X2+8x=-1 complete the square
1 answer:
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Step-by-step explanation:
Given x intercept is 1, So (x,y) is (1,0)
When x intercept is 1 then y value is 0
Another point on the line is (-2,3)
Two points are (1,0) and (-2,3)
Find out slope using the two given points
Use point slope formula
m=-1 and point(1,0)
Point slope equation is
Equation of the line in slope intercept form is
m∠1 = 30° (by Vertical angle theorem)
m∠A = 80° (by Triangle sum theorem)
m∠D = 80° (by Triangle sum theorem)
The value of x is 7.5 and y is 9.
Solution:
∠ACB and ∠DCE are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
⇒ m∠DCE = m∠ACB
⇒ m∠1 = 30° (by Vertical angle theorem)
In triangle ACD,
Triangle sum property:
<em>Sum of the interior angles of the triangle = 180°</em>
⇒ m∠A + m∠C + m∠B = 180°
⇒ m∠A + 30° + 70° = 180°
⇒ m∠A + 100° = 180°
⇒ m∠A = 100° – 180°
⇒ m∠A = 80° (by Triangle sum theorem)
Similarly, m∠D = 80° (by Triangle sum theorem)
In ΔACD and ΔDCE,
All the angles are congruent, so ΔACD and ΔDCE are similar triangles.
<em>In similar triangle corresponding sides are in the same ratio.</em>
Do cross multiplication.
90 = 12x
7.5 = x
Now, to find y:
Do cross multiplication.
9y = 72
Divide by 9, we get
y = 8
Hence the value of x is 7.5 and y is 9.