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Suppose that the functions f and g are defined for all real numbers x as follows.


Write the expressions for (f * g)(x) and (f - g)(x) and evaluate (f + g)(1).

Answer:

x=-5

Step-by-step explanation:

i just solved the problem

Answer:

=5±√23

Step-by-step explanation:

        -10+2√23

= -------------

               -2

         -10-2 √23

= -------------

                -2

Answer:

79/156

Step-by-step explanation:

we know that cosx is the adjacent side over the hypotenuse.

hence, we can find the opposite side using the pythagorean theorem.

sqrt(13^2 - 5^2)

therefore, the opposite side is 12

opposite: 12

adjacent: 5

hypotenuse: 13

not that cot is adjacent over opposite while sin is opposite over hypotenuse.

So,

12/13 - 5/12

the answer is 79/156

Answer:

2462.4 square inches

Step-by-step explanation:

we know the shorted side of the wall is 36 inches so we divide 2.5 to 36 to see how much bigger the actual wall is to the scale

36/2.5= 14.4

The actual wall is 14.4 times bigger than the scale

14.4 x 4.75= 68.4

68.4 x 36= 2462.4 inches

Answer:

Yes it its!!! It goes on for a long time!! Keep that in mind when you are doing problems like this!  

:)

Step-by-step explanation:

Answer:

1. The first statement is true

2. Answer will be 0. 2083

3. 1: 5

4. 0 takes in ten billions place

5. 1.38 * 10^10

Hope this helped

Correct me if i'm wrong

All the best !!

Answer:

30

Step-by-step explanation:

x=10

x^2+3x-130=0

x=10 or -13

there is no negative angle so the answer is ten

Answer:

z = 12.52 in.

Step-by-step explanation:

Because this is a right triangle, we can solve for z using on the trigonometric ratios.

If we allow 37° to be our reference angle, the 10 in. side is the adjacent side and z (directly across from the right angle) is the hypotenuse.

Thus, we can use the cosine ratio which is

\(cos(angle)=\frac{adjacent}{hypotenuse}\)

Now, we can plug everything into the formula and solve for z, the hypotenuse:

\(cos(37)=10/z\\z*cos(37)=10\\z=10/cos(37)\\z=12.52135658\\z=12.52\)

Answer:

I believe the answer will be 63 degrees not 100% sure tho

Step-by-step explanation:

The reason is because triangle FHE measures 27 degrees it looks like FHE is a right triangle so there needs to be a total of 90 degrees in a right triangle so 90-27=63 like I said not 100% correct

Answer:

is this weird but in all my years of school I've never learn something like this

Answer:

Every discontinuity of a rational function is either a removable discontinuity or an infinite discontinuity. It is NEVER a jump discontinuity.

9514 1404 393

Answer:

  P(M&P) = 0.05

Step-by-step explanation:

P(M+P) = P(M&P') +P(P&M') +P(M&P)

0.64 = 0.38 +0.21 +P(M&P)

P(M&P) = 0.64 -0.59 = 0.05

The probability the customer will select both items is 0.05.

_____

Additional comment

Inside parentheses, & = "and"; + = "or".

The height of the wall is 14 feet

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Therefore ;

TH/ JS = TV/VS

4/JS = 6/21

21× 4 = 6 JS

JS = 21× 4/6

JS = 84/6

JS = 14 feet

therefore the height of the wall is 14 feet

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Answer:

A)  Mr. Simpson's class; it has a larger median value 14.5 pencils.

Step-by-step explanation:

A box plot is a visual display of the five-number summary:

From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:

Mr Johnson's class:

Mr Simpson's class:

In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.

The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.

The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).

As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.

In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.

The possible values of x are 3 and 7

Given the rational expression below;

√60-8x = x - 9

Square both sides to have:

(60-8x)² = (x-9)²

60-8x = x²-18x+81

Equate to zero to have;

x²-18x+81 - 60 + 8x = 0

x² - 10x + 21 = 0

x² -3x-7x +21 = 0

x(x-3)-7(x-3) = 0

x = 3 and 7

Hence the possible values of x are 3 and 7

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The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealised relationship between two changing quantities.

We have given function as ,

f(x) = 1/√(x-4)

We have to find f(x) - f(5)/x-5

f(x) = f(5)/x-5 = 1/√(5-4)/(x-5)

= 1/√(5-4)/(x-5)

= (x-5)/√(5-4)

= (x-5)

Therefore, The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

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Answer:

(9,16)

Step-by-step explanation:

We Know

The equation y = 3x - 2

Find the y coordinate (9, ?)

We just simply put 9 in for x and solve for y

y = 3(9) - 2

y = 18 - 2

y = 16

So, the coordinate are (9,16)

After answering the given query, we can state that If -2 is the absent equation number, the total becomes -2 + 6 + 16 = 20.

A mathematical equation is a process that links two statements and indicates equality with the equals sign (=). A mathematical assertion that proves the equality of two mathematical statements is known as an equation in algebra. For instance, the equal symbol separates the numbers 3x plus 5 and 14 in the equation 3x + 5 = 14. A mathematical formula can be used to understand the connection between the two lines that are written on opposite sides of a letter. Frequently, the emblem and the particular program are identical. as in 2x - 4 = 2, for example.

Let x serve as the omitted number. Next, we have

? + 6 + x = 16

6 is subtracted from both parts to yield:

? + x = 10

Any figure with x that sums up to 10 would be a proper response. For instance:

If the absent number is 4, the total will be 4 + 6 + 6, which equals 16.

If 7 is the omitted number, the total would be 7 + 6 + 3 = 16.

If -2 is the absent number, the total becomes -2 + 6 + 16 = 20.

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1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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When a particle is moving so that its position at time t is given by the parametric equations x = 5*sin(-2t) and y = 5*cos(2t), the speed of the particle is 10.

Speed is the rate of change of position of a particle with respect to time.

Here we are given the parametric equations of positions of particle, in order to obtain the rate of change with respect to time we have to differentiate the equation with respect to time.

Speed of particle in x-direction can be obtained by

Vx = dx/ dt

= -2 × 5 × cos(-2t)

= -10cos(-2t)

= -10cos(2t)

Speed of particle in y-direction can be obtained by

Vy = dy/ dt

= 2 × 5 × (-sin(2t))

= -10sin(2t)

Therefore speed of particle can be obtained by

speed = √( (-10cos(2t))² + (-10sin(2t))² )

= 10√( cos(2t))² + (sin(2t))² )

= 10

-- The question is incomplete, answering to the question given below--

"A particle is moving so that its position at time t is given by the parametric equations : x = 5*sin(-2t) and y = 5*cos(2t). What is the speed of the particle?"

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The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

We have,

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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complete question:

Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.

By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Answer:

The Z-score for that day's temperature is 2.41, and since Z > 2, this temperature is significantly high.

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

If \(|Z| > 2\), the measure X is significantly high(Z > 2) or significantly low(Z < -2).

The mean high temperature on a particular day in January is 31 degrees F and the standard deviation is 8.7 degrees.

This means that \(\mu = 31, \sigma = 8.7\)

One year, the temperature was 52 degrees F on that day.

This means that \(X = 52\).

What is the Z-score for that day's temperature?

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{52 - 31}{8.7}\)

\(Z = 2.41\)

The Z-score for that day's temperature is 2.41, and since Z > 2, this temperature is significantly high.

The x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be 36x^7y^2.

In the given problem, we have the binomial expansion of (x - y)^n, which includes the term 126x^5y^4.

We will use the binomial coefficient formula to find the coefficients of the desired terms.

The general term of the binomial expansion is given by:

T(k) = C(n, k) * x^(n-k) * y^k

where C(n, k) is the binomial coefficient and can be calculated as:

C(n, k) = n! / (k!(n-k)!)

From the given term, 126x^5y^4, we have:

126 = C(n, 4)

x^5 = x^(n-4)

y^4 = y^4

Now we can find the value of n:

126 = n! / (4!(n-4)!)

Let's solve for n:

126 * 4! = n! / (n-4)!

504 = n! / (n-4)!

Now, we will find the coefficients of the terms x^6y^7 and x^7y^2.

The x^6y^7 term in the expansion will be:

T(k) = C(n, 7) * x^(n-7) * y^7

Since x^5 = x^(n-4), we have n - 4 = 5, so n = 9.

Substituting the value of n:

T(k) = C(9, 7) * x^2 * y^7

Using the binomial coefficient formula:

C(9, 7) = 9! / (7!2!) = 36

So, the x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be:

T(k) = C(n, 2) * x^(n-2) * y^2

We already found that n = 9, so substituting the value of n:

T(k) = C(9, 2) * x^7 * y^2

Using the binomial coefficient formula:

C(9, 2) = 9! / (2!7!) = 36

So, the x^7y^2 term in the expansion will be 36x^7y^2.

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The values of the missing angles are:

x = 6

∠m =  75°

∠k = 45°

We know that the exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.

Thus:

m + k = 120

Since ∠m = 9x + 21 and ∠k = 8x - 3, then:

9x + 21 + 8x - 3 = 120

17x + 18 = 120

17x = 102

x = 102/17

x = 6

∠m = 9(6) + 21

= 75°

∠k = 8(6) - 3 = 45°

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Answer:

540 and 282

Step-by-step explanation:

x + y = 822

x - y = 258

Combine the equations

---------------------

2x = 1080

x = 540

Plug in x to the first equation

--------------------

y + 540 = 822

   - 540   -540

y = 282

--------------------

x = 540 and y = 282

Answer: the first thing is your answer :)

thx for the points

Step-by-step explanation:

g

(

x

)

=

x

2

−

3

The parent function is the simplest form of the type of function given.

f

(

x

)

=

x

2

The transformation being described is from

f

(

x

)

=

x

2

to

g

(

x

)

=

x

2

−

3

.

f

(

x

)

=

x

2

→

g

(

x

)

=

x

2

−

3

The horizontal shift depends on the value of

h

. The horizontal shift is described as:

g

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left

h

units.

g

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right

h

units.

In this case,

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of

k

. The vertical shift is described as:

g

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up

k

units.

g

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down

k

units.

Vertical Shift: Down

3

Units

The graph is reflected about the x-axis when

g

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when

g

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of

a

.

When

a

is greater than

1

: Vertically stretched

When

a

is between

0

and

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

f

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: Down

3

Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.

Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:

(90%)^5 = (0.9)^5 = 0.59049.

The correct answer is therefore (d) 0.59.

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The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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Hello!

area

= 2*25 + (20 - 2)*(25-8)

= 50cm² + 306cm²

= 356cm²