What is an equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15

Answer:

Step-by-step explanation:

1. y=2x-3

2. y=2x+3

3. y=-2x+3

4.  y=-2x-3

The equations of the lines which goes with their graphs.

1. y=2x-3

2. y=2x+3

3. y=-2x+3

4.  y=-2x-3

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (1.5,0) and, (0,-3)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>3x-1.5y=4.5

y=2x-3

Again,

Here, we have to points (-1.5,0) and, (0,-3)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>3x+1.5y=-4.5

y=2x+3

Here, we have to points (1.5,0) and, (0,-3)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>-3x+1.5y=4.5

y=-2x+3

Here, we have to points (-1.5,0) and, (0,3)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>3x+1.5y=4.5

y=-2x-3

Hence, the required equations are,

1. y=2x-3

2. y=2x+3

3. y=-2x+3

4.  y=-2x-3

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Answer:

Give the triangle area so we can solve it for you.

Step-by-step explanation:

½*base*height

Step-by-step explanation:

the triangle is not given so let us take its base=b,and height=h

by using the formula=½*base*height

½*b*h

Answer:

x/2

Step-by-step explanation:

2/2=1=y

4/2=2=y

6/2=3=y

Slope=2

x−intercept=  2/10  =5

y−intercept=  −10/-1  =−10.00000

Answer:

2x+y-10=0

Step-by-step explanation:

6x+3y=30 move the constant to the left and change its sign

6x+3y-30=0

6x+3y-30=0 divide both sides of the equation by 3

2,094 cm^3

==========================================================

Explanation:

The diameter of 20 cm divides in half to the radius r = 10 cm.

The height is h = 20 cm.

V = volume of the cone

V = (1/3)*pi*r^2*h

V = (1/3)*pi*10^2*20

V = 2,094.3951023932 is approximate

I used my calculator's stored version of pi when computing the volume

That value then rounds to 2,094 cm^3 when rounding to the nearest whole number.

Answer:

9x

Step-by-step explanation:

9 packages and x pencils

9x

Answer:

1/4

Step-by-step explanation:

0.25

25/100

25 ÷ 25 = 1

100 ÷ 25 = 4

1/4

Answer:

120%

Step-by-step explanation:

Answer:

First, we need to figure out the total amount of students:

+ 10 students(ten students leave)

+ 15 students(15 students left)

10 + 15

= 25 students.

x = will represent the total amount of students in each group, so:-

5 groups per x students.

5x = 25(total students before alteration)

÷5    ÷5

x = 5, there are 5 students in each group.

Answer: It must be A

Step-by-step explanation:

The reason is because it is the only that is a integer and a fraction

Answer:

AB = 36

Step-by-step explanation:

Since E is the midpoint of AB, then

AE = EB , substitute values

4x + 6 = 10x - 12 ( subtract 10x from both sides )

- 6x + 6 = - 12 ( subtract 6 from both sides )

- 6x = - 18 ( divide both sides by - 6 )

x = 3

Thus

AB = AE + EB = 4x + 6 + 10x - 12 = 14x - 6 = 14(3) - 6 = 42 - 6 = 36

Answer:

$10.80

Step-by-step explanation:

Final Price = Original Price - Discount

Final Price = 18 - 7.2

Final Price = $10.80

Answer:

[see below]

Step-by-step explanation:

"The product of 5 and a number x is 14" would be:

[tex]5x=14[/tex]

[tex]5x=14\\\\\frac{5x=14}{5}\\\\ \boxed{x=2 \frac{4}{5}}[/tex] or 2.8

Hope this helps.

The amount of wrapping paper needed for the square pyramid gift box is: 96.72 in.².

Surface area of a square pyramid = area of the square base + area of the 4 triangular faces = s² + 4(1/2bh).

We are asked to find the amount of wrapping paper that would be needed to wrap the gift box, which is the surface area of the gift box that has a square pyramid shape.

Given the following dimensions of the gift box:

s = 5.2 in.

b = 5.2 in.

h = 6.7 in.

Plug in the values into s² + 4(1/2bh):

Surface area of a square pyramid = 5.2² + 4(1/2 × 5.2 × 6.7).

Surface area of a square pyramid = 96.72 in.²

Therefore, the amount of wrapping paper needed for the square pyramid gift box is: 96.72 in.².

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Answer:

p=2l+2w

p=2(57)+2(47)

p=208 feet

The perimeter of rectangle is 208 ft.

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.

Therefore, the Perimeter of a rectangle = 2(l + w).

Given:

length = 47 ft

width = 57 ft

So, the perimeter of rectangle

= 2( l + w)

=2( 47 + 57)

= 2 x 104

= 208.

Hence, the perimeter of rectangle is 208 ft

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Answer: 28.8

Step-by-step explanation:

Answer:

5 m

Step-by-step explanation:

A nonagon has 9 sides. You get individual side length by dividing the perimeter by amount of sides. 45 divided by 9 is 5.

Answer:

315

Step-by-step explanation:

360 - 45 = 315

since a full circle is 360 degrees that is why we take away the 45 degrees.

Answer:

The first one is 12.0, the second one is 12.9, and the third one is greater than or equal to I believe

Step-by-step explanation:

1. because it wants the average but the average is 12.9 so we use the median which is 12.0

2. because it is basically making it into a fraction so 12.9 is the total average

3. 2.4 is greater than or it can be equal to 1.5

Answer:

See below.

Step-by-step explanation:

Given numbers :-

⇒ 176, 231, 247, 256, 272, 299, 325, 343, 366, 375

⇒ Median = 272 + 299 / 2 = 285.5

⇒ Mean = 2890/10 = 289

(a) median if 375 becomes 265

⇒ 176, 231, 247, 256, 265, 272, 299, 325, 343, 366

⇒ New median = 265 + 272 / 2 = 268.5

⇒ Decreases by 17

(b) mean if 375 becomes 265

⇒ New mean = 2890 - 110 / 10 = 2780/10 = 278

⇒ Decreases by 11

Answer:

5x + 4y = - 8

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 )

Given

4x - 5y = 20 ( subtract 4x from both sides )

- 5y = - 4x + 20 ( divide all terms by - 5 )

y = [tex]\frac{4}{5}[/tex] x - 4 ← in slope- intercept form

with slope m = [tex]\frac{4}{5}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex] , thus

y = - [tex]\frac{5}{4}[/tex] x + c ← is the partial equation

To find c substitute (- 4, 3) into the partial equation

3 = 5 + c ⇒ c = 3 - 5 = - 2

y = - [tex]\frac{5}{4}[/tex] x - 2 ← in slope- intercept form

Multiply through by 4

4y = - 5x - 8 ( add 5x to both sides )

5x + 4y = - 8 ← equation in standard form

Answer:

17.6 kg

Step-by-step explanation:

5 meters = 8 kg

8/5 = 1.6 kg per meter

16-5 = 11

11*1.6 = 17.6 kg

Answer: 3.5 hours

Step-by-step explanation:

From the question, we are informed that Ray's burns 326 calories every hour. We are further told that he ate a doughnut that had 320 calories, and a latte had 820 calories. The total calories will be:

= 320 + 820

= 1140 calories

The number of hours needed to burn the calories will be the total calories divided by the amount of calories burnt in an hour. This will be:

= 1140/326

= 3.5 hours

[tex]2~~,~~\stackrel{2-5}{-3}~~,~~\stackrel{-3-5}{-8}~~,~~...~\hspace{10em}\stackrel{common~difference}{d = -5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{64}\\ a_1=\stackrel{\textit{first term}}{2}\\ d=\stackrel{\textit{common difference}}{-5} \end{cases} \\\\\\ a_{64}=2+(64-1)(-5)\implies a_{64}=2+(-315)\implies a_{64}=-313[/tex]

Answer:

-313 is the 64th term

Step-by-step explanation:

you take the second term an minus the first term with the second one {2-(-3)}

{=5} then you take two an minus five

it gives you -3 then you press minus five again it gives you negative eight then you press (equals to)until you reach the term you looking for

Answer:

-6

Step-by-step explanation:

Using additive inverse you will get the answer 6 because additive inverse is the opposite of a number on the number line. But you will reverse it again so it would be -6

Answer:

the opposite of -6 = 6

the opposite of the opposite of -6 = -6

Step-by-step explanation:

easy?

Answer: The dot over a number signifies that it is a repeater which would go on for ever, as when we endeavor to describe 1/3 decimally as 0.33333 . . . . (etc) With a series of numbers we place the dot over the first and last, as with 0.97979797979 . . . (etc) The remarkable feature being that a proper fraction divided by 9s e.g. 46/99 is exactly equal to the numerator with the repeater sign followed by the decimal.

Step-by-step explanation: Hope This Helps, Have A Nice Day.

Answer:

1365 combinations

Step-by-step explanation:

This is 15C4

= 15!/ (4!11!

= 15*14*13*12 / 4*3*2*1

= 32760/24

= 1365.