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just olya [345]
3 years ago
10

What additional information do you need to prove that ∆LMO ≅ ∆LNO by the HL Theorem? ∠NLO ≅ ∠MLO ∠MOL ≅ ∠NOL

Mathematics
2 answers:
BabaBlast [244]3 years ago
7 0

For a better understanding of the solution given here please find the diagram in the file attached.

We know from the Hypotenuse Leg Theorem (the HL theorem) that "if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent."

Thus, as can be seen from the diagram, Side LO (also called leg LO) is common to both the triangles LMO and LNO. <u>Therefore, the additional information that will be required to prove the congruence is that the respective hypotenuses, MO and NO are equal.</u>

FromTheMoon [43]3 years ago
5 0
The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
The triangles ΔLNO and ΔLMO have the same leg Lo, therefore you need the equality of hypotenuses LM=LN.

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A water molecule is made up of 3 atoms. One third of the atoms are oxygen and the remaining atoms are hydrogen. If there are 114
Mashcka [7]

Answer:

228 hydrogen atoms

Step-by-step explanation:

In a water molecule,

1/3rd is oxygen atoms, and

2/3rd (1 - 1/3 = 2/3) is hydrogen atoms

If there are 114 water molecules,

Total number of atoms would be:

3 * 114 = 342 (1 oxygen and 2 hydrogen atoms in 1 water molecule)

Out of these, 2/3rd would be hydrogen atoms, so:

\frac{2}{3}*342=228

There would be 228 hydrogen atoms

7 0
3 years ago
Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answ
gulaghasi [49]

Answer:

Part a ) The degrees of freedom for the given two sample non-pooled t test is 24

Part b ) The degrees of freedom for the given two sample non-pooled t test is 30

Part c ) The degrees of freedom for the given two sample non-pooled t test is 30

Part d ) The degrees of freedom for the given two sample non-pooled t test is 25

Step-by-step explanation:

Degrees of freedom for a non-pooled two sample t-test is given by;

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Now given the information;

a) :- m = 12, n = 15, s₁ = 4.0, s₂ = 6.0

we substitute

Δf =  {[ 4²/12 + 6²/15 ]²} / {[( 4²/12)²/12-1] + [(6²/15)²/15-1]}

Δf  = 30184 / 1241

Δf  = 24.3223 ≈ 24 (down to the nearest whole number)

b) :- m = 12, n = 21, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/12 + 6²/21 ]²} / {[( 4²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 56320 / 1871

Δf = 30.1015 ≈ 30 (down to the nearest whole number)

c) :- m = 12, n = 21, s₁ = 3.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 3²/12 + 6²/21 ]²} / {[( 3²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 29095 / 949

Δf = 30.6585 ≈ 30 (down to the nearest whole number)

d) :- m = 10, n = 24, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/10 + 6²/24 ]²} / {[( 4²/10)²/10-1] + [(6²/24)²/24-1]}

Δf = 1044 / 41  

Δf = 25.4634 ≈ 25 (down to the nearest whole number).

6 0
3 years ago
Writebthe name of the period that has the digit 913
den301095 [7]
Nine hundred thirteen thousand
7 0
3 years ago
If 19 ounces is $5.32 then how much is 1 ounce worth?
Scilla [17]

Answer:

$3.57

Step-by-step explanation:

19/5.32=3.571...

rounded it equals 3.57

hope this helps :3

if it did pls mark brainliest

6 0
3 years ago
Spiral Review (5.NBTA.1, 5.NBT A.2, 5.NBTB.5, 5.NET.B.6) 3. A small company packs 12 jars of jelly into each of 110 boxes to bri
marysya [2.9K]
If there are 12 jars of jelly in one box, and we have 110 boxes
we will do the following operation:
12 x 110=1320 jars of jelly 
4 0
3 years ago
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