The temperatures of two cities were measured at the same time. The
temperature in city A was 60 degrees and rose at a constant rate of 2
degrees per hour.
The temperature in city B was 40 degrees and rose at a constant rate
of 10 degrees per hour.
Enter the number of hours it took for the temperature to be the same in
both cities.

The values of x are [tex]\frac{\sqrt{31} + 2 }{3} , \frac{-\sqrt{31} + 2 }{3}[/tex] and y are [tex]\frac{19\sqrt{31} + 146 }{9} , \frac{-19\sqrt{31} + 146 }{9}[/tex].

Given Equations,

4x² + x - y = 0 ...(1)

-x² - 5x + y - 9 = 0

The above equation can be written as:

-x² - 5x + y = 9 ...(2)

Using the elimination method, the second term of both equations can be eliminated by adding the equations.

Therefore,

4x² +  x  - y = 0

-x² - 5x + y = 9

_____________

3x² - 4x = 9

Using the Completing the square method,

3x² - 4x = 9

Divide the equation by 3 on both sides,

[tex]x^{2} - \frac{4}{3}x = 3[/tex]

[tex]x^{2} - \frac{4}{3}x + (\frac{2}{3}) ^{2} = 3 + (\frac{2}{3}) ^{2[/tex]

[tex]( x - \frac{2}{3})^{2} = 3 + \frac{4}{9}[/tex]

[tex]( x - \frac{2}{3})^{2} = \frac{31}{9}[/tex]

[tex]( x - \frac{2}{3}) = \sqrt{\frac{31}{9}}[/tex]

[tex]x = \frac{\sqrt{31} }{3} + \frac{2}{3} , - \frac{\sqrt{31} }{3} + \frac{2}{3}[/tex]

[tex]x = \frac{\sqrt{31} + 2 }{3} , \frac{-\sqrt{31} + 2 }{3}[/tex]

Now, Put the value of x  in equation (1), we get the value of y.

4x² + x - y = 0

y = 4x² + x

[tex]y = 4( \frac{\sqrt{31} + 2 }{3})^{2} + \frac{\sqrt{31} + 2 }{3} , 4( \frac{-\sqrt{31} + 2 }{3})^{2} + \frac{-\sqrt{31} + 2 }{3}[/tex]

[tex]y = \frac{19\sqrt{31} + 146 }{9} , \frac{-19\sqrt{31} + 146 }{9}[/tex]

Therefore,

the values of x are [tex]\frac{\sqrt{31} + 2 }{3} , \frac{-\sqrt{31} + 2 }{3}[/tex] and y are [tex]\frac{19\sqrt{31} + 146 }{9} , \frac{-19\sqrt{31} + 146 }{9}[/tex].

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given steps are :

[tex]\qquad \sf  \dashrightarrow \: 144 {x}^{2} - 100[/tex]

[tex]\qquad \sf  \dashrightarrow \: (12x + 10)(12x - 10)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2(6x + 5)(6x - 5)[/tex]

The error is in third step ~

Correct method :

[tex]\qquad \sf  \dashrightarrow \: (12x + 10)(12x - 10)[/tex]

[ take 2 common out of both ]

[tex]\qquad \sf  \dashrightarrow \:2 (6x + 5) \sdot2(6x - 5)[/tex]

[ 2 times 2 will be 4 ]

[tex]\qquad \sf  \dashrightarrow \: 4(6x +5 )(6x - 5)[/tex]

A tables in math is the multiplication table that includes the list of multiples of natural numbers.

Students learn the multiples of a number in math table, which is the foundation of the subject. Multiplication tables have been taught to us since we were in primary school. We may swiftly solve issues involving multiplication with the aid of these math tables. Thus, it is essential for pupils to memorize the math tables 1 through 20, enabling them to complete challenging calculations with ease.

Understanding mathematics requires the use of math tables. It is essential that the pupils have a firm grasp of math tables because failing to do so would make it difficult for them to comprehend other areas of mathematics. Students are likely to struggle with fundamental math concepts like decimals, percentages, fractions, ratios, etc. without even a basic understanding of math tables. Once you have learned these multiplication tables, you will remember them for the rest of your life.

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The domain and range of the function y = 3x + 2 is all real numbers

3. Domain: Real Numbers, Range: Real Numbers, Function: y = x

4. Domain: Real Numbers, Range: Real Numbers, Function: y = x^2

5. Domain: Real Numbers, Range: Real Numbers, Function: y = x^3

6. Domain: Real Numbers, Range: Real Numbers, Function: y = x^4

7. Domain: Real Numbers, Range: Real Numbers, Function: y = x^5

8. Domain: Real Numbers, Range: Real Numbers, Function: y = x^6

The domain and range of the function y = 3x + 2 is all real numbers

the complete question is :

relations domain range and functions 3-8

What is the domain and range of the function y = 3x + 2?

Domain: Real Numbers, Range: Real Numbers

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Yes, number 2 and number 3 represents they are prime number as the number has only two factors one and the number itself.

As given in the question,

Given numbers are equal to :

2 and 3.

Prime numbers are those number which has only two factors one and the number itself.

Prime number does not get exactly divided by any other number except itself and one.

Factors of 2 are as follow :

1 and 2

Factors of 3 are as follow :

1 and 3

Therefore, number 2 and number 3 are considered a prime numbers as both the numbers has only two factors one and the number itself.

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Answer:

Let x be the amount of currency deposited

The checks deposited were 2x

The total deposit is x+2x = 3*x = 793

x = 793/3 = $264

So, Alicia deposited $264 in currency.

For polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) after dilation the vertices will be

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem, for r = 1/4 we have

preimage                                     image

A (-4, 6)   → (1/4 * -4, 1/4 * 6) →   A' (-1, 3/2)

B (−2, 2)   → (1/4 * -2, 1/4 * 2) →  B' (-1/2, 1/2)

C (4, −2)  → (1/4 * 4, 1/4 * -2) →   C' (1, -1/2)

D (4, 4)   → (1/4 * 4, 1/4 * 4)   →  D' (1, 1)

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Answer:

Third Answer Choice....A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

Step-by-step explanation:

1/4 = 0.25

Multiply by every number

A' = ( -1, 1.5 )
B' = ( -0.5, 0.5 )
C' = ( 1, -0.5)
D' = (1, 1)

If it says its wrong i dont even know whys that, because this is the only way i know that everyone can solve easily

The diagram's representation of the subtraction sign between the models is 6 + 3c.

Multiplying, dividing, adding, and removing are all possible in mathematics. As an example, consider the following expression: Mathematical operation, expression, and number The elements that make up a mathematical expression include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) One can contrast two expressions or sentences. The terms "expression" or "algebraic expression" refer to any mathematical statement that has variables, numbers, and an arithmetic operation between them. For instance, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m from the given expression, all of which are separated by the arithmetic sign +.

given

The subtraction symbol between the models is depicted in the diagram.

4 + 2c + 2 + c = 6 + 3c

6 + 3c

The diagram's representation of the subtraction sign between the models is 6 + 3c.

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Answer:

D. 28 units

Step-by-step explanation:

Add up all the units on each side

Going clockwise starting from the top:

5, 5, 1, 2, 3, 1, 3, 8

Add them all together

5 + 5 + 1 + 2 + 3 + 1 + 3 + 8 = 28

Answer:

The solution is [tex]x=0.3[/tex]

Step-by-step explanation:

[tex]-0.4x-4.15=x-1.6-2.97[/tex]

Subtract [tex]2.97[/tex] from [tex]-1.6[/tex].

[tex]-0.4x-4.15=x-4.57[/tex]

Subtract [tex]x[/tex] from both sides of the equation.

[tex]-1.4x-4.15=-4.57[/tex]

Add [tex]4.15[/tex] to both sides of the equation.

[tex]-1.4x=-0.42[/tex]

Divide both sides of the equation by [tex]-1.4[/tex].

[tex]x=\frac{-0.42}{-1.4}[/tex]

[tex]x=0.3[/tex]

Answer: $270

Step-by-step explanation:

you multiply 10.00×9= 90 and then 15.00×10=150 then i took the answer out of both problems and added them. 150+90=240 then i took 240 + 30 = 270

Answer:

c=71

Step-by-step explanation:

852=12c

852=12x71

Answer:

[tex] \sf \: c = 71[/tex]

Step-by-step explanation:

Given equation,

→ 852 = 12c

Now the value of c will be,

→ 852 = 12c

→ 12c = 852

→ c = 852 ÷ 12

→ [ c = 71 ]

Hence, the value of c is 71.

The range of pixel values in digital images is typically 0-255 because it corresponds to the number of bits used to represent each pixel. Most image file formats use 8 bits per color channel (red, green, and blue) to represent each pixel, and 8 bits can store a maximum of [tex]2^8[/tex] = 256 different values, with one of the values being reserved for transparency.

When working with 8-bit images, each color channel can take on one of 256 different values, from 0 to 255. This is known as an 8-bit color depth. Each pixel in the image is represented by a combination of red, green, and blue values, so the total number of possible colors is 256 x 256 x 256 = 16,777,216.

The use of 8-bit color depth allows for a wide range of colors to be represented in an image, while also being small enough to be easily stored and transmitted.

Also, it's worth mentioning that with the development of technology, the use of high-bit color-depth images has become more common in the field of photography, digital art, and video, where 16-bit and 32-bit color depths are frequently used.

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Answer:

a=6, b=59, c=28

Step-by-step explanation:

48/a+9=17       b-10/7=7             0.25c-5=2

48/a+9-9=17-9 7 (b-10/7) =7(7)    0.25c-5+5=2+5

48/a=8             10+ b-10=49+10   0.25c=7

a(48/a) = a (8)        b=59                 0.25c/0.25=7/0.25

48=8a                                            c=28

a=6

Answer:

1-Pythagorean Theorem

2-Area

3-Perimeter

4-Pythagorean Triple

5-Hypotenuse

6-Pythagorean Theorem Converse

7-Pythagorean Theorem

8-Legs

The Pythagorean Theorem is a mathematical formula used to find the length of the missing side of a right triangle. It states that the sum of the squares of the lengths of the two shorter sides (known as the legs) of the triangle is equal to the square of the length of the longest side (the hypotenuse).

The area of a space refers to the amount of two-dimensional space that it occupies. For example, the area of a rectangle can be found by multiplying its length by its width.

The perimeter is the distance around the outside of a shape, often used in polygons and closed figures.

A Pythagorean triple is a set of three integers a, b, and c that satisfy the equation a^2 + b^2 = c^2. These integers correspond to the three sides of a right triangle, with c being the hypotenuse.

The hypotenuse is the side of a right triangle that is opposite from the right angle and is also the longest side of a right triangle.

The Pythagorean Theorem Converse states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the length of the longest side, then the triangle is a right triangle.

The Pythagorean Theorem can be used to find the diagonal distance on a coordinate plane. Given the coordinates of two points, the theorem can be used to calculate the distance between them by making the diagonal distance the hypotenuse.

The legs of a right triangle are the two sides of the triangle that are adjacent (next to) to the right angle.

Uday Tahlan

A statement which correctly describes the graph shown below is: A. The object moves away from the origin at a speed of 3 m/s, stands still 6 m away from the origin for 3 seconds, then moves toward the origin at a speed of 2 m/s.

In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled by an object from its starting position with respect to the time when it is started moving.

Generally speaking, the position or distance traveled by a physical object in a position vs time graph is always plotted on the y-coordinate while time is always plotted on the x-coordinate (x-axis).

In this scenario, the speed of the object from the origin can be calculated as follows:

Speed = distance/time

Speed = 6/2

Speed = 3 m/s.

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The coordinate of a point is its location on a grid. The point will be located halfway between -2 and -3 on the x-axis, on -4 on the y-axis

Coordinate points:

A set of values that show an exact position on graphs is usually a pair of numbers. The first number shows the distance along, and the second number shows the distance up or down.

One number line is horizontal and is called the x-axis, and the other number line is the vertical number line and is called the y-axis. The two axes meet at a point called the origin.

The coordinate is given as:

[tex]Point=(2\frac{1}{2} ,-4)[/tex]

Express as decimals

Point=(-2.5,-4)

The above point means that:

X=-2.5

y=-4

Therefore, The point will be located halfway between -2 and -3 on the x-axis, on -4 on the y-axis

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Answer:

x = 0

Step-by-step explanation:

1 - 3x = 3x + 1 ( subtract 3x from both sides )

1 - 6x = 1 ( subtract 1 from both sides )

- 6x = 0 ( divide both sides by - 6 )

x = [tex]\frac{0}{-6}[/tex] = 0

An image is a representation of something that can be seen, such as a picture or drawing.

An image can be thought of as a 2-dimensional array of pixels, where each pixel has a specific color value. Each color value can be represented by numerical values, such as red, green, and blue (RGB) values.

In mathematics, we can think of an image as a function that maps the x and y coordinates of a pixel to its color value. For example, f(x,y) = (R, G, B) where R, G, B are the red, green, and blue values of that pixel.

We can also think of an image as a grid of points, where each point represents a pixel.

It can be a photograph, drawing, graphic, or any other visual representation of something. Images can be created using different techniques, such as painting, drawing, or photography.

They can also be digital, such as a computer-generated image or a photograph that has been scanned into a computer. Images are used in many different fields, such as art, science, advertising, and education.

Images can be found in various forms such as on billboards, posters, books, magazines, newspapers, websites, and social media platforms. They can also be used to communicate information, tell a story, or express an idea.

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If we want to be able to represent every hexadecimal value from 016 to ff16, the number of bits we need would be 8 bits.

The term hexadecimal refers to a numbering system in base 16. It can be used to represent large numbers with fewer digits. Most number systems are in decimal or base ten, however, hexadecimal is a type of number system which is in base 16. Hexadecimal has the base ten numbers from 0 to 9 and followed by six alphabetic characters A, B, C, D, E, and F. To represent every hexadecimal value from 016 to ff16, 8 bits will be needed.

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Answer: Ash has eaten 2/7 of her 4 donuts, which is equal to 8/7 or approximately 1.143 donuts.

Answer:

There are three general classes of substitution reactions, depending on the following factors.

Reactant or substituent.

Intermediate – carbocation, carbanion, or free radical.

Substrate (compound) – aliphatic or aromatic.

Step-by-step explanation:

Hope it helps!

Answer:

f

Step-by-step explanation:

Answer:

do 3*4 then divide by 12

Step-by-step explanation:

The weight of the ice changes at the rate of 1.25 lbs. in a half of an hour.

How quickly something evolves over time is referred to as its rate of change (ROC).

Given:

As a block of ice melts,

its weight changes from 1.5 lbs to .25lbs.

That means, the total decay,

1.5 + n = 0.25

n = 1.25 lbs.

This change takes a half of an hour.

So, the rate of change,

1.25 lbs. in a half of an hour.

Therefore, the rate of change is 1.25 lbs. in a half of an hour.

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Answer:

4x-12

Step-by-step explanation:

do -1(2x+5)  -> -2x-5

combine like terms

6x - 7 - 2x - 5  -> 4x -12

Answer:

4(x-3)

Step-by-step explanation:

6x - 7 - 1(2x + 5)

6x - 7 - 2x - 5

6x - 7 - 2x - 5

6x - 12 - 2x

6x - 12 - 2x

4x - 12

4 (x - 3)

ANSWER

4(x- 3)

Manuel was incorrect, because the perimeter of a flower bed is 51 1/4 feet not 25 5/8 feet.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, Manuel says  feet of fencing is enough for a rectangular flower bed that measures  feet by  feet

Here, perimeter =2(9 7/8 + 15 3/4 ) feet

= 2(79/8 + 63/4)

= 2(79/8 + 126/8)

= 2(205/8)

= 410/8

Manuel was incorrect, because the perimeter of a flower bed is 51 1/4 feet not  25 5/8feet.

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The value of m from the exponent is 35.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

[tex](x^m)[/tex]³ = [tex](x^{13) ^5[/tex] x [tex](x^{-8}) ^{-5}[/tex]

Now, solving the exponents

[tex](x^m)[/tex]³ = [tex](x^{65})[/tex] x [tex](x^{40}) }[/tex]

Now, using the property

[tex]x^m . x^n = x^{m+n}[/tex]

So, [tex](x^m)[/tex]³ = [tex](x^{65+ 40})[/tex]

[tex](x^{3m})[/tex] = [tex](x^{105})[/tex]

Now, comparing the base

3m = 105

m= 105/3

m= 35

Hence, the value of m is 35.

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We can conclude that (π) represents a irrational & transcendental number.

An irrational number is a number that cannot be expressed as a fraction p/q for any integers {p} and {q}.

Given is a mathematical constant as {π}.

Therefore, we can conclude that (π) represents a irrational & transcendental number.

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Social inequality in class 9 refers to the unequal distribution of social status, power, and privilege among individuals or groups within a society. It can manifest in various forms, such as discrimination, prejudice, and bias, which can limit opportunities and access to resources for certain groups.

In class 9, social inequality may be discussed in relation to various social issues, such as racial and ethnic inequality, gender inequality, and inequality based on sexual orientation, disability, and age. These issues can have a significant impact on individuals and groups, leading to reduced opportunities, access to resources, and lower quality of life.

Social inequality in class 9 may also be discussed in relation to broader societal issues, such as poverty, unemployment, and lack of access to healthcare and education. These issues can contribute to a cycle of disadvantage and can perpetuate social inequality.

It's worth noting that social inequality is often interconnected with other forms of inequality such as economic and educational inequality, and understanding how these inequalities interact is crucial to understand and address social inequality.

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