What is the equation of the function that is graphed as line a?

y = -2 x
y = x + 1
y = x - 1
y = 2 x + 1

Sum of logarithm is [tex]\left(\log _3(5)+\log _3(a)\right) b$$[/tex]

The exponent or power that must be added to a base to produce a given number is called the logarithm. If bx = n, then the mathematical expression for x is x = logb n, where x is the logarithm of n to the base b.

For instance, since 23 = 8, 3 is the logarithm of 8 in base 2, or 3 = log2 8. In a similar manner, since 102 = 100, 2 = log10 100. Those of the latter type (base 10-based logarithms) are referred to as common, or Briggsian, logarithms and are denoted by the letter log n.

The time needed to multiply numbers with many digits was significantly reduced thanks to the development of logarithms in the 17th century, which was done to speed up calculations.

Simplifying [tex]$\log _3(5 a) b: \quad\left(\log _3(5)+\log _3(a)\right) b$$\log _3(5 a) b$[/tex]

[tex]\log _3(5 a) b[/tex]

Simplifying we get

[tex]$\log _3(5 a): \quad \log _3(5)+\log _3(a)$$$=\left(\log _3(5)+\log _3(a)\right) b$$[/tex]

Therefore the sum of logarithm is [tex]\left(\log _3(5)+\log _3(a)\right) b$$[/tex]

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Answer:

18.75

Step-by-step explanation:

"Of", in math, typically denotes multiplication, which means we multiply 75% and 25 to find "75% of 25":

75% = 0.75

0.75 * 25 = 18.75

The number of minutes Felipe should leave the bottle of water in the cooler is 27.7 minutes

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

C(t) = 10 + 12e⁻⁰°⁰²⁵ˣ

Where:

Also from the question, we understand that Felipe wants to drink the water when it reaches a temperature of 16 degrees Celsius

This means that

C(t) = 16

Substitute C(t) = 16 in the above equation, so, we have the following representation

10 + 12e⁻⁰°⁰²⁵ˣ = 16

Evaluate the like terms

12e⁻⁰°⁰²⁵ˣ = 6

Divide both sides by 12

e⁻⁰°⁰²⁵ˣ = 0.5

Take the natural logarithm of both sides

-0.025t = ln(0.5)

So, we have

-0.025t = -0.693

Divide

t = 27.72

Approximate

t = 27.7

Hence, the number of minutes is 27.7 minutes

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Answer:

4 - log3 (2)

Step-by-step explanation:

2log3 (9) = log3 (9^2)

log3 (27 * 9^2 / 54)

log3 ( 3^3 * 3^4 / 9 * 6)

log3 (3^7 / 3^2 * 3 * 2)

log3 (3^7 / 3^3 * 2)

log3 ( 3^4 /2)

log3 (3^4) - log3 (2)

4 - log3 (2)

The number of outstanding shares that BBQ Corp. will have post-split, given the number of outstanding shares is, 4, 050, 000 shares

A stock split refers to when the number of outstanding shares that a company has, are divided into a certain number of shares which is based on the split ratio.

For a 3:1 stock split ratio, the number of outstanding shares will be split into three shares each.

BBQ Corp. has 1. 35 million shares so post - split, they will have:

= Outstanding shares x  3

= 1, 350, 000 x  3

= 4, 050, 000 shares

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The number of tables is 100 and the number of chairs purchased is 800.

Given,

In the question:

To furnish a cafeteria, a school can spend $5200 on tables and chairs. Tables cost $200 and chairs cost $40. Each table will have 8 chairs around it.

To write and solve a system of equations for x and y and how many tables and chairs will the school purchase?

Now, According to the question:

We need to form an equation from this given information and solve it for x to find the number of tables and chairs that the school will purchase.

The number of tables is x, so number of chairs is 8x

Total cost of tables=200x

Total cost of chairs=40 × 8x=320x

Total expenditure=200x + 320x=520x

520x = 5200

x = 100

Therefore, the number of tables is 100 and the number of chairs purchased is 800.

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The third side of the triangle whose two sides are 11 cm and 19 cm can be between 9 and 29.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

The sides of triangles are 11 cm and 19 cm,

Let the third side of the triangle is x,

Since, a side of a triangle is greater than the difference of two sides and less than the sum of two sides,

implies that,

19-11<x<19+11

8 < x < 30

The possible range of third side is (9,29).  

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Answer:

8cm < x < 30cm

Step-by-step explanation:

To find the range of lengths for the third side of a triangle when two side lengths are known, first, assign a variable for the length of the third side.

Let x be the length of the unknown side.

Use the Triangle Inequality Theorem to write the three inequalities.

x + 11x > 19

x + 19 > 11

11 + 19 > x

Solve each inequality.

x > 8

x > -8

30 > x

Now find the range of values that satisfies all three inequalities.

The range between 8 and 30 satisfies all 3 inequalities. Therefore, this triangle's third side lengths range is 8cm < x < 30cm.

Key expansion is most responsible for this delay.

A block cipher encrypts and decrypts a block of data with an algorithm and symmetric key. In order to expand the keyspace of a block cipher and make it more difficult to break the key through brute force, an initialization vector (IV) must be added to the plaintext that is being used as input. Key Expansion: In the initial stage, it uses just one key, but in later rounds, it expands to multiple keys. Data bytes: Instead of working with bit data, the AES encryption algorithm performs operations on byte data. Consequently, during the encryption process, it treats the size of the 128-bit block as 16 bytes.

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Approximately 7 bags of soil are needed to fill the land.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is garden that needs 5 3/6 pounds of soil. The bag of soil contains only 5/6 of soil.

The total number of bags of soil you need to buy are -

n = (33/6)/(5/6)

n = 33/6 x 6/5

n = 33/5

n = 6.6

n = 7 (approx.)

Therefore, approximately 7 bags of soil are needed to fill the land.

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The asset's value should be recognized on the balance sheet at $1.61 million.

Given,

On January 1st, 2006, Trekkers Footwear paid $2.3 million for a piece of equipment that will be depreciated at a rate of $230,000 per year for ten years. As of December 31, 2008, IT was worth $1.75 million in the market. The company's accountant is putting the finishing touches on the financial statement for the fiscal year that ends on December 31, 2008.

The balance sheet should reflect the asset's value at,

Cost of Asset = $2.3 million

Annual depreciation = $230000

Total no. of years depreciated till December 31, 2008, = 3 years

Hence, total depreciation = $230000 x 3 = 690000 = 0.69 million

Hence, book value as on 31 December 2008 = $2.3 million - $0.69 million = 1.61 million

Given Market Value on Dec 31, 2008, = $1.75 million.

But as per accounting conventions, Assets are recorded at Book value.

Hence $1.61 million is the right answer.

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They were based on four key areas

1) Representation,

2) Reasoning and Proof

3) Communication,

4) Problem Solving,

1) Representation:

Students are being challenged to present a mathematical concept in multiple ways. There are five different ways to depict thought:

1) Plaything models

2) Still images

3) Printed signs

4) Verbal/written communication

5) actual circumstances or settings

2) Reasoning and Proof:

The habit of reasoning should serve as a backdrop for the development of key mathematical concepts. Asking questions is the key! Why not? Invite students to make conjectures and then to develop, improve, and assess them since mathematics includes discovery. Additionally, let pupils investigate and articulate their own logic. It's frequently beneficial to expand on what kids already know while teaching them.

Students can use technology and manipulatives to solve problems and test their hypotheses at this point.

3) Communication:

Both a method of transmission and a part of what it means to "do" mathematics, communication in mathematics encompasses both. Teachers must create a safe space where students can attempt to share their ideas in the beginning. Since kids don't naturally communicate in math, teachers must be patient while they learn to do so.

4) Problem solving:

Mathematical problem solving is defined as "participating in a task for which the solution approach is not known beforehand. Students must employ previously learned information to create a solution, and by doing so, they obtain new mathematical understandings. Problem-solving exercises ought to be a regular element of math classes. Problems can be derived from real-world applications and experiences.

Hence we get the required answer.

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The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

In this problem, the function is:

H(x) = 6x + 90.

Hence the slope and the intercept are given as follows:

m = 6, b = 90.

The domain and the range of the function are given as follows:

The problem is given by the image shown at the end of the answer.

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(-5, 8)

=========================================================

These are two rules to memorize

[tex]\text{x-axis reflection: } \ \ (\text{x},\text{y})\to (\text{x},-\text{y})\\\\\text{y-axis reflection: } \ \ (\text{x},\text{y})\to (-\text{x},\text{y})\\\\[/tex]

----------

I'll relabel the point X as point A.

We apply a y-axis reflection first.

So we have:

[tex](\text{x},\text{y})\to (-\text{x},\text{y})\\\\(5,-8)\to (-5,-8)\\\\[/tex]

after the y axis reflection is applied.

This is the location of point A'

----------

Then we apply an x-axis reflection.

[tex](\text{x},\text{y})\to (\text{x},-\text{y})\\\\(-5,-8)\to (-5,-(-8))\\\\(-5,-8)\to \boldsymbol{(-5,8)}\\\\[/tex]

This is the location of point A''

which points us to choice C as the final answer.

----------

Side note:

The composition of an x-axis reflection and y-axis reflection, in either order, is the same as a 180 degree rotation around the origin.

The rule for a 180 degree rotation is [tex](\text{x},\text{y})\to (-\text{x},-\text{y})\\\\[/tex]

The weight of the newborn baby in pounds is 7pounds

Proportion is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

The relationship between a pound and stone is

1 pound = 1/14stone

therefore 1stone = 14pounds

The weight of the newborn baby is 1/2 stone

in pounds ,the weight of the baby is 14/2= 7pounds

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The sum of integers is: S = n(a + l)/2

Integer numbers are those without fractional or decimal parts. When there are fewer numbers to add, it is possible to determine the sum of integers using basic mathematics. However, we employ the sum of integers formula if we need to add multiple consecutive integers at once. Our computations are made easier, and the amount of time we spend adding is reduced.

The sum of an arithmetic sequence's n terms is what is meant by the sum of integers formula. The formula for the sum of integers is:

S = n(a + l)/2

where,

S = sum of the consecutive integers

n= number of integers

a= first term

l = last term

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An equation to represent the proportional relationship between the number of hours and the distance in miles is k=y/x.

Given that, Percy rides his bike 11.2 miles in 1.4 hours at a constant rate.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

The number of hours Percy rides x, and the distance in miles, y, that he travels

So, the proportional relationship is speed = y/x

Thus, 11.2/1.4

= 8 miles per hour

Therefore, an equation to represent the proportional relationship between the number of hours and the distance in miles is k=y/x.

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The correct answer is 'the projected misstatement of this sample was $6,000.'

An auditor cannot obtain absolute assurance that material misstatements in the financial statements will be find out.

The purpose of intentional misstatements or omissions of amounts or disclosures in financial statements is to deceive the users of financial statements. These misstatements result from fraudulent financial reporting.

Misstatements arising from the misappropriation of assets (sometimes referred to as defalcation) involve the theft of an entity's assets where the effect of the theft causes the financial statements not to be represented in conformity with generally accepted accounting principles.

The risk of a material misstatement of the financial statements as a result of fraud should be expressly assessed by the auditor, and the audit processes should be designed with that judgement in mind.

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The equation of the line having equal intercepts on the axes is:

13x+13y=6.

Given:

the straight lines are:

4x-7y-3 and 2x-3y+1

we are asked to determine the equation of the straight line passing through the point of intersection of the lines 4x-7y-3 and 2x-3y+1 and cut with the equal intercept on the axes.

Let the equation of the line having equal intercepts on the axes be

x/a + y/a =1

x + y = a ... eq(1)

On solving equation 4x-7y-3 and 2x-3y+1 we obtain x = 1/13 and y = 5/13.

{1/13,5/13} is the point of intersection of the two given lines.

Since equation (1) passes through point {1/13,5/13}

{1/13+5/13} = a

⇒ a = 6/13

∴ Equation (1) becomes x+y=6/13

⇒ 13x+13y=6

Thus the required equation of the line is 13x+13y=6.

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Your question is incomplete. Please find the missing content here.

Find the equation of the line passing through the point of intersection of the lines 4x-7y-3 and 2x-3y+1  that has equal intercepts on the axes.

The equation which has exactly one solution is 4 (x + 3) = 7x – 6, and the solution is x = 6.

To solve the equations, we can use Multiplicative Distribution Law.

The first equation, 4 (x + 3) = 7x – 6, has exactly one solution that is x = 6.

4 (x + 3) = 7x – 6

4x + 12 = 7x – 6

4x – 7x = – 6 – 12

– 3x = – 18

x = 6

The second equation, 4 (x + 3) + 8 = 4x + 20, has all real numbers.

4 (x + 3) + 8 = 4x + 20

4x + 12 + 8 = 4x + 20

4x – 4x = 20 – 12 – 8

0 = 20 – 12 – 8

0 = 0

The third equation, 4 (x + 3) + 3x = 7x + 12, has all real numbers.

4 (x + 3) + 3x = 7x + 12

4x + 12 + 3x = 7x + 12

4x + 3x – 7x = 12 – 12

7x – 7x = 0

0 = 0

The last equation, 4 (x + 3) + 6 = 4x + 9, has no solution. It is a wrong equation.

4 (x + 3) + 6 = 4x + 9

4x + 12 + 6 = 4x + 9

4x – 4x = 9 – 12 – 6

0 = - 9

Hence, by using the Multiplicative Distribution Law, the equation which has exactly one solution is 4 (x + 3) = 7x – 6.

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Answer: (A)

Step-by-step explanation: 4(x + 3) = 7x - 6

trust

Answer:

No

Step-by-step explanation:

The sum of two sides of a triangle should be greater than the size of the third side.

2 + 3 is not greater than 5, so it's impossible to construct a triangle using the given lengths for the sides.

Simplified value of given expression is 2x³√10x.

What is simplification?

In arithmetic,  simplification is reducing the expression / fraction problem during a less complicated type.

Main body:

Factor 40 into its prime factors

          40 = 2³ • 5

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          4 = 2²

Factors which will remain inside the root are :

          10 = 2 • 5

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          2 = 2

At the end of this step the partly simplified SQRT looks like this:

        2 • sqrt (10x7)

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x⁸)=x4

    (3.2) sqrt(x-⁶)=x-3

     (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x²•sqrt(x)

    (4.2) sqrt(x-7)=x³•sqrt(x-1)

Applying these rules to our case we find out that

    SQRT(x7) = x³ • SQRT(x)

 sqrt (40x7) =

       2² x³• sqrt(10x)

Hence the simplification to the value is as 2² x³ • sqrt(10x)

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In given proportinal relation , Maila need 204 yards for make 68 bow.

What is proportion?

   In mathematics, proportional means that two quantities or variables are linearly related. When one quantity doubles, the other quantity also doubles. When one of the variables decreases to 1/10th of its previous value, the other also decreases. A ratio is a comparison of two numbers, each representing a part of a whole. Essentially, percentages show that two fractions are equal, even if they are of different magnitudes. For example, 1/2 of 10 marbles has the same ratio as 1/2 of 50 marbles.

Here the relationship between ribbon and bow is proportional. Let us take ribbon as r and bow as b.

=> r ∝b

=> r= kb . Where k is constant.

Now put r=51 and b =17 then,

=> 51=k*17

=> k = 3

then the equation is r = 3b.

Now b=68 then ,

=> r = 3*68

=> r = 204 yard.

Therefore Maila need 204 yard ribbon to make 68 bow.

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Answer:

1.72

Step-by-step explanation:

Let's solve the problem,

→ 18.92/11

→ 18.92 ÷ 11

→ 1.72

Hence, answer is 1.72.

The decimal division of 18.92 by 11 gives us; 1.72

When dividing decimals,  we first have to convert the divisor to a whole number by moving the decimal point to the right. Thereafter, we now carry the dividend's decimal point up to the exact same number of places to the right and then divide the resultant numbers in the normal way, like in regular long division.

We want to divide 18.92 by 11. Thus, let us apply that rule described above to get;

18.92/11 = 1892/1100

= 1 + (1892 - 1100)/1100

= 1 + (792/1100)

= 1 + 0.72

= 1.72

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The equation of the line that passes through the point (8,4) and has a slope of 0 is y = 4.

Given:

point (8,4) and has a slope of 0

slope m = 0

Standard line equation is y = mx + c

substitute (8,4) and m values in y = mx + c

4 = 0*8 + c

4 = 0 + c

c = 4

c , m values in y = mx + c

y = 0*x + 4

y = 0 +4

y = 4.

Therefore The equation of the line that passes through the point (8,4) and has a slope of 0 is y = 4.

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0.769 minutes of the ride is spent higher than 17 meters above the ground.

What is the unit conversion in mathematics?

Unit conversion is a multi-step process that includes multiplying or dividing by a numerical factor, determining the appropriate number of significant digits, and rounding.

The given figure is a Ferris wheel we have to find the time spent on the ride higher than 17 m.

It means we have to find time spent riding from A to C through B (i.e., Arc ABC)

From the figure, in ΔAOD, we have

         OA = 12.5 m

         OD = 12.5 - 1 = 11.5 m

Now find 'θ'

           θ = [tex]cos^{-1}(\frac{11.5}{12.5})[/tex]

                = 23.07°

The total angle of arc ABC = 2θ

                                       = 2 * 23.07

                                       = 46.14°

It is given that, 1 full revolution is completed in 6 minutes.

so 46.14° will be completed in = 6/360 * 46.14

                                                  = 0.769 minutes.

Hence, 0.769 minutes of the ride is spent higher than 17 meters above the ground.

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The green ornaments that Peter remove from the box will be; 30

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

We are given that box of 120 holiday ornaments, 75% are green and the rest are red.

Therefore, 120 ornaments = 100%

75% are green = 75% of 120

0.75 x 120 = 90

And the rest are red means

120 - 90 = 30

Peter removes green ornaments from the box until only 60% of the ornaments in the box are green that means;

60% of 90

0.60 x 90 = 54

Then the green ornaments that Peter remove from the box will be; 30

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The equation of the line that passes through the point (8,0) and is parallel to the line x + y = 5 is x + y = 8.

Two lines are parallel with each other if they do not intersect no matter how much you extend both lines. Parallel lines have equal slopes.

Get the slope of the given line x + y = 5.

y = -x + 5

m = -1

Hence, the equation of the line should also be equal to -1.

Using the point slope form, plug in the values of the slope and the point to set up the equation.

(y - y₁) = m(x - x₁)

(y - 0) = -1(x - 8)

y = -x + 8

Rearranging, x + y = 8.

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