Find domain, range, vertical asymptotic, horizontal asymptote, x-intercept, y-intercept of f(x)= -1/x-5+3

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Answer:

B

subtract 20

80,60,40.....

Step-by-step explanation:

it's the arithmetic sequence having difference of 20

The measurements of the diagonal distance across the middle school gym is given by the following persons and is rounded to the nearest hundredths

The calculation of Arturo = 31.75 yards

The calculation of Bonnie = 32.98 yards

The calculation of Courtney = 31.42 yards

The calculation of Dawson = 31 yards

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the measurements of the diagonal distance across the middle school gym be represented as A

Now , the measured values are

a)

The measurement of Arturo = 6√28 yards

The measurement of Arturo = 6 x 5.2915

On rounding , we get

The measurement of Arturo = 31.75 yards

b)

The measurement of Bonnie = 8√17 yards

The measurement of Bonnie = 8 x 4.123

On rounding , we get

The measurement of Bonnie = 32.98 yards

c)

The measurement of Courtney = 10π yards

The measurement of Courtney = 10 x 3.142

On rounding , we get

The measurement of Courtney = 31.42 yards

d)

The measurement of Dawson = 3.1√100 yards

The measurement of Dawson = 3.1 x 10

On rounding , we get

The measurement of Dawson = 31 yards

Hence , the measurements are rounded

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The estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.

To estimate the value of 5^(3/2), we can use the tangent line approximation of the function y = x^(3/2) at x = 4.

First, we need to find the slope of the tangent line at x = 4. To do this, we take the derivative of the function y = x^(3/2):

y = x^(3/2)

y' = (3/2)x^(1/2)

y'(4) = (3/2)(4)^(1/2) = 3

So the slope of the tangent line at x = 4 is 3.

Next, we need to find the equation of the tangent line at x = 4. To do this, we use the point-slope form of the equation of a line, using the point (4, 8):

y - 8 = 3(x - 4)

y = 3x - 4

Now we can estimate the value of 5^(3/2) by substituting x = 5 into the equation of the tangent line:

y = 3x - 4

y = 3(5) - 4

y = 11

Therefore, an estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.

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Employing the identity (a+b)² = a² + 2ab + b², where a and b are any real numbers.

Substituting  a and b with a and x/y, respectively:

(a + x/y)² = a² + 2a(x/y) + (x/y)²

(a + x/y)² = (a + x/y)(a + x/y)

= a² + ax/y + ax/y + x²/y²

= a² + 2ax/y + x²/y²

add a² to both sides of the equation:

a² + (a + x/y)² = a² + 2ax/y + x²/y² + a²

a² + (a + x/y)² = (a² + x²/y²) + 2ax/y + a²

xy = a² substitute a² for xy in the last term:

a² + (a + x/y)² = (a² + x²/y²) + 2axy/xy + a²

a² + (a + x/y)² = (a² + x²/y²) + 2a + a²

We have that  x²/y² = (xy)/(y²) = a/y, and substituting this back into the equation:

a² + (a + x/y)² = (a² + a/y + a/y) + 2a + a²

= 2a² + (2a/x) + (2a/y)

A real number is described as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

Therefore from the mathematical expression shown above, we have shown that:

a² + (a + x/y)² = 2a² + (2a/x) + (2a/y)

This is the mathematical expression we wanted to prove.

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The solutions to the system are -1 and 3.

What is system of equations?

equations simultaneously, or a system of equations Multiple equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). There must be an equal number of equations and unknowns for a system to have a singular solution. Even then, a solution may not be assured.

Given : y = x + 5  ... equation 1

           y = x² – x + 2 ...equation 2

Putting  y=x+5 in equation 2

We get, x+5 =  x² – x + 2

             x² - x - x +2 -5 = 0

             x² -2x - 3 = 0

It can written be solved as :

                x² -2x - 3 = 0

                x² -3x +x - 3 = 0

                x ( x-3) + 1(x-3) = 0

                (x+1) (x-3) = 0

So, x = -1 and 3.

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The triangle has a surface area of 12 square centimetres.

We can apply the following formula to determine the triangle's area:

Area = base x height x half

The triangle's height in this instance is 4 cm, while its base is 6 cm. We can therefore determine the area by substituting these values into the formula as follows:

Area: 0.5 by 6.4 by 4.4 cm

Amount = 12 cm2

Hence, the triangle has a surface area of 12 square centimetres.

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Answer:

Let's use algebra to solve this problem:

Let's use the variable "m" to represent the number of markers that Martin has.

We know that Hiro has 4 fewer highlighters than Martin, so we can set up an equation:

18 = m - 4

This equation says that the number of markers Martin has (m) minus 4 is equal to the number of highlighters that Hiro has (18).

To solve for "m", we can add 4 to both sides of the equation:

18 + 4 = m

Simplifying this gives us:

22 = m

So Martin has 22 markers.

A linear equation in the form p = mn + b that gives the price they can charge for n shirts is p = -0.003x + 22.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (1000, 19), a linear function in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 19 = (16 - 19)/(2000 - 1000)(x - 1,000)

y - 19 = -0.003(x - 1,000)

y = -0.003x + 3 + 19

p = y = -0.003x + 22

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Julie used direct proof because each statement is deduced from a previous statement. Samuel used indirect proof because the final statement contradicts the assumption.

What are direct and indirect proofs?

The complete question is given below.

Both Julie and Samuel are asked to prove m∠CBD  = 65°.

Let us look at Julie's proof.

She used the known facts which are given and finally proved that m∠CBD  = 65°. So Julie used direct proof.

Now let us observe Samuel's proof.

He started contradicting the statement when he wrote

 m∠CBD  + 65° ≠ 90°

So the last statement goes against what he was asked to prove.

Samuel used indirect proof.

Therefore Julie used direct proof because each statement is deduced from a previous statement. Samuel used indirect proof because the final statement contradicts the assumption.

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The amount of money in account A is decreasing by 8% per year. Account B recorded a greater percentage change in amount of money over the previous year.

Amount is an indefinite quantity of something, usually money or a measurement of quantity. It is often used to describe the total amount of money received or spent in a particular instance or over a period of time.

The amount of money in account A is decreasing by 8% per year. This can be seen by looking at the 0.92 in the equation. This is the rate of decay, and represents a 8% decrease every year.

Part B: Account B recorded a greater percentage change in the amount of money over the previous year. Looking at the table, the amount of money decreased by 10.51%, 10.22%, and 11.94% in the first, second, and third years respectively. This is greater than the 8% decrease in account A.

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The ordered pair that would make the function true is option 4 (-1, -4).

As the name implies, an ordered pair is a set of items where the order in which they are placed is of particular significance. In coordinate geometry, ordered pairs are typically used to represent a point on a coordinate plane. They may also be used to depict aspects of a relationship.

The given equation of the graph is y = -0.25x - 2.

Substituting the coordinates in the options we have:

For (0, - 3):

y = -0.25x - 2

- 3 = -0.25(0) - 2

- 3 = -2 False.

For (4, 3)

y = -0.25x - 2

3 = -0.25(4) - 2

3 = -3 False

For (8, 4):

y = -0.25x - 2

4 = -0.25(8) - 2

4 = - 4

False.

For (-4, -1)

-1 = -0.25(-4) - 2

- 1 = -1

True.

Hence, the ordered pair that would make the function true is option 4 (-1, -4)

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Answer: The word "addressee" has 8 letters. To find the number of arrangements that can be made by taking 4 letters from these 8 letters, we can use the formula for combinations, which is:

n C r = n! / (r! * (n-r)!)

where n is the total number of items, r is the number of items to be selected, and ! represents the factorial function.

In this case, we want to select 4 letters from the 8 letters in "addressee", so n = 8 and r = 4. Substituting these values into the formula, we get:

8 C 4 = 8! / (4! * (8-4)!)

= (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (4 * 3 * 2 * 1)]

= 70

Therefore, there are 70 different arrangements that can be made by taking 4 letters from the letters of the word "addressee".

Step-by-step explanation:

Answer:

$6981

Step-by-step explanation:

If you put $6981 in a deposit and your interest rate is 8.5% monthly it will give you $2,019.62 which then means your total will be $9,000.62

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The required correct match for the given problem has been shown below.

A number system is described as a process of composing to designate digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other symbols in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
3 2/7 = 23/7 = 3.2                      between 3 and 4
-3 7/8 = -31/8 = -3.875               between -3 and -4

-3/8 = -0.375                             between 0 and -1
-0.9                                          between 0 and -1
1/7                                             between 0 and 1.

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The total amount the mechanic will need in retirement savings to meet their retirement income goa is (B) $950,000, the correct option is B

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

Annual gross wage=  $47,500

Percentage saved= 80%

Draw in 1 year=4%

Now,

To calculate the total amount the mechanic will need in retirement savings to meet their retirement income goal, we can follow these steps:

Determine the retirement income goal: The mechanic wants to live off 80% of their current annual gross wage, which is:

0.8 x $47,500 = $38,000 per year

Calculate the amount of savings needed to generate the retirement income: The mechanic wants to draw 4% of their savings in the first year, so the amount of savings needed to generate $38,000 per year is:

$38,000 / 0.04 = $950,000

Therefore, by the given interest rate answer will be $950,000.

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The equation that represents the graph will be x = (1/12) y². Then the correct option is A.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of the upward parabola is written as,

y = 4ax²

The equation of the downward parabola is written as,

y = - 4ax²

The equation of the rightward parabola is written as,

x = 4ay²

The equation of the leftward parabola is written as,

x = - 4ay²

From the graph, the parabola opens rightward, then the equation is written as,

x = (1/12) y²

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The function P(t) = 3.5(0.91)^t is an exponential decay and the percentage rate of change is 9%.

option B.

The function P(t) = 3.5(0.91)^t is an exponential decay function because the base, 0.91, is between 0 and 1.

To find the percentage rate of change, we need to find the value of r in the exponential function;

P(t) = P(0) (1 + r)^t or

P(t) = P(0) e^(rt)

where;

In this case, the initial value is 3.5, and the function is P(t) = 3.5 (0.91)^t. Comparing this to the form P(t) = P(0) e^(rt),

we see that P(0) = 3.5 and r = ln(0.91) ≈ -0.094.

Therefore, the percentage rate of change is -9.4%, which means that the value decreases by about 9.4% with each unit of time.

So the correct answer is option B: Exponential decay; 9%.

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The complete question is below:

-Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of

change.

P(t) = 3.5 (0.91)^t

A) Exponential decay; 3.5%

B) Exponential decay; 9%

C) Exponential growth; 9%

D) Exponential growth; 3.5%

Juli earned $13.25 per candle sold.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

For a charity fundraiser, Juli sold 16 candles.

Juli earned a total of $212 ($12 in donations + $100 to Charity A + $100 to Charity B).

To find out how much she earned per candle, we need to divide the total amount earned by the number of candles sold:

$212 ÷ 16 candles = $13.25 per candle

Therefore, per candle, the earning amount is $13.25.

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Answer:

Step-by-step explanation:

the volume of a cylinder is found with the formula V=[tex]\pi r^{2} h[/tex] where r is the radius and h is the height of the cylinder

plugging the numbers given into the formula results in 32791.5 [tex]cm^{3}[/tex]

The value of the function g(x + a) - g(x) is a(-2x - a + 5).

To find the value of function g(x + a) - g(x), we first need to substitute g(x + a) and g(x) into the expression and simplify:

g(x + a) - g(x) = [- (x + a)^2 + 5(x + a)] - [-x^2 + 5x]

= [-x^2 - 2ax - a^2 + 5x + 5a] - [-x^2 + 5x]

= -x^2 - 2ax - a^2 + 5x + 5a + x^2 - 5x

= -2ax - a^2 + 5a

= a(-2x - a + 5)

Therefore, the value of g(x + a) - g(x) is a(-2x - a + 5).

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Answer:

Refer to photo above ......alright

Answer:

E

Step-by-step explanation:

For Company A, the monthly cost y in dollars can be represented by:

y = 0.12x + 20

where x is the number of minutes used.

For Company B, the monthly cost y in dollars can be represented by:

y = 0.06x + 50

where x is the number of minutes used.

To find the number of minutes of calls where the monthly bills will be the same, we need to set the two equations equal to each other and solve for x:

0.12x + 20 = 0.06x + 50

0.06x = 30

x = 500

Therefore, the monthly bills will be the same for both companies when the number of minutes used is 500.

Answer: (E) 500 minutes

The values of the piecewise function {h(x)} for different values of {x} is given above.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is the relation as -

y = {- x² - 6x - 9          for   x < - 2}

y = {x/3 - 4              for x > - 2}

The given function is a piecewise function. We can write the values for different values of {x} as -

{x} = - 4

y{4} = - (-4)² - 6(-4) - 9 = - 1

{x} = - 3

y{-3} = - (-3)² - 6(-3) - 9 = - 0

{x} = - 1

y{-1} = -1/3 - 4= -4.3

{x} = 0

y{-1} = 0/3 - 4 = - 4

Therefore, the values of the piecewise function {h(x)} for different values of {x} is given above.

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Answer:

Chef will have 15 pieces of butter.

Step-by-step explanation:

Chef has 3 blocks of butter,

weight of each block = 1 pound

she cuts each block into fifth pieces,

3 / 1/5 = 15 pieces

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The student's percentile will be 28.

Calculating percentiles is a common practise. The majority of the time, we can define percentile as a score below which a predetermined percentage of other scores fall. We might be able to tell when someone received a test score of 65 out of 90. But without knowing what percentile he belongs to, this number is meaningless. When a score is in the 90th percentile, it signifies that it is higher than the scores of 90% of test-takers.

Given : Student's rank = 144 out of 200

So, there are 56 (200-144) students whose rank is below that student.

We know that, percentile

= no. of ranks below that rank / total no. of ranks * 100

So, his percentile = 56/200 * 100

                             = 28 percentile.

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Answer:

7n + 14

Step-by-step explanation:

Multiply the number outside the parentheses by each quantity in the parentheses.

7(n + 2) = 7 × n + 7 × 2 = 7n + 14

Answer:

Step-by-step explanation:

distribute the 7 to the n.

then distribute the 7 to the 2.

=7n+14

Let me solve it down for you :)

The shape is a cuboid, so its dimensions will be:

[tex] \sf \: Surface \: area \: of \: cuboid = 2(lb + bh + hl)[/tex]

[tex] \sf \: S.A. = 2(12 \times 5 + 5 \times 10 + 12 \times 10)[/tex]

[tex] \sf \: S.A. = 2(60+ 50 + 120)[/tex]

[tex] \sf \: S.A. = 2(230)[/tex]

[tex] \sf \: S.A. = 460 \: {m}^{2} [/tex]

Dimensions of the cuboid:

[tex] \sf \: Volume = l \times b \times h[/tex]

[tex] \sf \: Volume = 12\times 5 \times 10[/tex]

[tex] \sf \: Volume = 600 \: {m}^{3} [/tex]

Convert m to cm, according to the question:

600 Cubic meter =

600,000,000 Cubic Centimeters

Answer:

Step-by-step explanation:

We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.

We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.

Now, we can use the Pythagorean theorem to find the length of the third side, LM:

LM^2 = LT^2 + TM^2

LM^2 = 9^2 + 16^2

LM^2 = 337

LM = sqrt(337)

Therefore, the perimeter of triangle LMO is:

LM + MO + LO = sqrt(337) + 2(12) + 32

Perimeter = sqrt(337) + 56

To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:

TP^2 = TJ^2 + JP^2

TP^2 = 18^2 + 24^2

TP^2 = 900

TP = 30

Therefore, the perimeter of triangle TJP is:

TJ + JP + TP = 18 + 24 + 30

Perimeter = 72

Therefore, the perimeter of triangle TJP is 72.

If Jenny has 50 square tiles and arranges them in a rectangular array with 4 rows, then she would have a total of 48 tiles, with 2 tiles left over.

If Jenny arranges the tiles in a rectangular array with 4 rows, this means each row will have 50/4 = 12.5 tiles. However, since we cannot have half a tile, we need to round down to the nearest whole number, which is 12.

Therefore, each row will have 12 tiles, and the total number of tiles used will be 4 x 12 = 48. To find out how many tiles are left over, we need to subtract the total number of tiles used from the original number of tiles: 50 - 48 = 2. So, there will be 2 tiles left over.

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