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3 years ago

Write the word sentence as an equation. Then solve.

Mathematics

1 answer:

scoundrel [369]3 years ago

6 0

Answer:

-1.5-21x

Step-by-step explanation:

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Find m∠IUV if m∠IUV=x+49, m∠TUI=x+63, and m∠TUV=106∘.?<br> I'll mark you brainliest!

8090 [49]

Answer:

Step-by-step explanation:

You have to do IVU+TUI=TUV

so... x+49+x+63=106

5 0

3 years ago

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

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

3 0

3 years ago

Help me asap wil mark crown i always doooooooo :D

Alexus [3.1K]

Answer:

The answer is the 1st one.

Step-by-step explanation:

Hope it helps! :)

4 0

3 years ago

Read 2 more answers

Solve 4(x-5)= 14 please answer nowww

Anna35 [415]

Answer:

x=8.5

Step-by-step explanation:

To solve this equation, we want to find out what x is. To do this, we need to get x by itself.

Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.

4(x-5)=14

4 is being multiplied by x-5. The opposite of multiplication is division. Divide both sides by 4.

4(x-5)/4=14/4

x-5=14/4

x-5=3.5

5 is being subtracted from x. The opposite of subtraction is addition. Add 5 to both sides.

x-5+5=3.5+5

x=3.5+5

x=8.5

Let's check our solution. Plug 8.5 in for x in the original equation.

4(x-5)=14

4(8.5-5)=14

4(3.5)=14

14=14

Both sides of the equation are the same, so we know our solution, <u>x=8.5 </u>is correct.

6 0

3 years ago

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149 cars are waiting to take a ferry across the channel. Each ferry can only hold 18 cars. How many cars will be on the last fer

STatiana [176]

Answer:

5 cars will be on the last ferry

Step-by-step explanation:

If you divide 149 by 8, you get 8.27.

Since each ferry can hold 18 cars, you multipy 18 by 8 which results in 144. Then you subtract 144 from 149 and you get 5 :)

4 0

3 years ago

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