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mojhsa [17]
3 years ago
14

During a sale, $2 bars of soap were sold at the rate of 3 for 5$. how much is saved on the 9 bars

Mathematics
2 answers:
yanalaym [24]3 years ago
6 0

Answer:

$3

Step-by-step explanation:

When a bar of soap is $2,

  Cost of  9 bars = 9* 2 = $18

When 3 bars for $5,

 Cost of 9 bars =3*5 = $15

Savings = 18 - 15= $ 3

Vinvika [58]3 years ago
4 0
3$

Solution: 2x9=18$
3x3=9 5x3=15$
15$ ] 18$
]= less than

= 3$
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How can the Angle-Angle Similarity Postulate be used to prove the two triangles below are similar? Explain your answer using com
zloy xaker [14]

To use the AA postulate directly, you need to show that two corresponding angles are congruent. In order to show that here, you must calculate the value of one of the missing angle measures. Either of the missing angles can be found by invoking the fact that the sum of angles in a triangle is 180°.

After finding either missing angle, you can show that the measures of two angles in one triangle are identical to the measures of two angles in the other triangle, hence the triangles are similar by the AA postulate.

5 0
3 years ago
Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow
Gala2k [10]

Answer:

a) dx / dt = - x / 800

b) x = 500*e^(-0.00125*t)

c) dy/dt = x / 800 - y / 200

d) y(t) = 0.625*e^(-0.00125*t)*( 1  - e^(-4*t) )

Step-by-step explanation:

Given:

- Out-flow water after crash from Lake Alpha = 500 liters/h

- Inflow water after crash into lake beta = 500 liters/h

- Initial amount of Kool-Aid in lake Alpha is = 500 kg

- Initial amount of water in Lake Alpha is = 400,000 L

- Initial amount of water in Lake Beta is = 100,000 L

Find:

a) let x be the amount of Kool-Aid, in kilograms, in Lake Alpha t hours after the crash. find a formula for the rate of change in the amount of Kool-Aid, dx/dt, in terms of the amount of Kool-Aid in the lake x:

b) find a formula for the amount of Kook-Aid in kilograms, in Lake Alpha t hours after the crash

c) Let y be the amount of Kool-Aid, in kilograms, in Lake Beta t hours after the crash. Find a formula for the rate of change in the amount of Kool-Aid, dy/dt, in terms of the amounts x,y.

d) Find a formula for the amount of Kool-Aid in Lake Beta t hours after the crash.

Solution:

- We will investigate Lake Alpha first. The rate of flow in after crash in lake alpha is zero. The flow out can be determined:

                              dx / dt = concentration*flow

                              dx / dt = - ( x / 400,000)*( 500 L / hr )

                              dx / dt = - x / 800

- Now we will solve the differential Eq formed:

Separate variables:

                              dx / x = -dt / 800

Integrate:

                             Ln | x | = - t / 800 + C

- We know that at t = 0, truck crashed hence, x(0) = 500.

                             Ln | 500 | = - 0 / 800 + C

                                  C = Ln | 500 |

- The solution to the differential equation is:

                             Ln | x | = -t/800 + Ln | 500 |

                                x = 500*e^(-0.00125*t)

- Now for Lake Beta. We will consider the rate of flow in which is equivalent to rate of flow out of Lake Alpha. We can set up the ODE as:

                  conc. Flow in = x / 800

                  conc. Flow out = (y / 100,000)*( 500 L / hr ) = y / 200

                  dy/dt = con.Flow_in - conc.Flow_out

                  dy/dt = x / 800 - y / 200

- Now replace x with the solution of ODE for Lake Alpha:

                  dy/dt = 500*e^(-0.00125*t)/ 800 - y / 200

                  dy/dt = 0.625*e^(-0.00125*t)- y / 200

- Express the form:

                               y' + P(t)*y = Q(t)

                      y' + 0.005*y = 0.625*e^(-0.00125*t)

- Find the integrating factor:

                     u(t) = e^(P(t)) = e^(0.005*t)

- Use the form:

                    ( u(t) . y(t) )' = u(t) . Q(t)

- Plug in the terms:

                     e^(0.005*t) * y(t) = 0.625*e^(0.00375*t) + C

                               y(t) = 0.625*e^(-0.00125*t) + C*e^(-0.005*t)

- Initial conditions are: t = 0, y = 0:

                              0 = 0.625 + C

                              C = - 0.625

Hence,

                              y(t) = 0.625*( e^(-0.00125*t)  - e^(-0.005*t) )

                             y(t) = 0.625*e^(-0.00125*t)*( 1  - e^(-4*t) )

6 0
3 years ago
Instructions:select all the correct locations on the tables. andrew wants to purchase a new television with a screen length that
DaniilM [7]

The <em>correct answers</em> are:


5x²+70x+245 ≥ 1050; and

Yes.


Explanation:


Let x be the width of the tablet. Since the width of the TV is 7 inches more than the tablet, the width of the TV would be x+7.


The length of the TV is 5 times the width; this makes the length 5(x+7) = 5x+35.


The area of the TV would be given by

(x+7)(5x+35).


Since Andrew wants the area to be at least 1050, we set the expression greater than or equal to 1050:

(x+7)(5x+35) ≥ 1050


Multiplying this, we have:

x*5x+x*35+7*5x+7*35 ≥ 1050

5x²+35x+35x+245 ≥ 1050


Combining like terms,

5x²+70x+245 ≥ 1050


To see if 8 is a reasonable width for the tablet, we substitute 8 for x:

5(8²)+70(8)+245 ≥ 1050

5(64)+560+245 ≥ 1050

320+560+245 ≥ 1050

1125 ≥ 1050


Since this inequality is true, 8 is a reasonable width.

5 0
2 years ago
I don’t know how to do this.
Ronch [10]

Answer:

(2,-3)

Step-by-step explanation:

When you reflect over the x-axis, you leave the x-axis the same and the y-axis is the opposite of that number. It is the same thing with the y-axis, but the x-axis is the opposite of that number.

5 0
3 years ago
which of the following is a result of shiftinga circle with equation (×-2)+(y-3)^2= 25 to the left 2 unit ?​
Paha777 [63]

Answer:

x^2+(y-1)^2=25

Step-by-step explanation:

eqn of circle : (x-h)^2+(y-k)^2=r^2

center of circle = (h,k)

hence, the center of the current circle is (2,3)

moving 2 units to the left would make the center (0,1)

the radius would remain the same (5) , hence the new eqn would be

(x-0)^2+(y-1)^2=25

x^2+(y-1)^2=25

4 0
2 years ago
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