Answer:
∠ADB≅∠ABC by the Alternate Interior Angles Theorem
∠CAD≅∠ACB by the Alternate Interior Angles Theorem
∠BAD and ∠ADV are supplementary by the Consecutive Interior Angle Theorem
∠ABC and ∠BCD are supplementary by the Consecutive Interior Angle Theorem
Answer:
28/7
Step-by-step explanation:
Answer:
a ) y = 1 and x = -1
d) y = 5 and x = -1/2
Step-by-step explanation:
<h2><u>
Substitution method</u></h2><h2><u>Question a</u></h2>
y = x+ 2
y = 2x + 3
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = x + 2
x = y - 2
now put y - 2 where x is in the second equation
y = 2x + 3
y = 2(y - 2) + 3
y = 2y - 4 +3
now solve
4 - 3 = 2y -y
y = 1
since y = 1 we can find what x is by putting into the first formula
y = x +2
x = y - 2
x = (1) -2
x = -1
<h3><u>hence y = 1 and x = -1 </u></h3><h3><u /></h3><h2><u>Question d</u></h2>
y = 2x + 6
y = 4 - 2x
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
now place (y-6)/2 where x is in the second formula
y = 4 -2x
y = 4 - 2 (
)
now solve
the multiplication by 2 and division by 2 are cancelled out
hence making the simplified equation as:
y = 4 - y + 6
2y = 4 + 6
2y = 10
y = 5
now place this into the first equation
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
x = (5-6)/2
x = -1/2
<h3><u>
hence y = 5 and x = -1/2</u></h3>
Answer:
4y^3/2
Step-by-step explanation:
The 4 will remain 4 so we'll leave that alone. √y³ can be written as y^3/2. The way I like to remember how to write fractional exponents is that the index of the radical is the denominator of the fractional exponent and the exponent inside the radical is the numerator.
Answer:
6
Step-by-step explanation:
The law of cosines is useful here.
a^2 = 8^2 +11^2 -2·8·11·cos(32.2°) ≈ 36.070003
a ≈ √36.070003 ≈ 6.00583
a ≈ 6