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erica [24]
3 years ago
7

Which expression has a value of -10?

Mathematics
1 answer:
lidiya [134]3 years ago
8 0
Hope it helps :)
If you need more help tell me

You might be interested in
1. Find the value of
spin [16.1K]

9514 1404 393

Answer:

  1. -√5
  2. 3/5
  3. -4/5

Step-by-step explanation:

The relevant relations are ...

  sec = ±√(tan² +1)

  cos = 1/sec

  csc = 1/sin = ±1/√(1 -cos²)

Sine and Cosecant are positive in quadrants I and II. Cosine and Secant are positive in quadrants I and IV.

__

1. sec(θ) = -√((-2)² +1) = -√5

2. cos(θ) = 1/sec(θ) = 1/(5/3) = 3/5

3. csc(θ) = -1/√(1 -(-3/5)²) = -√(16/25) = -4/5

8 0
2 years ago
A 12 ounce bottle of shampoo lasted Nina 8 weeks how long would an 18 once bottle of shampoo last her
natali 33 [55]

Answer:

12 weeks

Step-by-step explanation:

set up a proportion of ounces/weeks = ounces/weeks

12/8 = 18/w

12w = 144

w = 12

4 0
2 years ago
Solve the system of equations algebraically. Verify your
xz_007 [3.2K]

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

y=4x-5 ----> equation A

y=-3 ----> equation B

Solve the system by substitution

Substitute equation B in equation A

-3=4x-5

Solve for x

Adds 5 both sides

-3+5=4x

2=4x

Divide by 4 both sides

x=0.5

therefore

The solution is the point (0.5,-3)

<em>Verify your  answer using the graph</em>

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

8 0
3 years ago
Read 2 more answers
A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of
belka [17]

Let <em>s(t)</em> be the amount of salt in the tank at time <em>t</em>. Then <em>s(0)</em> = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (<em>s(t)</em>/300 lb/gal) = <em>s(t)</em>/150 lb/min

so that the net rate at which salt is exchanged through the tank is

d<em>s(t)</em>/d<em>t</em> = 12 - <em>s(t)</em>/150 … (lb/min)

Solve for <em>s(t)</em>. The DE is separable, so we have

d<em>s</em>/d<em>t</em> = 12 - <em>s</em>/150

150 d<em>s</em>/d<em>t</em> = 1800 - <em>s</em>

150/(1800 - <em>s</em>) d<em>s</em> = d<em>t</em>

Integrate both sides to get

-150 ln|1800 - <em>s</em>| = <em>t</em> + <em>C</em>

Solve for <em>s</em> :

ln|1800 - <em>s</em>| = -<em>t</em>/150 + <em>C</em>

1800 - <em>s</em> = exp(-<em>t</em>/150 + <em>C </em>)

1800 - <em>s</em> = <em>C</em> exp(-<em>t</em>/150)

<em>s</em> = 1800 - <em>C</em> exp(-<em>t</em>/150)

Now given that <em>s(0)</em> = 50, we solve for <em>C</em> :

50 = 1800 - <em>C</em> exp(-0/150)

50 = 1800 - <em>C</em>

<em>C</em> = 1750

Then the amount of salt in the tank at any time <em>t</em> ≥ 0 is

<em>s(t)</em> = 1800 - 1750 exp(-<em>t</em>/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for <em>t</em> in

100 = 1800 - 1750 exp(-<em>t</em>/150)

1700 = 1750 exp(-<em>t</em>/150)

34/35 = exp(-<em>t</em>/150)

ln(34/35) = -<em>t</em>/150

<em>t</em> = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for <em>s(t)</em>, we could have instead stopped with

-150 ln|1800 - <em>s</em>| = <em>t</em> + <em>C</em>

Solve for <em>C</em> - this <em>C</em> <u>is not</u> the same as the one we found using the other method. <em>s(0)</em> = 50, so

-150 ln|1800 - 50| = 0 + <em>C</em>

<em>C</em> = -150 ln|1750|

==>   <em>t</em> = 150 ln(1750) - 150 ln|1800 - <em>s</em>|

Then <em>s(t)</em> = 100 lb when

<em>t</em> = 150 ln(1750) - 150 ln(1700)

<em>t</em> = 150 ln(1750/1700)

<em>t</em> = 150 ln(35/34)

<em>t</em> ≈ 4.348

5 0
3 years ago
A punch makes 16 pints.If 10 guests equally share the punch,how many pints will each guest drink?
m_a_m_a [10]

Answer:

1.6 pints

Step-by-step explanation:

A punch=16 pints

If 10 guest shares the punch equally

Each guest get=16 pints/10

=1.6 pints

Each guest will drink 1.6 pints of punch

8 0
2 years ago
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