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Harman [31]
3 years ago
5

*44 POINTS*

Mathematics
1 answer:
egoroff_w [7]3 years ago
3 0

Answer:

The standard form is -x + 2y = 8

Step-by-step explanation:

To find this, start by using point-slope form with the given information.

y - y1 = m(x - x1)

y - 3 = 1/2(x + 2)

Now solve for the constant.

y - 3 = 1/2(x + 2)

y - 3 = 1/2x + 1

-1/2x + y - 3 = 1

-1/2x + y = 4

Now to get integers, multiply the whole thing by 2.

-x + 2y = 8

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Write an expression that can be used to multiply 6x198 mentally
Vilka [71]
6×100+6×90+6×8 I think that is the answer
4 0
3 years ago
Read 2 more answers
A factory makes 1500 cans per minute, the factory makes cans for 8 hours a day, each can is filled with 300ml of cola, how much
3241004551 [841]
1500 x 60 = the number of cans made in one hour (90,000)
90,000 x 8 = the number of cans made in 8 hours (720,000)
720,000 x 300 = 216,000,000 ml of cola

Hope this helps you out!

5 0
2 years ago
X=3 is a factor of x^3+3x^2-7x+19.
Andrew [12]

Answer:

52

Step-by-step explanation:

3^3+3(3)^2-7(3)+19

27+27-21+19

54-2

52

Hope this helps

7 0
3 years ago
Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k​
valkas [14]

Answer:

\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k​, the vector projection of B unto a is expressed as proj_ab = \dfrac{b.a}{||a||^2} * a

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k  =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||²  = 130

proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\

<em>Hence the projection of b unto a is expressed as </em>\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\<em></em>

7 0
3 years ago
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium d
nikitadnepr [17]

Answer:

a) k=2.08 1/hour

b) The exponential growth model can be written as:

P(t)=Ce^{kt}

c) 977,435,644 cells

d) 2.033 billions cells per hour.

e) 2.81 hours.

Step-by-step explanation:

We have a model of exponential growth.

We know that the population duplicates every 20 minutes (t=0.33).

The initial population is P(t=0)=58.

The exponential growth model can be written as:

P(t)=Ce^{kt}

For t=0, we have:

P(0)=Ce^0=C=58

If we use the duplication time, we have:

P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08

Then, we have the model as:

P(t)=58e^{2.08t}

The relative growth rate (RGR) is defined, if P is the population and t the time, as:

RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k

In this case, the RGR is k=2.08 1/h.

After 8 hours, we will have:

P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644

The rate of growth can be calculated as dP/dt and is:

dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)

For t=8, the rate of growth is:

dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140

(2.033 billions cells per hour).

We can calculate when the population will reach 20,000 cells as:

P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81

3 0
3 years ago
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