please answer all 3 questions

Answer:

(3xy - 1)/3x = b

Step-by-step explanation:

make b the subject of formula

then simply it

did you get it

Answer:

b=Y-x/3

Step-by-step explanation:

Solve for b by simplifying both sides of the equation, then isolating the variable.

have a great day and thx for your inquiry :)

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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The probability of getting Blue then Green while spinning the wheel is

3 / 32

Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.

From the given figure we can find out the following information

The probability of getting Blue While spinning the wheel = 3/8

The probability of getting Green While spinning the Wheel = 2 / 8

The probability of getting Blue then Green while spinning the wheel

= 3/8 * 2/8

= 6/64

= 3/32

Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32

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The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula [tex]A = s^2[/tex], where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

[tex]56 = s^2[/tex]

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = [tex]sqrt(s^2)[/tex]

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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Answer:

74,000

Step-by-step explanation:

use intelligence

The products of the matrices A and B are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]

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

Matrix A = [tex]\left[\begin{array}{cc}-3&-8\\2&8\end{array}\right][/tex]

Matrix B = [tex]\left[\begin{array}{cc}6&3\\4&-2\end{array}\right][/tex]

Using the above as a guide, we have the following:

[tex]AB = \left[\begin{array}{cc}-3 * 6 + -8 * 4 &-3 * 3 -8 * -2\\2 * 6 + 8 * 4 &2 * 3 + 8 * -2\end{array}\right][/tex]

Evaluate

[tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex]

Next, we have

[tex]BA = \left[\begin{array}{cc}6 * -3 + 3 * 2&6 * -8 + 3 * 8 \\4 * -3 + -2 * 2&4 * -8 + -2 * 8\end{array}\right][/tex]

Evaluate

[tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]

Hence, the values are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]

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Answer:

28

Step-by-step explanation:

let's assumed that

x = Jerry's age

y = Carrie's age

if Jerry 4 years older that Carrie

x = y + 4

x + y = 52

(y + 4) + y = 52

2y + 4 = 52

2y = 48

y = 24

x = y + 4

x = 24 + 4

x = 28

Answer:

The answer is B:14

Step-by-step explanation:

When you simply multiply 5% by 14, you get 0.7. So you know that 5% of 14 is 7.

Answer:

(- 2, 0 ) , (1, - 3 )

Step-by-step explanation:

the solutions to the system of equations are at the points of intersection with the curve and the straight line.

points of intersection are at (- 2, 0 ) and (1, - 3 ) , then

solutions are (- 2, 0 ) , (1, - 3 )

Answer:

B

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

7

Step-by-step explanation:

Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?

A single log statement from the many log statements to 1 is: [tex]log(7wy^{(-8)}/x^3)[/tex]

The exponent that indicates the power to which a base number is raised to produce a given number are called logarithm.

Use the logarithmic identity:

log[tex](a^n)[/tex] = n*log(a)

to convert the coefficients 2, 3, and 8:

log w + log 7 - 3log x - 8log y

= log w + log 7 - log [tex]x^3[/tex] - log [tex]y^8[/tex]

Combine the terms on the right-hand side using the logarithmic identity:

log(a) + log(b) = log(ab)

log w + log 7 - log[tex]x^3[/tex] - log [tex]y^8[/tex]

= log([tex]7wy^{-8}/x^3[/tex])

Therefore, the single log statement is from the many log statements to 1 is: log[tex](7wy^{-8}/x^3)[/tex]

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Answer:

A. 4ab² + 2x

Step-by-step explanation:

If you want to get rid of those pesky parentheses, you have to use the superpower of distributive property. It lets you multiply everything inside the parentheses by the number outside. For example:

4(ab²+1/₂c + x) = 4ab² + 2c + 4x

Boom! No more parentheses!

To combine like terms, you have to add or subtract the numbers in front of the terms that have the same variable and exponent. For example:

2x - 4x = -2x

Bam! Only one x left!

Here are the steps to simplify the expression:

4(ab²+1/₂c + x) - 2(c+x)

= 4ab² + 2c + 4x - 2c - 2x (use superpower)

= 4ab² + 4x - 2x (combine like terms)

= 4ab² + 2x (simplify)

So, the answer is A. 4ab² + 2x.

Answer:

3

Step-by-step explanation:

factorize whats common in the question

division turns to multiplication by Inverwing the fraction

at the end of the day you will be left with 3

I hope you understand

The requried, Multiplies(with switching factors.) area given below,

a.

693 x 83 = 57489

83 x 693 = 57489

The answer is 57489.

b.

910 x 45 = 40950

45 x 910 = 40950

The answer is 40950.

c.

38 x 84 = 3192

84 x 38 = 3192

The answer is 3192.

d.

409 x 89 = 36401

89 x 409 = 36401

The answer is 36401.

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a) The fourth and sixth data points have significantly different ratios.

a) Let's calculate the ratios:

For the first data point:

= 11.5 gallons / $25.23 = 0.4555 gallons per dollar

For the second data point:

= 7.2 gallons / $15.80 = 0.4557 gallons per dollar

For the third data point:

= 10 gallons / $21.94 = 0.4556 gallons per dollar

For the fourth data point:

= 14.3 gallons / $40.63 = 0.3519 gallons per dollar

For the fifth data point:

= 6.8 gallons / $14.92 = 0.4555 gallons per dollar

For the sixth data point:

= 9.7 gallons / $27.56 = 0.3517 gallons per dollar

However, the fourth and sixth data points have significantly different ratios.

b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.

The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.

To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.

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255 number of adults and 355 number of students bought ticket.

Here,  we have,

Let the number of adults bought tickets are x and the number of students that bought tickets is (x + 100).

Since it is given that 100 more students brought tickets than adults.

Now, each adult ticket costs $5 and each student's ticket costs $3.5 and the total collected value of tickets is $2517.5.

So, 5x + 3.5(x + 100) = 2517.5

⇒ 8.5x + 350 = 2517.5

⇒ 8.5x = 2167.5

⇒ x = 255

So, 255 number of adults and (255 + 100) = 355 number of students bought ticket. (Answer)

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The requried solution of the given derivative has been given below.

If F(t) is an antiderivative of t⁵, then we have:

F'(t) = d/dt(F(t)) = t⁵

According to the Second Fundamental Theorem of Calculus, we have:

[tex]\int_1^x t^5 dt = F(x) - F(1)[/tex]

Using this formula, we can find [tex]d/dx(\int_1^x t^5 dt)[/tex] as follows:

[tex]d/dx(\int_1^x t^5 dt) = d/dx(F(x) - F(1)) = F'(x) - 0 = t^5[/tex]

Therefore, [tex]d/dx(\int_1^x t^5 dt) = t^5.[/tex]

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Answer:

  x ≥ 5

Step-by-step explanation:

You want the domain of the equation y = √(x -5) -1.

The domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...

  x -5 ≥ 0

  x ≥ 5 . . . . . . the domain of this function

__

Additional comment

The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.

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Answer:

Step-by-step explanation:

$6.80 x 19 pounds = $129.2

$4.70 x 18 pounds = $84.6

            +___________________

             37 pounds = $213.8

$213.8 divided by 37 pounds = 5.77837......

                                                  = $5.78 per pound

Darlene's net proceeds from the investment into shares would be $ 8, 279 .

First, find the initial broker fee:

=  Initial investment × Broker fee rate

= 20, 000 x 1. 5 %

= 20, 000 x 0. 15

= $ 300

The total fees incurred to buy and sell are:

= 300 initial broker + 21 later broker

= $ 321

The net proceeds would then be:

= Final value of stock - Initial investment - Total fees

= 28, 600 - 20, 000 - 321

= 8, 600 - 321

= $ 8, 279

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Full question is:

Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $ 28,600  two years later, and uses a discount broker who charges $21 per trade. Compute Darlene's net proceeds after the broker fees are taken out.

The value of sin(θ) is 0.31 and it lies in the third and fourth quadrants. if the value of the cosine of θ is −0.95.

cos(θ) = -0.95

To calculate the value of sin(θ), we can use the Pythagorean theorem:

[tex]sin^{2}[/tex] (θ) +[tex]cos^{2}[/tex] (θ) = 1

We can rearrange the Pythagorean identity to solve for sin(θ):

[tex]sin^{2}[/tex] (θ)= 1 - [tex]cos^{2}[/tex]

sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)---------  (equation 1)

Substitute the value of the cosine of θ = −0.95 in Equation 1

sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)

sin(θ) = ±[tex]\sqrt{(1 - 0.9025)}[/tex]

sin(θ) = ±[tex]\sqrt{0.0975}[/tex]

The positive value determines that the value is in the first and second quadrants, Negative shows the third and fourth quadrants.

sin(θ) = [tex]\sqrt{ 0.0975}[/tex]

sin(θ) = 0.312

Therefore, we can conclude that the value of sin(θ) is 0.312.

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The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

Kenya needs to initially put in the amount of $2,208.2in the account to have at least $7,000 after 15 years.

We can use the formula for compound interest:

A = P(1 + r/n)ⁿ

where A is the amount of money in the account after t years, P is the initial principal, r is the annual interest rate (as a decimal), and n is the number of times per year the interest is compounded.

Here, we want to find P, so we can rearrange the formula as:

P = A / (1 + r/n)ⁿ

We are given that r = 0.08 (8% interest) and n = 1 (interest is compounded annually).

We also know that A = $7,000 and t = 15 years.

So we can plug in these values and solve for P:

P = 7000 / (1 + 0.08/1)¹⁵

P = 7000 / (1.08)¹⁵

P ≈ $2,208.2

Therefore, Kenya needs to initially put in approximately $2,208.2in the account to have at least $7,000 after 15 years.

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Answer:

Center: (-3, 2)

Radius: 4

Step-by-step explanation:

x2 + 6x + y2 - 4y = 3​

x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4

(x + 3)² + (y - 2)² = 16

(x + 3)² + (y - 2)² = 4²

Center: (-3, 2)

Radius: 4

Answer: I believe the answer is Yolanda.

Step-by-step explanation: Because Maurice ran 110 meters in 20.9 seconds, which is slower than Yolanda. Completing the race in 20 seconds is better than 20.9 seconds.

Given statement solution is :- Outputs and values g(2/3) = 2/3.

To summarize:

g(0) = 0

g(-1) = undefined

g(2) = undefined

g(2/3) = 2/3

To find the values of g(x) for the given inputs, we substitute each input into the function g(x) = x / √([tex]1 - x^2[/tex]). Let's calculate the values:

g(0):

Substitute x = 0 into the function:

g(0) = 0 / √([tex]1 - 0^2[/tex])

= 0 / √(1 - 0)

= 0 / √1

= 0

Therefore, g(0) = 0.

g(-1):

Substitute x = -1 into the function:

g(-1) = (-1) / √(1 - [tex](-1)^2[/tex])

= (-1) / √(1 - 1)

= (-1) / √0

Since the square root of 0 is undefined, g(-1) is undefined.

g(2):

Substitute x = 2 into the function:

g(2) = 2 / √([tex]1 - 2^2[/tex])

= 2 / √(1 - 4)

= 2 / √(-3)

Since the square root of a negative number is undefined in the real number system, g(2) is undefined.

g(2/3):

Substitute x = 2/3 into the function:

g(2/3) = (2/3) / √(1 - [tex](2/3)^2[/tex])

= (2/3) / √(1 - 4/9)

= (2/3) / √(5/9)

= (2/3) / (√5/√9)

= (2/3) / (√5/3)

= (2/3) * (3/√5)

= 2√5 / 3√5

= 2/3

Therefore, outputs and values g(2/3) = 2/3.

To summarize:

g(0) = 0

g(-1) = undefined

g(2) = undefined

g(2/3) = 2/3

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For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.

We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).

First, we need to find the value of cosA and sinB:

Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:

cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61

Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:

hypotenuse = √(4² + 3²) = 5

sinB = opposite/hypotenuse = 4/5

Now we can substitute these values into the formula:

cos(A-B) = cosA cosB + sinA sinB

= (60/61)(3/5) + (11/61)(4/5)

= 180/305 + 44/305

= 224/305

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An equation that satisfies all three pairs of a and b values listed in the table include the following: C. 3a - b = 10.

In order to determine an equation that satisfies all three pairs of a and b values listed in the table, we would substitute each of the numerical values corresponding to each variable into the given equations and then evaluate as follows;

a - 3b = 10

0 - 3(-10) = 30 (False).

3a + b = 10

3(0) - 10 = -10 (False).

3a - b = 10

3(0) - (-10)

0 + 10 = 10 (True).

3a - b = 10

3(1) - (-7)

3 + 7 = 10 (True).

3a - b = 10

3(2) - (-4)

6 + 4 = 10 (True)

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Complete Question:

Which equation satisfies all three pairs of a and b values listed in the table?

a b

0 -10

1 -7

2 -4

The equation is?

A.) a-3b=10

B.) 3a+b=10

C.) 3a-b=10

D.) a+3b=10

The total "surface-area" of cone having "slant-height" as 10, and base-radius as 6, is 301.44 square units.

The total surface area of a cone can be calculated by adding the area of the base to the lateral surface area.

Let us first calculate the lateral surface area of the cone:

Lateral surface area = πrl; where r is radius , and 'l" = slant-height,

The radius of base = 6 units and slant height is = 10 units.

So, we have:

Lateral surface area = π × 6 × 10

Lateral surface area = 60π square units

Next, Area of the base = πr²;

Area of the base = π × 6²,

Area of the base = 36π square units,

Total surface area = Lateral surface area + Area of the base

Total surface area = 60π + 36π

Total surface area = 96×3.14 = 301.44 square units.

Therefore, the total surface area of cone is 301.44 square units.

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