MATHEMATICS HIGH SCHOOL

Passes through (3,1) ,perpendicular to y=-3x+2

Answers

Answer 1
Answer:

The equation of line which passes through (3, 1) and perpendicular to y = -3x + 2 is;

⇒ x = 3y

Here,

Given that;

The point is (3, 1).

We have to find the equation which passes through (3, 1) and perpendicular to y = -3x + 2.

What is equation of line passes through a point?

Equation of line passes through a point (a, b) with slope m is;

⇒ (y - a) = m (x - b)

Now,

As it is perpendicular to y = -3x + 2 and the slope of this is m₁ = -3,

Hence, the slope of to find line is m₂ = -1 / -3 = 1/3

We have the general equation of a line;

( y - y₁ ) = m₂ (x - x₁)

Where, ( x₁ , y₁ ) = (3, 1) and m₂ = 1/3

So, after putting all values we get;

( y - 1 ) = 1/3 ( x - 3)

3 (y - 1) = (x - 3)

3y - 3 = x - 3

3y = x

x = 3y

Hence, The equation of line which passes through (3, 1) and perpendicular to y = -3x + 2 is;

⇒ x = 3y

Learn more about the equation of line visit:

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Answer 2
Answer: As it is perpendicular to y = -3x + 2 and the gradient of that is -3 we know that the gradient of our line must be -1 / -3 = 1/3.

Now we have the general equation of a line m = (y-y1)/(x-x1) to which we can substitute our values.

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

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Two numbers have a difference of 0.7 and a sum of 1. what are the numbers?

Answers

In order to determine the value of the numbers, we can set up algebraic equations to solve. For this case, we need to set up two equations since we have two unknown numbers. We do as follows:
 let x = first number and y = second number
 From the problem statement, we set up equations.
 Equation 1 - the numbers have a difference of 0.7
 x - y = 0.7
 Equation 2 - the numbers have a sum of 1
 x + y = 1
 Solving for x and y via substitution method,
 x - y = 0.7
(1-y) - y = 0.7
1 - 2y = 0.7
-2y = 0.7 - 1 = -0.3
y = 0.15 or 3/20
 x - 0.15 = 0.7
x = 0.85 or 17/20
 Thus, the two numbers are 0.15 and 0.85.

The width of a singles tennis court is 27 feet. this is 1 foot more than 1/3 of the lenght. what is the length of the court

Answers

w = 27
1 + 1/3L = w
1 + 1/3L = 27
1/3L = 26
L = 78

i am a mathematics teacher. if anything to ask please pm me

In the figure ,the equal sides of the iscoscles triangular are 5cm each,the base in 6 cm and the height is 4cm height.The length of the rectangle are all 10cm Calculate the TSA (total surface area )of the triangular prism

Answers

Answer:

284 square cm.

Step-by-step explanation:

To calculate the total surface area (TSA) of the triangular prism formed by an isosceles triangle and a rectangle, you need to find the surface areas of both the triangular faces and the three rectangular faces and then add them together.

1. **Triangular Faces**:

  You have an isosceles triangle with a base of 6 cm and a height of 4 cm. The total area of both triangular faces can be calculated using the formula for the area of a triangle:

  Area of one triangular face = (1/2) * base * height

  Area of one triangular face = (1/2) * 6 cm * 4 cm = 12 square cm

  Since there are two identical triangular faces, the total area of both triangular faces is 2 * 12 square cm = 24 square cm.

2. **Rectangular Faces**:

  You have a rectangular prism with dimensions 10 cm x 10 cm x 6 cm. There are three rectangular faces.

  - The two rectangular faces with dimensions 10 cm x 10 cm have an area of 100 square cm each.

  - The third rectangular face with dimensions 6 cm x 10 cm has an area of 60 square cm.

  The total area of all three rectangular faces is 2 * 100 square cm + 60 square cm = 260 square cm.

3. **Total Surface Area (TSA)**:

  Now, you can calculate the TSA of the triangular prism by adding the areas of the triangular faces and the areas of the rectangular faces:

  TSA = Area of Triangular Faces + Area of Rectangular Faces

  TSA = 24 square cm + 260 square cm = 284 square cm

So, the total surface area of the triangular prism is 284 square cm.

How are x intercepts and y intercepts different?

Answers

Answer:

The x intercept is the point where a line crosses the x axis, the y intercept is the point where a line crosses at the y axis (0)

Step-by-step explanation:

Answer:

they each go for different things. the x intercept could determine the number of something and the y intercept can stand for how many times something happened.

Step-by-step explanation:

Write an equation in standard form for the line that passes through th (6,0) and (0,7)

Answers

Answer:

y=-7/6 x+7

Step-by-step explanation:

Sandra conducted an observational study to learn how relationships with family affect happiness. She surveyed 500 people in her hometown and found that 85% say that positive relationships with family members make them happy. What could be the conclusion of her study?

Answers

She may conclude that in her hometown, a majority of people experience greater happiness thanks to positive relationships. However, in order to apply this to a greater population, she will have to use a larger sample of people.
Since this is an observational study and not an experiment, she can only conclude that there may be a link between closeness with family and happiness but we cannot say that closeness with family results in happiness.
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