If you are given the equation below, what operation would you need to use tosolve for x? 20 = −5x

To write the given equation in logarithmic form, we can use the definition of logarithms. The equation 10^m = w can be rewritten as a logarithm with base 10: log10(w) = m

The general relationship between exponents and logarithms is as follows:

base^(exponent) = result

In logarithmic form, it's written as:

log_base(result) = exponent

For our given equation, 10^m = w, we have:

base = 10

exponent = m

result = w

Applying the general logarithmic relationship, we write:

log10(w) = m

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Result:

sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).

For us to write the expression, we shall use this formular formula:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

where:

a = tan⁻¹(x)

b = tan⁻¹(y)

Next, we have:

tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))

= (x - y) / (1 + xy)

From both sides, we have sine:

sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))

So, sin(tan⁻¹(x) - tan⁻¹(y))  

= sin(tan⁻¹(x) - tan⁻¹(y))

= (x - y) / (1 + xy) in terms of x and y.

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Answer:

1/3

Step-by-step explanation:

There are six triangles

2/6 of them are green

We can simplify this to 1/3

Answer:

1/6

Step-by-step explanation:

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

Answer:(8,1)

Step-by-step explanation:

Answer: 4,000,000

Please, please give me brainliest! I'm trying to become the next rank :) Thanks!

Answer: Heyaa!

The Answer Is... 4000000

Step-by-step explanation:

Multiple them together :

Hopefully this helps you !

- Matthew ~

The best measure of center for the frequency of the data is Mean. The value of the measure of the center is 30.

The Mean value refers to an intermediate value between a discrete set of numbers. It is a measure of central tendency in a data set. In statistics, the term average refers to any of the measures of central tendency. The arithmetic mean of a set of observed data is defined as being equal to the sum of the numerical values of each and every observation, divided by the total number of observations. Fifty part time college students were asked how many hours they work per week.

Frequency 12 10 81 6 0 10 30 40 0 10 30 40 20 Hours 20 Hours.

we can calculate mean by adding all the frequencies and then divide it by the number of observations.

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Answer:

35n/17r

Step-by-step explanation:

The expression (x-10)(x-3) in standard form is x^2 - 13x + 30. The quadratic term comes first, followed by the linear term, and finally the constant term.

To put the expression (x-10)(x-3) in standard form, we need to expand it and simplify any like terms. Here are the steps:

Start with the given expression: (x-10)(x-3).

Use the distributive property to expand the expression. Multiply each term in the first set of parentheses by each term in the second set of parentheses:

x(x-3) - 10(x-3).

Apply the distributive property further to simplify the expression:

x^2 - 3x - 10x + 30.

Combine like terms: -3x - 10x = -13x.

Rewrite the expression in standard form by arranging the terms in descending order of degree:

x^2 - 13x + 30.

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Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

Answer:

b=0.7(3) The 3 in the parentheses means the 3 repeats forever

Step-by-step explanation:

If you simplify the sides, it will equal -1.5b=3b-3.3. This means that 4.5b=3.3. This means that b=0.7(3). The 3 will repeat forever.

Hopefully the explanation and the answer helps you!

Answer:

I believe it's D

Step-by-step explanation:

It says he reads 40 pages per hour.

254 is the total

x is the hours

and 40 is pages read per hour

The solution of the system of equations:

y = 3x - 4

y = (-1/2)*x + 3

Is (2, 2).

Here we have the following system of equations:

y = 3x - 4

y = (-1/2)*x + 3

To solve this graphically, we just need to graph both equations on the same coordinate axis, and find a point where these two graphs intercept.

Below you can see the graph of the system, and there you can see that the lines intercept at the point (2, 2), so that is the solution of the system.

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Answer

x | y | (x, y)

0 | -5 | (0, -5)

2 | 5 | (2, 5)

1 | 0 | (1, 0)

Explanation

The function is given as

y = 5x - 5

To fill in the table,

when x = 0

y = 5x - 5

y = 5(0) - 5

y = 0 - 5

y = -5

(x, y) = (0, -5)

when x = 2

y = 5x - 5

y = 5(2) - 5

y = 10 - 5

y = 5

(x, y) = (2, 5)

when x = 1

y = 5x - 5

y = 5(1) - 5

y = 5 - 5

y = 0

(x, y) = (1, 0)

Hope this Helps!!!

         In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x,

        So in other words, a logarithm is the power to which a number must be raised in order to get some other number . For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100.

Hope this helps. Have a good day!

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

45.05 seconds

Step-by-step explanation:

Use the formula: d = v\(i\) t + \(\frac{1}{2}\) a\(t^{2}\)

d = distance      v\(i\) = initial velocity (m/s)    

t = time (s)     a = acceleration (m/\(s^{2}\))

m is meters and s is seconds. They are units of measurement so leave them be.

Assuming the object is simply dropped, the initial velocity is 0 since the object was not moving before it was dropped.

The distance is 725 feet, which is 220.98 meters.

The acceleration is 9.81m/\(s^{2}\) since that is the acceleration of Earth's gravity, aka free fall.

Time is what we are trying to find so just leave it as the variable t.

So plug the values into the equation:

220.98m = (0)(t) + \(\frac{1}{2}\) (9.81m/\(s^{2}\))(t)

220.98m = (4.905m/\(s^{2}\))(t)

45.0519877676s = t

t = 45.05s

Remember to pay attention to units because your answer will be wrong otherwise

Answer:

15,240,960 numbers

Step-by-step explanation:

To solve this were going to use the principle of permutations. The formula for permutation is given as

P = n! / (n - r)!

Now, the question specifically stated that repeats aren't tolerated, thus for the needed number of serial numbers would be gotten by multiplying the permutation is 4 and 9, by that of the permutation of 4 and 10.

We then have something that is looking like this

Permutation of 4 and 9.

P = 9! / (9 - 4)!

P = 9! / 5!

P = 362,880 / 120

P = 3,024

Permutation of 4 and 10

P = 10! / (10 - 4)!

P = 10! / 6!

P = 3,628,800 / 720

P = 5,040

Multiplying both together would then fetch us our final answer

N = 5,040 * 3,024

N = 15,240,960

Answer:

Surface area: 250

Volume: 1375

Step-by-step explanation:

Scale factor: 4:5

This means that the dimensions of the larger figure are 5/4 of those in the smaller figure.

Surface area:

The surface area is found multiplying the square of the change(5/4) by the original surface area(160). So

\(S = (\frac{5}{4})^2 \times 160 = \frac{25}{16} \times 160 = 25 \times 10 = 250\)

Volume:

The volume is found multiplying the cube of the change(5/4) by the original volume(704). So

\(S = (\frac{5}{4})^3 \times 704 = \frac{125}{64} \times 704 = 125 \times 11 = 1375\)

Answer:

a = 21°

b = 70°

c = 89°

Step-by-step explanation:

a = 21° as vertically opposite angles are equal

to work out b:

angles on a straight line add up to 180

b + 110 = 180

b = 180 - 110

b = 70°

to work out c:

the sum of angles in a triangle add up to 180

we have a and b

21 + 70 + c = 180

91 + c = 180

c = 180 - 91

c = 89°

Answer: 375

Step-by-step explanation:

Ruling out each number:

6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.

3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.

2 & 4 & 8: Is proven wrong in the 4th clue.

7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.

1: Is proven wrong after 7 is proven true.

Figuring out placement:

5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.

3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.

7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

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Answer:

Volume = 27 cubic units

Step-by-step explanation:

First, the formula of volume is l x h x w.

Second, the l, h, and w, are all 3, so to get your answer you do 3 x 3 x 3 which equals 27.

Hope this helps!

Answer:

x = 4

Step-by-step explanation:

i. 8x + 1 = 7x + 5

ii. 8x - 7x = 5 - 1

iii. x = 4

Plotting the inequalities using online graphing calculator. The graph is attached.

What is the example of inequality?

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12   (1)

2x + y < -5    (2)

Plotting the inequalities using  online graphing calculator. The graph is attached.

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Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

Answer:

3

Explanation:

Given;

To be able to determine the quotient of the above, we have to introduce the multiplication sign and invert the second fraction as seen below;

The probability that Jessica picks a yellow pencil is 80%.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It is stated as a number ranging from 0 to 1, or as a percentage ranging from 0% to 100%, where 0 indicates an impossible occurrence and 1 (or 100%) represents a certain event.

Now,

The probability of picking a yellow pencil =  the number of yellow pencils / total number of pencils:

Probability of picking a yellow pencil = Number of yellow pencils / Total number of pencils

In this case, there are 8 yellow pencils out of a total of 10 pencils:

Probability of picking a yellow pencil = 8 / 10

Simplifying the fraction by dividing both the numerator and denominator by 2, we get:

Probability of picking a yellow pencil = 4 / 5

Probability of picking a yellow pencil = 4 / 5 x 100%

Probability of picking a yellow pencil = 80%

Therefore, the probability that Jessica picks a yellow pencil is 80%.

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Answer:

20months

Step-by-step explanation:

$580/ $29 = 20months