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Murrr4er [49]
1 year ago
13

Which of the following are among the five basic postulates of Euclidean geometry?

Mathematics
1 answer:
lana66690 [7]1 year ago
6 0

Answer:

Choices B, C, and D are correct.

Step-by-step explanation:

Euclid's Five postulates are as follows:

<em>1. A straight line segment may be drawn from any given point to any other.</em>

<em>2. A straight line may be extended to any finite length.</em>

<em />

<em>3. A circle can be drawn with any center and radius.</em>

<em />

<em>4. All right angles are congruent/equal to each other.</em>

<em />

<em>5. Through a point not on a given line, there is exactly one line parallel to the given line.</em>

Now looking at these postulates and the choices we are given we see that only choice B, C, and D match with above.

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In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) =x2 to the number of x-intercepts in
Natalija [7]
Important:  Please use " ^ " to indicate exponentiation:

<span>"f(x) =x^2 to the number of x-intercepts in the graph of g(x) = x^2 +2."

Notes:  the graph of f(x) = x^2 is a vertical parabola that opens up.  It has its vertex at (0,0).  This is the only point at which f(x)=x^2 has a horiz. intercept.

g(x) = x^2 + 2 has a graph that looks the same as that of f(x) = x^2, EXCEPT that the whole graph is moved 2 units UP.  This new graph never touches or intersects the x-axis.  Therefore, g(x) has NO horiz. intercepts (no x-int.).

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7 0
2 years ago
The chart below lists the original and sale prices of items at a clothing store.
Tom [10]

Answer: C) For every original price, there is exactly one sale price.

For any function, we always have any input go to exactly one output. The original price is the input while the output is the sale price. If we had an original price of say $100, and two sale prices of $90 and $80, then the question would be "which is the true sale price?" and it would be ambiguous. This is one example of how useful it is to have one output for any input. The input in question must be in the domain.

As the table shows, we do not have any repeated original prices leading to different sale prices.

5 0
1 year ago
Read 2 more answers
Triangle L N M is shown. Angle L N M is a right angle. An altitude is drawn from point N to point O on side L M, forming a right
zaharov [31]

Answer:

Therefore the value of k = 6.

Step-by-step explanation:

Given:

LN = m

NM = l

OM = k

NO = 4

LO = 8

LM = 8 + k and

Δ LNM ,Δ LON and Δ MON are right Triangle.

To Find :

Om = k = ?

Solution:

In Right angle Triangle By Pythagoras Theorem we have,

(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}

So, In Right angle Triangle Δ LON we have,

LN² = ON² + OL²

m² = 4² + 8²

m² = 80   ............( 1 )

Now in  Right angle Triangle Δ MON we have,

MN² =  ON² + MO²

l² = 4² + k² ....................( 2 )

Now In Right angle Triangle Δ LNM we have,

LM² = LN² + MN²

(8 + k)² = m² + l² .................( 3 )

Substituting equation  1 and equation 2 in equation 3

(8+k)² = 80 + 4² + k²

Applying (A+B)² = A² +2AB + B² we get

64 + 16k+k^{2} = 80+ 16 +k^{2} \\\\16k=96\\\\\therefore k=\frac{96}{16} \\\\\therefore k=6

Therefore the value of k = 6.

4 0
1 year ago
Read 2 more answers
Simplify this expression: One-half k squared + g minus 3 + one-half k squared minus 3 + 2 g k2 + 3g – 6 One-fourthk2 + 3g 3g + 9
Alborosie

Answer:

The answer is A, k2 + 3g – 6

Step-by-step explanation:

did the assignment on edge2020

7 0
2 years ago
Read 2 more answers
What is the missing statement in the proof? Scroll down to see the entire proof.
Eva8 [605]

Answer: C. \angle BCA\cong \angle DCB is the missing statement.

Explanation: Given: ΔABC with m∠ABC = 90° (view diagram)

Prove: AB^2 + BC^2 = AC^2

Proof:  1. Draw BD\perp AC (construction)

 2. \angle ABC\cong\angle BDC  (Angles with the same measure are congruent.)

3. \angle BCA\cong \angle DCB (Reflexive Property of Congruence)

4. \triangle ABC\sim \triangle BDC  (AA criterion for similarity)

5. BC:DC=AC:BC  (Corresponding sides of similar triangles are proportional.)

 6.BC^2= AC\times DC  (cross multiplication)----------(1)

7. \angle ABC\cong \angle ADB (Angles with the same measure are congruent)

8. \angle BAC\cong \angle DAB (Reflexive Property of Congruence)

9. \triangle ABC\sim \triangle ADB  (AA criterion for similarity)

10.  AB:AD=AC:AB⇒AB^2=AC.AD --------------(2)

equation (1) + equation (2) ⇒AB^2+BC^2= AC(DC+AD)⇒AB^2+BC^2= AC^2


6 0
1 year ago
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