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Leona [35]
3 years ago
10

Cassandra assigns values to some of the measures of triangle ABC. If angle A measures 30°, a = 6, and b = 18, which is true?

Mathematics
1 answer:
Anna [14]3 years ago
8 0

Answer:

The triangle does not exist because sin(A)/a can not be equal to sin(B)/b

Step-by-step explanation:

we know that

step 1

Find the measure of angle B

Applying the law of sines

\frac{sin(A)}{a}=\frac{sin(B)}{b}

we have

A=30\°

sin(30\°)=1/2

a=6\ units

b=18\ units

substitute

\frac{(1/2)}{6}=\frac{sin(B)}{18}

\frac{1}{12}=\frac{sin(B)}{18}

sin(B)=\frac{18}{12}

sin(B)=\frac{3}{2}=1.5

Remember that the value of sine can not be greater than 1

therefore

The triangle does not exist because sin(A)/a can not be equal to sin(B)/b

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Hi, I'm happy to help!

To simplify this expression, we need to first use the order of operations <u>(Parenthesis, Exponents, Multiplication or Division (Left to Right), and Addition or Subtraction (Left to Right)</u>), then combine like terms. (<u>80,40,57</u>, or <u>6t, 8t, 98t</u>, or<u> 2t²,7t²,83t²</u>)

When a number is next to parenthesis with no sign, it means we are using multiplication. We can change this expression to look like this, by changing all the numbers next to the parenthesis with no sign, to one with a multiplication sign.

8(5+t) - 2(t+1) 8(5 + t) - 2(t+1)=

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

We start with parenthesis and solve everything inside of those, but, because everything inside the parenthesis are unlike terms, we cannot combine them.

Next, We look for any exponents (x²). There are none in this equation.

We then look for multiplication or division. There is a lot of multiplication, so we start solving that from left to right.

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

Now, before we do anything else, we need to recheck the parenthesis, now that they have changed. We can further simplify the middle parenthesis by adding together like terms.

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - ((80t+16t)+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

Now, we look for addition or subtraction of like terms. We can now remove the parenthesis, since everything inside of the last two parenthesis is negative, we turn it negative, as long as we only combine the like terms.

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Once we find like terms, we can rearrange the expression.

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This doesn't have any like terms, so we don't alter it.

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We can now remove the parenthesis.

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Since there are no more like terms this is the furthest we can simplify. We can then rearrange the expression to be arranged completely correct.

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I hope this was helpful, keep learning! :D

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Learn more on function and values here: brainly.com/question/10439235

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