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drek231 [11]
2 years ago
7

If an equation has no solution, then the solution set is the _____ And is denoted by _____

Mathematics
1 answer:
Art [367]2 years ago
5 0

Answer:

If an equation has no solution, then the solution set is the _<u>empty set</u>_ and

is denoted by _<u>{ } </u><u>or </u><u>∅</u>__.

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An animal shelter spends $4.50 per day to care for each bird and $8.50 per day to care for each cat. Dominic noticed that the sh
Nimfa-mama [501]

Answer:

Step-by-step explanation:

4.5b + 8.5c = 175

b + c = 22.......b = 22 - c

4.5(22 - c) + 8.5c = 175

99 - 4.5c + 8.5c = 175

-4.5c + 8.5c = 175 - 99

4c = 76

c = 76/4

c = 19......there are 19 cats

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b = 3 <==== there are 3 birds

3 0
4 years ago
In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S
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Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a \triangle RST, RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

Using the cosine rule:

cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ

Now, let us use Sine rule to find other angles:

\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}

\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ

\Rightarrow sin S = \dfrac{10 \times 0.695}{7}\\\Rightarrow S = 83.14^\circ

Smallest angle is \angle T

Correct answer is option A. T

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4 years ago
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