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3 years ago

Solve the inequality 2x+10<-28

Mathematics

1 answer:

Otrada [13]3 years ago

8 0

Answer:

x < -19

Step-by-step explanation:

2x+10<-28

Subtract 10 from each side

2x+10-10<-28-10

2x< -38

Divide each side by 2

2x/2 <-38/2

x < -19

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3x-2y=13 2x+3y=-16 are these lines parallell or perpendicular or neither

Lelechka [254]

3x - 2y = 13
-2y = -3x + 13
y = 3/2x - 13/2...slope is 3/2, y int is -13/2

2x + 3y = -16
3y = -2x - 16
y = -2/3x - 16/3...slope = -2/3, y int is -16/3

perpendicular lines will have negative reciprocal slopes. To find the negative reciprocal of a number, flip the number and change the sign.
On the 1st equation, the slope was 3/2....find its negative reciprocal.....flip it, making it 2/3....change the sign...making it -2/3. So the negative reciprocal of 3/2 is -2/3.

So if one equation has a slope of 3/2 and another equation has a slope of -2/3, then these lines are perpendicular <==

6 0

4 years ago

A countrys population in 1990 was 145 million. In 1998 it was 151 million. Estimate the population in 2015 using the exponential

alexandr402 [8]

Answer:

The population in 2015 will be 165 million.

Step-by-step explanation:

The exponential growth formula is given by:

$f(t) = a(1 + r)^{\Delta t}$

Where:

a: is the initial population

r: is the rate of increase

Δt: is the time

With the initial information we can find the rate:

$151 = 145(1 + r)^{1998-1990}$

Using logarithm:

$ln(151) = ln(145) + 8[ln(1 + r)]$

$ln(1 + r) = \frac{ln(151) - ln(145)}{8}$

$ln(1 + r) = 5.0683 \cdot 10^{-3}$

Using exponential:

$e^{ln(1 + r)} = e^{5.0683 \cdot 10^{-3}}$

$r = 5.081 \cdot 10^{-3}$

Now, we can find the estimated population in 2015:

$f(t) = 151(1 + 5.081 \cdot 10^{-3})^{2015-1998}$

$f(t) = 165$

Therefore, the population in 2015 will be 165 million.

I hope it helps you!

5 0

3 years ago

What is the value of x? 6(x-4)=10

Mrac [35]

Answer:

$\boxed{\sf{x=\dfrac{17}{3}=5.6 }}$

Step-by-step explanation:

Use a distributive property.

Distributive property:

$\Longrightarrow: \sf{A(B+C)=AB+AC}$

⇒ 6(x-4)=10

First, divide by 6 from both sides.

⇒ 6(x-4)/6=10/6

Solve.

⇒ x-4=5/3

Add by 4 from both sides.

⇒ x-4+4=5/3+4

Solve.

5/3+4

4*3/3+5/3

4*3+5/3

4*3=12

12+5=17

x=17/3

Dividing is another option.

17/3=5.6

x=17/3=5.6

Therefore, the final answer is x=17=5.6.

I hope this helps you! Let me know if my answer is wrong or not.

7 0

2 years ago

water in a swimming pool evaporates at the rate of 3% per day. If there is 16000 gallons of water in a swimming pool. How many g

damaskus [11]

11,798.786 gallons (Don't know what place you want it rounded to, if at all) Assuming 3% evaporates per day, that is how many gallons will be left after 10 days.

7 0

4 years ago

Which term best describes the expression 137 rabbits per km2?

Murrr4er [49]

I believe the correct answer from the choices listed above is option D. The term that best describes the expression 137 rabbits per km2 would be density. It is a population density. It is the number of an entity per unit of area, usually quoted per square kilometer or square mile.

5 0

4 years ago