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Korolek [52]
3 years ago
6

6. Find the measure of each marked angle.

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
8 0
ANSWER : both angles are 60 degrees and x is equal to 8.
10x - 20 = 7x + 4
Move the terms
3x = 24
x= 8
Sub back in to find the value:
80 - 20 = 60
56 + 4 = 60

Please mark as brainliest
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Need some math help please!
stellarik [79]

Hello!

In our triangle, c is the hypotenuse. We are given an adjacent side length to our angle. This means we will use the cosine. Let's find it first.

cos54≈0.59

This gives us the equation below.

0.59=9/c

0.59c=9

c≈15.25

Therefore, c is equal to about 15.25

I hope this helps!

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3 years ago
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The difference of 15 and x is 12
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A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min
sesenic [268]
A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})
\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}
A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4

We're given that A(0)=30. Multiply both sides by the integrating factor e^{t/100}, then

e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4
\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4
e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C
A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}

Given that A(0)=30, we have

30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02

so the amount of salt in the tank at time t is

A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}
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