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Mekhanik [1.2K]
2 years ago
10

Write the slope intercept equation of a line that has a 3 slope of 5 & y-intercept of (0, –4). y =​

Mathematics
1 answer:
Karo-lina-s [1.5K]2 years ago
3 0
If the question is asking what the equation is when the slope is 5 then the equation will be y=5x-4 since the stem of the equation is going to be y=mx+b, m is the slope and b is the y intercept
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Find a homogeneous linear differential equation with constant coefficients whose general solution is given by
frez [133]

Answer:

y" + 2y' + 2y = 0

Step-by-step explanation:

Given

y=c_1e^{-x}cosx+c_2e^{-x}sinx

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)

Where

\alpha = -1 and \beta = 1

For a homogeneous linear differential equation, the repeated value m is given as:

m = \alpha \± \beta i

Substitute values for \alpha and \beta

m = -1 \± 1*i

m = -1 \± i

Add 1 to both sides

m +1= 1 -1 \± i

m +1= \± i

Square both sides

(m +1)^2= (\± i)^2

m^2 + m + m + 1 = i^2

m^2 + 2m + 1 = i^2

In complex numbers:

i^2 = -1

So, the expression becomes:

m^2 + 2m + 1 = -1

Add 1 to both sides

m^2 + 2m + 1 +1= -1+1

m^2 + 2m + 2= 0

This corresponds to the homogeneous linear differential equation

y" + 2y' + 2y = 0

6 0
3 years ago
an item is regularly priced at $70. It is on sale for 30% off the regular price. how much in dollars is discounted from the regu
sleet_krkn [62]
$9 is discounted from the regular price. If you find the discounted price you get $21. Then subtract the 21 from 30 and you get 9
7 0
3 years ago
Hello I don’t understand question 9 a and b. Please show working out.<br> Thanks
brilliants [131]
A) I would make the positive integer x and then form an equation.

x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6

Since the question asks for a positive integer the answer is 7.

B) two positive numbers x and y.

X - y = 3
x^2 + y^2 = 117

Use these simultaneous equations to figure out each number.

Rearrange the first equation

x = y + 3

Then substitute it into the second equation.

(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)

This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.

Use y to find x

x = y + 3
x = 6 + 3
x = 9

So the answers are x = 9 and y = 6.
3 0
3 years ago
How many eighth-size parts do you need to model 3/4
Molodets [167]
8 divided by 2 is 4, so multiply 3/4 by 2, 6/8, than you have your answer, 6.
8 0
2 years ago
Ms. Snyder is giving a 28-question test that is made up of multiple choice questions worth 2 points each and open response quest
zlopas [31]

Answer:

x *2 + (28-x)*4 = 100

Step-by-step explanation:

Given

Total number of questions in the paper = 28

Out of these 28 questions let us say that x number of questions are of 2 points and 28-x questions are of 4 points.

Also, the complete test is of 100 marks

Thus, the linear equation representing the

x *2 + (28-x)*4 = 100

8 0
2 years ago
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