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3 years ago

Combine the like terms to create an equivalent expression: -3r- 6+ (-1)

Mathematics

2 answers:

Norma-Jean [14]3 years ago

7 0

Answer:

-3r+5 is that answer hdj

GenaCL600 [577]3 years ago

5 0

Answer:

-3x-7

Step-by-step explanation:

-6 + -1 = -7

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Jerome is writing a coordinate proof to show that the midsegment of a trapezoid is parallel to its bases. He starts by assigning

Bingel [31]

Answer:

coordinates of R(b,c)

slope of NM is 0.

Step-by-step explanation:

The midpoint of the line joining the points (x₁,y₁) and (x₂,y₂) is given by

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

The midpoint of the line segment NK is given by

$(\frac{0+2b}{2},\frac{0+2c}{2})$

∴R(b,c)

The slope of the line joining the points (x₁,y₁) and (x₂,y₂) is given by

$m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Slope of RS is

$m_{RS} =\frac{c-c}{a+d-b} = 0$

Hence

coordinates of R(b,c)

and slope of NM is 0.

8 0

3 years ago

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Please help. I will give brainliest(:

Tanzania [10]

Distribute the -4. Then combine like terms.

24 - 4(5y - 6z) + 3y - 7z =

= 24 - 20y + 24z + 3y - 7z

= - 20y + 3y + 24z - 7z + 24

= -17y + 17z + 24

7 0

3 years ago

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Could someone please help me? Find the domain and range of the graph

Elan Coil [88]

Answer:

C = D all real Numbers ; R y>= -2

Step-by-step explanation:

for discover the domain we have to look the x axis and check for what x the graph exist. If we look this graph we can see that there are two solid lines.

the two arrows indicate that the graph continues both to left and to the right

so the domain is all real numbers

for the range we have to check the y axis. If we look at the graph we can see that under -2 there is nothing, while up -2 the graph continues to raise,

so the range is y>= -2

so the final answer is C

5 0

3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

If f(x) varies directly with x and f(x)=40 when x=8, find the value of f(x) when x=2.

melamori03 [73]

f(x)=40

x=8

so if x=2 it would be 40/8 which is 5

6 0

3 years ago

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