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miskamm [114]
3 years ago
12

Find an equation for a line perpendicular to y= 3x – 5 , with a y- intercept of -2

Mathematics
1 answer:
damaskus [11]3 years ago
8 0

Answer:

Since the lines are Perpendicular..

The Product of their Gradients = -1

m'm"=-1

m' from y=3x - 5 is 3

3.m" = -1

m" = -1/3.

Since Intercept on y axis = -2...

That of x at that point is =0

y-y' = m"(x-x")

y-(-2) = -1/3( x - 0)

y+2 = -1/3(x)

Multiplying through by 3

3y + 6 = -x

3y + x = -6. This is your Equation

To verify this.

Let's turn it into the Intercept form which is

x/a + y/b = 1

To get 1 at the right hand side... Divide through by -6

3y/-6 + x/-6 = 1

y/-2 - x/6 = 1

You could see directly below y is its intercept and thats -2

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Factor completely: 2x4 − 32.
vazorg [7]

Answer:

Option b) is correct.

The completed factor of given expression is  2(x-2)(x+2)(x^2+4)

Step-by-step explanation:

Given expression is 2x^4-32

To find the completed factor for the given expression:

2x^4-32:

Taking the common number "2" outside  to the above expression we get

2x^4-32=2(x^4-16)

Now rewritting the above  expression as below

=2(x^4-2^4)  (since 16 can be written as the number 2 to the power of 4)

=2((x^2)^2-(2^2)^2)

The above expression is of the form a^2-b^2=(a+b)(a-b)

Here a=x^2 and  b=2^2

Therefore it becomes

=2(x^2+2^2)(x^2-2^2)

=2(x^2+4)(x^2-2^2)  

The above expression is of the form a^2-b^2=(a+b)(a-b)

Here a=x and  b=2

Therefore it becomes

=2(x^2+4)(x+2)(x-2)  

=2(x+2)(x-2)(x^2+4)  

Therefore =2(x+2)(x-2)(x^2+4)  

2x^4-32=2(x-2)(x+2)(x^2+4)  

Option b) is correct.

The completed factor of given expression is  2(x-2)(x+2)(x^2+4)

3 0
3 years ago
Read 2 more answers
Ou are mailing a package that weighs 5 pounds, and sending it first class. The post office charges $0.44 for the first ounce, an
Inga [223]
5 pounds= 80 ounces
total cost= ($0.44×1)+($0.20×79)=$16.24
3 0
3 years ago
The half of the day from midday to midnight can be described as
Serjik [45]

Answer:

24hours divided by 2 is 12

Step-by-step explanation:

8 0
3 years ago
An observer, whose eyes are 1.98 m above the ground, is standing 39.2 m away from a tree. The ground is level, and the tree is g
lozanna [386]

Answer:

The tree is 16.25 m tall.

Step-by-step explanation:

Attached is a diagram that better explains the problem.

From the diagram we see that the distance between the top of the tree and the line of sight of the observer is x.

To find the height of the tree, we need to first find x and then add it to the height of the observers line of sight from the ground.

Using SOHCAHTOA trigonometric function:

tan(20) = x/39.2

=> x = 39.2 * tan(20)

x = 39.2 * 0.364

x = 14.27m

Hence, the height of the tree is:

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The tree is 16.25 m tall.

5 0
3 years ago
Convert the linear equation 8x − 2y = 12 into function form.
alex41 [277]

Answer:

y=4x-6

Step-by-step explanation:

8x-2y=12

8x-2y-12=0

8x-12=2y

4x-6=y

8 0
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