equation of the line through (3,5) and parallel to y=2x-2

Assume to contrary that the sum of the squares of two odd integers can be the square of an integer. Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.

A quadrilateral with four equal sides is called a square. There are the numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about square's characteristics, mathematics, and design.

A square has four corners and is closed, two-dimensional (2D) object.

Assume to contrary that the sum of the squares of two odd integers can be the square of an integer.

Suppose that x,y,z∈Z such that [tex]x^{2} +y^{2} =z^{2}[/tex], and x and y are odd.

Let, x=2m+1 and y=2n+1.

Hence,

[tex]x^{2} +y^{2} =(2m+1)^{2} + (2n+1)^{2}[/tex]

           =[tex]4m^{2}+4m+1+4n^{2}+4n+1[/tex]

           =[tex]4(m^{2}+n^{2}) + 4(m+n)+2[/tex]

           =[tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex]

Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.

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Answer:

26000:48000

26000/48000

26/48(cancel the zeros)

13/24

fractional form=13/24

Answer:

(-4,0)

ignore this line

Answer:

When A = 0 and y = 1 and C = 2

0x + 1y = 2

y = 2 No matter what x is, y will always be 2 and this will create a horizontal line.

Step-by-step explanation:

Step-by-step explanation:

your answers are right in my pov

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Hello! In this question, we will be solving the given equation for the variable "y".

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Explanation:

In our question, we were given the following equation:

To solve for our "y" variable, we will perform distributive property and simplify to get the value of "y".

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Solve:

[tex]0.3(6y + 15) = 1.8y + 4.5\\\\\text{Use the distributive property to distribute the "0.3"}\\\\1.8y+4.5=1.8y+4.5\\\\\text{Since both sides of the equal sign are equal, there will be infinite solutions}[/tex]

Proof:

[tex]\text{To prove that there are infinite solutions, we could continue to solve the}\\\text{equation:}\\\\1.8y+4.5 =1.8y+4.5 \\\\\text{Subtract 1.8y from both sides}\\\\4.5=4.5\\\\\text{Subtract 4.5 from both sides}\\\\0=0[/tex]

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Answer:

[tex]\boxed{\text{Infinite solutions}}[/tex]

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Answer:

13 units

Step-by-step explanation:

[tex]d=√((x_2-x_1)²+(y_2-y_1)²) [/tex]

[tex] \sqrt{( - 2 - ( -14)^{2} } + ( - 4 - 1) {}^{2} [/tex]

[tex] \sqrt{12 {}^{2} } + ( - 5) {}^{2} [/tex]

[tex] \sqrt{169} [/tex]

The sets of numbers which each of the numbers given belong to as required in the task content is as follows;

As evident in the task content, the sets to which the three numbers belong is to be determined.

Hence, taking the numbers one after the other; we have;

15 => The number 15 belongs to the set of real numbers, rational numbers and most particularly, integers.

-5.075 => The number -5.075 belongs to the set of real numbers, rational numbers, and most particularly, decimals.

π => The number represented by π belongs to the set of real numbers, irrational numbers and it's numerical value is a non-terminal and non-repeating decimal.

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Answer:

x-intercept equals 5

y-intercept equals -10

Step-by-step explanation:

y-intercept: solve when x=0. y=-2|x-5|= -10

Answer:

6.6 is the correct number

Step-by-step explanation:

The base is 2.2 inches. The height is 3 inches. So the area is 2.2 × 3 = 6.6 square inches.

After factorization, the absolute value of the variable 'x' is 9.

What is factorization method?

The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.

According to the question, the given linear equation is: |2x - 4| = 15

Now, to calculate the value of the variable 'x' by using factorization method. And to remove the bars which represent absolute value that means positive values

Required expression: |2x - 4| = 15

⇒ 2x = 15 + 4 = 19

⇒ x = 19/2 = 9.5

After factorization, the absolute value of the variable 'x' is 9.

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Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, you can calculated in this case:

Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:

m= (-4 - (-8))÷ (4 - (-1))

m= (-4 + 8)÷ (4 + 1)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-8= 4/5× (-1) + b

-8= -4/5 +b

-8 + 4/5= b

-36/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.

Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:

m= (-5 - (-9))÷ (7 - 2)

m= (-5 + 9)÷ (5)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-9= 4/5× (-2) + b

-9= -8/5 +b

-9 + 8/5= b

-37/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.

You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.

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Answer: 13

Step-by-step explanation:

As the sum of the angles of a triangle is 180, we have that 39 + 90 + 3x+12 = 180.

3x = 180 - 39 - 90 - 12

3x = 39

x = 13

Answer: The answer I came up with is:  $237,737

Check the picture below.

The number of rectangular containers will be necessary to package 6,400 candles is 143

The number of cylindrical containers will be necessary to package 6,400 candles is 157.

The container that would minimise cost is the rectangular container because it would $67 less to use the rectangular container.

The first step is to determine the total cost of packing 6400 candles using the rectangular container.

Total cost = number of containers needed x cost of one rectangular container

Number of containers needed = total number of candles to be packages / number of candles the container can hold

6400 / 45 = 142.22 = 143 rectangular containers

Total cost = $16 x 143 = $2,288

The next step is to determine the total cost of packing 6400 candles using the cylindrical container.

Total cost = number of containers needed x cost of one cylindrical container

Number of containers needed = total number of candles to be packages / number of candles the container can hold

6400 / 41 = 156.1  = 157 cylindrical containers

Total cost = $15 x 157 = $2,355

Difference in costs = $2,355 - $2,288 = $67

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Finding the numeric value of the regression line, it is found that the electric bill in a month with temperature of 48 degrees is of $157.59.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

In the context of this problem, the function is given as follows:

y = 227.19 - 1.45x.

Which y giving the electric bill for a month of temperature x degrees.

The temperature is of 48 degrees, hence to find the electric bill, the lone instance of x in the function is replaced by 48, hence:

y = 227.19 - 1.45(48) = $157.59.

Hence the electric bill in a month with temperature of 48 degrees is of $157.59.

The regression line is missing in this problem, as is defined as follows:

y = 227.19 - 1.45x.

In which:

The problem asks for the electric bill in a month with temperature of 48 degrees.

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Answer: 25.5 miles per gallon. 16.8 gallons x 25.5 miles = 428.4 miles

Answer: 1/4

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that A'D'=2 and AD=8, so the scale factor is 2/8 = 1/4.

Let's begin by listing out the information given to us:

The elevator starts at 80 m

The elevator descends 2 meters every 0.5 seconds for 4 seconds

The inequality is given by:

The set notation is given by:

The most appropriate choice for Independent event and multiplicative counting rule will be given by

This is known as multiplicative counting rule.

What is Independent event and multiplicative counting rule?

Event that is not dependent on any other event is called independent event.

Let A and B be two independent events.

P(A∩B) = P(A) [tex]\times[/tex] P(B)

If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.

Here,

Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on

Also assuming that the events are independent

The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways

This is known as multiplicative counting rule.

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The rate of interest is 10% and the sum is Rs 10,1000.

The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.

The compound interest formula is given by

Compound Interest = Amount – Principal

Here, the amount is

[tex]A=P(1+\frac{r}{100} )^{n}[/tex]  where,

A = amount

P = principal

r = rate of interest

n = time (in years)

Given:

C.I. of a sum of money in 3 years = Rs 13310

C.I. of a sum of money in 4 years = Rs 14641

Let the principal be P and the rate of interest be r%

Then, according to the question,

For 3 years:

[tex]13310=P(1+\frac{r}{100} )^{3}[/tex]       ..... (1)

For 4 years:

[tex]14641=P(1+\frac{r}{100} )^{4}[/tex]       ..... (2)

Dividing equation (2) by (1), we obtain

[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]

⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]

⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]

⇒[tex]r=\frac{100}{10}[/tex]

⇒ r = 10%

Now, substituting r in equation (1),

[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]

⇒[tex]13310=P(\frac{1331}{1000} )[/tex]

⇒P = Rs 10,000

Therefore, the rate of interest is 10% and the sum is Rs 10,1000.

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Answer:

f(4) = 11

Step-by-step explanation:

f(x) = 3 x -1

Let x = 4

f(4) = 3*4 -1

     = 12-1

     = 11

f (x) = 3x - 1

f (4) = 3 × 4 - 1

f (4) = 12 - 1

f (4) = 11

Hope Helpful :-;

The term "if and only if" makes the sentence bi-conditional. A triangle is equilateral if and only if it has three congruent sides.

A conditional statement with its opposite expressed in the form of "if and only if," collectively known as a bi-conditional statement. Bi-conditional logic is the theory behind bi-conditional assertions.

This can be compared to the conditional sentence, "if this, then that." Due to the lack of a "if and only if," it is not bi-conditional. The reversal of a conditional statement's ability to produce a bi-conditional depends on whether it is also true.

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They could buy 8 small notebooks or 3 large notebooks and 3 small notebooks.

Answer: just one way to do it. You can buy 3, large books and 3 small books

Step-by-step explanation:

10x3=30

48-30=18

18 divided by 3 = 6

Answer:

Factoring polynomials is the inverse process of multiplying polynomials. After factoring a polynomial, if we divide the polynomial with the factors then the remainder will be zero.