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3 years ago

A conjecture and the two-column proof used to prove the conjecture are shown.

Mathematics

2 answers:

Nonamiya [84]3 years ago

8 0

Answer:a=29939¥…§|3

Step-by-step explanation:

aliina [53]3 years ago

5 0

Answer: the statements and resons, from the given bench, that fill in the blank are shown in italic and bold in this table:

Statement Reason

1. K is the midpoint of segment JL Given

2. segment JK ≅ segment KL Definition of midpoint

3. L is the midpoint of segment KM Given

4. segment KL ≅ segment LM Definition of midpoint

5. segment JK ≅ segment LM Transitive Property of

Congruence

Explanation:

1. First blank: you must indicate the reason of the statement "segment JK ≅ segment KL". Since you it is given that K is the midpoint of segment JL, the statement follows from the very Definition of midpoint.

2. Second blank: you must add a given statement. The other given statement is segment KL ≅ segment LM .

3. Third blank: you must indicate the statement that corresponds to the definition of midpoint. That is segment KL ≅ segment LM .

4. Fourth and fith blanks: you must indicate the statement and reason necessary to conclude with the proof. Since, you have already proved that segment JK ≅ segment KL and segment KL ≅ segment LM it is by the transitive property of congruence that segment JK ≅ segment LM.

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Please answer! I crossed out the ones you don’t have to complete.

Nina [5.8K]

Answer:

1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

5. $x^-6 = \frac{1}{x^6}$

6. $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7. $a^{-3}b^0c^4=\frac{c^4}{a^3}$

Step-by-step explanation:

Question 1:

We need to rewrite the expression using exponents

5.a.b.b.5.c.a.b.5.b

We will first combine the like terms

5.5.5.a.a.b.b.b.b.c

Now, if we have 5.5.5 we can write it in exponent as: $=5^{1+1+1}=5^3$

a.a as $a^{1+1}=a^2$

b.b.b.b as: $b^{1+1+1+1}=b^4$

So, our result will be:

$5^3a^2b^4c$

Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

Question:

Rewrite using positive exponent:

The rule used here will be: $a^{-1}=\frac{1}{a^1}$ which states that if we need to make exponent positive, we will take it to the denominator.

Applying thee above rule for getting the answers:

5) $x^{-6} = \frac{1}{x^6}$

6) $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7) $a^{-3}b^0c^4=\frac{b^0c^4}{a^3}$

We know that $b^0=1$ so, we get

$a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}$

4 0

3 years ago

"Sofia went on a road trip to visit her family. She first traveled from West Palm Beach to Fort Myers which is 108 miles away. T

m_a_m_a [10]

Answer:

Sofia went on a road trip to visit her family. She first traveled from West Palm Beach to Fort Myers which is 108 miles away. The next day, she drove to Miami for a distance of 135 miles. Finally, driving back home for 81 miles. Determine if the three towns on Sofia’s road trip form a right triangle. Which statement is correct?"

3 0

3 years ago

The monthly output P of a light bulb factory is given by the formula P = 450LK, where L is the amount invested in labor and K th

Tems11 [23]

Answer:

C(p) = 4,96 (in thousands of dollars)

l = 2980 $ invest in labor

k = 2980 $ invest in equipment

Step-by-step explanation:

Information we have:

Monthly output P = 450*l*k ⇒ k = P/450*l

But the production need to be 4000

Then k = 4000/450*l

Cost of production = l * k (in thousands of dollars)

C(l) = l + 4000/450*l

Taking derivatives (both members of the equation)

C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0

45*l² - 400 = 0 ⇒ l² = 400/45

l = 2.98 (in thousands of dollars)

l = 2980 $ And

k = 400/45*l ⇒ k 400/45*2.98

k = 2.98 (in thousands of dollars)

C(p) = l + k

C(p) = 2980 + 2980

C(p) = 5960 $

4 0

3 years ago

9. In a rhombus whose side measures 34 and the smaller angle is 42°. Find the length of the larger diagonal, to the nearest tent

Veseljchak [2.6K]

Answer:

63.5

Step-by-step explanation:

The diagonals of a rhombus bisect opposite angles.

The longer diagonal bisects the 42° angle

The larger angle of the rhombus is 180 - 42 = 138

Let x = the length of the longer diagonal

You know two sides and the included angle of a triangle.

Using the law of cosines we get

$x^{2} = 34^{2} + 34^{2} -2(34)(34) cos 138\\ = 1156 + 1156 - 2312 cos 138\\ = 4030.150837...\\x = \sqrt{4030.150837} = 63.48$ $x^{2} = 34^{2} + 34^{2} -2(34)(34)cos 138\\ = 1156 + 1156 - 2312 cos 138\\ = 4030.1508...\\ x = \sqrt{4030.1508} \\ = 63.48$ x^2 = 34^2 + 34^2 - 2(34)(34) cos 138