What is an equation of the line that passes through the point (-6,-2) and is parallel to the line 2x-3y=12?

The length of one edge of a cube with a volume of 1331 cm³ is 11 cm, derived by taking the cube root of the volume.

To calculate the length of one edge of a cube when the volume is given, we use the formula for the volume of a cube: Volume = side³, where 'side' is the length of one edge of the cube.

The cube in question has a volume of 1331 cm³. To find the length of one edge of the cube, we need to take the cube root of the volume. The cube root of 1331 cm³ is 11 cm, meaning each side of the cube measures 11 cm.

The cube root is calculated because raising a number to the third power cubes it, and taking the cube root is the inverse operation. This process allows us to determine the original value that was cubed to get the volume.

Answer: -50

Step-by-step explanation: A withdrawal means that you're decreasing the amount of money you have.

So a withdrawal of $50 can be written as -50.

Answer:

165

Step-by-step explanation:

55* 3 = = 165

The initial fee of a train ticket, given a constant fee per stop, can be calculated by finding the constant fee per stop and subtracting the total of this fee for a given number of stops from the total price for those stops. By this calculation, the initial fee is $2.50.

To determine the initial fee that is related to the price of a train ticket, which consists of an initial fee plus a constant fee per stop, we should first calculate the cost per stop. We can do this by subtracting the price of a ticket for 3 stops from the price of a ticket for 7 stops. So, we get $12.50 - $6.50 = $6.00. We find the difference in the number of stops, which is 7 - 3 = 4 stops. Divide the total price difference by the difference in the number of stops to get the constant fee per each stop: $6.00 / 4 stops = $1.50 per stop. Now we know the constant fee for each stop, so we subtract that from the total price for 3 stops to find the initial fee: $6.50 - ($1.50 * 3) = $2.50. So, the initial fee is $2.50.

To find the initial fee, we need to determine the additional cost per stop. We can do this by using the formula y = mx + b, where y represents the price of the ticket, x represents the number of stops, m represents the constant fee per stop, and b represents the initial fee.

Using the given data, we can set up two equations using the points (3, 6.50) and (7, 12.50).

By subtracting these two equations, we can determine the value of b, which represents the initial fee. Thus, the initial fee is $3.

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Answer:

The sum of the first 35 terms of the arithmetic sequence when a = 5 and d = 4 is 2555.

Step-by-step explanation:

Given:

a = 5

d =  4

To Find :

The sum of first 35 terms of the arithmetic sequence  = ?

Solution:

Step 1 : finding the 35th term

[tex]a_n = a_1 +(n-1)d[/tex]

[tex]a_35 = 5 +(35-1)4[/tex]

[tex]a_35 = 5 +(34)4[/tex]

[tex]a_35 = 5 +136[/tex]

[tex]a_35 = 141[/tex]

Step 2: Finding the sum of first 35 terms

[tex]S_n = \frac{n(a_1 +a_n)}{2}[/tex]

Substituting the values

[tex]S_n = \frac{35(5+141)}{2}[/tex]

[tex]S_n = \frac{35(146)}{2}[/tex]

[tex]S_n = \frac{35(146)}{2}[/tex]

[tex]S_n = \frac{5110)}{2}[/tex]

[tex]S_n = 2555[/tex]

Answer:

- 133

Step-by-step explanation:

To find the 30 th term substitute n = 30 into the formula, that is

[tex]a_{30}[/tex] = 12 - 5(30 - 1) = 12 - (5 × 29) = 12 - 145 = - 133

Final answer:

The 30th term of the sequence defined by an = 12 – 5(n – 1) is – 133.

Explanation:

To calculate the 30th term of the sequence given by an = 12 – 5(n – 1), we start by substituting the value of n with 30.

[tex]a_{30}[/tex] = 12 – 5(30 – 1)

[tex]a_{30}[/tex] = 12 – 5(29)

[tex]a_{30}[/tex]   = 12 – 145

[tex]a_{30}[/tex] = – 133

The 30th term of the sequence is – 133.

Answer:

15 sec.

Step-by-step explanation:

Given: Object travels 1/20 of the length of the path in 3/4 seconds.

Let the entire length of the path be "x".

Now, solving to find the total time taken to travel entire length.

First step, Object travel= [tex]\frac{1}{20}\times x = \frac{x}{20}[/tex]

Next putting the value in the ratio of Length: time.

[tex]\frac{\frac{x}{20} }{\frac{3}{4} }[/tex]

And another ratio of entire length and total time

[tex]\frac{x}{Total\ time}[/tex]

Now, using scissor method fractioning to solve the ratio or fraction

⇒[tex]\frac{\frac{x}{20} }{\frac{3}{4} }= \frac{x}{Total\ time}[/tex]

To divide fraction, take reciprocal of the divisor and multiply the dividend.

⇒ [tex]\frac{x}{20} \times \frac{4}{3} = \frac{x}{Total\ time}[/tex]

⇒[tex]\frac{4x}{20\times 3} = \frac{x}{Total\ time}[/tex]

Cross multiplying both side.

⇒ [tex]Total\ time= \frac{20x\times 3}{4x}[/tex]

⇒ [tex]Total\ time= \frac{20\times 3}{4}[/tex]

⇒[tex]Total\ time= 5\times 3= 15\ sec[/tex]

∴ Total time taken by Object to travel entire length is 15 sec.

Answer:

$16,991

Step-by-step explanation:

Rate = r = 2.5%

Times = b = 4

A = P [1 + (r / b)]ⁿᵇ

A = $15,000 [1 + (0.025 / 4]⁵ ˣ ⁴

A = $15,000 [1 + 0.00625]²⁰

A = $15,000 [1.00625]²⁰

A = $15,000 x 1.132708

A = $16,991

For this case we have the following inequality:

[tex]0.4 + y\geq 7[/tex]

If we subtract 0.4 from both sides of the inequality we have:

[tex]y \geq7-0.4\\y \geq6.6[/tex]

Thus, the solution is given by all the values of "y" greater than or equal to 6.6.

The graph of the solution is attached.

Answer:

[tex]y\geq6.6[/tex]

The length of the line segment that connects vertex A and vertex B is 5 units

Step-by-step explanation:

Let us revise some facts about the horizontal and vertical segments

In Δ ABC

∵ A = (1 , -1)

∵ B = (1 , 4)

∵ C = (8 , 4)

∵ The x-coordinate of point A = 1

∵ The x-coordinate of point B = 1

∴ The x-coordinates of points A and B are equal

- The x-coordinates of A and B are equal, then the line AB is a

  vertical segment

∴ The length of AB is the difference between the y-coordinates

   of points A and B

∵ The y-coordinate of point A = -1

∵ The y-coordinate ob point B = 4

∴ The length of AB = 4 - (-1)

∴ The length of AB = 4 + 1

∴ The length of AB = 5 units

The length of the line segment that connects vertex A and vertex B is 5 units

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Answer:

5 units

Step-by-step explanation:

Answer:

The points each have scored are Susie 45.5 points and jack 40.5 points.

Step-by-step explanation:

Given:

Susie and jack are on a basketball team.

The total amount of points scored was 86.

Susie has 5 more than as many points as jack.

Now, to find the points they each have:

Let the points of jack be [tex]x[/tex].

Then the points of Susie be [tex]5+x[/tex].

There total points scored =  86.

According to question:

[tex]x+(x+5)=86.[/tex]

⇒ [tex]x+x+5=86.[/tex]

⇒ [tex]2x+5=86.[/tex]

Subtracting both sides by 5 we get:

⇒ [tex]2x=81.[/tex]

Dividing both sides by 2 we get:

⇒ [tex]x=40.5.[/tex]

Jack scored = 40.5 points.

Putting the value of [tex]x[/tex] to get the points of Susie:

[tex]x+5[/tex]

⇒ [tex]40.5+5 = 45.5[/tex]

Susie scored = 45.5 points.

Therefore, the points each have scored are Susie 45.5 points and jack 40.5 points.

To compare the two plans and find the amount of driving for which they cost the same, we can set up an equation and solve for x. The two plans cost the same for 450 miles of driving.

To compare the two plans and find the amount of driving for which they cost the same, we need to set up an equation. Let's assume the amount of driving is represented by the variable x. The total cost for Plan 1 can be calculated as:

Total cost = $46 + $0.13x

The total cost for Plan 2 can be calculated as:

Total cost = $55 + $0.11x

We can set the two equations equal to each other and solve for x:

$46 + $0.13x = $55 + $0.11x

$0.02x = $9

x = $9 / $0.02 = 450

Therefore, the two plans cost the same for 450 miles of driving.

Answer:

180° rotation

Step-by-step explanation:

sign changes when we rotate a point to 180 degrees. so 9 became -9 and -1 became 1, which gave us the clue that it's 180° rotation

The given situation described 180° rotation

Andrew's rotation maps point M(9, -1) to M'(-9, 1).

Since signing is changed when we rotate a point to 180 degrees. So here 9 became -9 and -1 became 1, which provides us the clue that its 180° rotation.

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Answer:

as illustrated

Step-by-step explanation:

X-4y= - 18

find 2 points on the line

x = 0     y = 4.5      (0, 4.5)

x = 4   y = 5.5         (4, 5.5)

Answer:

Please Check the image for the answer to your question hope this helps!

Should be 5812.95 Students

Answer:

Step-by-step explanation:

4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10

5.5-8.1=-2.6

-5-5/3=-15/3-5/3=-20/3

-8 3/8-10 1/6=-67/8-61/6=-445/24

-4.62-3.51=-8.13

Answer: Search it up

Step-by-step explanation:

It shows you all the steps and will help you

Step-by-step explanation:

DCF is 90°

so to find BCE

BCE+64+90=180

BCE=26°

CBE is (180-3x)

taking triangle BEC

(180-3x)+x+26=180

180-3x+x+26=180

-2x+26=0

-2x=-26

x=13

Answer:

[tex]6x + 4x - 3x = 10x - 3x = 7x[/tex]

Answer:

Yes, y varies directly with x.

[tex]y=\frac{11}{8} x[/tex]

Step-by-step explanation:

[tex]\frac{y}{x}=\frac{11}{8} =\frac{22}{16} =\frac{33}{24}[/tex]

Hence [tex]y[/tex] varies directly with [tex]x[/tex].

[tex]\frac{y}{x}=\frac{11}{8} \\\\ y=\frac{11}{8} x[/tex]

Answer:

Hector has spent $37.5.

Step-by-step explanation:

Given:

Total money he cashed = $50

Also Given:

Hector spent [tex]\frac{3}{4}[/tex] of his money the day after he cashed his paycheck of $50.

Let 'm' be the amount of money hector spent.

Now according to question;

amount of money hector spent is equal to [tex]\frac{3}{4}[/tex] times the amount of money he cashed his paycheck.

framing in equation form we get;

[tex]m =\frac{3}{4}\times 50 = \$37.5[/tex]

Hence hector has spent $37.5.

Answer:

10 go into 450 45 times

Step-by-step explanation:

Answer:

Step-by-step explanation:

8) a) No: of sides of a regular polygon = 360° / exterior angle

                                                                = 360°/18° = 20 sides

b) Sum of interior angles of regular polygon = (n-2) * 180°   {n-no:of sides}

                   = (20-2)*180° = 18*180° = 32400°

9) Let the exterior angle be x.

So, interior angle = 140° + x

Interior angle + exterior angle  = 180°

140° +x + x = 180°

140° +2x = 180°

2x = 180° - 140°

2x =40°

x = 40°/2 = 20°

Exterior angle = 20°

Interior angle  = 160°

No: of sides of a regular polygon = 360° / exterior angle

                                                                = 360°/20° = 18 sides

Hint: Always sum of exterior angles of regular polygon is 360°

Answer:

see explanation

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

(A)

To find k use the given condition y = 2 when x = 10

k = yx = 2 × 10 = 20, thus

y = [tex]\frac{20}{x}[/tex] ← equation of variation

(B)

When x = 4, then

y = [tex]\frac{20}{4}[/tex] = 5

The midline equation for the sinusoidal function is y = 4 sin(ωx + ∅) - 3, derived by calculating the amplitude and vertical shift within the general function equation.

A function is a mathematical expression, rule, or law that defines the relationship between one variable and another. In mathematics, functions play a crucial role in representing physical relationships and various mathematical concepts. One specific type of function is the sinusoidal function, characterized by its repetitive pattern within a specific time interval.

The general form of a sinusoidal function is given by the equation:

y = A sin(ωx + ∅) + c

Here, A represents the amplitude, ω is the argument, ∅ is the phase difference, and c is the vertical shift known as the midline.

To find the equation of the midline, we use the formula:

A = (Maximum value - Minimum value) / 2

Given that the maximum value is 1 and the minimum value is -7, the amplitude (A) is calculated as:

A = (1 - (-7)) / 2 = 4

The vertical shift (c) is determined to be -3. Substituting these values into the general equation, we obtain the equation of the midline for the sinusoidal function:

y = 4 sin(ωx + ∅) - 3

In summary, the equation of the midline for the sinusoidal function is y = 4 sin(ωx + ∅) - 3.

The amplitude and vertical shift inside the general function equation are used to obtain the midline equation for the sinusoidal function, which is y = 4 sin(ωx + ∅) - 3.

A mathematical phrase, rule, or law that establishes the connection between two variables is called a function.

Functions are essential to the representation of both mathematical concepts and physical relationships in mathematics.

The sinusoidal function is one particular kind of function that is distinguished by its repeating pattern inside a predetermined time frame.

The following formula provides the generic form of a sinusoidal function:

sin(ωx + ∅) + c = A

In this case, amplitude is denoted by A, argument by ω, phase difference by ∅, and vertical shift, or midline, by c.

We utilise the to determine the midline's equation.

A is equal to (Maximum - Minimum) / 2.

A = (1 - (-7)) / 2 = 4 is the formula for calculating the amplitude (A), given that the maximum value is 1 and the minimum value is -7.

It is found that the vertical shift (c) is -3. The equation of the midline for the sinusoidal function is obtained by substituting these values into the general equation: y = 4 sin(ωx + ∅) - 3

In conclusion, y = 4 sin(ωx + ∅) - 3 is the equation of the midline for the sinusoidal function.

Answer:

y=-2x-2

Step-by-step explanation:

y+4=-2(x-1)

y+4=-2x+2

y=-2x+2-4

y=-2x-2

Answer:

6.32

Step-by-step explanation:

There's an easy trick for this. Move the decimal point once to the left, and then multiply by 2.

31.60 turns into 3.16 (which is 10% btw)

Multiply 3.16 by 2 and you get 6.32, or 20% of 31.60. Hope this helped!

Answer:

The graph of y = f(x) will shift left 6 units, as shown in figure a.

Step-by-step explanation:

A translation means we are able to move the graph of a function up or down - normally called Vertical Translation -  and right or left - commonly called Horizontal Translation.

If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the  x, so it is f(x + 6).

For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.

So, the graph of y = f(x) will shift left 6 units.

Keywords: graph shift, translation

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The graph of y = f(x) will shift left 6 units. The correct option is the third one.

For any function y = f(x), we define an horizontal translation of N units as:

y = f(x + N)

Where if:

N > 0, the translation is to the left.

N < 0, the translation is to the right.

Here we have:

y = f(x + 6)

So this is a translation of 6 units to the left.

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Answer:

420cal = 2 cups

Step-by-step explanation:

140cal = 2/3 cup

xcal= 2 cups

Divide 2/(2/3) = 3

Multiply both sides by 3 (answer)

140cal= 2/3 cups (3)

420cal = 2 cups

The 2 cups Contain 420 Cal.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

2/3 Cup contain = 140 Cal

So, 1 cup contain = 140 ÷ ( 2/3)

                             = 140 x 3/2

                             = 70 x 3

                             = 210

Then, In 2 cups = 210 x 2

                          = 420 Cal

Hence, 2 cups Contain 420 Cal.

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