*. If (2,3) and (-6,5) are the end points of diagonal of a square. Find the equation of another diagonal. Please help with this question..

 y = 4x + 12    (edited to reflect a SQUARE)

Step-by-step explanation:

Opposite Diagonal of a square means the line goes through the midpoint and has the opposite reciprocal slope.

Use the Midpoint formula:    

Use the Slope formula:  

Opposite Diagonal slope is opposite (change the sign) and reciprocal (flip the fraction)  → m⊥ = + 4

Now use the Point-Slope formula:   y - y₁ = m⊥(x - x₁)    where

y - 4 = 4(x + 2)

y - 4 = 4x + 8

   y = 4x + 12

Simple question

slope of on le diagonal,whose coordinates are given=

now we know that diagonals of square are perpendicular to each other

and we also know that if there are two perpendicular lines have slope m1 and m2 respectively,then

so if one diagonal's slope is -1/4 then other diagonal's slope will be 4

now we know that all the equation of a line is in the form

y=mx+c

where m is slope

so simply put the value of m=4

y=4x+c...i)

we also know that the line of equationi) will pass through the midpoint coordinates of first diagonal

mid point of first diagonal ={(2-6)/2 ,(5+3)/2}=(-2,4)

put this value of x and y in i) equation

4=-8+c

c=12

hence putting the value of c in equation I) we get the equation of line as

y=4x+12

y-4x-12=0

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places