Y = mx + b
slope(m) = 3/4
(3,7)...x = 3 and y = 7
now we sub and find b, the y int
7 = 3/4(3) + b
7 = 9/4 + b
7 - 9/4 = b
28/4 - 9/4 = b
19/4 = b
so ur equation is : y = 3/4x + 19/4
if point A (x,5) lies on the line.....
y = 3/4x + 19/4......when y = 5
5 = 3/4x + 19/4
5 - 19/4 = 3/4x
20/4 - 19/4 = 3/4x
1/4 = 3/4x
(1/4) / (3/4) = x
1/4 * 4/3 = x
4/12 reduces to 1/3 = x......so point A is (1/3,5)...with x being 1/3
The best method that will work for any quadratic equation is to use the quadratic formula: x = (-b±√(b² - 4ac))/2a, this will work for any quadratic of the form ax² + bx + c = 0.
As for the last equation in the attachment, that is a cubic equation, these are much trickier to solve and as such the formula is much longer and very complicated. Therefore it is easier to see if it can be broken down into a linear term and a quadratic. This can be done by substituting integer values of x into the equation to see if it holds true. If both sides of the equation are equal for a given value of x then the equation ax³ + bx² + cx + d can be rewritten as (Ax + B)(px² + qx + r). This can then be put into the quadratic formula mentioned above.
Answer:
33.45
Step-by-step explanation:
Just multiply
Just put it like normally, forget the decimal for now, you don’t have to line it up due to it not being addition Or subtraction
You’ll get 3345 without the decimal
now there are 2 decimal places from 0 so
just move the decimal place 2 times to the left
33.45
Answer:
The answer to your question is
Step-by-step explanation:
Data
Foci (-2, 2) (4, 2)
Major axis = 10
Process
1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.
From the graph we conclude that it is a horizontal ellipse.
2.- Determine the foci axis (distance between the foci)
2c = 6
c = 6/2
c = 3
3.- Determine a
2a = 10
a = 10/2
a = 5
4.- Determine b using the Pythagorean theorem
a² = b² + c²
-Solve for b
b² = a² - c²
b² = 5² - 3²
b² = 25 - 9
b² = 16
b = 4
5.- Find the center (1, 2) From the graph, it is in the middle of the foci
6.- Find the equation of the ellipse

Answer:

Step-by-step explanation:
Given two expressions ,
And , we need to find the LCM , that is lowest common factor . So , let's factorise them seperately .
<u>Factorising</u><u> </u><u>x²</u><u> </u><u>-</u><u> </u><u>9</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Factorising</u><u> </u><u>3x</u><u>³</u><u> </u><u>+</u><u> </u><u>8</u><u>1</u><u> </u>
Hence we can see that (x+3) is common factor in both expressions.
<u>Hence</u><u> </u><u>the</u><u> </u><u>LCM</u><u> </u><u>is</u><u> </u><u>(</u><u> </u><u>x</u><u>+</u><u>3</u><u> </u><u>)</u><u> </u><u>.</u>