Solve for x. Pls explain your answer.

x = 8

Step-by-step explanation: The question shows two separate trapeziums DEFG and QRSP. In figure DEFG two sides and three angles are given. However, if we turn figure QRSP upside down, we can see that what we have is two similar trapeziums, DEFG and SPQR. Upon closer examination, we would see that line DE = line SP

Similarly line GF = line RQ

Also angle F = angle Q.

Having take note of these similarities, we can now express them as follows;

2x - 4 = 12 {i.e RQ = GF}

6y + x = 68 {i.e Q = F}

What we now have is a pair of simultaneous equations

2x - 4 = 12 ————(1)

6y + x =68 ————(2)

From equation (2)

x = 68 - 6y (by rearranging and making x the subject of the formula)

We can now substitute for the value of x into equation (1)

2x - 4 = 12

2(68 - 6y) - 4 = 12

By expanding the bracket, we now have

136 - 12y - 4 = 12

By regrouping and collecting like terms,

136 - 4 - 12 = 12y

Remember that if a negative number crosses to the other side of the equality sign, it becomes positive, and vice versa. Hence, negative 12y crosses to the right hand side of the equation and becomes positive 12y.

136 - 4 - 12 = 12y

120 = 12y

Divide both sides of the equation by 12

10 = y

Now we can substitute for the value of y = 10 into equation (2)

6y + x = 68

6(10) + x = 68

60 + x =68

Subtract 60 from both sides of the equation

x = 8.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0