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1 year ago

Solve the system of equations 4x + 3y = 3 and y = 2x + 6.

Mathematics

1 answer:

muminat1 year ago

8 0

Step-by-step explanation:

4x + 3y = 3

y = 2x + 6 ->

2x - y = -6

let's multiply the modified second equation by 3 and add both equations :

4x + 3y = 3

6x - 3y = -18

--------------------

10x + 0 = -15

x = -1.5

4x + 3y = 3

4×-1.5 + 3y = 3

-6 + 3y = 3

3y = 9

y = 3

and so the solution is (-1.5, 3).

which is not in the list of your answer options.

so, something must have been wrong in your problem definition.

either you changed something in the 2 equations, or subverting is missing in the answer options, or you even mixed up problem and answer options of 2 different questions.

but I also checked by using the numbers in the 2 equations, but (-1.5, 3) is indeed the correct solution for the given 2 equations.

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A bacterial culture starts with 500 bacteria and doubles in size every half-hour.

tekilochka [14]

Answer:

a). 32000

b). $T_{t}=500\times 4^{t}$

c). 1259

Step-by-step explanation:

Growth of a bacteria is always exponential. Therefore, population of the bacteria is represented by the the geometric sequence.

Sum of the bacterial population after t hours will be represented by

$T_{n}=ar^{n}$

Where a = population at the start

r = ratio with the population is growing

n = time or duration of the growth in one hour

a). Population of 500 bacteria gets doubled after half an hour.

Or gets 4 times after an hour

This sequence will have a common ratio r = 4

and initial population a = 500

Therefore, population of the bacteria after 3 hours will be

$T_{3}=500\times 4^{3}$

$T_{3}=32000$

b). After t hours number of bacteria will be represented by

$T_{t}=500\times 4^{t}$

c). We have to calculate the population after 40 minutes.

That means duration 't' = 40 minutes of $\frac{2}{3}$ hours

By the formula,

$T_{\frac{2}{3}}=500\times 4^{\frac{2}{3}}$

$T_{\frac{2}{3}}=1259.92$ ≈ 1259

Therefore, number of bacteria after 40 minutes will be 1259.

8 0

3 years ago

Read 2 more answers

Joe heard from a reliable source that only 22% of people actually sleep 8 hours or more per night. You do a survey and find 58 o

Juliette [100K]

Answer:

95% Confidence interval: (31.32%,47.04%)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 148

Number of people who sleep for 8 hours or longer, x = 58

$\hat{p} = \dfrac{x}{n} = \dfrac{58}{148} = 0.3918$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.3918\pm 1.96(\sqrt{\dfrac{0.3918(1-0.3918)}{148}})\\\\ = 0.3918\pm 0.0786\\\\=(0.3132,0.4704)=(31.32\%,47.04\%)$

(31.32%,47.04%) is the required 95% confidence interval.

8 0

3 years ago

HELP PLEASE HELP!!!!!

babunello [35]

Answer:

(i): A triangle where all three sides are equal and the same.

(ii): A triangle where all three sides are unequal in length.

(iii): A triangle that has two sides of equal length.

(iv): A triangle where all three internal angles are acute(they measure less than 90 degrees.

(v): A triangle where all three internal angles are obtuse(measure above 90 degrees).

(vi): A triangle where one internal angle is a right angle(90 degrees).

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Step-by-step explanation:

6 0

2 years ago

Which answer choice is a solution to the inequality 1.5x + 3.75 greater than or equal to 5.5

irga5000 [103]

Answer:

x≥ $\frac{7}{6}$

Step-by-step explanation:

given 1.5x+3.75≥5.5

→ 1.5x≥5.5-3.75

→ 1.5x≥1.75

→ x≥ $\frac{1.75}{1.5}$

→ x≥ $\frac{7}{6}$

8 0

3 years ago

Read 2 more answers

Select a letter for the correct ans

Natasha_Volkova [10]

Answer:

251.4cm² is the area of the cone-shaped vase.

8 0

2 years ago