Answer:
Option 4: 0
Step-by-step explanation:
Given the function, f(x) = 3x, and the domain. {-3, 1, 4}:
Substitute the values of each domain as inputs into the function:
<h3>x = -3</h3>
f(-3) = 3(-3)
f(-3) = -9
<h3>x = 1</h3>
f( 1 ) = 3( 1 )
f( 1 ) = 3
<h3>x = 4</h3>
f(4) = 3(4)
f(4) = 12
Therefore, the correct answer is option 4) 0, because there is no input value that provides an output of 0. You were only given three domain values that provided its corresponding outputs.
The volume of the first pan is (length x width x depth) =
(20cm x 16cm x 4.4cm) = 1408 cm³ .
The batter fills it, so we know there is 1408 cm³ of batter.
Somehow, Carla manages to transfer every drop and smidgen of batter to
the new pan, leaving not a single drip of it in the first pan. So we know that
there is 1408 cm³ of batter in the new pan. It will spread out to fill the whole
length and width of the new pan, and we're to calculate how deep it will be.
(length x width x depth) = 1408 cm³
(20cm x 20cm) x (depth) = 1408 cm³
(400 cm²) x (depth) = 1408 cm³
Divide each side by 400cm² : depth = 1408 cm³ / 400cm²
= 3.52 cm
Since the new pan is 5 cm deep, this works. The batter doesn't
overfill it and glurb out over the top and all over the counter.
The question asked how far the batter is <em>from the top of the pan</em>.
The pan is 5 cm deep.
The batter is 3.52cm deep.
The batter comes up to (5 - 3.52) = 1.48 cm from the top of the pan.
Rounded to the nearest tenth of a cm, that's <em>1.5 cm </em>from the top.
Answer:
15°,105°,195°,285°
Step-by-step explanation:
\frac{2 tan ~x}{1-tan^2 x} =\frac{1}{\sqrt{3} } \\tan ~2x=tan~30,tan~210,tan~ (30+360),tan~(210+360)\\2x=30,210,390,570\\x=15^\circ,105^\circ,195^\circ,285^\circ
Among the four choices, theorems is the best possible answer. Postulate, by definition, is a statement that is assumed to be true without proof while theorems are true statements that can be proven. Both of these types of statements are used to justify geometrical equations, illustrations and statements.
<em>Answer:</em>
Complete proof is written below.
Facts and explanation about the segments shown in question :
- As BC = EF is a given statement in the question
- AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
- AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
- AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.
Below is the complete proof of the observation given in the question:
<em />
<em>STATEMENT REASON </em>
___________________________________________________
1. BC = EF 1. Given
2. AB + BC = AC 2. Betweenness
3. AC > BC 3. Def. of segment inequality
4. AC > EF 4. Def. of congruent segments
<em />
<em>Keywords: statement, length, reason, proof</em>
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