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kirza4 [7]
2 years ago
7

What is the Hinge Theorem used to show? A. that two triangles are similar B. the relative lengths of the corresponding sides in

two triangles C. the congruency of adjacent sides D. the relative measures of the corresponding angles in two triangles
Mathematics
1 answer:
Montano1993 [528]2 years ago
8 0

Answer:

B. The relative lengths of the corresponding sides in two triangles.

Step-by-step explanation:

We know that, Hinge theorem states that if two sides of one triangle is congruent to two sides of another triangle and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Or we can also say it as, if two triangles have two congruent sides (sides of equal length), then the triangle with the larger angle between those sides will have a longer third side.

So basically,Hinge theorem compares the relative lengths of the corresponding sides in two triangles.

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Complete the sentence below. If (3x2 + 22x + 7) ÷(x + 7) = 3x + 1, then (x + 7)(???????) =???? .
g100num [7]

Answer: The answer is (x+7)(3x+1)=33x^2+22x+7.

Step-by-step explanation: Given that

(3x2 + 22x + 7) \div(x + 7) = 3x + 1,

and we are to complete the following sentence:

(x+7)(???)=???

We have the following division algorithm for polynomials

\textup{If }a(x)\times b(x)=c(x),\\\textup{then, we have }\\\\\dfrac{c(x)}{b(x)}=a(x)~~~~~\textup{or}~~~~~~c(x)\div b(x)=a(x).

Here, a(x) = quotient, b(x) = divisor and c(x) = dividend.

Applying this rule in the given problem, we have

\textup{since }(3x2 + 22x + 7) \div(x + 7) = 3x + 1,\\\\\textup{so, }\\\\(x+7)(3x+1)=3x^2+22x+7=0.

Thus, the complete sentence is

(x+7)(3x+1)=3x^2+22x+7=0.

7 0
2 years 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
If sin(x) = 1/3 and sec(y) = 25/24 , where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities
Dominik [7]
<span>sin(x-y) = (24-14*sqrt(2))/75 Write down what you know sin(x) = 1/3 sec(y) = 25/24 cos(y) = 1/sec(y) = 24/25 cos(x) = sqrt(1-sin(x)^2) = sqrt(1-1/9) = sqrt(8/9) = 2*sqrt(2)/3 sin(y) = sqrt(1-cos(y)^2) = sqrt(1-576/625) = sqrt(49/625) = 7/25 We now know the sin and cos of both x and y. Now to get the sin of x-y. sin(x-y) = sin(x)cos(y) - cos(x)sin(y) Substitute the known values for sin and cos of x and y, then evaluate and simplify sin(x-y) = (1/3)(24/25) - (2*sqrt(2)/3)(7/25) sin(x-y) = 24/75 - 14*sqrt(2)/75 sin(x-y) = (24-14*sqrt(2))/75</span>
5 0
2 years ago
Melissa practiceted piano for 5/6 of an hour. On Monday and 8/9 of an hour on Tuesday. How many more minutes did she practice on
Charra [1.4K]

Answer:

24 hrs

Step-by-step explanation:

99594iu58

3 0
2 years ago
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A coin was tossed 60 times and the coin landed on Heads 35 times. What proportion of the time did the coin land on Heads?
SVETLANKA909090 [29]

Answer: Hence, the proportion of head lands obtained from the total number of tosses is 0.583

Step-by-step explanation:

Given the following :

Total number of coin tosses = 60

Total number of times coin landed on head = 35

Proportion of head landings obtained :

Total number of head landings obtained / total number of coin tosses

Proportion of head landing obtained :

= 35 / 60 = 7 / 12 = 0.5833

4 0
2 years ago
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