Answer:
the last option is the correct one
Step-by-step explanation:
first one is C and second is D
Answer:
Step-by-step explanation:
The axis of symmetry lies exactly halfway between the given x = 1 and x = -5.
The axis of symmetry is x = -2.
The 'halfway' value is also the 'average' of 1 and -5: -4/2, or -2.
The axis of symmetry is x = -2.
<h3>
Answer:</h3>
C. Two-thirds vote
<h3>
Step-by-step explanation:</h3>
To help with checks and balances, the consitution allows congress to override a presidential veto with a two-thirds vote; also known as a constitutional majority.
Intial Vote
When Congress first votes on a normal bill (not a consitutional change) all that is required is a simple majority. A simple majority means more than 50 percent.
Presidential Veto
Just because something is passed by Congress does not mean that it will be a law. The President still has to sign the bill into law. However, the President has the option to veto the bill.
Overriding a Veto
If a bill is overridden, Congress can move to override the veto. If they want to override the veto, there must be a 2/3's majority that agrees to pass the bill again.
Additionally, when overriding a veto any votes that are not affirmative, this includes abstentions and absent voters, are considered opposing votes. For example, if 2 congressmen did not show up to vote, then their votes would automatically be counted against the bill.
<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
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Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
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See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
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Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction
