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Digiron [165]
3 years ago
8

Select the equation of the line parallel to the equation 2x + 4y = -5 that passes through the point (-4, -8).

Mathematics
1 answer:
marusya05 [52]3 years ago
7 0
The equation for the line will be x+2y=-20 
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The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.
Ratling [72]
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x

The equation to represent the perimeter of the triangle would be:
y = 3x - 6

The solutions to the system would be (12, 30) or (1, -3).  The only viable solution is (12, 30).

Explanation
The area of a triangle is found using the formula
A = 1/2bh

For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x

We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x

The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)

Combining like terms we get:
P = 3x - 6

We will replace P with y, so we have:
y = 3x - 6

Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:

3x - 6 = 1/2(x²) - (7/2)x

It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x

We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x

When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12

This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)

Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.

Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)

We cannot have a negative perimeter, so the only viable solution is (12, 30).
8 0
3 years ago
Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0. 36y'' − y = x
viktelen [127]
Try this solution, note, checking was not performed.

5 0
3 years ago
Brainliest question please help me please I need right answer please show your work
Oksana_A [137]

Answer:

outside the circle

Step-by-step explanation:

diameter and radius are the main attractions in maths regarding circles.

7 0
3 years ago
"flower, heart, circle." what is The 35th shape is
kramer

Answer:

heart

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Susan has purchased a whole life policy with a death benefit of $200,000. Assuming that she dies in 10 years and the average inf
Anika [276]

Answer:

Answer is: $148,809.52

Step-by-step explanation:

Susan has purchased a whole life policy with a death benefit of $200,000.

Assuming that she dies in 10 years.

Rate = 3% or 0.03

Future value after 10 years = (1+r)^{n} = (1.03)^{10} = 1.344

Purchasing power of proceeds = \frac{200000}{1.344}= $148,809.52

5 0
3 years ago
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