\log_{ 6 }({ 3x }) + \log_{ 6 }({ x-1 }) = 3

What's the answer and how do you get it

Answer:

Solution given:

3(5x+8)

distribute

15x+8*3

15x+24 is a required answer.

Answer:

15x + 24

Step-by-step explanation:

Apply the Distributive Property of Multiplication.  Multiply each of the two terms inside parentheses by 3:

3(5x + 8) = 15x + 24

For the student the lift increased for the weight will be 50%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A student doing resistance exercise.

After one week, She can lift the weight = 2 kg

And, After four weeks, she can lift the weight = 3 kg

Since, We know that;

Percent = (increased weight - Actual weight) / Actual weight  x 100

Substitute all the values, we get;

Increased percent = (3 - 2) / 2 x 100

Increased percent = 1 / 2 x 100

Increased percent = 100 / 2

Increased percent = 50%

Therefore,

For the student the lift increased for the weight will be 50%.

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Step-by-step explanation:

=81m⁴-n⁴

={(3m)²}²-(n²)²

=(3m²+n²)(3m²-n²)

hope it helps.

Answer:

a. 0.17

b. 0.95

Step-by-step explanation:

The key to answering both questions is that we should understand that the probability of an event happening = 1 - the probability of the event not happening

Firstly, we want to calculate the probability of less than four

Probability of less than four = 1 - probability of four or more heads

that is 1 - 0.83 = 0.17

Probability of less than 8 = 1 - probability of 8 or more = 1-0.05 = 0.95

Given the exponential expression

Give the general exponential equation

The equivalent logarithmic functions is given as:

Compared with the exponential function:

• a = 8

• b = 2/3

• y = 4

Substitute into the logarithm equivalent:

Answer:

n = 6

Step-by-step explanation:

f(n) = 0 is on the n- axis at (6, 0 )

When f(n) = 0 then n = 6

The length of a side of regular hexagon with area 35 inch² is 3.7 inches.

The formula to be used for calculation of the length of a side of regular hexagon is -

Area = 3√3/2 a², where a is the side.

Keep the values in formula -

35 = 3√3/2 a²

Rewriting the equation to find the length of side of regular hexagon

a² = 35×2/3√3

Performing multiplication in numerator and denominator of the equation

a² = 70/5.2

Performing division

a² = 13.5

a = ✓13.5

Taking square root

a = 3.67 inches

Rounding to nearest tenth = 3.7 inches

Thus, the side is 3.7 inches.

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The value of the missing angle is calculated as: ∠BGC = 76°

The parameters are given as:

∠AGB = 35°

∠AGE = 69°

From angle theorems, we know that the sum of angles on a straight line is 180°. If we split any straight line into smaller angles, all of these angles would then be summed up to make 180° which is the same as with a triangle. Angles in a straight line are a very useful problem solving tool for many geometric problems.

Thus:

∠AGB + ∠AGE + ∠BGC = 180°

Thus:

35 + 69 + ∠BGC = 180

∠BGC = 180 - (69 + 35)

∠BGC = 76°

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Answer:

20/27

Step-by-step explanation:

Answer:

Step-by-step explanation:

let amount invested at 12%=x

amount invested in 10 %=y

amount invested in 8 %=z

z=2x

x+y+z=290,000

x+y+2x=290,000

3x+y=290,000  

multiply by 5

15x+5y=1,450,000  ... (1)

12/100 x+10/100 y+8/100 z=27,600

12x+10 y+8z=2,760,000

6x+5y+4z=1,380,000

6x+5y+4(2x)=1,380,000

14x+5y=1,380,000   ... (2)

(1)-(2) gives

x=1,450,000-1,380,000=70,000

z=2(70,000)=140,000

70,000+y+140,000=290,000

y+210,000=290,000

y=290,000-210,000=80,000

invested in 12 %=$ 70,000

invested in 10 %=$ 80,000

invested in 8 %=$ 140,000

(b)

annual income from 12 %=12/100 ×70,000= $8,400

annual income from 10 % =10/100×80,000=$ 9,600

annual income from 8 %=8/100×140,000= $11,200

Answer:

r = -6

Step-by-step explanation:

Use the slope formula and solve for r.

slope = y2 -y1

            x2 -x1

Since you know all the numbers except for r, plug everything in and you get:

5  = 9 - r

        9 - 6

So then do the arithmetic, you find that 9 - r = 15. So r must = -6.

Answer:

3:5

Step-by-step explanation:

just

simplify

The final equation of the line is   y = (-2/3)x - 3   in the coordinate system.

what is coordinate system?

A coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the position of a point or an object in space. In mathematics, the most common coordinate system is the Cartesian coordinate system

what is equation ?

In mathematics, an equation is a statement that shows the equality between two expressions. It contains an equals sign (=) between the two expressions that are being compared. Equations can be used to describe relationships between variables, to solve problems, or to represent real-world situations.

In the given question,

To draw the line going through (-6,1) with a slope of -2/3, we can follow these steps:

Plot the point (-6,1) on a coordinate system. This will be one point on the line.

From that point, use the slope to find another point on the line. A slope of -2/3 means that for every 3 units to the right we move, we must move 2 units down. So starting from (-6,1), we can move 3 units to the right and 2 units down to get to the point (-3,-1). This is another point on the line.

Draw a straight line through the two points to represent the line going through (-6,1) with a slope of -2/3.

To write the equation of the line, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1,y1) is one point on the line, m is the slope, and (x,y) are the coordinates of any other point on the line. Let's choose (-6,1) as our point:

y - 1 = (-2/3)(x - (-6))

Simplifying, we get:

y - 1 = (-2/3)x - 4

Adding 1 to both sides, we get the final equation of the line:

y = (-2/3)x - 3

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The probability that it will rain (event r), which formula would we use is

P(AB) = P(A) P(BA)/ P(B).

Bayes' theorem is a way to find probabilities when we know other probabilities.

Formula:

P(AB) = P(A) P(BA)/ P(B)

Tells how often A occurs when B occurs. If we know how often B occurs when A occurs, then P(BA)

and how likely it is that A is independent, write P(A)

and how likely it is that B is independent, write P(B)

Now,

The meteorological woman said, “The probability of rain on Saturday is 40% and the probability of rain on Sunday is 40%, so the probability of rain this weekend is 100%.”

I decided to simplify the problem by saying P(non-Saturday) = 0.5 and P(non-Sunday) = 1.0.

This obviously means P(non this weekend) = 1.0. Rain this weekend I started with p(rain on Saturday) x p(rain on Sunday) but I gave 0.5 and tried p(it didn't rain this weekend) = p(it didn't rain on Saturday) x. P (it did not rain on Sunday) is 0.

So P(rain this weekend) = 1 - P(no rain this weekend) = 1.0

Using this method, P(rain this weekend) = 0.75 or 75% of the original statement.

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Answer:

Need help with what?

Step-by-step explanation:

1. Newmont Mining Corporation is a mining company, but the comparison company has not been specified. Therefore, I am unable to provide specific calculations or comparisons.

2. The three ratios that determine Return on Equity (ROE) can be used to compare and contrast the ROE values of the two companies once the comparison company is selected.

3. The top three risks identified by Newmont Mining Corporation can be found in their 10-K report.

1. Without knowing the specific comparison company within the same industry, I cannot perform calculations or provide a detailed comparison of ratios. Once the comparison company is specified, financial ratios such as liquidity ratios (current ratio, quick ratio), profitability ratios (gross profit margin, net profit margin), and leverage ratios (debt-to-equity ratio, interest coverage ratio) can be calculated for both companies to assess their relative strengths and weaknesses.

2. The three ratios that determine Return on Equity (ROE) are the net profit margin, asset turnover ratio, and financial leverage ratio. These ratios can be used to compare and contrast the ROE values of Newmont Mining Corporation and the selected comparison company. The net profit margin measures the company's profitability, the asset turnover ratio assesses its efficiency in generating sales from assets, and the financial leverage ratio evaluates the extent of debt used to finance assets.  

3. To identify the top three risks identified by Newmont Mining Corporation, one would need to review the company's 10-K report. The 10-K report is an annual filing required by the U.S. Securities and Exchange Commission (SEC) and provides detailed information about a company's operations, financial condition, and risks. Within the 10-K, the "Risk Factors" section typically outlines the significant risks faced by the company. By reviewing this section of Newmont Mining Corporation's 10-K report, the top three risks identified by the company can be identified, providing insights into the challenges and potential vulnerabilities the company faces in its industry.

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Answer:

A, B, E  

explanation:                                                                                                                                            

Answer:

A: The range of scores is 38.

B: Without the outlier, the range of scores would be 12.

C: The outlier impacts the range more than it impacts the interquartile range.

D: The interquartile range is 9.

F: Without the outlier, the interquartile range would be 9.5.

Step-by-step explanation:

edg2020

The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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Answer:

x = - 9

Step-by-step explanation:

Given

- (5x - 4) = 49 ← distribute the parenthesis by - 1

- 5x + 4 = 49 ( subtract 4 from both sides )

- 5x = 45 ( divide both sides by - 5 )

x = - 9

Answer:

5 acorns, 4 seed pods, and 4 feathers

Step-by-step explanation:

Answer:

v - 18

Step-by-step explanation:

( 7v - 9 ) - ( 6v + 9 )

= 7v - 9 - 6v - 9

= 7v - 6v - 9 - 9

= v - 18

Answer:

v - 18

Step-by-step explanation:

(7v-9)-(6v+9)

Distribute the minus sign

7v-9-6v-9

Combine like terms

7v -6v  -9-9

v -18

Answer:

The equation that matches this situation is y = 8.34x + 25 ⇒ B

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = Δy/Δx, where

∵ Lisa collects rainwater in a barrel that weighs 25 pounds

∴ The initial value of the weight is 25 pounds

∴ b = 25

∵ When there are 10 gallons of water in the barrel, the total weight

  of the barrel and the water is 108.4 pounds

∴ At x = 10, y = 108.4

∵ When there are 20 gallons of water, the total weight is 191.8 pounds

∴ At x = 20, y = 191.8

→ Find Δx and Δy

∵ Δx = 20 - 10 = 10

∵ Δy = 191.8 - 108.4 = 83.4

→ Substitute them in the rule of the slope above

∴ m = \(\frac{83.4}{10}\)

∴ m = 8.34

→ Substitute the values of m and b in the form of the equation above

∵ y = 8.34x + 25

∴ The equation that matches this situation is y = 8.34x + 25

Answer:

y = 1.4x + 5.6

Step-by-step explanation:

plug the slope and y-intercept into the formula: y = ax + b (a is the slope and b is the y-intercept)

thus, y = 1.4x + 5.6

The required answer is a square cross-section with a side length of 3.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,

The cross-section we are interested in is a square that lies in the plane y=-1. To find this square, we need to find the value of x where the curve  y=x³ intersects the plane y=-1.

y=x³ and y=-1 intersect when,
x = (-1)^(1/3)
x = -1,  since (-1)³ = -1.

The curve y=x³ intersects the plane y=-1 again when x=2, since 2³=8 and -1<8. Therefore, the square cross-section perpendicular to the y-axis that we are looking for has a side length 2-(-1)=3.

Hence, the answer is a square with a side length of 3.

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Answer: 5

explanation:

x -5 apples = x^2 - 25

1 apple = x

cross multiply:

x (x-5) = 1 (x^2 - 25)

x^2 - 5x = x^2 - 25

the "X^2" WILL CANCEL OUT

-5x = -25

x = -25/-5

x = 5

The cost of one apple is x + 5

Let the cost of one apple be y.

So, we have the following equation

y * (x - 5) = x^2 - 25

Express x^2 - 25 as a difference of two squares

y * (x - 5) = (x + 5)(x - 5)

Divide both sides by x - 5

y = x + 5

Hence, the cost of one apple is x + 5

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Answer:

Solution,

Let the points be A and B

A(-3,2)------->( X1,y1)

B(-2,5)------>( x2,y2)

Now,

gradient means slope.

\(slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: = \frac{5 - 2}{ - 2 - ( - 3)} \\ \: \: \: \: \: = \frac{ - 3}{ - 2 + 3} \\ \: \: \: \: \: = \frac{ - 3}{1} \\ \: \: \: = - 3\)

Hope this helps..

Good luck on your assignment..

Answer:

\(\boxed{x=3}\)

Step-by-step explanation:

Let's solve now

\(\red{( - 3 \: \: \: \: \: \: 2)} = >\green{ (x1 \: \: \: \: \: y1) }\\ \red{( - 2 \: \: \: \: \: \: 5 ) }= >\green{ (x2 \: \: \: \: \: y2)}\\ \)

\(\blue{slope = \frac{y1 - y2}{x1 - x2} } \\ = \frac{2 - 5}{ - 3 - ( - 2)} \\ = \frac{ - 3}{ - 3 + 2} \\ = \frac{ - 3}{ - 1} \\ = 3\)

Yes, an angle in a right-angled triangle is always present.  Without any additional information about the triangle, it is impossible to determine the value of the angle in question.

In a right-angled triangle, one of the angles is a right angle, which measures 90 degrees. The other two angles in the triangle are acute angles and their measures always add up to 90 degrees.

To find the value of the angle in question, we need to know some additional information about the triangle. If we have the lengths of two sides of the triangle, we can use trigonometric ratios to find the measure of the angle.

For example, if we know the length of the side opposite the angle and the length of the hypotenuse (the longest side of the triangle), we can use the sine ratio to find the measure of the angle.

If we know the length of the side adjacent to the angle and the length of the hypotenuse, we can use the cosine ratio.

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

The answer is C.

Step-by-step explanation:

The theory of vertical angles, often known as the theorem of vertically opposite angles. According to the theorem, two opposed vertical angles created when two lines cross one other are always equal (congruent) to each other no matter what the circumstances are.