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kotykmax [81]
2 years ago
8

What is the equation of a line that is perpendicular to the line y = -3x + 2 and passes through the point (6,8)?

Mathematics
1 answer:
aivan3 [116]2 years ago
3 0

Answer:

y = 1/3x+6

Step-by-step explanation:

y = -3x+2 is in slope intercept form  y = mx+b  where m is the slope and b is the y intercept

The slope is -3

Perpendicular lines have slopes that are negative reciprocals

The slope of the perpendicular line is  -1/-3 = 1/3

The equation of the new line is

y = 1/3x +b

Using the point that passes through the line ( 6,8) and substituting in for x and y

8 = 1/3(6) +b

8 = 2+b

8-2 =b

6 =b

The equation becomes

y = 1/3x+6

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A family has two cars. the first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of
marusya05 [52]
Car 1 consumes 30 gallons of gas.Car 2 consumes 20 gallons of gas.
7 0
3 years ago
One number is times a first number. A third number is 100 more than the first number. If the sum of the three numbers
icang [17]

When a number is 3 times a first number. A third number is 100 more than the first number and the sum of the three numbers is 450, the numbers are 70, 170 and 210.

<h3>How to calculate the numbers?</h3>

Let the first number = x

Second number = 3x

Third number = x + 100

Sum = 450

The numbers will be:

x + 3x + x + 100 = 450

5x + 100 = 450

5x = 450 - 100

5x = 350

Divide

x = 350 / 5

x = 70

First number = 70

Second number = 3x = 3 × 70 = 210

Third number = x + 100 = 70 + 100 = 170

Therefore, the numbers are 70, 170 and 210.

Learn more about numbers on:

brainly.com/question/24644930

#SPJ1

One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 450 , find the numbers.

8 0
11 months ago
What is f(g(x)) when f(x) = x2 + 5, and g(x) = 10 - 5x?
Mashutka [201]

Answer:

D

Step-by-step explanation:

To obtain f(g(x)) substitute x = g(x) into f(x), that is

f(10 - 5x)

= (10 - 5x)² + 5 ← expand (10 - 5x)²

= 100 - 50x - 50x + 25x² + 5 ← collect like terms

= 25x² - 100x + 105 → D

5 0
3 years ago
A triangular pyramid has a base with an area of 43 cm squared and lateral faces with bases of 10 cm and heights of 8.6 cm. What
Jet001 [13]

Answer:

The total surface area of triangular pyramid is 172 cm squared

Step-by-step explanation:

Triangular pyramid:

  • Number of faces 4.
  • Number of vertices of a triangular pyramid is 6.
  • The volume  is \frac13 AH. A= area of the pyramid's base and H= height of the pyramid.
  • The surface area of triangular pyramid B+L. B= area of base, L= area of lateral surface.

Given that, the area of the base is 43 cm squared. Lateral faces with bases of 10 cm and heights 8.6 cm.

The 3 sides of the triangular pyramid is triangle in shape.

The area of triangle is \frac12 \times base \times height.

The lateral surface area of the triangular pyramid is

=3(\frac12 \times base \times height)

=3(\frac12\times 10\times8.6) cm squared

=129 cm squared

The total surface area of triangular pyramid is

=Area of the base + lateral surface area

=(43+129) cm squared

=172  cm squared

8 0
3 years ago
What is the explicit formula for the sequence?
Aleksandr [31]

Answer:

a_{n} = n - 2

Step-by-step explanation:

Note the difference between consecutive terms is constant, that is

0 - (- 1) = 0 + 1 = 1

1 - 0 = 1

2 - 1 = 1

3 - 2 = 1

This indicates the sequence is arithmetic with n th term

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 1, thus

a_{n} = - 1 + n - 1 = n - 2

7 0
3 years ago
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