Could someone help me for this?
1 answer:
Answer:
x = - , x =
Step-by-step explanation:
to find the points of intersection equate the 2 equations , that is
7x - 15 = 10 + 12x - 6x² ( subtract 10 + 12x - 6x² from both sides )
6x² - 5x - 25 = 0 ← factor the quadratic on left side
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × - 25 = - 150 and sum = - 5
the factors are - 15 and + 10
use these factors to split the x- term
6x² - 15x + 10x - 25 = 0 ( factor the first/second and third/fourth terms )
3x(2x - 5) + 5(2x - 5) = 0 ← factor out (2x - 5) from each term
(2x - 5)(3x + 5) = 0
equate each factor to zero and solve for x
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = -
2x - 5 = 0 ⇒ 2x = 5 ⇒ x =
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Answer:
<h3>B. 4units</h3>Step-by-step explanation:
Find the diagram attached. The diagram is a similar triangle.
From the diagram, XZ/XY = CA/AB
Given XZ = 2x-2+2x-2 = 4x-4
XY =5x-7
CA = 2x-2
AB= x+1
On substituting this parameters into the formula to get x first
4x-4/5x-7 = 2x-2/x+1
cross multiply
(4x-4)(x+1) = 5x-7(2x-2)
open the parenthesis
4x²+4x-4x-4 = 10x²-10x-14x+14
4x²-4 = 10x²-24x+14
10x²-4x²-24x+14+4 = 0
6x²-24x+18 = 0
x²-4x+3 = 0
x²-3x-x+3 = 0
x(x-3)-1(x-3) =0
(x-3)(x-1) = 0
x = 3 and 1
Next is to get length AX.
Given AX = 2x-2
Substitute x = 3 into the expression
AX = 2(3)-2
AX = 6-2
AX = 4 units
Hence the measure of length AX is 4 units
