of sides in the hexagon (n) = 6 ;

let the side length of hexagon be (s) = 2x ;

the perimeter is = [tex]n\times s[/tex] = 12x ;

So , the area is = [tex]\frac{1}{2} \times a\times (12x)[/tex] = 6 × a × x ;

the central angle of one triangle in the hexagon is(2θ)  = 60 degree ;

So , θ = 30 degree .

we use the trigonometric ratio to find the value of "a" and "x" by using "r" and "θ" ,

⇒ [tex]\frac{Sin30}{1} =\frac{x}{r}[/tex]  ⇒ [tex]\frac{Sin30}{1} =\frac{x}{5}[/tex]

⇒ [tex]x=5Sin(30) = \frac{5}{2}[/tex] ;

and ⇒ [tex]\frac{Cos30}{1} =\frac{a}{r}[/tex]  ⇒ [tex]\frac{Cos30}{1} =\frac{a}{5}[/tex]

⇒ [tex]a=5Cos(30) = \frac{5\sqrt{3} }{2}[/tex] ;

substituting the values of "a" and "x" in the Area ,

we get ;

Area = 6 × a × x = [tex]6\times (\frac{5\sqrt{3} }{2} )\times(\frac{5}{2} )[/tex] ;

= [tex]\frac{75\sqrt{3} }{2}[/tex] = 64.95 ≈ 65 square units .

Therefore , Area of regular hexagon is ⇒ 65 square units .

The given question is incomplete , the complete question is

How do you find the area of a regular hexagon with only the radius as 5 units ?

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The greatest common factor of the expression 2ax² + 2ax + 2a is 2a.

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,

2ax² + 2ax + 2a

There are three terms.

The greatest common factor in each term is 2a

Now,

2a (x² + x + 1)

Thus,

The expression with the greatest common factor is 2a (x² + x + 1).

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The translation that describe the path of the 8 tile to reach it's final position is given as follows:

(x,y) -> (x + 3, y - 1).

This same translation cannot be used to describe the path of all tiles, as some will move up, some down, some left and some right, but the movement is not the same for all tiles.

There are four translations that are standard, and their rules are defined as follows:

The tiles will be placed in order, meaning that the tile number eight should be the second row and fourth column.

As the tile with the number eight is at the first row and the first column, the movements are given as follows:

Hence the compound translation is given as follows:

(x,y) -> (x + 3, y - 1).

This, however, cannot be used for all the points, as some of them, for example 5 and 6, are already in their final position, while the movement for tile 1 is 2 units up.

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Answer:

6.4 x10^ -4

Step-by-step explanation:

the number has to berween 1 and 9 ao multiply by 10000 and because you went from a small number to a bigger number ,it is a negative power

The train will travel 354.6km in 4hr 45 min.

Step-by-step solution:

GIVEN-

Distance=112km in 1hr and 30min(3/2h)

TO FIND-

Distance in 4hr and 45 min

Let the required distance be x km.

More distance → more time

Therefore the two quantities are directly proportional.

∴Distance=x

Time (in hours)=4hr 45min= 19/4h

[tex]\frac{x1}{y1}[/tex]=[tex]\frac{x2}{y2}[/tex]

⇒

[tex]\frac{112}{x}[/tex]=[tex]\frac{1.5}{19/4}[/tex]

⇒3/2 x= 112×19/4

∴x=354.6km

Hence, the required distance =354.6 km.

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The algebraic expression for the payment of the plan with y dollar surge is A = x/2 + y.

The concept of algebraic expressions is the use of letters or alphabets to represent numerical values without stating their exact meanings. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given that the annual premium plan is x dollars.

The payment is made semi-annually this is represented as follows:

x/2

There is a surplus charge of y, this is written as:

A = x/2 + y

Hence, the algebraic expression for the payment is A = x/2 + y.

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The statements that are true include;

An inequality can be described as a relation with a non-equal comparison between two elements, values, variables, numbers or other algebraic expressions.

Inequalities are mostly used to compare two numbers on the number line on the basis of their size.

It is important to note that the positive values are greater than the negatives .

Also, zero(0) is greater than the negative numbers from the left side of the number line.

Hence,  -1. 5 is less than -0. 5, -0. 5 is less than 0, -2. 5 is less than -2

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Triangle 1 and triangle 2 are concurrent if, Triangle 1 has vertices at (A, B), (C, D), and (E, F), Triangle 2 has vertices at (-A, B), (-C, D), and (-E, F) and are reflected so, option D is correct.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.

Given:

Triangle 1 has vertices at (A, B), (C, D), and (E, F),

Triangle 2 has vertices at (-A, B), (-C, D), and (-E, F).

Triangle 1 is reflected on the y-axis and we get triangle 2,

Both, triangle 1 have the same magnitude of dimension as triangle 2,

Thus, both are concurrent also.

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Answer: D is the correct answer

Step-by-step explanation:

imagine math

Answer:

2.65

Step-by-step explanation:

a^2 + b^2 = c^2 (Pythagorean theorem)

square root of 3 = 1.73205080757

2 x square root of 3 = 3.4

2^2 + 3.4^2 = C^2

4+ 11.6= C^2

The value of m in the given triangle will be 10.39.

According to the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of a right triangle. In other words, a² + b² = c² for the triangle depicted below. The right triangle's legs, a, and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.

where a, b, and c are the base, height, and hypotenuse of the triangle.

Given in the figure there is one big triangle whose height is m and whose hypotenuse is 24 or (18 + 6). let x be the base of the triangle.

From the Pythagorean theorem

x² + m² = 24²

x² = 576 - m²

For another triangle whose base is n and height is 18.

From the Pythagorean theorem

n² + 18² = x².......(1)

from equation (1)

n² + 18² = 576 - m²

n² + m² = 576 - 324

n² + m² = 252........(2)

For another triangle whose base is 5 and height is n.

From the Pythagorean theorem

n² + 6² = m²

n² - m² = 36.....(3)

From comparing equations 2 and 3

n² + m² - (n² - m²) = 252-36

2m² = 216

m² = 108

m = ± 10.39

since the length can not be n negative.

m = 10.39

therefore the value of m in the given triangle is 10.39.

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Answer:

8v+3c

Step-by-step explanation:

Given 2v+6v+3c

1) Add all like terms

-Since both 2 and 6 have "v" and the two together

2) 8v+3c

Answer: 8v+3c

Hope this helps :)

The surface area of the composite figure is 217.28yd²

The volume of the composite figure is 141.12yd³

A composite figure can be defines as a shape created with two or more basic shapes.

The composite figure consist of a triangular prism and cuboid

The surface area of the cuboid =2(lh+lb+bh)

= 2 ( 4.8×2.8 + 8× 2.8 + 4.8×8)

= 2( 13.44+22.40+38.4)

= 2(74.24)

= 148.48yd²

The surface area of the prism = 2B+ph

Base area = 1/2 × 3×8 = 12

The perimeter = 3+8+5 = 16

SA = 2×12+ 16×2.8

SA = 24+44.8

SA = 68.8yd²

the surface area of the composite figure = 148.48+68.8 = 217.28yd²

The volume of the cuboid = 4.8× 2.8 × 8 = 107.52yd³

Volume of the prism = base area × height = 12×2.8 = 33.6yd³

Therefore the volume of composite figure= 107.52+33.6 = 141.12 yd³

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Answer:

[tex](x, y)=\{(-2,-1), (3,14)\}[/tex]

Step-by-step explanation:

[tex]y=x^2+2x-1, y=3x+5 \\ \\ \implies x^2+2x-1=3x+5 \\ \\ x^2-x-6=0 \\ \\ (x-3)(x+2)=0 \\ \\ x=-2, 3 \\ \\ x=-2 \implies y=-1 \\ \\ x=3 \implies y=14 \\ \\ \therefore (x, y)=\{(-2,-1), (3,14)\}[/tex]

Answer: 45cm^2

Step-by-step explanation:

The area of the parallelogram is the base x the height.

So in this question, you multiply 5 (which is the base) by 9, (which is the height).

Answer:

A = 45 cm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 5 and h = 9 , then

A = 5 × 9 = 45 cm²

On solving the provided question, we can say that - here it the given inequality equation [tex]36x - 72 > 24x + 36 = > 12x > 108 = > x > 9[/tex]

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

[tex]4(9x - 18) > > 3(8x + 12)\\36x - 72 > 24x + 36\\12x > 108\\x > 9[/tex]

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Answer: men: 120 men, 310 women, and 170 children

600*0.2=120

600*0.35=310

600-120-310=170

Ryosuke drove his friend 24 miles, which used 1.14 gallons of gas. The total cost of the gas was $4.64, calculated by multiplying 1.14 gallons by the price of one gallon which was $4.05.

1. Calculate the number of miles driven: Subtract the odometer reading when Ryosuke picked his friend up (74,568) from the odometer reading when he dropped his friend off (74,592). This gives us the total number of miles driven (24).

2. Calculate the number of gallons used: Divide the total number of miles driven (24) by the car's gas mileage (28). This gives us the number of gallons used (1.14).

3. Calculate the cost of the gas: Multiply the number of gallons used (1.14) by the price of one gallon of gas ($4.05). This gives us the cost of the gas used ($4.64).

28 miles

= [tex]$\frac{74,592-74,568}{28}$[/tex]

= 1.14 gallons

Cost of gas

= 1.14 gallons x[tex]$\$4.05$[/tex]

= [tex]$\$4.64$[/tex]

1. 74,592 - 74,568 = 24

2. 24 / 28 = 1.14

3. 1.14 x $4.05 = $4.64

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The total available number of pizza is 576 and yes, they are falsely advertising their choices

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

The number of pizza is the products of the individual numbers above

So, we have the following representation

Pizza = 3 * 3 * 4 * 8 * 2

Evaluate the products

This gives

Pizza = 576

The number 576 is less than 150,000 (the number of different pizza advertised)

Since this is incorrect, then they are they falsely advertising their choices

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The 50th derivative of y=cos2x is [tex]& y^{50}(x)=-2^{50} \cos (2 x)[/tex].

Consider y=cos 2x

Derivative: The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

Finding the nth derivative means to take a few derivatives (1st, 2nd, 3rd…) and look for a pattern. If one exists, then you have a formula for the nth derivative. To find the nth derivative, find the first few derivatives to identify the pattern.  Apply the usual rules of differentiation to a function, then find each successive derivative to arrive at the nth.

The first derivative is

[tex]$$\begin{aligned}& y^{\prime}=-2 \sin 2 x \\& =-2\left[\cos \left(2 x+\frac{\pi}{2}\right)\right]\end{aligned}$$[/tex]

The second derivative is

[tex]$$y^{\prime \prime}=-2^2\left[\cos \left(2 x+2 \cdot \frac{\pi}{2}\right)\right]$$[/tex]

Similarly, we get the [tex]n^{th}[/tex] derivative

[tex]$$y^n(x)=-\left[2^n \cos \left(2 x+n \frac{\pi}{2}\right)\right]$$[/tex]

When n=50

[tex]$$\begin{aligned}& y^{50}(x)=-\left[2^{50} \cos \left(2 x+50 \cdot \frac{\pi}{2}\right)\right] \\& y^{50}(x)=-2^{50} \cos (2 x)\end{aligned}$$[/tex]

Therefore, the [tex]50^{th}[/tex] derivative of y = cos 2x is [tex]& y^{50}(x)=-2^{50} \cos (2 x)[/tex].

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The tangent line approximation for f(-1.2) is defined as follows:

f(-1.2) = -5.

The point-slope format for the equation of the tangent line is given as follows:

y - y* = m(x - x*).

In which the parameters are given as follows:

The derivative for this problem is given as follows:

f'(x) = 4x - 1.

f(-1)= -6, hence the coordinates of the point are given as follows:

x* = -1, y* = -6.

Hence the slope is given as follows:

m = f'(-1).

m = 4(-1) - 1

m = -5.

Thus the tangent line is defined as follows:

y + 6 = -5(x + 1).

y = -5(x + 1) - 6.

At x = -1.2, the approximation is calculated as follows:

y = -5(-1.2 + 1) - 6

y = -5.

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Answer:

(f - g)(x) = 2x + 7

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x + 5 - (x - 2) ← distribute parenthesis by - 1

= 3x + 5 - x + 2 ← collect like terms

= 2x + 7

The graph that shows the solution to the inequality, would be Graph A.

The inequality is :

x - 4 ≤ - 1

What this means is that all values of x should be able to deduct 4 such that the result would be less than or equal to - 1.

This means that the largest number that x can take is :
x - 4 = - 1

x = -1 + 4

x = 3

x can be a maximum of 3 and then all other x values have to be less than 3. This is shown as a solution in the first graph.

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The new coordinate pair of A' is (0,4) when dilated by a scale factor of 1/2

Given,

The coordinates A(0,8),and C(-4,-6) are dilated by a scale factor of 1/2

let the scale factor be k.

What are coordinates?

coordinates can be defined as the pair of numbers which are used to determine the position of a given point.

k = 1/2

and coordinates A(0,8) and C(-4,-6)

the rule of dilation

If a point (x,y) dilated for the scale factor of 'k', we do get image as (kx,ky)

Using this concept, we know scale factor is  , we could get image as

A' (0*1/2 , 8*1/2)

A' ( 0 , 4)

And for C(-4,-6)

C'(-4*1/2 , -6*1/2)

C' (-2,-3)

Hence, The new coordinate pair of A' is (0,4) when dilated by a scale factor of 1/2 .

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Answer:

Experian, Equifax, and/or Transunion

Step-by-step explanation:

None