For what values of x is x² + 2x = 24 true?
A -6 and 4
B -4 and 6
C 4 and -6
D 6 and 4

x=6 or x=-4

Step-by-step explanation:

This question is under the topic factorisation... which means we will have to factorise the given equation before getting the answer

x^2+2x=24

To be able to factorise,we will have to substrate 24 from both sides

X^2+2x-24=0

Factorisation is when you get two numbers that when you add up it will give you one of the number given in the question as well as when you multiply it will also give you another number in the question

The general formula for factorisation

X^2-(sum of the two numbers)x+(product of two numbers)

Considering the question, we have -24, what will we multiply to get -24 and when add together it can give us +2

Let's consider+6&+4

If we should multiply them we will get +24 instead of-24 and if we should add up it will give 10 instead of 2...so it is not possible to use them

Let's consider +6 and-4

If we multiply them we will get -24

And if we add we will get +2

Therefore we are taking -6 and+4

X2-6x+4x-24=0

x(x-6)+4(x-6)=0

(x-6)(x+4)=0

x=6 or x=-4

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.