What reason can be used to prove that the triangles are congruent?
A. ASA
B. AAS
C. SAS
D. SSS

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The height equation is:

h(t) = 25*(5/8)^n

And the height after the 8th bounce is 0.582 yards.

We know that the ball returns to 5/8 of its height each time it bounces, so if the initial height is H, then the height after n bounces will be a simple exponential equation:

h(t) = H*(5/8)^n

And here the initial height is 25 yards, then the exponential equation is:

h(t) = 25*(5/8)^n

Now that we have the equation, we can seethat the height after 8 bounces is:

h(8) = 25*(5/8)^8 = 0.582

The height is 0.582 yards.

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Answer:

4275

Step-by-step explanation:

You have to do 95 * 45

The way I do this would be, 95 is close to 100, and doing 100 * 45 is much easier than 95 * 45.

100 * 45 is 4500 but ofc that isn't the answer, since we are using 100 and not 95 we have to subtract 5 * 45 which is also a fairly simple equation to solve

5*45 is 225, so what we have to do now is take our 4500 and subtract our 225

4500 - 225 = 4275

Answer:

4,275

Step-by-step explanation:

Give 95 people for each game.

there is only one easy step, you multiply:

\(95*45=4275\)

hope this helped!
Brainliest Please!

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

Ximena can use 1 gigabytes of data

Step-by-step explanation:

The first thing you want to do is subtract

51.10 - 44.50 =  5.6

5.6 is the amount of money she will have to spend on data

With each gigabyte costing 4 dollars and only 5 dollars to spend

she can only use one gigabyte

9514 1404 393

Answer:

  it is less expensive to purchase a new car

Step-by-step explanation:

The expected cost of gas, insurance, and repairs for the old car are ...

  Total miles in 5 years = (325 mi/wk)(52 wk/yr)(5 yr) = 84,500 mi

Old car

  Gas cost in 5 years = (84,500 mi)/(14 mi/gal)($3.50/gal) = $21,125

  Insurance cost in 5 years = (5 yr)($600/yr) = $3,000

  Repair cost in 5 years = ($1500/yr)(5 yr) = $7,500

  Total operating cost in 5 years = $21125 +3000 +7500 = $31,625

__

New Car

  Gas cost in 5 years = (84,500 mi)/(47 mi/gal)($3.50/gal) ≈ $6,293

  Insurance cost in 5 years = (5 yr)($1000/yr) = $5,000

  Repair cost in 5 years = (0)(5 yr) = 0

  Total operating cost in 5 years = $6293 +5000 = 11,293

__

Difference in operating costs is $31,625 -11,293 = $20,332.

It is less expensive to purchase a new car for any price less than $20,300. If the new car costs only $16,000, it is the less-expensive option.

Purchase of a new car is the least-expensive option.

__

Additional comments

The cost of financing, annual license fees, and resale value of the new car may also come into play. In addition, the relative non-economic values of consumption of new materials, adding old materials to the scrap heap, and environmental pollution may figure in the decision. While the car dealer may pay for maintenance costs of a new car, it seems likely that at least one set of tires will be required in 5 years (85000 miles). (Assuming wheel alignment is not an issue for tire wear, that cost may balance out for the two cars.)

Answer:

5 km/h

Step-by-step explanation:

Average speed = total distance/total time

total distance = 5 + 5 = 10 km

total time = 45 + 25 + 50 = 120 min = 2 hours

so average speed = 10/2 km/h = 5 km/h

Answer:

c

Step-by-step explanation:

Answer:

2/3 x 1/5 is your answer.

Step-by-step explanation:

because if you count all the blocks in total then you get 18, if you look at the way they shaded the blocks and the order they shaded them then you'll see that the two purple blocks are facing down, and the blue one is below, which show that they where whole but split and so what we make of that is that whole three line so we count that row so it will give us 2 which would be the purple color and we put 3 which was the whole until it was shaded with blue, continuing on, we look at the pink blocks, which look like they don't make much since since they are a number that is not one of the answers, and yes your right! its just their as a distraction, what you should be looking at is whats below, if you look at the white and that blue block and you count that across, you've counted 5 which is and answer in the work, next you'll look at the blue block and as it show, yes, its shaded as 1 so what we do is look work 1/5 and boom theirs your answer! and if you don't think its right you can always multiply the 2/3 x 1/5 and your answer will be 18 which is the number of blocks in total

Answer:

100.

Step-by-step explanation:

By proportion the number of apples sold  is (6/4) * 40

= 6 *10

= 60.

Total fruit = 40 + 60 = 100.

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad \qquad \stackrel{slope}{m}\implies 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{5}(x-\stackrel{x_1}{(-2)})\implies y-4=5(x+2)\)

Answer:

x is 600 and y is 128:

so the answer is 472!

Answer:

Which one or do you mean something way different.

Quotient of 8 + 7 = 15

Quotient of 8 + ? + 7 = ??

What is the missing number?

If its wrong I hope you know I tried!

Thanks, 0Drink0Milk0

Answer:

324

Step-by-step explanation:

Answer:

0.159

Step-by-step explanation:

Given that:

Sample size (n) = 100

Population mean(pm) = 50

Standard deviation (s) = 8

Probability that Sample mean (m) will be greater Than 50.8

Using the relation :

(sample mean - population mean) / (standard deviation /sqrt(n))

P(m > 50.8)

Z = (50.8 - 50) / (8/ sqrt(100))

Z = 0.8 / (8/ 10)

Z = 0.8 / 0.8

Z = 1

P(Z > 1) = 0.15866 ( Z probability calculator)

Hence,

P(Z > 1) = 0.159 ( 3 decimal places)

The probability that a sample mean will be greater than 50.8 is P(Z > 1) = 0.159.

Given that,

Suppose that a random sample of size 100 is to be selected from a population with a mean of 50 and a standard deviation of 8.

We have to determine,

What is the probability that a sample mean will be greater than 50.8?

According to the question,

Sample size (n) = 100

Population mean(pm) = 50

Standard deviation (s) = 8

The probability that Sample mean (m) will be greater than 50.8.

Therefore,

\(\dfrac{(sample \ mean - population \ mean) \times \sqrt{n}}{standard \ deviation}\)

Where P(m > 50.8)

\(Z = \dfrac{50.8 - 50 \times \sqrt{100}}{8}\\\\Z =\dfrac{ 0.8 \times 10 }{8}\\\\Z = \dfrac{0.8 }{0.8}\\\\Z = 1\)

P(Z > 1) = 0.15866 ( Z probability calculator)

Hence,  The probability that a sample mean will be greater than 50.8 is P(Z > 1) = 0.159.

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Answer:

1/2(-1.4m+0.4)=-0.7m+0.2

Answer: The one that starts with (-4,10)

Step-by-step explanation:

Linear means that the numbers are going up at a constant rate. It means, that the y will go up corrosponding x.

1) Linear

X goes up 2 per 4 y

2)  Linear

X goes up 1 per 3y

3)  Linear

X goes up 2 per 4y

4) Not Linear

X goes up 2 per Unequal growth y.

You can tell because it goes up by +5 until the last where it goes up +7

We are given a quadratic function and the rather than the equation for this function we already have the outputs at each given input as shown in the table provided. This means, for example, for the function given, when the input is -10, the output is 184. Thus the table includes among other values;

To calculate the average rate of change we shall apply the formula for the slope (which is also the average rate of change). This is given below;

Note that the variables are;

The first input value is -10 and the function at that value is 184

The second input value is 0 and the function at that value is -6

We now have;

We can now substitute these into the formula shown nearlier and we'll have;

ANSWER:

The average rate of change over the given interval is -19

Answer:

a.8

Step-by-step explanation:

y=-16

-16=-2x

16=2x

x=16/2=8

Answer:

A

Step-by-step explanation:

330 m/s=330×60 m/min=19800/1000 km/min=198 km/min=1.98×10^1 km/min

Answer:

Step-by-step explanation:

The expression 2x - 11x - 6 can be simplified as follows:

2x - 11x - 6 = -9x - 6

So, the equivalent expression is -9x - 6.

The answer is:

-9x - 6

Work/explanation:

To simplify this expression, we combine the like terms :

\(\huge\text{2x - 11x - 6} \\ \\ \\ \text{-9x - 6}\)

There's nothing that we can do for this expression. It's been simplified as much as possible.

Answer:

\(y < 3x - 4\)

Step-by-step explanation:

We can tell right away, that the line has a positive slope, since it goes upwards and to the right. To find the slope exactly, we will use rise/run. We will count the units from the first given point until we reach the next point.

So we can tell that the slope is 3/1 or just 3.

Also, since the line crosses the y-axis at -4, this will be the y-intercept.

Next, since the line is dotted, we know that the inequality sign will either be the "greater than" sign, or the "lesser than" sign. In this case, since the shaded area is below the line, we will use the "lesser than" sign.

So all together, we have y < 3x - 4.

Hope this helps you :)

Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

The formula used to calculate the variance of a set of data is Variance = \(s^2\)=1n−1n∑i=1(xi−¯x\()^2\).(Option-A)

To calculate the variance, each data point is subtracted from the mean, squared, and then added together. This gives the sum of the squared deviations from the mean. This sum is then divided by the total number of data points to get the average squared deviation from the mean, which is the variance.

Variance is a measure of the spread or variability of a set of data. It is useful in statistical analysis to understand how much the data points differ from the mean, and to compare different sets of data. Lower variance values indicate that the data is more tightly clustered around the mean, while higher variance values indicate that the data is more spread out.(option-A)

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A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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The moment of inertia for rotation about the z axis is  \(I & =\frac{a^2 M}{3}\).

A triangular prism of mass m, whose two ends are equilateral triangles.

Two ends are equal.

The xy plane with side 2a, is centered on the origin with its axis along the z axis.

Find the moment of inertia for rotation the z-axis.

It is divide into 4 triangles with side 'a' k one side is 3cm.

\($$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$\)

It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.

Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.

\($$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$\)

\($$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$\)

⇒ Now, by using the \($I_{\text {Big }}=I$\)

⇒\(I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\\)

⇒\(4 I & =I+a^2 m\)

⇒\(4 I-I & =a^2 m \\\)

⇒\(3 I & =a^2 M . \\\)

⇒\(I \quad & =\frac{a^2 M}{3}\)

Therefore, the moment of inertia is \(I & =\frac{a^2 M}{3}\).

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Answer:

x

Step-by-step explanation:

We need to solve this equation by graphing. We need to find what roots will make our equation equal zero. This is the same as drawing a line

\(y = 0\)

and see what points intercepts both graphs.

According to the graph above, one root are between 0 and 0.5 and the other are between 4 and 4.5.

We can find it actual value by solving it

\( - 1 + \frac{9}{2} x - {x}^{2} = 0\)

\( - {x}^{2} + \frac{9}{2} x - 1 = 0\)

Apply Quadratic Formula, we get

\( \frac{9 + \sqrt{65} }{4} \)

and

\( \frac{9 - \sqrt{65} }{4} \)

Which gives us approximately

x=4.27 and 0.23

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

You have a graph of the function ...

  y = 3 +4x -x^2

You want to find solutions to the equation ...

  0 = -1 +9/2x -x^2

This second equation can be made equivalent to ...

  3 +4x -x^2 = p

for some suitable function p.

We can find that function using the relation ...

  (3 +4x -x^2) -p = 0 = -1 +9/2x -x^2

Solving for p, we get ...

  (3 +4x -x^2) -(-1 +9/2x -x^2) = p

  3 +4x -x^2 +1 -9/2x +x^2 = p . . . . . . . eliminate parentheses

  4 -1/2x = p . . . . . . . . . . . . . . . . . . simplify

The line we want is ...

  p = -1/2x +4 . . . . . . . line with y-intercept 4 and slope -1/2

Where this line crosses the graph you have, the x-coordinates are the solutions of the equation -1 +9/2x -x^2 = 0.

Answer: the average rate of f(x) from x=-6 to x=6 is 12.

Step-by-step explanation:

-6+6=0

-6+12=6

Hope this helps :)