3. Your friend Juan says the perimeter of the rectangle can be represented by the expression,
8x +4. Determine if the expression you wrote in #2 and the expression Juan wrote are
equivalent. Justify your answer.

Answer:

(5, 4 )

Step-by-step explanation:

under a counter- clockwise about the origin of 180°

a point (x, y ) → (- x, - y ) , then

(- 5, - 4 ) → (- (- 5), - (- 4) ) → (5, 4 )

The combination of samples is 80% likely to contain no defective televisions.

A combination appears to be a statistical technique for estimating the number of potential configurations in a collection of objects where the sequence of anything like the option is immaterial. Organize the elements in every order to choose. Permutations & combinations are commonly misunderstood.

Evaluate just non-faulty TVs to identify the same amount of ways in which the picked TVs are not defective. Because there are two faulty televisions out of 16, the amount of non-faulty sets is two.

= 10 - 2

= 8

Two non-defective televisions must be picked from a pool of twelve. There are several ways to accomplish this:

= ((10 × 9 × 8 × 7 ....) ÷ ((2 × 1) × (8 × 7 × 6...))  = 8!/2!((10- 2)!) = 80.

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Answer:

62.18

Step-by-step explanation:

The new value =

63 - The value of the percentage decrease =

63 - (1.3% × 63) =

63 - 1.3% × 63 =

(1 - 1.3%) × 63 =

(100% - 1.3%) × 63 =

98.7% × 63 =

98.7 ÷ 100 × 63 =

98.7 × 63 ÷ 100 =

6,218.1 ÷ 100 =

62.181 ≈

62.18

1/5/2023

7:00PM

The measure of m∠6 is 123° and is equal to m∠1 because there are corresponding angles formed by parallel lines cut by a transversal.

Corresponding angles are the angles that are formed when two parallel lines are cut or intersected by the transversal and they are equal.

The angles 1, 2, 3, 4, 5, 6, 7, and 8 all lie on a transversal line that cuts the parallel lines, hence m∠1 and m∠6 are corresponding angles are they are equal.

so;

m∠1 = (15x + 3)° = m∠6 = (10x + 43)°

collect like terms, we have;

15x - 10x = 43° - 3°

5x = 40°

divide through by 5

x = 40°/5

x = 8

m∠6 = [10(8) + 43]°

m∠6 = (80 + 43)°

m∠6 = 123°

Therefore, the corresponding angle m∠6 have the measure of 123°.

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Fraction 10/16 is not equivalent to 3/4 among the other given fractions.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given some fractions.9/12, 6/8, 18/24, 10/16, and 15/20.

Simplifying this given fraction by taking the common term out

[tex]\frac{9}{12}, \frac{6}{8} , \frac{18}{24} , \frac{10}{16} , \frac{15}{20}[/tex]

[tex]\frac{9/3}{1/3}, \frac{6/2}{8/2} , \frac{18/6}{24/6} , \frac{10/2}{16/2} , \frac{15/5}{20/5}[/tex]

Thus we will get

3/4, 3/4, 3/4, 5/8, 3/4

Therefore, Among the other fractions listed, fraction 10/16 is not equal to fraction 3/4.

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The equation of the line that passes through the two points (3,1) and (9,5) is y= (5-1)/(9-3) * (x-3) + 1.

y - y1 = (y2 - y1)/(x2 - x1) * (x - x1)

y - 1 = (5 - 1)/(9 - 3) * (x - 3)

y - 1 = 4/6 * (x - 3)

y = 4/6 x + 5/3

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The equation to find the amount deposited each month is 160 + 12m = 400.

The amount deposited each month is $20.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Amount in account = $160

Amount at the end of the year = $400

Now,

There are 12 months in a year.

The amount deposited each month = m

Now,

160 + 12m = 400

Solve for m.

12m = 400 - 160

12m = 240

m = 20

Thus,

The equation is 160 + 12m = 400.

The amount deposited each month is $20.

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The length of the CD is 66.

Similar triangles are triangles that have the same shape but can be different sizes. Two triangles are similar if and only if the corresponding angles are congruent and the corresponding side lengths are in proportion. The symbol for similarity is '~' . Similarity can be determined by using the Angle-Angle (AA) similarity, the Side-Angle-Side (SAS) similarity, or the Side-Side-Side (SSS) similarity. If two triangles are similar, the ratio of the corresponding side lengths is called the scale factor. If this scale factor is k, then the ratio of any pair of corresponding sides is k.

In ΔBCD and ΔEFD,

side BC ≈ side EF            ....(given E is on CD)

∠ BCD ≅ ∠EFD                .....(given)

side CD ≈ side FD           ......( given F is on BD)

∴ΔBCD ≈ ΔEFD               ....(By Side Angle Side criteria)

[tex]\frac{BC}{EF} = \frac{CD}{FD}[/tex]

∴ [tex]\frac{77}{35} = \frac{CD}{30}[/tex]

∴ CD = 77 × 30/ 35

∴ CD = 66

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The two expressions which are similar to the given expressions are 45 (0.5x - 1)  and 22.5 ( x - 2 ) .

What is linear Equation ?

linear equation can be defined as the equation in which the highest degree is one.

Given expression,

15(1.5x-3)

expression 15(1.5x-3) can also written as 15 (15/10 -3)

that is

15 ( 3/2 - 3 )

15 * 3 (1/2 x -1 )

45 (0.5x - 1)

And

45 ( 0.5x -1 )

45 (x-2/2)

22.5 ( x - 2 )

Hence , The two expressions which are similar to the given expressions are 45 (0.5x - 1)  and 22.5 ( x - 2 ) .

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The area of shaded figure is  272 square units  

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

Area of trapezium = (1/2)(a+b)*h

a=18 , b= 34, h - 16

So,  area of trapezium = (1/2)(18+34)*16 =  52*8 =  416 square units

Area of unshaded triangle = (1/2) * base*height

                                            = (1/2) * 18*16 = 18*8 = 144 square units

Area of shaded figure = area of  trapezium - Area of unshaded triangle

                                     = 416 - 144

                                     = 272 square units  

So, the Area of shaded figure =  272 square units  

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To find the third side of an inequality of a triangle, you must first use the Triangle Inequality Theorem.

This theorem states that for any triangle, the sum of any two sides of the triangle must be greater than the third side. This means that in order to find the length of the third side, you must subtract the sum of the two known sides from the smaller of the two sides, then the length of the third side will be equal to the difference between these two numbers. For example, if two sides of a triangle have lengths of 4 and 3, the third side must be greater than 1 (4 + 3 = 7 and 4 - 3 = 1). Therefore, the length of the third side must be greater than 1.

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Answer: (D) --> 4 2/3

Step-by-step explanation:

1st --> Turn the problem into an improper fraction using the reciprocal

2nd --> Turn the improper fraction into a mixed answer

The AAS Triangle Congruence Theorem states that if two angles and the side between them of one triangle are equal to two angles and the side between them of another triangle, then the two triangles are congruent.

The AAS Triangle Congruence Theorem states that if two angles and the side between them of one triangle are equal to the two angles and the side between them of another triangle, then the two triangles are congruent. This theorem is an important tool in geometry that can be used to determine if two triangles are congruent and to find missing side lengths or angles. This theorem is based on the idea that if two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles must be congruent. This is because the third side of the triangle, and the remaining angles must also be equal in order for the triangles to be congruent. Therefore, the AAS Triangle Congruence Theorem can be used to determine if two triangles are congruent, and to find missing side lengths or angles.

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To determine whether two functions are inverses of each other, we can use function composition to check if the composition of the two functions is the identity function. The identity function is a function that always returns its input.

What does the term "inverse function" mean?

A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the inverse of a function f. (y). Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.

The composition of two functions f and g is denoted by f(g(x)) or f o g.

If f(g(x)) = x and g(f(x)) = x for all x in the domain of the functions, then f and g are inverse functions.

In this case,

f(g(x)) = f((x-2)/5) = 5((x-2)/5) + 2 = x

so, f and g are inverse functions.

and also

g(f(x)) = g(5x+2) = (5x+2-2)/5 = x

so, f and g are inverse functions.

Therefore the functions f(x)= 5x+2 and g(x) = x-2/5 are inverses of each other.

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For right triangle LMN, the required ratio equivalent to tan(L) is 5 /13.

In this case, in order to find the ratio equivalent to tan (L).

tan(L) = opposite / adjacent side

tan(L) = NM /LN

Here given

NM = 5cm

LN = 13cm

We already know that tan(L) = perpendicular / adjacent

from given,

tan (L) = 5 / 13

As a result, the required ratio for triangle LMN is 5/13.

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In Grade 6, students typically learn about angles and their properties. Some of the key concepts that students may study include:

These are some of the key concepts that students may learn about angles in Grade 6, but the specific curriculum can vary depending on the school district and state.

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If 8x ≤ g(x) ≤ 4x4 − 4x2 + 8 for all x,  x will be evaluated as lim x→1 g(x), 1 is 8.

To evaluate the limit of g(x) as x approaches 1, we must first examine the given inequality. It states that if 8x is less than or equal to g(x), and g(x) is less than or equal to 4x4 - 4x2 + 8, then this is true for all x.

Calculating the limit of g(x) as x approaches 1, we start by substituting x = 1 into the given inequality. This gives us 8(1) ≤ g(1) ≤ 4(1)4 - 4(1)2 + 8. Simplifying, this gives us 8 ≤ g(1) ≤ 8, so g(1) must be equal to 8.

Therefore, the limit of g(x) as x approaches 1 is 8.

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The number of toothpicks Arun could have used to make his bigger square than Jitesh's 8-toothpick square was B. 16.

We are told that Jitesh made a square using 8 toothpicks.

The toothpicks have the same length as Arun's.  We also know that Arun made a bigger square than Jitesh.

The same number of toothpicks must be on the four sides to make a square.  Otherwise, it cannot form a perfect square.

Thus, it is unlikely that 14 toothpicks can make a square because 14 is not evenly divisible by 4, just like 22.  However, 16 is evenly divisible by 4 and forms a perfect square of 4, giving each side an equal size.

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The length of diagonal KM of square is 11.31 inch.

What is square?

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

A square has four equal sides, four vertices, and is a closed, two-dimensional shape. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.

Given:

The Square JKLM, the area of JKLM is 64 sq in.

We have to find the length of diagonal KM.

Since,

Area of square = (side)^2

64 = (side)^2

Side = 8

Length of each side of square is 8 in.

By using the Pythagorean theorem,

(KL)^2 + (LM)^2 = (KM)^2

       8^2 + 8^2 = (KM)^2

          64 + 64 = (KM)^2

                 128 = (KM)^2

                 KM = 11.31

Hence, the length of diagonal KM of square is 11.31 inch.

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Its speed is closest to 414m/s

given that

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in metres (m), centimetres (cm), or millimetres (mm) (mm). The wavelength is more frequently described in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (UV), and gamma radiation ().

Frequency, which is defined as the quantity of wave cycles per second, and wavelength have an inverse relationship. The wavelength of the signal decreases with increasing signal frequency.

a wave has a wavelength = 25.4cm

a frequency = 1.63khz

now, we need to find speed of the wave

speed = wavelength × frequency

speed = 25.4 × 16.3

           = 414m/s

speed = 414m/s

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The function is 130/2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

According to question,

[tex]\int\limits^9_0 {f(x)} \, dx \\ \int\limits^7_0 {f(x)} \, dx+\int\limits^9_7 {f(x)} \, dx\\ \int\limits^7_0 {7} \, dx + \int\limits^9_7 {x} \, dx\\ (7x)^{7} _{0} + (\frac{x^{2} }{2})^{9} _{7}[/tex]

7x7 - 7x0 + 81/4 - 49/4

49 + 32/2

130/2

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Answer:

u = 2

Step-by-step explanation:

The slope of a line between points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is equal to [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], so, given our slope of 8, we need to find the first y-coordinate:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\8=\frac{10-u}{3-2}\\\\8=\frac{10-u}{1}\\\\8=10-u\\\\-2=-u\\\\2=u[/tex]

Hence, the value of "u" is 2.

Answer:

To find the value of u, you can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

In this case, (x1, y1) = (2, u) and (x2, y2) = (3, 10). Plugging these values into the formula gives:

slope = (10 - u) / (3 - 2)

Simplifying this expression gives:

slope = (10 - u) / 1

Since the slope is 8, we can set this expression equal to 8 and solve for u:

8 = (10 - u) / 1

8 = 10 - u

u = 10 - 8

u = 2

Therefore, the value of u is 2.

Certainly! The slope of a line is a measure of how steep the line is. It is calculated by finding the ratio of the difference in the y-coordinates of two points on the line to the difference in the x-coordinates of those same two points. For example, in the line you gave, the two points are (2, u) and (3, 10). The difference in the x-coordinates of these two points is 3 - 2 = 1, and the difference in the y-coordinates is 10 - u. The slope of the line is then (10 - u) / 1. We know that the slope of this line is 8, so we can set the expression for the slope equal to 8 and solve for u. This gives us the value of u, which is 2. I hope this helps! Let me know if you have any questions.

Answer:

.5

Step-by-step explanation:

2.5/5 = .5

Answer:

After a reflection in the y-axis, the quadratic function would have the following formula:

y = -(2x² - 8x + 3)

= -2x² + 8x - 3

Therefore, the answer is option D: y=2x² +8x-3.

Step-by-step explanation:

The area of a page of the book, "flowers of the four seasons". would be = 5.6× 10^-⁷ m²

To calculate the area of a book, the length and weight of the book must be determined which is then multiplied to give it's area in square metres or mm².

The number of pages that makes up the book, "flowers of the four seasons". = 22 pages.

Since the book has a square shape, the length and width is the same = 0.75 mm

To convert 0.75 mm to meter, divide by 1000= 0.00075m

The area of a page = Length× width = 0.00075×0.00075

= 0.0000005625= 5.6× 10^-⁷ m²

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The population grow fastest in the 5th decade (1950) because that is the highest point in the graph

A graph is a visual representation of a set of data or a mathematical function. It is a way to represent data or relationships between different variables in a clear and concise way.

There are several types of graphs, including line graphs, bar graphs, scatter plots, and pie charts. Each type of graph is used to represent different types of data and convey different types of information.

Examining the given graph:

The population grow fastest in the 5th decade (1950)

You will notice that the peak point (highest point) on the graph with a population of 45 thousand is in 1950 i.e. 5th decade (Check the attached image)

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The Seed, where the range is 100, is the initial value of an algorithm used to produce a set of numbers.

Difference between the greatest and lowest value is referred to as the range. To get the range, find the variable's greatest observed value and deduct its lowest observed value. The data points in the center of the distribution are not taken into account; the range only considers these two values. Between the lowest and greatest values, there is a range of values. Values at each end of the range make up the range. Use the data set 4, 6, 10, 15, 18 as an example. Its range is 18-4 = 14, and its minimum and maximum values are 4, 4, and 4.

The term "seed" refers to the initial value of an algorithm used to produce a set of integers.

[tex]20, 25, 30, 45, 55, 90, 110,115,120[/tex]

Range = 120 - 20 = 100

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On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

the sum of the areas of the circle, the triangle, and the square.

Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.

A = 210-123 = 87 sq unit

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Answer:

Area of a Trapezoid = [tex]136cm^{2}[/tex]

Step-by-step explanation:

Area of a Trapezoid = [tex]\frac{1}{2} X(a+b)h[/tex]

Area of a Trapezoid = [tex]\frac{1}{2} X(12+22)8[/tex]

Area of a Trapezoid = [tex]\frac{1}{2} X34X8[/tex]

Area of a Trapezoid = [tex]136cm^{2}[/tex]

Function that represents the expression is f (y) = $150 + $35Y

In mathematics, function is an expression that creates a relationship between an independent variable and a dependent variable.

The set of values of independent variable is called input and the set of values for dependent variable is called output.

given, bus rental fee = $150

fee for private group tour per person = $35

let, the amount of people included in this tour = Y

total fee for private group tour for Y people= $35Y

Therefore, the total charge for the Brazil tour = bus rental fee + fee for private group

total charge = $150 + $35Y

if total charge for Brazil tour can be modelled by a function

then function f (y) = $150 + $35Y

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