In the function y= 5x, what is the value of x?
08
O There is only one solution for x.
It can be any number.
OIt is unknown and can't be found.

Answer: Choice B

\((f * g)(x) = \frac{x^2+6x+8}{x^2+2x-15}, \ \text{ for } x \ne -5 \text{ and } x \ne 3\\\\\)

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Work Shown:

\(h(x) = (f * g)(x)\\\\h(x) = f(x) * g(x)\\\\h(x) = \frac{x^2-16}{x^2+3x-10}*\frac{x^2-4}{x^2-7x+12}\\\\h(x) = \frac{(x-4)(x+4)}{(x+5)(x-2)}*\frac{(x-2)(x+2)}{(x-3)(x-4)}\\\\h(x) = \frac{x+4}{(x+5)(x-2)}*\frac{(x-2)(x+2)}{x-3} \ \ \text{ ... see note 1}\\\\h(x) = \frac{x+4}{x+5}*\frac{x+2}{x-3} \ \ \text{ ... see note 2}\\\\h(x) = \frac{(x+4)(x+2)}{(x+5)(x-3)}\\\\h(x) = \frac{x^2+6x+8}{x^2+2x-15}\\\\\)

note 1: A pair of (x-4) terms canceled

note 2: A pair of (x-2) terms canceled

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Extra info (optional section):

The fact that \(x \ne -5 \text{ and } x \ne 3\) is to avoid a division by zero error in the simplified version of h(x).

I would argue that \(x \ne 2 \text{ and } x \ne 4\) should be thrown in as well simply so that the domains match up perfectly with the original f(x) and g(x) functions.  

So I think the full domain should be that x is any real number but

\(x \ne -5 \text{ and } x \ne 2\\x \ne 3 \text{ and } x \ne 4\)

Put another way: if x = 2 is allowed in h(x), then that clashes with the fact that it's not allowed in f(x). The same idea happens with x = 4 but with g(x) this time. It's possible your teacher glossed this fact over, or ran out of room.

Answer:

48

Step-by-step explanation:

4*2*3 for the 4 flaps

2*4*3 for the 2 tops

(4*2*3) + (2*4*3) = 48

Answer:

52 square inches

Step-by-step explanation:

to find the surface area of a rectangular prism the formula is

S.A.=2(l*w+l*h+w*h)

2(4*3+4*2+3*2)

=52 square inches

here l is length w is width and h is height

Answer: The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:

Debit Allowance for Doubtful Accounts account: $500

Credit Bad Debt Expense account: $500

The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.

Step-by-step explanation:

Yes, the previous balance in the Allowance for Doubtful Accounts account does come into play when you add $500 to the account. The Allowance for Doubtful Accounts account is a contra asset account that is used to offset the Accounts Receivable account. It represents an estimate of the amount of accounts receivable that are expected to be uncollectible.

The balance in the Allowance for Doubtful Accounts account is based on the estimated amount of uncollectible accounts, which is typically a percentage of the total accounts receivable balance. When you add $500 to the account, you are increasing the estimated amount of uncollectible accounts.

To record this journal entry, you would debit the Allowance for Doubtful Accounts account for $500 and credit an expense account (such as Bad Debt Expense) for the same amount. The previous balance of $2,000 would also be included in the account balance and would be reflected in the new balance of $2,500.

The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:

Debit Allowance for Doubtful Accounts account: $500

Credit Bad Debt Expense account: $500

The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.

Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

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Answer:

x=8

Step-by-step explanation:

Since m and n are parallel, the two given angles are equal (opposite exterior).  Therefore,

7x-2=5x+14

7x-5x=14+2

2x=16

x=8

Positive numbers are always greater than -15. Therefore, it's a greater than.

-2x = - 15

Dividing both sides by -2, we get

x = 7.5

Negative cancels on both sides, so we get a positive equation.

Positive numbers are always greater than -15. Therefore, it's a greater than.

What is greater than or less than?

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The value of z is 8633/137 or 63.01, approximately.

\(\frac{x}{y} =\frac{z}{100}\)

\(\frac{x}{y}*100 =\frac{z}{100}*100\\ \\100\frac{x}{y} =z\\ \\z=100\frac{x}{y}\)

\(z=100\frac{(86.33)}{(137)}\\ \\z=\frac{8633}{137}=63.01\)

If the calculated value of "z" is correct, then the original equation should return the same value on both sides of the equal symbol (=) when substiting all the variables by their respective value.

\(\frac{86.33}{137} =\frac{\frac{8633}{137}}{100}\\ \\0.63=0.63\)

That's correct!

Hence, the value of z is 8633/137 or 63.01.

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Answer:

length = 8 ft

width = 4 ft

Step-by-step explanation:

Let the width = x.

Then the length = x + 4.

perimeter = x + x + x + 4 + x + 4 = 4x + 8

4x + 8 = 24

4x = 16

x = 4

x + 4 = 4 + 4 = 8

Answer:

length = 8 ft

width = 4 ft

Answer:

The correct answer is $0

Step-by-step explanation:

The taxable income (line 6) on the 1040EZ form is:  

Taxable Income = -$3,650.

If the result is negative, it means the taxpayer's income is below the standard deduction threshold, and her taxable income would be $0.

Here,

To calculate the taxable income (line 6) on the 1040EZ form, we need to subtract the standard deduction from the adjusted gross income (AGI).

For the tax year 2021 (the last available information before my knowledge cutoff in September 2021), the standard deduction for a taxpayer filing as Single is $12,550.

Given that the taxpayer's adjusted gross income (AGI) is $8,900, we calculate the taxable income as follows:

Taxable Income = AGI - Standard Deduction

Taxable Income = $8,900 - $12,550

Taxable Income = -$3,650

If the result is negative, it means the taxpayer's income is below the standard deduction threshold, and her taxable income would be $0.

The taxpayer would not owe any federal income tax in this case.

However, she may still want to file her tax return to claim any potential tax credits or receive a refund if she had taxes withheld from her paycheck during the year.

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Answer:

64 inches squared

Step-by-step explanation:

Answer:

Two rays conjoined with a vertex

In Geometry, an angle is when two rays intersect/conjoin with a vertex. The answer is Two rays conjoined with a vertex. Hope it helps!

Answer:

an angle can be defined as the figure formed by two rays meeting at a common end point.

An angle is represented by the symbol ∠.

Step-by-step explanation:

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I'm new here......

Step-by-step explanation:

4x+15y= 40-5y= 20

= 4x+15y+5y= 40-20

4x+20y= 20

Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.

Answer:

85.33%

Step-by-step explanation:

64/75=0.8533333...

x100 = 85.33%

Answer:

ry using words that might appear on the page you’re looking for. For example, "cake recipes" instead of "how to make a cake."

You can also try these searches:

triangle omg has vertices

the points 4 0 4 0 and 0 3 are the vertices of a ______ triangle *

Step-by-step explanation:

Answer:

About 25 years.

Answer:

A. Reflection over the y axis and a translation 4 units down

B. Yes because glide reflections preserve side and angle measures.

Answer:

− + 3 + 4 − 1 2

Step-by-step explanation:

Answer:

--you would decompose it into a rectangle and triangle along the dotted line then add the two areas together to get the total area. the area of the trapezoid is 59.375 ft²

--i havent seen the other problem so i cant answer the convince me part, but you should be able to say how its different from the answer above^^^

Step-by-step explanation:

hope this helps :)

The hourly pay that was charged for the repairs to Victor's car was $ 57.14

To find the hourly wage, find the total labor wages that were charged as a cost to Victor's repairs. This cost would be:

= 272 - 6 - 28. 50 - 20 .00 - 15. 00 - 2. 50

= $ 200

The total hourly wage charged was $ 200 for 3 . 5 hours of work.

This means that the hourly pay charged was :

= Total labor wages / Number of hours

= 200 / 3 . 5

= $ 57.14

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The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².

The side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²

= 75.69 cm²

Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²

Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².

In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².

Total surface area = surface area of the cube + surface area of the cylinder

Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²

Total surface area ≈ 583.31 cm²

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Answer:

\(\textrm {D. The derivative is }\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}\)

Step-by-step explanation:

Given

\(f(x) = \dfrac{u(x)}{v(x)}\)

the derivative of f(x) wrt x is

\(f'(x) = \dfrac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}\)

\(u(x) =x^9 \;so \; u'(x) = 9x^8\)

\(v(x) = x^3 , v'(x) = 3x^2\\\\\[v(x)\]^2 = [x^3]^2 = x^6\)

Putting all these together we get

\(f'(x)=y'=\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}\)

Missing entries are in bold

Answer:

The answer to this question is 17.5 hours due to dividing

Step-by-step explanation:

35÷2=17.5

The biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.

A formula in Microsoft Excel is an expression that modifies values in a set of cells.

Even if the result is incorrect, these formulas nonetheless return a result.

We may execute calculations like addition, subtraction, multiplication, and division using Excel formulae.

To make complex computations simpler, Excel features prewritten formulas known as functions.

A function takes one or more values, runs an operation, and then outputs the outcome to a cell.

Arguments are the values that you pass to a function.

So, in the given situation of Jenny, the excel formula PV(.035/12, 15*12, -485)will be used to determine the largest mortgage loan she can afford.

Therefore, the biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.

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Complete question":
Jenny has decided that she can afford a monthly mortgage payment of $390. She has been offered a 3.5% 20-year mortgage from her bank. What formula could you type into Excel to determine the largest mortgage loan she can afford is?

(A) PV(.035/12, 15*12, -485)

(B) PMT(.035/12, 15*12, -485)

(C) PV(.035, 15*12, -485)

(D) 390*.035/20

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Répondre:

76 km / heure

Explication étape par étape:

Étant donné que:

Heure à laquelle Simon a quitté la maison = 9 h 15

Heure à laquelle Simon est arrivé au travail = 10h30

Distance domicile-lieu de travail = 95 km

La vitesse moyenne = (distance totale parcourue / temps total pris)

Temps total pris = 10h30 - 9h15 = 1 heure 15 minutes = 1 heure (15/60) = 1,25 heure

Distance / temps

95 km / 1,25 heure

= 76 km / h

The dimensions of the rectangular room are 12 feet by 16 feet

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

Represent the length with x

So, we have

Width = x + 4

The area is then represented as

Area = x * (x + 4)

This means that

x * (x + 4) = 192

So, we have

x * (x + 4) = 12 * 16

This means that

x = 12 and x + 4 = 16

Evaluate

x = 12 and x = 12

So, the dimensions of the figure are 12 feet by 16 feet

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Answer:

I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion * 360° = 0.6 * 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.

The area of the first, second, and third is a triangle30square in,18 square cm,130 Square yards the surface area of the triangular top of the end table is  640 square centimetres the length of the third side of the triangle is 17 yards the length of the missing side of the right triangle is 6√2 feet.

According to the given information:

a. The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. Therefore, for the first triangle:

A = (1/2)(10 in)(6 in) = 30 square inches

b. For the second triangle:

A = (1/2)(4 cm)(9 cm) = 18 square centimeters

c. For the third triangle:

A = (1/2)(20 yd)(13 yd) = 130 square yards

d. The surface area of the triangular top of the end table is also given by the formula A = (1/2)bh, where b is the base and h is the height. Therefore:

A = (1/2)(40 cm)(32 cm) = 640 square centimeters

e. Using the Pythagorean theorem, we can find the length of the third side of the right triangle:

c² = a² + b²

c² = 8² + 15²

c² = 289

c = √289

c = 17 yards

Therefore, the length of the third side of the triangle is 17 yards.

f. Using the Pythagorean theorem, we can find the length of the missing side of the right triangle:

c² = a² + b²

c² = 6² + 6²

c² = 72

c = √72

c = 6√2 feet

Therefore, the length of the missing side of the right triangle is 6√2 feet.

g. The length of the missing hypotenuse can be found using the Pythagorean theorem:

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5

Therefore, the length of the missing hypotenuse is 5.

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Answer:

a. a2 + b2 = c2

a2 + (12 in.)2 = (20 in.)2

a2 + 144 sq. in. = 400 sq. in.

a2 = 144 sq. in. – 144 sq. in. = 400 sq. in. – 144 sq. in.

a2 = 256 sq. in.

√a2 = 256 sq. in.

a = 16 in.

Answer: The length of the missing side is 16 inches.

b. a2 + b2 = c2

(7 cm)2 + b2 = (25 cm)2

49 cm2 +  b2 = 625 cm2

49 cm2 – 49 cm2 + b2 = 625 cm2 – 49 cm2

b2 = 576 cm2

√b2 = √576 cm2

b = 24 cm

Answer: The length of the missing side is 24 centimeters.

c. a2 + b2 = c2

(8 yd.)2 + (15 yd.)2 = c2

64 sq. yd. + 225 sq. yd = c2

289 sq. yd. = c2

√289 sq. yd. = √c2

17 yd. = c

Answer: The third side of the fence will be 17 yards long.

Step-by-step explanation: