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3 years ago

Find the equation of a line that is parallel to

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

7 0

Answer:

g(x) = 3x - 3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

If a line is parallel to another, they have the same slope.

Step 1: Define variables

m = 3

Random pt (2, 3)

y = 3x + b

Step 2: Find b

3 = 3(2) + b

3 = 6 + b

b = -3

Step 3: Write parallel linear equation

y = 3x - 3

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3x + 5y = -19 5x - 2y = 16 solve for x and y

beks73 [17]

Step-by-step explanation:

2(3x + 5y = -19)

6x + 10y = -38

5 (5x -2y = 16)

25x - 10y = 80

19x = 42

but idk from there the rest doesn't work Soo if u can find the prob and tell me I'll fix it.

7 0

3 years ago

the length of a tangent from a point a at distance 5 cm from the centre of the circle is 4 cm find the radius of the circle

Semenov [28]

The radius of the circle is 3 cm.

Step-by-step explanation:

Refer the attached diagram, the circle with centre O. In that given, AB is tangent given as 4 cm and distance of point from the circle, OA = 5 cm

As AB is tangent, OB (radius of circle) is perpendicular to AB (tangent at any point of circle). Therefore the angle of OBA is 90 degree.

Also, triangle OAB is a right angled triangle (refer attached diagram). By using Pythagoras theorem in right angled triangle,

$(\text {Hypotenuse})^{2}=(\text {Height})^{2}+(\text {Base})^{2}$

$(O A)^{2}=(O B)^{2}+(A B)^{2}$

Substitute the given values in the above expression, we get

$(5)^{2}=(O B)^{2}+(4)^{2}$

$(O B)^{2}=25-16=9$

Taking square root on both side, we get

Radius of the circle, OB = 3 cm

5 0

3 years ago

2 glasses of milk and 3 snack bars have a total of 73 carbohydrates (carbs), and 4 glasses of milk and 2 snack bars have a tota

Lena [83]

Answer:

There are 14 Carbs in 1 glass of milk.

8 0

3 years ago

Match the following items by evaluating the expression for x = -6.

Kryger [21]

Step-by-step explanation:

Put the value of x = -6 to all expressions:

$x^{-2}=(-6)^{-2}=\dfrac{1}{(-6)^2}=\dfrac{1}{6}\qquad\text{used}\ a^{-n}=\dfrac{1}{a^n}\\=====================\\x^{-1}=(-6)^{-1}=\dfrac{1}{(-6)^1}=-\dfrac{1}{6}\\=====================\\x^0=(-6)^0=1\qquad a^0=1\ \text{for all real numbers except 0}\\=====================\\x^1=(-6)^1=-6\qquad a^1=a\ \text{for all real numbers}\\=====================\\x^2=(-6)^2=36$

5 0

3 years ago

04.03 HC)

faust18 [17]

Part A:

To find the average rate of change, let us first write out the equation to find it.

Δy/Δx = average rate of change.

Finding average rate of change for Section A

Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5

Δx = 1- 0 = 1

Plug the numbers in: Δy/Δx = 5/1 = 5

Therefore, the average rate of change for Section A is 5.

Finding average rate of change for Section B

Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

Δx = 3 - 2 = 1

Plug the numbers in: Δy/Δx = 36/1 = 36

Therefore, the average rate of change for Section B is 36.

Part B:

(a) How many times greater is the average rate of change of Section B than Section A?

If Section B is on the interval [2,3] and Section A is on the interval [0,1].

For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.

(b) Explain why one rate of change is greater than the other.

Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.

6 0

3 years ago