Can y’all pls answer this

Money with Tom = ×

Money with Aaron = x + 8

Their sum = $20

This can be written as :

= x + x + 8 = 20

= 2x + 8 = 20

= 2x = 20 - 8 ( transposing +8 from LHS to RHS changes +8 to -8 ) .

= 2x = 12

= x = 12 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 ) .

= x = 6

Which means ,

Tom has = x = $6

Aaron has = x + 8 = $6 + $8 =

= $14

Therefore , Tom has = $6 and Aaron has = $14 .

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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The function that models the population t years after 2000 is22300 × e^(0.06t), The estimated fox population in the year 2008 is 36081. This can be answered by the concept of exponential function.

The question asks to find a function that models the population of foxes in a certain region with a continuous growth rate of 6 percent per year starting from the year 2000. It also asks to estimate the fox population in the year 2008 using this function.

a. Let P(t) be the population of foxes t years after 2000. Since the growth rate is continuous, we can use an exponential function with base e to model the population. We know that P(0) = 22300 (the population in the year 2000), and the annual growth rate is 6%. Therefore, we can write:

P(t) = 22300 × e^(0.06t)

b. To estimate the fox population in the year 2008, we need to find P(8) since t = 8 represents 8 years after 2000. Substituting t = 8 into the equation above, we get:

P(8) = 22300 × e^(0.06×8) = 22300 × e^0.48 ≈ 36081

Therefore, the estimated fox population in the year 2008 is 36081.

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It this an actual school question or a question from a satanic worshiper?

Answer:

420 calories

Step-by-step explanation:

Multiply 140 by 3 because there are three servings in a can, and each serving is 140 calories, so the number of calories in the can is the product of the numbers.

Answer:

The correct numerical expression using PEDMAS for "subtract the sum of 2 and 9 from the product of 4 and 3" is:

4 x 3 - (2 + 9)

Using the order of operations, first, we perform the addition inside the parentheses, then we multiply 4 and 3, and finally, we subtract the result of the sum from the product:

= 4 x 3 - 11

= 12 - 11

= 1

Therefore, the correct numerical expression is (4 x 3) - (2 + 9) = 1.

Step-by-step explanation:

Answer:

  1244.3 square units

Step-by-step explanation:

The area of a composite figure can be found by decomposing it into its parts, then adding the areas of those parts. This figure can be decomposed into a square of side length 22 units, and two circles, each with radius 11 units.

The area of a square is the square of its side length.

  A = s²

  A = 22² = 484 . . . . square units

The area of a circle is given by the formula ...

  A = πr²

  A = π(11²) = 121π

The area of the two circles is twice this value, or ...

  2A = 2(121π) = 242π ≈ 760.3 . . . . square units

The area of the figure is the sum of the areas of its parts:

  total area = square area + area of circles

  total area = 484 +760.3 = 1244.3 . . . . square units

Answer:

3

Step-by-step explanation:

If 6 numbers have a mean value of 10, it means that the sum of the numbers divided 6 is equal to 10. This can be expressed as:

x÷6=10

x=60

The new number added will be the 7th number and now the mean is 9. You have to ask what number divided by 7 is equal to 9? This can be expressed as:

y÷7=9

y=63

63-60=3

So the new number added is 3

Answer:

3

Step-by-step explanation:

Mean is calculated as

mean = \(\frac{sum}{count}\)

Given the mean of 6 numbers is 10, then

\(\frac{sum}{6}\) = 10 ( multiply both sides by 6 )

sum = 60

When another number x is added then count is 7

\(\frac{60+x}{7}\) = 9 ( multiply both sides by 7 )

60 + x = 63 ( subtract 60 from both sides )

x = 3 ← the number added

Answer:

113,046

Step-by-step explanation:

Add inside of parentheses first to get

(498)x(227)

Multiply to get

113,046

Answer:

5 r o 2 t

Step-by-step explanation:

(√3+√7)²

We know ,[(a+b)²=a²+2ab+b²]

=>(√3+√7)²=(√3)²+2(√3)(√7)+(√7)²

=>(√3+√7)²=3+2√21+7

=>(√3+√7)²=10+2√21

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

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Answer:

S = 1/2 . x^2 + 11/2 . x + 15

Step-by-step explanation:

- Let S = the area of the shaded region

- From the figure we see that S = 1/2 the area of the rectangle

- The area of the rectangle is (x+5)(x+6) = x^2 + 11x + 30

--> S = 1/2 (x^2 + 11x + 30)

--> S = 1/2 . x^2 + 11/2 . x + 15

Given function:y = √(1 – x³)We need to find dy/dx.As per the chain rule of differentiation, if y = f(u) and u = g(x), then the derivative of y with respect to x is given by dy/dx = dy/du * du/dx.

Now, let u = 1 – x³. Then, y = √u ⇒ y = u^(1/2).

dy/dx = dy/du * du/dxdy/du = 1/(2√u) = 1/(2√(1 – x³))du/dx = -3x²Therefore, dy/dx = dy/du * du/dx = 1/(2√(1 – x³)) * (-3x²) = (-3x²)/(2√(1 – x³)).

Therefore,  (A) 3(1 - x²)².Option (A) is the correct answer.

The given function is y = √(1 – x³) and we need to find dy/dx. As per the chain rule of differentiation, if y = f(u) and u = g(x), then the derivative of y with respect to x is given by dy/dx = dy/du * du/dx.

Let u = 1 – x³. Then, y = √u ⇒ y = u^(1/2).

We need to find dy/dx.dy/dx = dy/du * du/dxdy/du = 1/(2√u) = 1/(2√(1 – x³))du/dx = -3x².

Therefore, dy/dx = dy/du * du/dx = 1/(2√(1 – x³)) * (-3x²) = (-3x²)/(2√(1 – x³)).

Thus, dy/dx = (-3x²)/(2√(1 – x³)).Therefore, the correct option is (A) 3(1 - x²)².  

The derivative of the given function y = √(1 – x³) with respect to x is (-3x²)/(2√(1 – x³)) and the correct option is (A) 3(1 - x²)².

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______________________________

- This is also known as PEMDAS.

- This is the parenthesis and exponents step.

- This is the multiplication step.

______________________________

Answer: ASA

Step-by-step explanation:

Its obvious!! Two angles and one side (ASA).

"ASA" is when we know two angles and a side between the angles. "ASA" means "Angle, Side, Angle"

Answer:

Please check the formatting when posting.  I'm assuming these are the equations:

y=x^2 - 2

y=−x

Step-by-step explanation:

We can either graph the equations or solve them.  I use graphing - see the attachment.  The lines intersect at (-2, 2) and (1,-1)

1.  Graphing

See attached graph

(-2, 2) and (1,-1) are the intersection points

2.  Solving

y=x^2 - 2  Use y=−x in this equation:

-x = x^2 - 2

0 = x^2 + x - 2

0 = (x+2)(x-1)

x = -2 and +1

(-2, 2) and (1,-1) are the intersection points

Answer:

No problems here!

Great Job!

Step-by-step explanation:

Answer:

x = 18.0

Step-by-step explanation:

You must memorize the definitions of the trig functions and then these types of problems are easy.

In your problem,  sin of an angle = opposite side/hypotenuse

So,  sin 51 = 14/x

      x sin 51  = 14

            x = 14/sin 51 = 18.0

(a) The function f(x) = x² + 2, has a one-to-one correspondence.

    The function f(x) = (x+3)/(x+2), has a one-to-one correspondence.

(b) fog = {(a, 3), (b, 8), (c, 2), (d, 3)}.

       \(f^{-1_}\)= {(8,1), (3,2), (2,3)}.

Problem (a)

The given function is

f(x) = x² + 2,

we can check whether it is a one-to-one correspondence by checking if it passes the horizontal line test.

This means that if we draw a horizontal line through the graph of the function, it should intersect at most one point on the graph.

To do this,

we can take the derivative of the function: f'(x) = 2x.

This derivative is always positive except for at x = 0, where it is zero.

This means that the function is increasing everywhere except at x = 0, where it has a minimum value.

Since the function is always increasing and has a minimum value at x = 0, this means that it passes the horizontal line test and is a one-to-one correspondence.

For the second function f(x) = (x+3)/(x+2),

we can also check whether it is a one-to-one correspondence by using the horizontal line test.

To do this, we can set f(x) equal to a constant value y, and then solve for x in terms of y.

We get x = (2y - 3)/y.

This means that f(x) is not defined when y = 0,

since we would be dividing by zero.

Therefore, we need to exclude y = 0 from the range of the function in order for it to be a one-to-one correspondence.

Also, we can take the derivative of the function,

f'(x) = 1/(x+2)².

This derivative is always positive, which means that the function is always increasing.

Therefore, if we exclude y = 0 from the range of the function, we can conclude that it passes the horizontal line test and is a one-to-one correspondence.

Problem (b) ;

(1) To find fog,

we have to perform the composition of functions f and g. That is,

we have to put in g into f as follows:

⇒ fog(a) = f(g(a))

              = f(2)

              = 3

fog(b) = f(g(b))

          = f(1) = 8

fog(c)  = f(g(c))

          = f(3)

          =  2

fog(d) = f(g(d))

          = f(2)

          = 3

Therefore, fog = {(a, 3), (b, 8), (c, 2), (d, 3)}.

2) To find inverse of f,

we have to find the inverse of function f.

We can switch the positions of the elements in each ordered pair and then solve for the new y values as follows,

⇒ (8,1), (3,2), (2,3)

Thus, \(f^{-1_}\)= {(8,1), (3,2), (2,3)}.

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Part A - (f + g)(x) = 5x + 12.

Part B -  (f + g)(4) = 32.

Part C - We evaluate (f + g)(4) and get 32, it means that after 4 months, the two shelters combined have adopted a total of 32 animals.

Part A: To find (f + g)(x), we need to add the two functions f(x) and g(x) together.

(f + g)(x) = f(x) + g(x)

= (x + 5) + (4x + 7)

= x + 5 + 4x + 7

= 5x + 12

Therefore, (f + g)(x) = 5x + 12.

Part B: To evaluate (f + g)(4), we substitute x = 4 into the function (f + g)(x).

(f + g)(4) = 5(4) + 12

= 20 + 12

= 32

Therefore, (f + g)(4) = 32.

Part C: In terms of the scenario, the function (f + g)(x) represents the total number of animals adopted at both shelters combined in a given number of months. The equation 5x + 12 indicates that for every month (x), the total number of animals adopted at both shelters is 5 times the number of months plus 12.

For example, if we evaluate (f + g)(4) and get 32, it means that after 4 months, the two shelters combined have adopted a total of 32 animals.

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Answer:

Step-by-step explanation:

Part A: (f + g)(x) = 5x + 12.

My work for Part A:

Step 1: Write the functions without the parentheses: x + 5 + 4x + 7.

Step 2: Rewrite the function so like terms are next to each other: x + 4x + 5 + 7.

Step 3: Combine like terms: x + 4x = 5x, and 5 + 7 = 12.

Step 4: Write the final function in standard form: (f + g)(x) = 5x + 12.

Part B: (f + g)(4) = 32.

My work for Part B:

Step 1: Write the first function substituting x for 4: f(4) = 4 + 5.

Step 2: Solve the function: f(4) = 4 + 5 = 9.

Step 3: Write the final answer for the first function: f(4) = 9.

Step 4: Write the first function substituting x for 4: g(4) = 4 x 4 + 7.

Step 5: Solve the function: g(4) = 4 x 4 = 16, and 16 + 7 = 23.

Write the final answer for the second function: g(4) = 23.

Step 6: Add the output answers together: 9 + 23 = 32.

Step 7: Write the final output answer for both functions: (f + g)(4) = 32

Part C: 32 represents the total number of animals adopted at two shelters in 32 months.

Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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The probability that the sum of the three recorded numbers is less than 6 is 19/27

To find the probability that the sum of the three recorded numbers is less than a certain value, we can use the technique of generating functions.

Let's first write the generating function for one draw from the bag. Each ball has a 1/3 probability of being drawn, and the number on the ball contributes that amount to the sum. So the generating function for one draw is

g(x) = (1/3)x + (1/3)x^2 + (1/3)x^3

To find the generating function for the sum of three draws, we can cube the generating function for one draw

g(x)^3 = [(1/3)x + (1/3)x^2 + (1/3)x^3]^3

Expanding this expression using the binomial theorem, we get

g(x)^3 = (1/27)x^3 + (1/9)x^4 + (5/27)x^5 + (5/18)x^6 + (5/27)x^7 + (1/9)x^8 + (1/27)x^9

The coefficient of each term tells us the number of ways to get that sum. For example, there is only one way to get a sum of 3 (draw 1, 1, and 1), but there are five ways to get a sum of 5 (draw 1, 1, 2; 1, 2, 1; 2, 1, 1; 1, 3, 1; and 3, 1, 1).

Now, we want to find the probability that the sum of the three recorded numbers is less than s. We can do this by finding the sum of the coefficients of the terms with exponents less than or equal to s

P(sum < s) = [coefficient of x^0 + coefficient of x^1 + ... + coefficient of x^(s-1)] / 27

For example, if we want to find the probability that the sum is less than or equal to 6, we need to find the sum of the coefficients of x^0 through x^5:

P(sum ≤ 6) = (1/27) + (1/9) + (5/27) + (5/18) + (5/27) + (1/9) = 19/27

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Answer:

x = 101

Step-by-step explanation:

\(x+(-21)=21-(-59)\\x-21=21+59\\x-21=80\\x=101\)

Answer:

1. At 1/3 cup per person, the amount of tomato juice needed is \(1\tfrac{1}{3} \ cups\) of tomato juice

2. At 2/3 cup per person, the amount of tomato juice needed is \(2\tfrac{2}{3} \ cups\)  of tomato juice

Step-by-step explanation:

1. Here we have that each person gets 1/3 cup of juice

Number of people in the group = 4

Amount of tomato juice each person gets = 1/3 cup

Total amount of tomato juice required = 4 × 1/3 = 4/3 cups of tomato juice

In proper fractions, we have;

Total amount of tomato juice required = \(1\tfrac{1}{3} \ cups\) of tomato juice.

2. Where we have that;

Amount of tomato juice each person gets = 2/3 cup

Number of people in the group = 4

∴ Total amount of tomato juice required = 4 × 2/3 = 8/3 cups of tomato juice

In proper fractions, we have;

Total amount of tomato juice required = \(2\tfrac{2}{3} \ cups\) of tomato juice.

The midpoint of the line segment is (1, 2). Then the correct option is B.

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints of the line segment are (-1, 7) and (3, -3). Then the mid-point of the line segment will be given as,

(x, y) = [(-1 + 3) / 2, (7 - 3) / 2]

(x, y) = (2/2, 4/2)

(x, y) = (1, 2)

The midpoint of the line portion is (1, 2). Then the right choice is B.

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Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

Answer:

y=61°

Step-by-step explanation:

(y-8°)+(y+15°)+(y-10°)=180°

y-8°+y+15°+y-10°=180°

3y-3°=180°

3y=180°+3°

3y=183°

3y÷3=183°÷3

y=61°

The value of y from the given triangle can be calculated using the angle sum property as 61.

Given that:

A triangle has three angles given.

The measures of the angles are y - 8°, y - 10°, and y + 15°.

The angle sum property of triangles is defined as the property which states that the sum of the angles of the triangle is 180°.

Equating the angle measures:

y - 8 + y - 10 + y + 15 = 180

Add the like terms together.

3y - 3 = 180

Take 3 as common.

3(y - 1) = 180

Divide both sides of the equation by 3.

y - 1 = 60

Add 1 on both sides.

y = 61

Hence, the value of y is 61.

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