x=√40-3x can someone help solve

Answer:

[tex]A.\;\; \left(\dfrac{21}{3}\right)^x\\\\\\C. \;\;\dfrac{7^{x}\cdot3^{x}}{3^{x}}\\\\E. \;\;7^x[/tex]

Step-by-step explanation:

[tex]\dfrac{21^x}{3^x} = \left(\dfrac{21}{3}\right)^x[/tex][tex]21 = 7 \cdot 3\\\\So\; \dfrac{21^x}{3^x} = \dfrac{7^x \cdot 3^x}{3^x}[/tex]
So choice A is correct

[tex]------------------------[/tex]

[tex]21 = 7 \cdot 3\\\\So\; \dfrac{21^x}{3^x} \\\\\\= \dfrac{(7\cdot3)^{x}}{3^{x}}=\dfrac{7^{x}\cdot3^{x}}{3^{x}}[/tex]

So Choice C is correct

[tex]------------------[/tex]

[tex]\text{SInce $\dfrac{21}{3} = 7$}\\\\\text{ $\left(\dfrac{21}{3} \right)^x = (7)^x = 7^x$}[/tex]

Therefore choice E is correct

All the other three are incorrect

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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Step-by-step explanation:

a) The probability that Stephen wins can be estimated by dividing the number of times he wins by the total number of matches:

P(Stephen wins) = 11/27 = 0.407 (or 40.7%)

b) The probability that Natasha wins can be estimated by subtracting the probability of Stephen winning from 1:

P(Natasha wins) = 1 - P(Stephen wins) = 1 - 0.407 = 0.593 (or 59.3%)

Answer:

After 100 days, the amount of the substance will decrease to half its original value, so Yo/2 = 5 mg. The half-life of a substance is the time it takes for half of it to decay or disappear. So, every 100 days, the amount of the substance will be halved until there is none left.

Question is not clear.

Answer:

5.6 is greater than 5.

Answer:

5.6>5

Step-by-step explanation:

5.6 is more than 5 :)

Situations with constant rates are represented using linear equations.

The parameters that have been provided are:1 third of an ounce of milkshake every second, 20 ounces at first.

A linear equation is denoted by the following:

Where:

The rate is shown by m.

The starting value is represented by b.

The equation that summarizes Lin's circumstance is as follows:

The graph is shown in the attachment.

Since the other equation is missing, the solution cannot be found.

Situations with constant rates are represented using linear equations.

The parameters that have been provided are:

1 third of an ounce of milkshake every second

20 ounces at first.

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Answer:

Step-by-step explanation:

Solve the System of Equations

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−1,7)

Equation Form:

x=−1,y=7

Answer:

working on a answer one second

Step-by-step explanation:

The value of the given number after division is 10c² + 5c - 9.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

Given to divide  (40c³ +20c² −36c) ÷ (4c)

dividing each term separately,

40c³/4c + 20c²/4c - 36c/4c

dividing constant by constant and variables by variable,

10c² + 5c - 9

Hence the division is 10c² + 5c - 9.

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(the tail points right on the number line), the mean is higher than the median.

What is median?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simples to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the center of a sequence to determine its value.

Every student learns one of the fundamental principles of statistics, which is that in a skewed distribution, the mean is closer to the tail, in around the second week of introductory statistics.

Every student learns one of the fundamental principles of statistics, which is that in a skewed distribution, the mean is closer to the tail, in around the second week of introduction to statistics. Therefore, the mean is greater than the median in a right-skewed distribution (where the tail points directly to the right on the number line).

Hence, (the tail points right on the number line), the mean is higher than the median.

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Step-by-step explanation:

we only have the graph.

it looks like the y-value from the lowest point (= the absolute minimum) is -16.

Answer:

Represent Wilbur with W and Orville with O

The equation connecting both flights is

W - 120 = O

W = 364 feet

364 - 120 = 246

O = 246

Step-by-step explanation:

wish you best of luck

The correct form of the equation can be written as y = 35/6 x + 2

We have to know that the equation have been given to us in the point that we have as; y - 5/7 = 5x - 6/6. We would then have to multiply both sides with the LCM of the equations and then we have that;

42(y - 5/7) = 42(5x - 6)/6

6(y - 5) = 7(5x - 6)

6y - 30 = 35x - 42

Collecting the like terms we have that;

6y - 35 x = -42 + 30

6y - 35x = -12

6y = 35x + 12

y = 35/6 x + 12/6

y = 35/6 x + 2

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Step-by-step explanation:

brackets are missing.

it should look like

lim x→2 (x² + 3x - 10)/(x² - x - 2) =

= (x - 2)(x + 5)/((x - 2)(x + 1)) = (x + 5)/(x + 1) =

= (2 + 5)/(2 + 1) = 7/3

content-wise there is nothing wrong with the argument.

left and right limits are the same.

so, the result is correct.

The equivalent expression is t - 9

From the question, we have the following parameters that can be used in our computation:

− 3 +t-6

Collect the like terms

So, we have the following representation

t - 3 - 6

Evaluate the like terms

This gives

t - 9

Hence, the expression is t - 9

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1: Unique solution: the solution: (0, 3)

2: The system have no solution.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two system of equations,

1.  x + y = 3

   x - y = -3

Adding both the equations,

2x = 0,

x = 0

And y = 3.

The solution: (0, 3)

And 2. 5x + y = 7

   10x + 2y = 16

The system have no solution.

Because lines are parallel.

Therefore, all the required solutions are given above.

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Answer:

The solution is Option C.

The annual percentage rate of Penny is 22.4 %

Step-by-step explanation:

Answer:

X = 50

Z = 50

W = 130

Y = 130

Sum of Interior Angles: 360 degrees

Step-by-step explanation:

We can infer from the diagram, X = 50, therefore Z must be as well. W is congruent to Y, so 260 / 2 = 130. Quadrilateral is equal to 360 degrees.

Six times the difference of a number and two us forty - two less than the number is 6.

What are the arithmetic calculations?

Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division, and their properties and applications. Arithmetic calculations are mathematical operations that involve one or more numbers and result in a numerical answer. These operations can be performed using mental arithmetic, pencil, and paper, or with the help of a calculator.

Let the number be x. We can write the given expression as:

6(x - 2) = x - 42

Expanding the left side:

6x - 12 = x - 42

Solving for x:

5x = 30

x = 6

Therefore, the number is 6.

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Answer:

1620 lines / minute.

Step-by-step explanation:

Proportions:

1 minute = 60 seconds

Then:

108 lines ⇒ 4 seconds

A lines ⇒ 60 seconds

A = 108 lines * 60 seconds / 4 seconds

A = 1620 Lines

The average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] is 1.

A function is a process or set of instructions that takes inputs, performs a specific task, and produces an output. Functions are key components of programming languages, allowing the coder to create complex commands with simple instructions. For example, a function can be used to add two numbers together or to generate a random number. Functions can also be combined to create more complex sequences of instructions.

The average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] can be determined by taking the difference of the output values of the function at the endpoints of the interval, and then dividing it by the difference of the input values of the interval.

The output of the function at x=3 is f(3)=9/-3*3 +4 = -5,
and the output of the function at x=5 is f(5)=9/-3*5 +4 = -3.

Therefore, the difference of the output values is f(5)-f(3) = -3 - (-5) = 2

The difference of the input values is 5-3 = 2

Therefore, the average rate of change of the function on the interval [3,5] is f(5)-f(3) / (5-3) = 2/2 = 1.

Hence, the average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] is 1.

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The time required to paint the cone when the base area is doubled is determined as 5.0 minutes.

The amount of time requires to paint the entire cone when the area of the base of the cone is doubled is calculated using simple proportion as shown below;

                                                               time

Area of base of  cone = 49π in². ----------------------->   2.5 minutes

Area of base of  cone = 2 (49π in² ) ------------------->   ?

49 x = ( 2 x 49 x 2.5 )

x = 2 x 2.5 min

x = 5.0 minutes

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A series of terms is referred to as a geometric progression if each next term is produced by multiplying each previous term by a fixed amount. (GP), whereas the common ratio is the name given to the constant value. In the case of the GP 2, 4, 8, 16, 32, 64, for instance, the common ratio is 2.

The phrase that comes after the previous one in the GP, having a common ratio of r = l/[r(n-1)]. S=a/(1 - r), where 0 r 1, is the sum of infinite, or the sum of a GP with infinite terms.

A number progression is said to as a geometric progression if any two consecutive terms is always same.

Hence we have a=3,n=9,r=2

Now [tex]t=ar^n^-^![/tex]

=[tex]3*2^9^-^1[/tex]

=[tex]3*2^8[/tex]

=3×256

=768

∴ The ninth term of the G.P. is 768.

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Answer:

5

Step-by-step explanation:

The greatest common factor between all 3 fruits is 5. There would be 3 apple slices, 4 oranges, and 12 grapes per cup.

The result is the same, $2.7048. This result is not surprising because as the number of compounding periods increases, the difference between the amount after each compounding period becomes smaller and smaller. Eventually, the amount after compounding reaches a limit, which is $2.7048 in this case.

a. To calculate the value of the investment compounded monthly, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (12 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 12)^(12 * 1)

A = $1.00 * (1 + 100% / 12)^12

A = $1.00 * (1.0083)^12

A = $1.0083^12

A = $2.682

b. To calculate the value of the investment compounded weekly, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (52 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 52)^(52 * 1)

A = $1.00 * (1 + 100% / 52)^52

A = $1.00 * (1.00192)^52

A = $1.00192^52

A = $2.7005

c. To calculate the value of the investment compounded daily, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (365 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 365)^(365 * 1)

A = $1.00 * (1 + 100% / 365)^365

A = $1.00 * (1.00027)^365

A = $1.00027^365

A = $2.7048

d. To calculate the value of the investment compounded 1000 times in a year, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (1000 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 1000)^(1000 * 1)

A = $1.00 * (1 + 100% / 1000)^1000

A = $1.00 * (1.001)^1000

A = $1.001^1000

A = $2.7048

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The expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

We break up a number according to its place value and expand it to show the value of each digit.

Given that to write expanded form of 706.039

Expanded Factors Form:

706.039 = 7 × 100  + 0 × 10 + 6 × 1  + 0 × 0.1 + 3 × 0.01 + 9 × 0.001

Expanded Notation Form:

706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

Hence, the expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

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Object A moves with variable speed and Object B moves with constant speed.

The correct option is D.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

A graph titles Distance vs time.

A curved line is drawn through point 10 on y-axis and this line is labeled Object A.

The graph of the object A is shown as a curved line.

The graph for Object B is a straight slanting line passing through the origin.

The graph for Object B is a linear proportional relationship.

So, Object A moves with variable speed and Object B moves with constant speed.

Therefore, object A moves with variable speed and Object B moves with constant speed.

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The expression represents a quadratic polynomial.

The constant term is 1.

The leading term is -x².

The coefficient of the leading term is -1.

What is a polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

Given expression is -x² + 1

The variable of the expression is x.

The constant term is 1.

Leading term: The highest power of the variable that occurs in the polynomial is its degree. The term with the highest degree—i.e., the term with the highest power of the variable—is the leading term. The leading coefficient is the leading term's coefficient.

The leading term of the expression is  -x² .

The coefficient of  -x²  is -1.

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Answer: 1730

Step-by-step explanation:

subtract 270 from 2000

a) The sample and the population are given as follows:

b) The numbers are classified as follows:

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

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