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LekaFEV [45]
3 years ago
11

Determine whether the triangles must be congruent. If so, name the postulate or theorem that justifies your answer. If not, expl

ain. Is 16 and 18 Angle-Side-Angle or Angle-Angle-Side? Please help ASAP!

Mathematics
1 answer:
Alona [7]3 years ago
6 0
Problem 16)

We use ASA (angle side angle) to show the two triangles are congruent. Why ASA instead of AAS? Because the single pair of sides are between the two angles. 

--------------------------------------------

Problem 18)

Similar to problem 16, we'll have two pairs of congruent angles, and a pair of congruent sides. However, the sides are NOT between the two angles. So that means we use AAS in this case.
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3 years ago
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Green thumb landscaping want to build a $124000.00 greenhouse in 2 years. The company sets up a sinking fund with payments made
DENIUS [597]

Answer:

$<em>150,858.5</em>

Step-by-step explanation:

The formula for calculating compound interest is expressed as;

A = P(1+r/n)^nt

P is the Principal = $124000.00

r is the rate = 12% = 0.12

t is the total time = 2 years

n is the time of compounding = 1/4 = 0.25(quarterly)

Substitute into the formula;

A= 124000(1+0.12/(0.25))^(0.25)(2)

A = 124000(1+0.48)^0.5

A = 124000(1.48)^0.5

A = 124000(1.2166)

A = 150,858.5

<em>The amount after 2 years if compounded quarterly is  150,858.5</em>

8 0
3 years ago
Calcula en cada caso las restantes razones trigonométricas de un angulo agudo si se conoce que:
olchik [2.2K]
A) cos a = (√22)/5; tan a = (√66)/22
B) sin a = (2√2)/3; tan a = 2√2
C) sin a = (√30)/6; cos a = (√6)/6
D) sin a = 3/5; tan a = 3/4
E) sin a = (5√26)/26; cos a = (√26)/26
F) sin a = 3/5; tan a = 3/4

Explanation
The ratio for sine is opposite/hypotenuse.  This means the side opposite the angle is √3 and the hypotenuse is 5.  Using the Pythagorean theorem to find the adjacent side,
(√3)² + A² = 5²
3+A² = 25
A² = 22
A=√22
This means that cos a = adjacent/hypotenuse = (√22)/5 and tan a = opposite/adjacent = (√3)/(√22) = (√66)/22.
B)  The ratio for cosine is adjacent/hypotenuse; this means the side adjacent to the angle is 1 and the hypotenuse is 3.  Using the Pythagorean theorem to find the side opposite the angle (p),
1² + p² = 3²
1+p² = 9
p² = 8
p=√8 = 2√2
This means that sin a = opposite/hypotenuse = (2√2)/3 and tan a = opposite/adjacent = (2√2)/1 = 2√2.
C) The ratio for tangent is opposite/adjacent; this means that the side opposite the angle is √5 and the side adjacent the angle is 1.  Using the Pythagorean theorem to find the hypotenuse,
(√5)²+1² = H²
5+1=H²
6=H²
√6 = H
This means that sin a = opposite/hypotenuse = (√5)/(√6) = (√30)/6 and cos a = adjacent/hypotenuse = 1/(√6) = (√6)/6.
D)  The ratio for cosine is adjacent/hypotenuse; this means that the side adjacent the angle is 4 and the hypotenuse is 5.  Using the Pythagorean theorem to find the side opposite the angle, p:
4²+p²=5²
16+p²=25
p²=9
p=3
This means that sin a = opposite/hypotenuse = 3/5 and tan a = opposite/adjacent = 3/4.
E)  The ratio for tangent is opposite/adjacent;; this means that the side opposite the angle is 5 and the side adjacent the angle is 1.  Using the Pythagorean theorem to find the hypotenuse,
5²+1²=H²
25+1=H²
26=H²
√26 = H
This means that sin a = opposite/hypotenuse = 5/(√26) = (5√26)/26 and cos a = adjacent/hypotenuse = 1/(√26) = √26/26.
F) 0.8 = 8/10; The ratio for cosine is adjacent/hypotenuse.  This means that the side adjacent the angle is 8 and the hypotenuse is 10.  Using the Pythagorean theorem to find the side opposite the angle, p:
8²+p² = 10²
64+p² = 100
p² = 36
p=6
This means that sin a = opposite/hypotenuse = 6/10 = 3/5 and tan a = opposite/adjacent = 6/8 = 3/4.
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3 years ago
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OI 00<br>R<br>b) From the given figure:<br>write the alternate<br>angle of angle RUN<br>P<br>$<br>2​
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Answer:

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Step-by-step explanation:

Alternate angles are defined as angles that are located in opposite positions when we look at them relative to a transverse line that intersects two horizontal lines.

Now, we want to find the alternate angle to angle RUN.

The same transverse line cuts the other horizontal line PQ at point O.

Therefore the alternate angle to angle RUN is angle POU

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3 years ago
Multiple Choice: Please select the best answer and click "submit."
Airida [17]
The answer is c first 2×6= 12 then 12-5=7
then do -7×-2=14 the minus signs cancel
finaly we have two bracket so we multiply both number (7)×(14)=98
6 0
3 years ago
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