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2 years ago

Select all the correct answers.

Mathematics

1 answer:

Vlad1618 [11]2 years ago

3 0

Answer:

The measure of reference angle is $30^{\circ}$ .
$\cos \theta=\frac{\sqrt{3}}{2}$

Step-by-step explanation:

Converting $\theta$ to degrees,

$\theta=\left(\frac{11\pi}{6} \right) \left(\frac{180}{\pi} \right)=330^{\circ}$

This means $\theta$ lies in Quadrant 4, and thus its reference angle is $360^{\circ}-330^{\circ}=\boxed{30^{\circ}}$

Since $\theta$ lies in the fourth quadrant, $\sin \theta$ and $\tan \theta$ are negative.

Since $\theta$ lies in the fourth quadrant, $\cos \theta$ is positive, and is equal to $\cos (30^{\circ})=\boxed{\frac{\sqrt{3}}{2}}$

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I don't understand this. Please help!:::: Provide an answer for a, b, c, and d.

OleMash [197]

Answer for part A is $\angle A \cong \angle D$ which in English means "angle A is congruent to angle D"

The reason why we know that angle A and angle D are congruent is because they are both right angles. By the right angle congruence theorem (the reason just below the blank for part A), we can say that angle A = angle D. They are both 90 degree angles.

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Answer for the blank in part B is "Given" without quotation marks of course. This is the first "given" while the second given is coming up in part C

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For part C, the other given is $\angle C \cong \angle F$ so that's what will go in the blank. It may seem silly, but all we're doing is repeating verbatim what is given to us. With any proof, you always start with what you are given and somehow connect it with what you're trying to prove

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Finally, the answer for the blank in part D is "AAS Congruence Theorem" (without quotes)

The AAS congruence theorem allows us to prove two triangles congruent if we know if two pairs of angles are congruent plus if we know two sides are congruent as well.

The angle portions are covered by part A and part C. The side portions are part B's territory. Combining A, B, & C allows us to use the AAS theorem

Note: It is NOT the ASA theorem because the two angles do not sandwich the sides. In other words, the side AB is not between the two angles A and C. Similarly, DE is not between the two angles D and F. The order is very important as ASA is slightly different than AAS.

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3 years ago

Bus A and Bus B leave the bus depot at 5 pm. Bus A takes 30 minutes to complete its route once and bus B takes 35 minutes to com

shepuryov [24]

Answer:

Step-by-step explanation:

Bus A will take 1 hour and will arrive back at 6pm, because 30+30=60 and there are 60 min is one hour. Bus B will arrive 1 hour 10 minuets. 35+35=70, Knowing that it will arrive there in over an our because there is more than 60 min, and the extra ten is the amount of minuets. SO bus B will arrive at 6:10pm. Hope I explained this right.

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3 years ago

How do I find angles a, b, and c?

LenaWriter [7]

For angle A, you need to do 180-130 which is 50
for angle B, you need to do 180- 90 - 50 which is 40
for angle C, you need to do 180 - 60 - 40 which is 80

If you want me to explain you with further details with how exactly I got those answers and how I knew what to do, then ask me.

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3 years ago

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Slove for X= what would this be for Mai poured 2.6 liters of water into a partially filled pitcher. The pitcher then contained 1

alexandr1967 [171]

Answer:

x + 2.6 = 10.4

x = 7.8

Step-by-step explanation:

If 2.6 liters are added to x liters with the result that 10.4 liters then exist, the model is ...

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The commutative property of addition lets you rewrite this to ...

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2 years ago

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const2013 [10]

Answer:

1.) Triangle ABC is congruent to Triangle CDA because of the SAS theorem

2.) Triangle JHG is congruent to Triangle LKH because of the SSS theorem

Step-by-step explanation:

Alright. Let's start with the 1st figure. How do we prove that triangles ABC and CDA (they are named properly) are congruent? First, we can see that segments BC and AD have congruent markings, so that can help us. We also see a parallel marking for those segments as well, meaning that the diagonal AC is also a transversal for those parallel segments. That means we can say that angle CAD is congruent to angle ACB because of the alternate interior angles theorem. Then, the 2 triangles also share the side AC (reflexive property).

So, we have 2 congruent sides and 1 congruent angle for each triangle. And in the way they are listed, this makes the triangles congruent by the SAS theorem since the angle is adjacent to the 2 sides that are congruent.

The second figure is way easier. As you can clearly see by the congruent markings on the diagram, all the sides on one triangle are congruent to the other. So, since there are 3 sides congruent, we can say the triangles JHG and LKH are congruent by the SSS theorem.

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