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3 years ago

6

Which represents the solution set of the inequality 2.9(x+8)<26.1

2 answers:

harina [27]3 years ago

5 0

First you had to multiply by ten from both sides of equation form.

$2.9(x+8)*10$

Then refine by simplify.

$29(x+8)$

Next, you divide by twenty-nine from both sides of equation form.

$\frac{29(x+8)}{29}< \frac{261}{29}$

Simplify.

$x+8$

Then you subtract by eight from both sides of equation form.

$x+8-8$

Finally, simplify by equation.

$9-8=1$

$x$

Final answer: $\boxed{x$

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

alukav5142 [94]3 years ago

4 0

The answer is x is less than 1.

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PLEASE HELP I ONLY NEED THIS TO GET A 100 IN HOMEWORK!!! HELP PLEASE!

DerKrebs [107]

Answer:

12

Step-by-step explanation:

First fraction:

Numerator:

(17/40 + 0.6 - 0.005) = 1.02

1⅕ = 1.2

(1.2 ÷ 1.02)×1.7 = 2

Denominator:

5/6 + 4/3 - 53/30

Lcm: 30

(5×5 + 4×10 - 53)/30

12/30 = 0.4

Fraction value: 2/0.4 = 5

Second fraction:

4.75 + 7.5 = 12.25

33 ÷ 33/7

33 × 7/33 = 7

12.25/7 = 1.75

1.75 ÷ 0.25 = 7

Final answer:

5 + 7 = 12

7 0

3 years ago

What is twice 230? Write using exponents. Explain your reasoning.

Zielflug [23.3K]

2 x 230 = 231
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6 0

3 years ago

A 200-gal tank contains 100 gal of pure water. At time t = 0, a salt-water solution containing 0.5 lb/gal of salt enters the tan

Artyom0805 [142]

Answer:

1) $\frac{dy}{dt}=2.5-\frac{3y}{2t+100}$

2) $y(t)=(50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}$

3) 98.23lbs

4) The salt concentration will increase without bound.

Step-by-step explanation:

1) Let $y$ represent the amount of salt in the tank at time t, where t is given in minutes.

Recall that: $\frac{dy}{dt}=rate\:in-rate\:out$

The amount coming in is $0.5\frac{lb}{gal}\times 5\frac{gal}{min}=2.5\frac{lb}{min}$

The rate going out depends on the concentration of salt in the tank at time t.

If there is $y(t)$ pounds of salt and there are $100+2t$ gallons at time t, then the concentration is: $\frac{y(t)}{2t+100}$

The rate of liquid leaving is is 3gal\min, so rate out is $=\frac{3y(t)}{2t+100}$

The required differential equation becomes:

$\frac{dy}{dt}=2.5-\frac{3y}{2t+100}$

2) We rewrite to obtain:

$\frac{dy}{dt}+\frac{3}{2t+100}y=2.5$

We multiply through by the integrating factor: $e^{\int \frac{3}{2t+100}dt }=e^{\frac{3}{2} \int \frac{1}{t+50}dt }=(50+t)^{\frac{3}{2} }$

to get:

$(50+t)^{\frac{3}{2} }\frac{dy}{dt}+(50+t)^{\frac{3}{2} }\cdot \frac{3}{2t+100}y=2.5(50+t)^{\frac{3}{2} }$

This gives us:

$((50+t)^{\frac{3}{2} }y)'=2.5(50+t)^{\frac{3}{2} }$

We integrate both sides with respect to t to get:

$(50+t)^{\frac{3}{2} }y=(50+t)^{\frac{5}{2} }+ C$

Multiply through by: $(50+t)^{-\frac{3}{2}}$ to get:

$y=(50+t)^{\frac{5}{2} }(50+t)^{-\frac{3}{2} }+ C(50+t)^{-\frac{3}{2} }$

$y(t)=(50+t)+ \frac{C}{(50+t)^{\frac{3}{2} }}$

We apply the initial condition: $y(0)=0$

$0=(50+0)+ \frac{C}{(50+0)^{\frac{3}{2} }}$

$C=-12500\sqrt{2}$

The amount of salt in the tank at time t is:

$y(t)=(50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}$

3) The tank will be full after 50 mins.

We put t=50 to find how pounds of salt it will contain:

$y(50)=(50+50)- \frac{12500\sqrt{2} }{(50+50)^{\frac{3}{2} }}$

$y(50)=98.23$

There will be 98.23 pounds of salt.

4) The limiting concentration of salt is given by:

$\lim_{t \to \infty}y(t)={ \lim_{t \to \infty} ( (50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }})$

As $t\to \infty$ , $50+t\to \infty$ and $\frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}\to 0$

This implies that:

$\lim_{t \to \infty}y(t)=\infty- 0=\infty$

If the tank had infinity capacity, there will be absolutely high(infinite) concentration of salt.

The salt concentration will increase without bound.

6 0

2 years ago

The sum of the three consecutive integers is -27. What is the product of the smallest and largest of the three integers?

Aleksandr [31]

Answer:

B. 80

Step-by-step explanation:

3 consecutive integers: x-1 , x , x+1

(x-1) + x + (x+1) = -27

3x = -27

x = -9

smallest: -9-1 : -10

largest: -9+1 : -8

product of the smallest and largest of the three integers: (-10)*(-8)=80

4 0

2 years ago

Which statement is true?

Y_Kistochka [10]

Answer:

D

Step-by-step explanation:

15 + 2x + x + 3 = 3x + 18

hope this helps

3 0

2 years ago

Read 2 more answers