3x-6y=6. Solve for y

To answer this question we will use the following property of logarithms:

Dividing the given equation by 4 we get:

Simplifying the above result we get:

Applying the natural logarithm we get:

Applying the property of logarithms we get:

Therefore:

Answer: Option D.

Remove the brackets.

Take the like terms closer.

Now do the addition and subtraction

Let us split the middle term

Now take x as common from the first two terms and -1 from the next two terms.

Answer:

(x - 1)(7x + 12)

Hope you could understand.

If you have any query, feel free to ask.

Solve (6x² + 5x - 3) + (x² - 9)

(x-1) (7x+12)

please look at the attached picture :)

Answer:

C

Step-by-step explanation:

The add to 180 because that's a straight line    

The equation of the tangent line to the curve y = (1 + 2x)¹² at the point (0, 1) is y = 24x + 1.

To find the equation of the tangent line to the curve at the given point, we need to determine the slope of the tangent line and then use the point-slope form of a linear equation.

Given the equation of the curve: y = (1 + 2x)¹² and the point (0, 1), we can find the slope of the tangent line by taking the derivative of the curve with respect to x.

Let's differentiate y = (1 + 2x)¹²:

dy/dx = 12(1 + 2x)¹¹ * 2

At the point (0, 1), x = 0. Substituting this value into the derivative, we have:

dy/dx = 12(1 + 2(0))¹¹ * 2

= 12(1)¹¹ * 2

= 12 * 2

= 24

So, the slope of the tangent line at the point (0, 1) is 24. Now we can use the point-slope form to find the equation of the tangent line:

y - y₁ = m(x - x₁)

Plugging in the values: x₁ = 0, y₁ = 1, and m = 24, we have:

y - 1 = 24(x - 0)

Simplifying, we get:

y - 1 = 24x

Finally, let's rewrite the equation in slope-intercept form (y = mx + b):

y = 24x + 1

Therefore, the equation of the tangent line to the curve y = (1 + 2x)¹² at the point (0, 1) is y = 24x + 1.

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The surface area of the solid pyramids are as follows;

First figure; 436 square units

Second figure; 319 square units

Third figure; 673 square units

A pyramid is a shape that consists of a polygon base and side faces that are triangular.

First figure

The figure is a pentagonal pyramid of height 8 units and side length of 10 units

The apothem, a, can be obtained from the formula;

\(a = \dfrac{s}{2\cdot tan \left(\dfrac{180}{n} \right)}\)

s = 10

n = 5

\(a = \dfrac{10}{2\cdot tan \left(\dfrac{180}{5} \right)} \approx 6.88\)

Slant height ≈ √(8² + 6.88²) ≈ 10.55

Area of the 5 triangles = 5 × (1/2) × 10 × 10.55 ≈ 263.75

Area of pentagonal base ≈ (1/2) × 6.88 × 5 × 10 = 172
Area of the figure ≈ 263.75 + 172 ≈ 436

Second figure;

Square pyramid

n = 4

When s = 8, we get;

\(a = \dfrac{12}{2\cdot tan \left(\dfrac{180}{4} \right)} =6\)

Slant height of the 8 units long side = √(6² + 10²) ≈ 11.66

Area of two of the four triangle surfaces = 2×(1/2)×8 ×11.66≈ 93.28

When s = 12 we get;

\(a = \dfrac{8}{2\cdot tan \left(\dfrac{180}{4} \right)} =4\)

Slant height of the 12 units long side = √(4² + 10²) ≈ 10.77

Area of two of the four triangle surfaces = 2×(1/2)×12 × 10.77 ≈ 129.24

Area of the rectangular base = 12 × 8 = 96

Area of the figure = 93.28 + 129.24 + 96 ≈ 319

Third figure

Octagonal pyramid

n = 8

s = 8

\(a = \dfrac{8}{2\cdot tan \left(\dfrac{180}{8} \right)}\approx 9.66\)

Slant height = √(9.66² + 6²) ≈ 11.37

Area of the 8 triangles = 8 × (1/2) × 8 × 11.37 ≈ 363.84

Area of the octagonal base = 2×(1 + √2)×s²

Therefore;

2×(1 + √2)×8² ≈ 309.02

Area of the figure ≈ 363.84 + 309.02 ≈ 673

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Answer:

11%/ 0.11

Step-by-step explanation:

I=prt

154=700*x*2

154=1400x

divide 1400 by both sides

=0.11

or 11%

The ratio of cost to the number of cans = 5: 2  

A ratio is a mathematical concept that represents the relationship between two or more values.

In the given problem, the ratio represents the relationship between the cost of the soup and the number of cans purchased.

Ratios are commonly used in mathematics, finance, and other fields to express comparisons and relationships between different quantities.

Here we have

$10 for 4 cans of soup  

The required ratio can be formed as follows

=> 10: 4

=> 10/2: 4/2   [ Divided by 2 ]

=>  5: 2

Therefore,

The ratio of cost to the number of cans = 5: 2    

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Based on these calculations, the estimated instantaneous velocity at t = 9 is approximately 31376 ft/s.

(a) To find the distance traveled by the ball during the time interval [9, 9.5], we substitute the values of t into the equation \(s(t) = 16t^2:\)

\(s(9) = 16(9)^2 = 1296 ft\)

\(s(9.5) = 16(9.5)^2 = 1712 ft\)

The ball travels Δs = s(9.5) - s(9) = 1712 ft - 1296 ft = 416 ft during the time interval [9, 9.5].

(b) The average velocity over the time interval [9, 9.5] can be calculated by dividing the change in distance by the change in time:

Δs/Δt = (s(9.5) - s(9)) / (9.5 - 9)

Substituting the values, we get:

Δs/Δt = (1712 ft - 1296 ft) / (0.5) = 416 ft / 0.5 = 832 ft/s

The average velocity over [9, 9.5] is 832 ft/s.

(c) To estimate the object's instantaneous velocity at t = 9, we can calculate the average velocity over smaller time intervals that approach t = 9.

Δt = 0.01:

V(9) ≈ Δs / Δt

= (s(9.01) - s(9)) / (9.01 - 9)

= (1609.76 ft - 1296 ft) / 0.01

= 31376 ft/s

Δt = 0.001:

V(9) ≈ Δs / Δt

= (s(9.001) - s(9)) / (9.001 - 9)

= (1615.68016 ft - 1296 ft) / 0.001

= 319680 ft/s.

Δt = 0.0001:

V(9) ≈ Δs / Δt

= (s(9.0001) - s(9)) / (9.0001 - 9)

= (1615.6800016 ft - 1296 ft) / 0.0001

= 31996800 ft/s.

Δt = 0.0001:

V(9) ≈ Δs / Δt = (s(8.9999) - s(9)) / (8.9999 - 9)

= (1615.6799984 ft - 1296 ft) / (-0.0001)

= -31996800 ft/s

Δt = 0.01:

V(9) ≈ Δs / Δt = (s(8.999) - s(9)) / (8.999 - 9)

= (1609.76 ft - 1296 ft) / (-0.001)

= -313760 ft/s

Δt = 0.01:

V(9) ≈ Δs / Δt

= (s(8.99) - s(9)) / (8.99 - 9)

= (1592.896 ft - 1296 ft) / (-0.01)

= -29600 ft/s

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Answer:

A scalar quantity is defined as the physical quantity with only magnitude and no direction.

Answer:

18

Step-by-step explanation:

2x9=18

The margin of error is approximately $18.35, and the 99% confidence interval for the population mean repair cost is ($56.65, $93.35). This means we are 99% confident that the true population mean repair cost falls within this interval.

To calculate the margin of error, we use the formula: Margin of Error = t × (standard deviation / √n), where t is the critical value for the desired confidence level, standard deviation is the sample standard deviation, and n is the sample size.

With a sample mean repair cost of $75.00 and a standard deviation of $11.50, and a sample size of 6, we need to determine the critical value associated with a 99% confidence level. Since the sample size is small (n < 30), we use a t-distribution instead of a z-distribution.

Using the t-distribution with (n-1) degrees of freedom, where n is the sample size, and a confidence level of 99%, we find the critical value to be approximately 3.707.

Next, we calculate the margin of error: Margin of Error = 3.707 × (11.50 / √6) ≈ 18.35.

To construct the 99% confidence interval, we take the sample mean and add/subtract the margin of error: 75.00 ± 18.35. This gives us a confidence interval of approximately (56.65, 93.35).

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An observational study would be the most appropriate type of study to compare lawyer salaries to doctors' salaries.

When comparing lawyer salaries to doctors' salaries, conducting an observational study would be the most appropriate approach. An observational study involves observing and analyzing existing data without any intervention or manipulation of variables. In this case, researchers would collect salary data from a representative sample of lawyers and doctors and analyze the differences between the two groups.

Conducting an experiment without blinding, experiment with single blinding, or experiment with double blinding would not be suitable for this question. Blinding refers to the process of concealing information about the intervention or treatment from the participants or researchers to reduce bias. Since the question involves comparing salaries, there is no direct intervention or treatment that can be manipulated, making blinding unnecessary.

A case-control study would also not be appropriate for this question. A case-control study is typically used to investigate the association between an outcome (case) and potential risk factors (control). In the case of lawyer salaries versus doctors' salaries, there is no specific outcome or risk factor to compare; rather, the focus is on comparing the salaries themselves.

Therefore, an observational study would be the most suitable approach to compare lawyer salaries to doctors' salaries, as it allows for the collection and analysis of existing data without the need for manipulation or blinding.

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Answer:

1st=2. (-7,9) (-18,9)

2nd=4. y= 5/9x+10

Noise levels at 5 volcanoes were measured in dB, and the z value is 2.326 with a 98% confidence interval.

The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. It differs from simple interest in that simple interest does not take the principal into account when calculating the interest for the following period. In math, compound interest is typically represented by the letter C.I.

You only have a 5% chance of being wrong with a 95 percent confidence interval. There is a 10% chance that you could be incorrect with a 90% confidence interval. In comparison to a 95% confidence interval, a 99 percent confidence interval would be larger. A 95% confidence interval is a range of values that, to a 95% degree of certainty, contains the population's actual mean.

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Answer:

13.71 m

Step-by-step explanation:

Draw the tunnel so the width marks the zeroes at   (-12,0) and (12,0)

    then      y = a ( x+12)(x-12)   is the equation..

      ..to calculate 'a' sub in the point 9, 6   (where the width is 18)

               6 = a ( (9+12)(9-12)    shows a = -2/21

y = -2/21 (x+12)(x-12)       Max is when x = 0

      -2/21 ( 12)(-12)  = 288/21     =    13.71 m

Answer:

  ∠LMN = 90°

Step-by-step explanation:

Ordinarily, you would rotate the protractor so the 0° mark lines up with one of the sides of the angle you want to measure. You have not done that here, but you can still find the measure of the angle.

Subtract the smaller scale value from the larger one to find the angle measure:

  ∠LMN = 180° -90° = 90°

_____

Additional comment

Most physical protractors are marked with two scales. One goes counterclockwise, as this one does. The other goes clockwise. At each point on the scale, the markings total 180°.

Answer:

A D E

Step-by-step explanation:

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To multiply decimals, first line up the decimal points in the two numbers.

Then multiply the numbers as if they were whole numbers, ignoring the decimals. After multiplying, count the number of digits after the decimal points in both numbers. Finally, add the number of digits after the decimal points together and place the decimal point in the answer that number of places from the right. For example, to multiply 5.2 and 3.1, line up the decimals like this:

5.2

× 3.1

Then multiply the numbers as if they were whole numbers:

52

× 31

= 1612

There are one digit after the decimal in the first number and one digit after the decimal in the second number, so add one and one to get two. Place the decimal point two places from the right to get the answer 16.12.

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Answer:

Probably the first one because the other two questions would be un-reliable

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

1/7)(x^2 + 2)^7 - (2/3)(x^2 + 2)^6 + C. This is the final result.

To evaluate the integral ∫x(x^2 + 2)^5 dx, we can use the substitution method.

Let's substitute u = x^2 + 2. Taking the derivative of both sides with respect to x, we get du/dx = 2x. Rearranging this equation, we have dx = du / (2x).

Substituting dx and u into the original integral, we have ∫x(x^2 + 2)^5 dx = ∫(u - 2)(u)^5 (du / (2x)).

Now we can simplify the integral by canceling out the x in the denominator.

The integral becomes ∫(u - 2)(u)^5 (du / 2).

Expanding the terms, we have ∫((u^6) - 2(u^5)) (du / 2).

Now we can integrate term by term.

∫(u^6) (du / 2) = (1/7)(u^7) + C1, where C1 is the constant of integration.
∫(2u^5) (du / 2) = (1/3)(u^6) + C2, where C2 is the constant of integration.

Putting it all together, the final result is:

(1/7)(u^7) - (2/3)(u^6) + C, where C is the constant of integration.

Substituting back u = x^2 + 2, we get: 1/7)(x^2 + 2)^7 - (2/3)(x^2 + 2)^6 + C

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To the nearest tenth of a year, it will take 31.1 years until the population reaches 41,500.Given that a town has a population 14,000.

It increases at a rate of 4.5% each year. We need to determine to the nearest tenth of a year how long it will be until the population will reach 41,500.

Let t be the number of years it will take for the population to reach 41,500.

Then the population after t years will be:

P(t) = \(14,000(1 + 0.045)^t\)

Notice that we are multiplying by (1 + 0.045) rather than adding 0.045.

This is because the population is increasing by 4.5% of the previous year's population, not just by a flat 4.5% of 14,000.

Now we need to solve the equation:

P(t) =\(41,50014,000(1 + 0.045)^t\)

= \(41,500(1.045)^t\)

Divide both sides by

14,000: \((1.045)^t\)= 2.964286...

Take the natural log of both sides of the equation:

t * ln(1.045) = ln(2.964286...)t

= ln(2.964286...) / ln(1.045)

≈ 31.1 years

Therefore, to the nearest tenth of a year, it will take 31.1 years until the population reaches 41,500.

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Answer:

m=1/2

Step-by-step explanation:

your answer is right

11w11(w)11×wthat a few different ways

Step-by-step explanation:

:)

Answer:

x = - 7

Step-by-step explanation:

- 2x = 5 + 9

- 2x = 14

x = - 14 / 2

x = - 7

Hope this answer helps you  :)

Have a great day

Mark brainliest

Answer:

x ≤ -7

Step-by-step explanation:

−2x−9 ≥ 5

add 9 to both sides

-2x -9 +9 ≥ 5+9

-2x ≥ 14

divide -2 on both sides

since we're dividing by a negative number we need to flip our inequality sign

-2x/-2 ≥ 14/-2

x ≤ -7

The number of blue marbles in the jar are 8.

Given,  the total number of marbles in the jar = 24.

therefore, total number of all possible outcomes = 24.

Let the number of green marbles in Jar be x.

therefore, the number of favourable outcomes = x.

The probability that the marble drawn is green  = x/24

But we have the probability of drawing a green marble = 2/3

x/24 = 2/3

3x = 2 (24)

x = 16

Thus , the number of green marbles in the jar = 16

The number of blue marbles = 24 - 16 = 8

Hence, the number of blue marbles in the jar is 8.

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

There are 24 marbles in a jar out of them some are green and remaining are blue. If a marble is drawn from the jar at random, the probability that the green marble drawn is 2/3.Find the number of blue marbles in the jar.

Answer:

negative 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

1.

a mother is a she, not a he ...

anyway, we need to make 2/3 and 3/4 comparable.

for this we need to bring both fractions to a common denominator, which is usually the smallest common multiple of the denominators.

yes, 12 is the smallest number that can be divided by 3 and by 4 without remainder.

to transform a fraction too another denominator, we need to multiply it by a fraction a/a, which has the value 1, of course (so we don't change the value of the original fraction), but changes the denominator to the desired number.

what do I multiply with 4 to get 12 ? 3.

so, I multiply 3/4 by 3/3 = 9/12.

what do I multiply with 3 to get 12 ? 4.

so, I multiply 2/3 by 4/4 = 8/12.

now we can compare and calculate :

out of the total of 9/12kg 8/12kg were used.

that means

1/12kg of carrots are left.

2.

this is a strange question, as watermelons, bananas and melons are very differently sized. so, for example 1/2 watermelon and 1/2 banana are very different quantities.

so, what does e.g. 1 fruit mean ?

or if we understand the fractions as shares of the overall smoothie, then we have too much. 4/6 (watermelon) + 2/6 (melon) = 6/6 = 1 (whole smoothie).

so, what to do with the banana ?

this question does not make any sense at all.

but if it is just to add fractions, we can do that :

4/6 + 1/2 + 2/6

as mentioned above, 4/6 + 2/6 = 6/6 = 1

1 + 1/2 = 2/2 + 1/2 = 3/2 = 1.5 or 1 1/2

so there is 1 1/2 fruit in the smoothie (whatever that means).

3.

1 1/2 + 2 1/2 = 2/2 + 1/2 + 4/2 + 1/2 = 8/2 = 4

in total, there are 4 cups of sugar needed.

The general solution to the given Cauchy-Euler equation for t > 0 is:

y(t) = C1 * t⁻⁵ + C2 * t⁴

Let's consider the given Cauchy-Euler equation for t > 0:

t²(d²y/dt²) + 2t(dy/dt) - 20y = 0

To solve this equation, we can assume a solution of the form y(t) = tⁿ, where r is a constant to be determined.

Now, let's find the derivatives of y(t) with respect to t:

dy/dt = rtⁿ⁻¹ d²y/dt² = r(r-1)tⁿ⁻²

Substituting these derivatives back into the Cauchy-Euler equation, we get:

t²(r(r-1)tⁿ⁻²) + 2t(rtⁿ⁻¹) - 20tⁿ = 0

Simplifying this equation, we have:

r(r-1)tⁿ + 2rtⁿ - 20tⁿ = 0

Factoring out tⁿ, we get:

tⁿ [r(r-1) + 2r - 20] = 0

Since t > 0 for the given equation, we can divide both sides of the equation by tⁿ to obtain:

r(r-1) + 2r - 20 = 0

Expanding and rearranging this equation, we get:

r² + r - 20 = 0

Now, we can solve this quadratic equation for r. Factoring it, we have:

(r + 5)(r - 4) = 0

Setting each factor equal to zero, we find two possible values for r:

r + 5 = 0, which gives r = -5 r - 4 = 0, which gives r = 4

These values of r represent the roots of the characteristic equation associated with the Cauchy-Euler equation. Since we have two distinct roots, the general solution to the Cauchy-Euler equation can be written as a linear combination of the corresponding solutions:

y(t) = C1 * t⁻⁵ + C2 * t⁴

Where C1 and C2 are arbitrary constants that can be determined using initial conditions or boundary conditions if provided.

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Elspeth can find the circumference by dividing 9.42 centimeters by π, the mathematical constant. she can use this radius value to calculate the circumference of the circle using the formula C = 2πr.

The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.

In this case, Elspeth knows that π times r approximately equals 9.42 centimeters. To find the circumference, she needs to divide 9.42 centimeters by π.

Dividing by π will cancel out the π on the right side of the equation, leaving only the value of the radius r. By dividing 9.42 centimeters by π, Elspeth will obtain the value of the radius.

Then, she can use this radius value to calculate the circumference of the circle using the formula C = 2πr.

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