Comparati numerele urmatoare, aducand mai intai puterile la aceeasi baza
a) 5 la puterea 87 si 25 la puterea 36

This is a transformation of the parent square root function, and it can be written as:

f(x) = √(-x + 4) - 2

It is ratter easy to identify the shape of the general square root function:

f(x) = √x

The only difference is that now it opens to the left, and it starts at the point (4, -2)

Then:

The sign of the x must be negative.

And with the known vertex we can write the equation:

f(x) = √(-x + 4) - 2

That is the graphed function.

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The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.

Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.

Simplifying this, we get 2x - 80 = $670  + 80 2x = $750  x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.

The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.

The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.

Therefore, the cost of the bench is $375, and the cost of the garden table is $295.

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Answer:

4 2/3

Step-by-step explanation:

From the given expression, it is found that:

a) When x = 7 and y = 11, the numeric values are given as follows:

b) They will only have the same numeric value when x = y.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.

The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.

In the context of this problem, the expressions are given as follows:

When x = 7 and y = 11, the numeric values are given as follows:

The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.

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Answer:

h = 1,268 cm

Step-by-step explanation:

                   V = (π·r²·h)/3, general formula

                 83 = (π·4²·h)/3, substitute what is given V= 83 cm³ and r = 4 cm

             83 ·3 = (π· 16·h)·3/3, multiply both sides by 3 and solve 4² = 16

               249 = π·16·h, multiply 83·3 = 249 and 3/3 = 1

      249/ π·16 = h , divide both sides by π·16

1,268.146587 = h, solve

             1,268 ≈ h , is rounded to the nearest cm

\( = 4 - 4 \: log_{5}(10) - 4 log_{2}(10) + 4 log_{2}(10) log_{5}(10) \\ \\ or \: \\ \\ = 4\)

the answer is 2

see the attachment for explanation

Answer:

Answer is 2). 4

Explanation:

\({ \rm{(2 - log_{ \sqrt{2} }10)(2 - log_{ \sqrt{5} }10)}}\)

• let's open the brackets:

\({ \rm{(2 \times 2) + (2 \times - log_{ \sqrt{5} }10 ) + (2 \times - log_{ \sqrt{2} }10) + ( log_{ \sqrt{2} }10 \times log_{ \sqrt{5} }10) }} \\ \\ = { \rm{4 - 2 log_{ \sqrt{5} }10 - 2 log_{ \sqrt{2} }10 + ( log_{ \sqrt{5} }10)( log_{ \sqrt{2} }10)}}\)

• change log√5 to log√2:

\({ \rm{4 - 2 log_{ \sqrt{2} }10 - (\frac{2 log_{ \sqrt{2} }10 }{ log_{ \sqrt{2} } \sqrt{5} } ) + ( log_{ \sqrt{2} }10)( \frac{ log_{ \sqrt{2} }10 }{ log_{ \sqrt{2} } \sqrt{5} } )}} \\ \\ = { \rm{4 - 2 log_{ \sqrt{2} }10 - ( \frac{4 log_{ \sqrt{2} }10}{ log_{ \sqrt{2} } \sqrt{5} }) }} \\ \\ = { \rm{4 - 2 log_{ \sqrt{2} }10 - ( \frac{8 log_{ \sqrt{2} }(5 \times 2) }{ log_{ \sqrt{2} }5} )}} \\ \\ = { \rm{4 - 2 log_{ \sqrt{2} }(5 \times 2) - \frac{8 log_{ \sqrt{2} }2}{ log_{ \sqrt{2} }5 } }} \)

• now let's change log√2 to log10

\( = { \rm{4 - \frac{2 log_{10}10}{ log_{10} \sqrt{2} } - \frac{8 log_{10}2}{ log_{10} \sqrt{2} } \div \frac{ log_{10}5 }{ log_{10} \sqrt{2} } }} \\ \\ = { \rm{4 - \frac{2}{0.3} - \frac{2.41}{0.3} \times \frac{0.3}{0.7} }} \\ \\ = { \rm{4 + \frac{41}{70} }} \\ \\ { \rm{ = 4 \frac{41}{70} \: \approx \: 4 }}\)

The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

-2(x + y) = -2(1) --

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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Answer:

negative 2 is bigger

............. .

Answer:

-5 is less than -2 it's mean that -2 is bigger.

Step-by-step explanation:

Answer: 21.15 ft²

Step-by-step explanation:

We can use the formula for the area of a triangle:

(b×h)/2

In this case, the base is 9 and the height is 4.7.

So, we substitute the variables with the numbers in this problem.

(9 × 4.7)/2

9 × 4.7 = 42.3

42.3/2 = 21.15

So, our final answer is 21.15 ft²

Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12

Answer:

C

Step-by-step explanation:

 2

+2

-----

 4

Let's find the seconds as an improper fraction:

He ran 100 meters in 48/5 seconds or 9.6 seconds. To find the speed in meters per second we have to divide the distance (in meters) by the time (in seconds):

The average speed is 125/12 m/s (or 10.42 m/s, rounded to the nearest hundredth)

In mixed numbers the speed is 10 5/12 m/s

Answer: below i've attached a file that you view  for ---> 4x-3y=1 and 3y=x-1 using  the  substitution method  (please let me know if you can see it ..you might need to zoom in )

Step-by-step explanation:

The percentage of data items that lie below the z-score of 3 is 99.87%.

In a normal distribution, the z-score represents the number of standard deviations a particular data point is away from the mean. The table provided gives the percentiles corresponding to different z-scores.

To find the percentage of data items that lie below a z-score of 3, we can look up the corresponding percentile in the table. In this case, the percentile for a z-score of 3 is given as 99.87%.

This means that approximately 99.87% of the data items in a normal distribution are below a z-score of 3.

Similarly, to find the percentage of data items that lie above a z-score of 3, we can subtract the percentage below the z-score from 100%. In this case, it would be 100% - 99.87% = 0.13%.

This means that approximately 0.13% of the data items in a normal distribution are above a z-score of 3.

Thus, these percentages indicate the relative position of the data points within the distribution. It provides a measure of how extreme or rare a particular value is in comparison to the rest of the distribution.

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The number of times that Greg is on time to class is 4

The given parameters are:

Probability that Greg is on time, p = 14%

The sample size, n = 30

The estimate of the number of times that Greg is on time to class is

E(x) = np

Substitute the known values in the above equation

E(x) = 30 * 13%

Evaluate the product

E(x) = 3.9

Approximate

E(x) = 4

Hence, the number of times that Greg is on time to class is 4

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Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

The question is an example of a ratio problem. This implies that

Therefore, le the number of domestic vehicles be x. We can say that;

Answer: 1458

Answer:

1350 km yw!

Step-by-step explanation:

Answer:

B and C

Just see if there is any number that can divide both top and bottom

If there isnt, its in simplest form

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

Answer:

Can you give a picture of what we are answering

Step-by-step explanation:

Answer:

Using the Empirical Rule, we find that .997 (99.7%) of students have grade point averages that are between 1.23 and 3.81.

Step-by-step explanation:

Calculate the z-scores corresponding to a GPA of 1.23 and 3.81.

We want to find the area between the z-scores of -3 and 3.

The Empirical Rule tells us that 99.7% of the data lies within three standard deviations under the normal curve.

Therefore, the area between -3 < z < 3 is about .997, or around 99.7%.

Answer:

88.9%

Step-by-step explanation: