Answer:
12
Step-by-step explanation:
18*2=36, 60-36=24, 24/2=12
Answer:
Parallel
Step-by-step explanation:
The equation of a line in slope - intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Both given equations are in this form, that is
y = 
x + 1 → m =
y = x - 7 → m =
Parallel lines have equal slopes thus the lines are parallel
Answer:
x = 10°
Step-by-step explanation:
a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"
Therefore, in cyclic quadrilateral ABDE,
m∠ABD + m∠AED = 180°
110° + m∠AED = 180°
m∠AED = 180° - 110°
= 70°
b). AD = ED [Given]
m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]
m∠EAD = m∠AED = 70°
By triangle sum theorem in ΔABD,
m∠BAD + m∠ABD + m∠ADB = 180°
m∠BAD + 110° + 40° = 180°
m∠BAD = 180 - 150
= 30°
m∠AEB = m∠AED + m∠DAB [By angles addition postulate]
m∠AEB = 70° + 30°
= 100°
By triangle sum theorem in the large triangle,
x° + m∠AEB + m∠EAB = 180°
x° + 100° + 70° = 180°
x = 180 - 170
x = 10°
Answer:
x² -3/4x +1/4 = 0
Step-by-step explanation:
Consider the two equations in factored and expanded forms:
(x -p²)(x -q²) = x² -(p²+q²)x +p²q² = 0 ⇒ p²+q² = 1, p²q² = 16
and
(x -1/p)(x -1/q) = x² -(1/p+1/q)x +1/(pq) = 0
Consider the squares of the sum and product of roots:
constant term: (1/(pq))² = 1/(p²q²) = 1/16 ⇒ 1/(pq) = √(1/16) = 1/4
x-term: (1/p +1/q)² = (p +q)²/(pq)² = (p² +q² +2pq)/(p²q²)
= (p² +q²)/(p²q²) +2/(pq)
= 1/16 +2/√16 = 9/16 ⇒ (1/p +1/q) = √(9/16) = 3/4
Then the equation with roots 1/p and 1/q is ...
x² -3/4x +1/4 = 0
Answer:
(6, 3)
General Formulas and Concepts:
<u>Pre-Alg</u>
- Order of Operations: BPEMDAS
<u>Alg I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define systems</u>
4x = 8y
2x + 5y = 27
<u>Step 2: Rewrite systems</u>
x = 2y
2x + 5y = 27
<u>Step 3: Solve for </u><em><u>y</u></em>
- Substitute: 2(2y) + 5y = 27
- Multiply: 4y + 5y = 27
- Combine like terms: 9y = 27
- Isolate <em>y</em>: y = 3
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Plug in y into an original equation to find x.</em>
- Substitute: 4x = 8(3)
- Multiply: 4x = 24
- Isolate <em>x</em>: x = 6
