Identify all the hyperbolas which open horizontally

The hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Step-by-step explanation:

A hyperbola with equation of the form:

(x-h)^2/a^2-(y-k)^2/b^2)=1 opens horizontally

Then, the hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

and

Step-by-step explanation:

There are 2 types of hyperbolas:

Horizontal:

Vertical:

If the x term is positive then parabola is horizontal.

If the y term is positive then parabola is vertical.

so, only first two equations are in which x term is positive.

hence, equations are

and

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

14

step-by-step explanation:

14 x 3 = 42