Poppy gets semi-monthly paycheck of $2,375. What is her annual income?

Considering the figure the value of angle b is

According to the vertical angle theorem, the opposing angles of two crossing lines must have the same value, or be congruent.

hence angle a = angle y

Then from exterior angle of a triangle theorem: If a triangle's side is created, the outside angle that results is equal to the sum of the two opposite internal angles.

angle b = angle a + 90

= 34 + 90

= 124 degrees

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Answer:

1.33

Step-by-step explanation:

2.87349 rounded to the nearest thousandth is 2.873 because the number next to it (4) is less than 5.

1.54324 rounded to the nearest thousandth is 1.54324 is 1.543 because the number next to it (2) is less than 5.

Then you do 2.873 - 1.543 and that = 1.33. So 1.33 is your final answer :)

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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1.

We are told that the coordinates of the image are of the formula:

P'(x-2 , y-3) where x and y are the actual points and x-2 and y-3 are the reflections

Finding the coordinates of point A:

We are given that the coordinates of reflection of A are: A'(-4 , 3)

we also know that reflected point follow the formula: P'(x-2 , y-3)

So, the points of A'(-4 , 3) follow the formula P'(x-2 , y-3)

So, their respective x and y coordinates will be equal

Hence,

x - 2 = -4

x  = -2                 [adding 2 on both sides]

Also,

y - 3 = 3

y  = 6                 [adding 3 on both sides]

Therefore, the coordinates of A are A(-2,6)

Finding the coordinates of B:

We are given the coordinates of B' are B'(-4 , 2)

So,

x - 2 = -4

x = -2             [adding 2 on both sides]

also,

y-3 = 2

y = 5             [adding 5 on both sides]

Therefore, the coordinates of B are: B(-2,5)

Finding the coordinates of C:

We are given that the coordinates of reflection of C are: C'(-2,3)

Using the general formula given in the question:

x - 2 = -2  

x = 0            [adding 2 on both sides]

y - 3 = 3

y = 6            [adding 3 on both sides]

Therefore, the coordinates of C are: C(0,6)

Finally, the coordinates of A, B and C are:

A(-2,6)   ,    B(-2,5)   ,    C(0,6)

__________________________________________________________

2.

Reflecting the pre-image along the x-axis

To reflect along x-axis, we multiply the y-coordinate by -1

Coordinates of the pre-image:

A(-2,6)   ,    B(-2,5)   ,    C(0,6)

Coordinates of points reflected along the x-axis:

A(-2,-6)   ,    B(-2,-5)   ,    C(0,-6)

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

A-1/P=n

Step-by-step explanation:

step 1. look at the parentheses and use inverse operations on both sides

A=P(1+n)

-1       -1

step 2. divide both sides by P

A-1=P(n)

/P    /P

n= A-1/P

The value of n on solving the equation A = P (1 + n) is A / P - 1.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

A = P (1 + n),

Here we can solve the parentheses by using the distributive property as shown below,

A = P × 1 + P × n

A = P + nP

Transform as shown below,

nP = A - P

n = (A - P) / P

n = A / P - 1

Thus, the value of n is A / P - 1.

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An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.

The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.

For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following

form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.

The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.

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Answer:

Hola? divertido

Step-by-step explanation:

Answer: y = x + 5

Step-by-step explanation:

If x>5:

Then all of these values will be positive. So the absolute value symbols are unnecessary!

so we can re-write as:

y = x-3 + x+3 - x + 5

which simplifies to:

y = x + 5

The equation is rewritten without absolute value is y=3x-6.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To find the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.

The given equation is y=|x-3|+|x+2|-|x-5|.

Here, y=x-3+x+2-x-5

y=3x-6

Therefore, the equation is rewritten without absolute value is y=3x-6.

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Answer:

18 ounces of water.

Step-by-step explanation:

So, you see, there are 6 ounces of water in one bottle. When you have three bottles with 6 ounces in each, then that would be 18. You would add 6, 3 times, or just simply multiply 3 by 6 which would be 6 × 3, which would turn out to be 18.

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

cool

Step-by-step explanation:

Answer:

Step-by-step explanation: Just do 0.25+0.25 then the answer x 0.18 and then divide the answer by 2 and it should equal 0.045

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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Answer:

Adults: 134

Senior: 241

Step-by-step explanation:

Known

Number of adult tickets sold: x

Revenue from adult tickets: $11x

Number of senior tickets sold: y

Revenue from senior tickets: $8y

From the problem, we found the equation \(y = 2x - 27\) and 3,402 = 11x + 8y

Combining the two equation:

\(3,402 = 11x + 8(2x-27)\\3,402 = 11x + 16x - 216\\3,402 + 216 = 27x\\27x = 3,618\)

Divided both side by 27

\(x = 134\)

Since

\(y = 2x - 27\)

Inserting the value of x,

\(y = 2(134) -27\\y = 268 - 27\\y = 241\)

So, there are 134 adult tickets sold and 241 senior tickets sold.

The volume of the cylindrical shaped pool with water is V = 75.4 feet³

Given data ,

Let the diameter of the pool be d = 8 feet

So , radius r = 4 feet

And , the height of the cylindrical pool is h = 3 feet

Now , the water is half full

So , Volume of Cylindrical pool is V = ( 1/2 ) πr²h

V = ( 1/2 ) ( 3.14 ) ( 4 )² ( 3 )

On simplifying , we get

V = 75.4 feet³

Hence , the amount of water in pool is V = 75.4 feet³

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The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

9

Step-by-step explanation:

4 * 2 + 3 - 2 =

= 8 + 1 =

= 9

The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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Answer:

(x^2 + 4)(x^2 + 8)

Step-by-step explanation:

Below are some general reasons why a questionnaire might not be suitable:

Poorly constructed questions: If the questions in the questionnaire are not clear, ambiguous, leading, or biased, then the responses obtained may not be accurate or reliable. Poorly constructed questions may also lead to confusion, misunderstandings, and errors.

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Answer:

option b -8x-6y=-126

2x+6y=72

Step-by-step explanation:

please mark me as brainlest

Answer:

Use Photomath

Step-by-step explanation:

Answer:

To calculate the radius of the circle, you need to use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. Therefore, in your triangle, the ratio of the length of the side opposite the 60° angle to the sine of the 60° angle is the same as the ratio of the length of the other two sides to their respective sines.

Let's call the two adjacent sides of the triangle a and b, respectively. The Law of Sines states that:

a/sin(60°) = b/sin(30°)

The length of side a is 12, and the length of side b is 12 times the square root of 3. This means that:

12/sin(60°) = (12√3)/sin(30°)

We can rearrange this equation to calculate the radius of the circle:

r = 12 * sin(30°) / sin(60°)

This gives us a radius of 12√3.

Part a

The domain is the set of x-values, which is \((-\infty, \infty)\)

Part b

The range is the set of y-values, which is \((-\infty, -2]\)

Part c

The x-intercepts is when y=0, which there are none of.

Part d

The y-intercept is when x=0, which is at (0, -2).

The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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Answer: 434,524

Step-by-step explanation:

We know 36,500 is 8.4% of the total. To find 100%, we must divide 36500 by 8.4 to find 1% which is 4345.238...

To get from 1% to 100%, we must multiply our answer by 100 to get 434523.8 which we can then round to the nearest whole number 434524

Answer:

The answer is the third option

Step-by-step explanation:

When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.

So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.