3a + 2b = 35 find a and b​

Answer:

• (a)80 mg

• (c)f(t)=80(0.5)^t

• (d)0.625 mg

Explanation:

Part A

From the point (0, 80), we see that the person took 80 mg of the medicine at the start.

Part B

From the graph:

From points (0,80) and (2,20); and (2,20) and (4,5)

• After 2 hours, the amount of medicine has been reduced by a factor of 1/4.

Therefore, after 1 hour, the amount of medicine is reduced by a factor of 1/2.

The completed table is attached below:

Part C

An exponential function is written in the form:

Since the amount of medicine is halved every 1 hour:

The rate of decrease = 1/2

The starting amount, Ao = 80 mg

Therefore, an equation that defines f is:

Part D

After 7 hours, when t=7

After 7 hours, 0.625 mg of medicine remains in the person's body.

Answer:

c

Step-by-step explanation:

Answer:

data set A is linear, and data set B is linear

Step-by-step explanation:

From midnight to 5:00 am, the temperature dropped for 5 hours at 0.5°C each hour, so the total temperature drop was:

5 x 0.5°C = 2.5°C

Let the temperature at midnight be T°C. Then, we can use the information given to set up an equation:

Temperature at 5:00 am = Temperature at midnight - total temperature drop

11.5°C = T°C - 2.5°C

Solving for T, we can add 2.5°C to both sides of the equation:

11.5°C + 2.5°C = T°C - 2.5°C + 2.5°C

14°C = T°C

Therefore, the temperature at midnight was 14°C.

Answer:

you can because the real cube root of any negative real number is negative.

Step-by-step explanation:

Answer: The reason that we can't have the square (or quartic) root of a negative number is that two negatives always cancel to give a plus; so the square root of a negative number is undefined. ... The Real cube root of any negative Real number is negative.bc. a negativ number multiplied by it self 3 time result negativ too

hope this helps ❤️

Step-by-step explanation:

The amount for handle soend on Christmas present will be 240.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.

Now,

Since, Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.

Let the amount for handle soend on Christmas present = x

Hence, The amount for handle soend on Christmas present will be;

⇒ x - 1/4x = 180

⇒ 3/4x = 180

⇒ 3x = 180 × 4

⇒ 3x = 720

⇒ x = 240

Thus, The amount for handle soend on Christmas present will be 240.

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Answer:

5 and 13

Step-by-step explanation:

Answer:

13

is the answer

Hope it help u

The required marks solution of the given system of equations is incorrect.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Mark made a solution to determine the common solution for the equation x + y ≤ 10 and 2x+3y = 24.

Since Mark's calculation is wrong he must have solved the equaiton by making the inequality an equaiton as x + y = 10 and solved it by any of the methods with another equation 2x + 3y =24. Where we would get (6,4) as a common solution between the two lines.

Thus, the required marks solution of the given system of equations is incorrect.

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The probability that a junior is taking physics, given they are in Algebra II, is approximately 0.3846 or 38.46%.

1. First, let's find the number of juniors taking only Algebra II and not physics. We do this by subtracting the number of juniors taking both courses from the total number of juniors taking Algebra II:
  468 (Algebra II) - 180 (both courses) = 288 (only Algebra II)

2. Now, we have two groups of juniors enrolled in Algebra II:
  - 288 juniors taking only Algebra II
  - 180 juniors taking both Algebra II and physics

3. Since we want to find the probability that a junior is taking physics, given they are in Algebra II, we'll focus on the group taking both courses.

4. To calculate the probability, divide the number of juniors taking both courses by the total number of juniors taking Algebra II:
  Probability = (number of juniors taking both courses) / (total number of juniors in Algebra II)
  Probability = 180 / (288 + 180)
  Probability = 180 / 468
  Probability ≈ 0.3846 or 38.46%

So, if one of the 650 juniors was picked at random and we know they are in Algebra II, the probability that they are also taking physics is approximately 38.46%.

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Answer:

One solution

Step-by-step explanation:

Let us first expand the left side of the equation to rid of the parenthesis:

\(3*12x-3*9+9=2x+4\\36x-27+9=2x+4\\36x-18=2x+4\)

Now let us isolate the variable to sove for x:

\(36x-2x=4+18\\34x=22\\x=\frac{22}{34}\\x=\frac{11}{17}\)

Therefore, x=\(\frac{11}{17}\). As you can see, there is just one solution.

I hope this helps! Please let me know if you have any further questions :)

Answer:

Steps:

600 - 480 = 120

100(120/480) = 25

Answer:

increase in percentage = 25%

Step-by-step explanation:

here's your solution

==> Total number of students last year = 480

==> Number of students this year = 600

==> Number of increased students = 600 - 480

= 120 students

==> now , in percentage = (120/480)*100

==> percentage increase = 25%

hope it helps

Answer:

subtract 6 from 3 and a is -3

Step-by-step explanation:

Answer:

a= -3

Step-by-step explanation:

a=3-6

a=-3

Answer:

One is 8x+12y= 112

Step-by-step explanation:

I don't know if it's right tho. SO don't come at me.

The value of cos A in the triangle is 1 / 9.

The triangle is given as ABC. The side lengths are a, b and c. Therefore, cos A of the triangle can be found using cosine rule as follows:

a² = b² + c² - 2bc cos A

a = 4

b = 3

c = 3

Therefore,

4² = 3² + 3² - 2(3)(3) cos A

16  = 9 + 9 - 18 cos A

16 - 18 = - 18 cos A

-2 = - 18 cos A

divide both sides by - 18

cos A = - 2 / - 18

cos A = 1 / 9

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Answer:

what is this

<1=43°

Answer:

pls see attached

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Substituting the given radius, we get:

V = (4/3)π(18³) ≈ 24,389 cm³

Rounding to the nearest whole number, we get:

V ≈ 24,389 cm³ ≈ 24,389 cubic centimeters

Therefore, the volume of the sphere is approximately 24,389 cubic centimeters.

\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=18 \end{cases}\implies V=\cfrac{4\pi (18)^3}{3}\implies V\approx 24429~cm^3\)

x=14

Mark me as brainliest

Answer:

Step-by-step explanation:

Minimum: 2

Quartile Q1: 4.5

Median: 10

Quartile Q3: 15

Maximum: 19

Answer:

y=-2x-6

Step-by-step explanation:

Answer:

\(Probability\ of\ picking\ a\ 7=\frac{1}{10}\\Probability\ of\ picking\ a\ card\ less\ than\ 5=\frac{4}{9}\)

Step-by-step explanation:

\(We\ are\ given\ that,\\The\ total\ outcomes\ to\ the\ Random\ Experiment\ A\ are\ 1,2,3,4,5,6,7,8,9,10.\\ (We\ don't\ consider\ Ace\ Cards\ or\ Face\ Cards, here.)\\Hence,\\Lets\ consider\ picking\ the\ first\ Card:\\\\Here,\\The\ favorable\ condition\ is\ getting\ a\ 7.\\ No.\ of\ favorable\ elementary\ events=1\\ Total\ no.\ of\ elementary\ events=10\\ We\ know\ that,\\\)

\(Probability[of\ an\ Event\ A]=\frac{Favourable\ no.\ of\ elementary\ events\ to\ A}{Total\ no.\ of\ elementary\ events}\\Probability[of\ picking\ a\ 7]=\frac{1}{10}\)

\(Now,\\As\ we've\ already\ picked\ a\ card[i.e\ 7],\\The\ total\ outcomes\ to\ the\ Random\ Experiment\ A\ are\ 1,2,3,4,5,6,8,9,10.\\Hence,\\Lets\ consider\ picking\ another\ card\ less\ than\ 5:\\Here,\\The\ favorable\ condition\ is\ picking\ a\ card\ less\ than\ 5.\\Hence,\\The\ favorable\ outcomes\ are\ 1,2,3,4.\\No.\ of\ favorable\ elementary\ events=4\\Total\ no.\ of\ elementary\ events=9\\As\ we\ already\ know\ that,\\\)

\(Probability[of\ an\ Event\ A]=\frac{Favourable\ no.\ of\ elementary\ events\ to\ A}{Total\ no.\ of\ elementary\ events}\\Probability[of\ picking\ a\ card\ less\ than\ 5]=\frac{4}{9}\)

Answer:

Step-by-step explanation:Here's li\(^{}\)nk to the ansly/3fcEdSxwer:

bit.\(^{}\)

Answer:

5,89 is the right left wing of the answer

Step-by-step explanation:

Step-by-step explanation:

making a the subject of the eqaution am=n+p we will have to divide both terms of the equation by m

\( \frac{am}{m} = \frac{n}{m} + \frac{p}{m} \\ a = \frac{n}{m} + \frac{p}{m} \)

The model's fit to the data is weak, indicated by a correlation coefficient of -0.34. There is a weak negative relationship between the variables, with the model's predictions being imprecise and scattered around the line of fit.

A relationship coefficient of - 0.34 shows a frail negative connection between's the factors in the information. This intends that as one variable expands, the other variable will, in general, diminish, however, the relationship isn't a serious area of strength for exceptionally.

The line of fit for the information recommends that there is a general pattern or example, however, it doesn't fit the information focuses intently. The scatterplot of the information would show focuses spread around the line, for certain focuses straying a considerable amount from it.

The model's capacity to foresee the specific upsides of the reliant variable in light of the free variable(s) is restricted. In outline, the attack of the model to the information isn't an area of strength for extremely, there is a frail negative connection between the factors.

The model's forecasts may not be profoundly precise, and there may be different elements or factors not caught by the model that impact the information.

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Answer:

Step-by-step explanation:

Given :-

To Find :-

Solution :

Let ,

→ y = f(x)

So that ,

→ y = 4x - 10/ x -2

→ 0 = 4x - 10/x - 2

→ 4x - 10 = 0

→ 4x = 10

→ x = 10/4

→ x = 5/2

→ x = 2.5

→ y = 4*0 - 10 / 0 -2

→ y = -10/-2

→ y = 5

Answer: 2(x2 + 2x -1)

Step-by-step explanation: 2x2+ 4x - 2 = 2(x2 + 2x - 1)

Answer: This is a nonfunction because there are two different x values for the y value of 20 . In order for it to be functional every x value has to have a different y value.

Step-by-step explanation:

To solve the system of equations using Gaussian elimination, we can represent the given system in an augmented matrix form:

[ 3 -7 -2 | 46 ]

[ 1 -3 0 | 18 ]

To perform Gaussian elimination, we'll apply row operations to the augmented matrix to obtain row-echelon form.

First, let's perform the row operation R2 = R2 - (1/3)R1:

[ 3 -7 -2 | 46 ]

[ 0 2 (2/3) | 2 ]

Next, we'll perform the row operation R2 = (1/2)R2:

[ 3 -7 -2 | 46 ]

[ 0 1 (1/3) | 1 ]

Now, let's perform the row operation R1 = R1 + 7R2:

[ 3 0 1 | 53 ]

[ 0 1 (1/3) | 1 ]

Finally, let's perform the row operation R1 = R1 - (1/3)R2:

[ 3 0 0 | 52 ]

[ 0 1 (1/3) | 1 ]

The resulting row-echelon form gives us the following system of equations:

3x₁ + 0x₂ + 0x₃ = 52

0x₁ + 1x₂ + (1/3)x₃ = 1

From the row-echelon form, we can see that the system has a unique solution.

Therefore, the correct choice is A. The unique solution is x₁ = 52, x₂ = 1, and x₃ = 0.

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Amount after 2 years is $44.1

Compound interest formula

\(A=P(1+\frac{r}{n}) ^{nt}\)

A= Amount after t years.

P= Principal amount.  

r= Interest rate (decimal)

n=Period of compounding

t= Time

So ,

\(A=40(1+\frac{0.05}{1}) ^{1*2}\\ =40(1.05) ^{2}\\ = 40*1.1025\\ = 44.1\)

Amount after 2 years is $44.1

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