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3 years ago

Which property justifies this statement?

Mathematics

2 answers:

dalvyx [7]3 years ago

8 0

D. <span>Transitive Property of Equality</span>

marissa [1.9K]3 years ago

7 0

Answer:

option D

Transitive property of equality

Explanation:

Transitive property of equality justifies the statement:

x=y+2 , y+2=8 then; x= 8

Transitive property of equality states that if we have two things that are equal to each other and the second thing is equal to a third thing then, the first thing is also equal to the third thing.

In mathematical terms: if a=b and b=c then a=c.

As per the given statement:

a = x , b= y+2 and c= 8

then,

a=b i.e, x=y+2 and

b=c i.e, y+2 =8 then

by using transitive property of equality, we get;

a=c i.e, x=8

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Four balls of wool will make 8 knitted hats. How many balls of wool will Janet need to make 6 hats?

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3 balls of wool would make 6 hats.

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3 years ago

HELPPP!!! I NEED HELP WITH 1-6!!!

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3 years ago

A tank initially contains 60 gallons of brine, with 30 pounds of salt in solution. Pure water runs into the tank at 3 gallons pe

adoni [48]

Answer:

the amount of time until 23 pounds of salt remain in the tank is 0.088 minutes.

Step-by-step explanation:

The variation of the concentration of salt can be expressed as:

$\frac{dC}{dt}=Ci*Qi-Co*Qo$

being

C1: the concentration of salt in the inflow

Qi: the flow entering the tank

C2: the concentration leaving the tank (the same concentration that is in every part of the tank at that moment)

Qo: the flow going out of the tank.

With no salt in the inflow (C1=0), the equation can be reduced to

$\frac{dC}{dt}=-Co*Qo$

Rearranging the equation, it becomes

$\frac{dC}{C}=-Qo*dt$

Integrating both sides

$\int\frac{dC}{C}=\int-Qo*dt\\ln(\abs{C})+x1=-Qo*t+x2\\ln(\abs{C})=-Qo*t+x\\C=exp^{-Qo*t+x}$

It is known that the concentration at t=0 is 30 pounds in 60 gallons, so C(0) is 0.5 pounds/gallon.

$C(0)=exp^{-Qo*0+x}=0.5\\exp^{x} =0.5\\x=ln(0.5)=-0.693\\$

The final equation for the concentration of salt at any given time is

$C=exp^{-3*t-0.693}$

To answer how long it will be until there are 23 pounds of salt in the tank, we can use the last equation:

$C=exp^{-3*t-0.693}\\(23/60)=exp^{-3*t-0.693}\\ln(23/60)=-3*t-0.693\\t=-\frac{ln(23/60)+0.693}{3}=-\frac{-0.959+0.693}{3}= -\frac{-0.266}{3}=0.088$

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3 years ago

In a volcano, erupting lava flows continuously through a tube system about 15 kilometers to the sea. Assume a lava flow speed o

koban [17]

9514 1404 393

Answer:

30 hours

Step-by-step explanation:

The relation between time, speed, and distance is ...

time = distance/speed

time = (15 km)/(0.5 km/h) = 30 h

It takes 30 hours for the lava to reach the sea.

5 0

3 years ago

How do you factorize p2 + 2p - 3 =0

julia-pushkina [17]

Answer:

Solution

p = {-3, 1}

Step-by-step explanation:

Simplifying

p2 + 2p + -3 = 0

Reorder the terms:

-3 + 2p + p2 = 0

Solving

-3 + 2p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.

(-3 + -1p)(1 + -1p) = 0

Subproblem 1

Set the factor '(-3 + -1p)' equal to zero and attempt to solve:

Simplifying

-3 + -1p = 0

Solving

-3 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + -1p = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -1p = 0 + 3

-1p = 0 + 3

Combine like terms: 0 + 3 = 3

-1p = 3

Divide each side by '-1'.

p = -3

Simplifying

p = -3

Subproblem 2

Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying

1 + -1p = 0

Solving

1 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -1p = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -1p = 0 + -1

-1p = 0 + -1

Combine like terms: 0 + -1 = -1

-1p = -1

Divide each side by '-1'.

p = 1

Simplifying

p = 1

Solution

p = {-3, 1}

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3 years ago