The graph shows the distance y, in centimeters, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x.

What is the pendulum's maximum displacement?

the answer is the second one

Answer:

The answer is b!!

Answer:

15/8.

Step-by-step explanation:

Tan A = opposite / adjacent side

= 15/8.

The value of tan A is 15/8.

Given: Right angled triangle

AB = 8

AC = 17

BC = 15

We have to find tan A.

We know,

tan A = Opposite side / Adjacent side

In the given right angle triangle:

Opposite side = BC

Adjacent side = AB

⇒ tan A = BC/AB

⇒ tan A = 15/8

Therefore, the value of tan A is 15/8.

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B, C, and D is the answer

This question most likely pertains to a mathematical figure or diagram. The student is asked to identify true statements applying to the figure, which might illustrate a problem-solving process or the form of a disjunctive syllogism. Without the actual figure, a more detailed analysis isn't possible.

Without having the actual figure to analyze it's difficult to state definitively, but from the context provided, it sounds like this could be a diagram or figure related to problem-solving in mathematics. Figures are often used in mathematics to illustrate complex concepts and provide visual representation to support understanding. It seems like the figure might be used to demonstrate the process of solving mathematical problems or possibly, the process of argumentation using a disjunctive syllogism. Based on this information, the student may have to identify true statements about the figure in question. Potential statements could relate to the type of problem the figure represents, the process it illustrates, or specific features or attributes depicted in the figure itself.

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Answer:

[tex]\boxed{\text{Min = 400; Max = 960}}[/tex]

Step-by-step explanation:

F = 8x + 5y

At (0, 100):  F = 8×0    + 5×100 =     0 + 500 = 500

At (0, 80):   F = 8×0    + 5×80   =     0 + 400 = 400 — MINIMUM

At (80, 60): F = 8×80  + 5×60  = 640 + 300 = 940

At (80, 0):   F = 8×80  + 5×0    = 640  +     0 = 640

At (120, 0):  F = 8×120 + 5×0   = 960  +     0 = 960 — MAXIMUM

The minimum value is [tex]\boxed{ 400}[/tex]and the maximum value is [tex]\boxed{ \text{ 960}}[/tex].

Answer:
Minimum; 400
Maximum; 960

☆

EDGE2022; Good Luck :D

The compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.

If n is the number of times the interest is compounded each year and r is the yearly rate of compound interest, the final amount after 't' years is:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

The function b(x) is expressed as follows:

[tex]\rm b(x) = 33741(1+\frac{0.028}{1} )^x\\\\[/tex]

Where ;

Rate(r)=2.8 percent

Total after x years(b)

Initial amount ( P)= 33741

x represents the number of years since 2015.

Hence, the compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.

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Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as[tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right][/tex]

A= [tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] [/tex]

X= [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex]

B= [tex] \left[\begin{array}{c}3\\7\end{array}\right][/tex]

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

                                    = (-24)-(-27)

                                    = (-24) + 27 = 3

so, |A| = 3

Adj A=  [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex]

A⁻¹ =  [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex]/3

A⁻¹ =  [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] [/tex]

X= A⁻¹ B

X=  [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right][/tex]

X= [tex]\left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right][/tex]

X= [tex]\left[\begin{array}{c}-4+21\\-3+14\end{array}\right][/tex]

X= [tex]\left[\begin{array}{c}17\\11\end{array}\right][/tex]

x= 17, y= 11

solution set= (17,11).

Answer:

a. (17,11)

Step-by-step explanation:

The given system is ;

[tex]6x-9y=3[/tex]

[tex]3x-4y=7[/tex]

The augmented matrices is

[tex]\left[\begin{array}{ccc}6&-9&|3\\3&-4&|7\end{array}\right][/tex]

Divide Row 1 by 6

[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\3&-4&|7\end{array}\right][/tex]

Subtract 3 times Row 1 from Row 2

[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&\frac{1}{2}&|\frac{11}{2}\end{array}\right][/tex]

Divide Row 2 by [tex]\frac{1}{2}[/tex]

[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&1}&|11\end{array}\right][/tex]

Add [tex]\frac{3}{2}[/tex] times Row 2 to Row 1

[tex]\left[\begin{array}{ccc}1&0&|17\\0&1}&|11\end{array}\right][/tex]

Hence the solution is (17,11)

Answer:

The equation of the circle in standard form is: (x - 2)² + (y - 4)² = 9

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- If the center of the circle is point (h , v) and the radius of the

 circle is r, then the standard form of the equation of the circle

 is (x - h)² + (y - v)² = r²

- (x , y) a general point on the circle

* Lets look to the picture

- The center of the circle is point (2 , 4)

- The highest point on the circle is (2 , 7) and the lowest point

 on the circle is (2 , 1)

∴ The diameter of the circle = 7 - 1 = 6

∵ The radius = 1/2 the diameter

∴ The radius of the circle = 1/2 × 6 = 3

* Now we can write the equation of the circle

∵ h = 2 and v = 4

∵ r = 3

∴ (x - 2)² + (y - 4)² = 3²

∴ The equation of the circle in standard form is:

   (x - 2)² + (y - 4)² = 9

Answer:

1 9

2 11

3 13

4 15.

Step-by-step explanation:

When x = 1 y = 2(1) + 7 = 9.

x = 2, y = 2(2)+7 = 11

x = 3, y = 2(3) + 7 = 13

x = 4, y = 2(4) + 7 = 15.

Answer:

$20

Step-by-step explanation:

4×5=$20

this is random do not look

For this case we will indicate expressions equivalent to 6 ^ {16}:

We can write the following:

[tex]6 ^ {16} = 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6\\6 ^ {16} = (6 ^ 8) ^ 2\\6 ^ {16} = 6 ^ {\frac {32} {2}}[/tex]

Answer:

The equivalent expressions are shown in the previous part.

Answer:

Step-by-step explanation:

You can think of an inverse function as a function that “unwraps” x from whatever operations are attached to it. In the case of F(x) = √x, we can ”unwrap” x by squaring it. This narrows our options down to either A or D. Keep in mind that since there are no real number solutions to the square root of a negative number, we need to limit our domain to non-negative values. In other words, x ≥ 0. With that restriction, our answer is A.

The answer is:

The inverse of the given function is:

A. [tex]f(x)^{-1}=x^{2}[/tex]

Where,

[tex]x\geq 0[/tex]

Inversing a function involves inversing the function variables. If we want to inverse a function, we need to rewrite the variable "x" with "y" and rewrite the variable "y" with "x", and then, isolate the variable "y".

Also, the domain of the original function will be the range of its inverse function, and the range of the original function, will be the domain of the its inverse function.

We are given the function:

[tex]f(x)=\sqrt{x}[/tex]

[tex]f(x)=y=\sqrt{x}[/tex]

So, inversing we have:

[tex]y=\sqrt{x}[/tex]

[tex]x=\sqrt{y}[/tex]

[tex](x)^{2}=(\sqrt{y})^{2}\\\\x^{2}=(y^{\frac{1}{2}})^{2}\\\\x^{2}=y^{\frac{2}{2} }\\\\x^{2}=y[/tex]

So, we have that the given function is only "part" of its inverse function, since negative square roots does not exist, it means that the domain of the given function starts from the number 0 taking only positive numbers.

Hence, we have that the answer is:

A. [tex]F(x)=x^{2}[/tex]

Where,

[tex]x\geq 0[/tex]

Have a nice day!

Answer:

  82

Step-by-step explanation:

The sum resolves to ...

  13 + 18 + 23 + 28 = 82

_____

for n=2, the term is 5·2 +3 = 10+3 = 13

The coefficient of n is 5, so you know the next term will be 5 more than this:

for n=3, the term is 5·3 +3 = 15+3 = 18

Additional terms are each 5 more than the one before. Since there are so few terms, you can add them up directly as quickly as you can use any other formula. For a longer series, you might find the average term (here, 41/2), then multiply by the number of terms (here, 4). The result is the sum of the series:

  4·(41/2) = 82

Answer:

  c.  5, 8, 17, 44

Step-by-step explanation:

Put the given number into the formula and do the arithmetic:

  3·4 -7 = 5 . . . . . matches answer choice C only

___

You know the correct answer at this point. You can check the other numbers if you wish:

  3·5 -7 = 8

  3·8 -7 = 17

  3·17 -7 = 44

Answer:

It is a right triangle.

Step-by-step explanation:

By the  Inverse Pythagoras Theorem if 39^2 = 36^2 + 15^2  then it is a right triangle.

39^2 = 1521

36^2 + 15^2 = 1296 + 225 = 1521.

So it is a right triangle.

Based on the converse of the Pythagorean Theorem, the triangle with the following side lengths is a right triangle.

What is the Converse of the Pythagorean Theorem?

The converse of the Pythagorean Theorem states that a triangle is a right triangle if the sum of the squares of two of its legs are equal to the square of the length of the longest side (hypotenuse).

The longest side in the triangle is 39 in. Therefore:

39² = 36² + 15²

1,521 = 1,521

Based on this, we can conclude that the triangle given is a right triangle.

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Answer:

[tex]\texttt{Probability that the first ball will be red and the second will be blue = }\frac{9}{55}[/tex]

Step-by-step explanation:

Total number of balls = 3 + 2 + 6 = 11

Probability is the ratio of number of favorable outcome to total number of outcomes.

[tex]\texttt{Probability that the first ball will be red = }\frac{\texttt{Total number of red balls}}{\texttt{Total number of balls}}\\\\\texttt{Probability that the first ball will be red = }\frac{3}{11}[/tex]

Now we have 10 balls in which 6 are blue.

[tex]\texttt{Probability that the second ball will be blue = }\frac{\texttt{Total number of blue balls}}{\texttt{Total number of balls}}\\\\\texttt{Probability that the first ball will be red = }\frac{6}{10}=\frac{3}{5}[/tex]

[tex]\texttt{Probability that the first ball will be red and the second will be blue = }\frac{3}{11}\times \frac{3}{5}\\\\\texttt{Probability that the first ball will be red and the second will be blue = }\frac{9}{55}[/tex]

Answer:

[tex]\large\boxed{x=7}[/tex]

Step-by-step explanation:

[tex]5^{x+2}=5^9\iff x+2=9\qquad\text{subtract 2 from both sides}\\\\x+2-2=9-2\\\\x=7[/tex]

The value of x if 5ˣ⁺²=5⁹ is 7. Therefore, the correct answer is option C.

The given equation is 5ˣ⁺²=5⁹.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

We know that, when the bases are equal their exponents are equal.

x+2=9

x=9-2

x=7

Therefore, the correct answer is option C.

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Independent, means the first event won't affect the second event.

The independent events would be :

A, B, E, F

I think it's C. Trout increased its predicted average population.

Answer:

b

Step-by-step explanation:

because it increases the most

The cost of 11 laptops is 11c

Using the parameters given :

The expresssion to determine the cost is :

Now we have;

33 = 30000

11 = c

cross multiply

33c = 330000

c = 10000

The cost of 11 laptops : 11*c

Answer:

A, B, C

Step-by-step explanation:

Answer:

"a period change"

Step-by-step explanation:

Simple ways of understanding transformations are:

Phase shift: 2 graphs would be shifted version of each other, all other things constant.

Period change: the 2 graphs would have different cycles, one would be compressed/stretched version of the other, all other things constant

Amplitude Change: The height/crest of the graphs would vary, that is the amplitude. All other things constant.

Addition of Negative constant: this would shift the 1 graph downwards with respect to the other graph, it is a vertical shift. All other things constant.

Now carefully looking at the 2 graphs given, we can see that the cycles are different. One is a more "relaxed", or "stretched" version of the other. This means, the period is changed.

2nd answer choice is right.

Answer: try question cove but brainly is good so keep using it

]

Answer:

  152 in³

Step-by-step explanation:

Each cube's volume is the cube of its edge length, so the total volume is ...

  (5 in)³ + (3 in)³ = 125 in³ +27 in³ = 152 in³

Multiply corresponding components, then add the products:

[tex]v\cdot w=3(-4)+(-8)(-2)+(-3)(-6)=22[/tex]

The resultant of the dot product of two vectors is:

                     [tex]v\cdot w=22[/tex]

We are asked to find the dot product of the two vectors v and w.

The vectors are given by:

r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>

This means that  in the vector form they could be written as follows:

[tex]r=8\hat i+8\hat j -6\hat k\\\\v=3\hat i-8\hat j -3\hat k\\\\w=-4\hat i-2\hat j -6\hat k[/tex]

Hence, the dot product of two vectors is the sum of the product of the entries corresponding to each direction component.

i.e. the x-component get multiplied to each other, y-component get multiplied to each other and so happens with z.

Hence, the dot product of v and w is calculated as:

[tex]v\cdot w=3\times (-4)-8\times (-2)-3\times (-6)\\\\i.e.\\\\v\cdot w=-12+16+18\\\\i.e.\\\\v\cdot w=22[/tex]

Answer:

Step-by-step explanation:

105 years old. Since if he 35 the mother is 105>>------->(35 x 3= 105)

85 years old. 25•3=75 the difference between 75 and 25 is 50, which means she is 50 years older than him. 35+50=85.

Answer:

The volume is equal to [tex]112\frac{1}{2}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

we have

[tex]L=4\frac{1}{2}\ cm=\frac{4*2+1}{2}=\frac{9}{2}\ cm[/tex]

[tex]W=5\ cm[/tex]

[tex]H=5\ cm[/tex]

substitute the values

[tex]V=(\frac{9}{2})(5)(5)[/tex]

[tex]V=112.5\ cm^{3}[/tex]

Convert to mixed number

[tex]112.5\ cm^{3}=112\frac{1}{2}\ cm^{3}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

54.5 amps to the nearest tenth.

Step-by-step explanation:

V = IR  where V = volts, I = current and R = resistance.

12 = I * 0.22

I = 12/0.22

I = 54.5 Amps.

When the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.

The question regarding how many amps will be drawn from the 12-volt battery when a car engine with a resistance of 0.22 ohms is started can be solved using Ohm's Law. Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. The formula is given by I = V / R.

Therefore, the current drawn from the battery can be calculated as follows:

So, when the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.

Answer:

The side length of the original patio was [tex]12\ ft[/tex]

Step-by-step explanation:

Let

x----> the side length of the original square patio

we know that

[tex]441=(x+9)^{2}\\ \\x^{2} +18x+81=441\\ \\ x^{2} +18x- 360=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=12\ ft[/tex]

see the attached figure

Answer:

for study island it is 11 feet

Step-by-step explanation:

let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.

[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}[/tex]

now let's check for the asymptotes.

[tex]\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2[/tex]

Answer:

A

Step-by-step explanation:

We can use a simple formula to solve for SST. The formula is:

[tex]SST=\frac{SSE}{1-R^2}[/tex]

Where

the coefficient of determination is  [tex]R^2[/tex]

Now, we are given  [tex]R^2[/tex]  is 0.25 and SSE is 12 (not SEA, it's SSE). we simply put it into the formula and solve for SST:

[tex]\\SST=\frac{12}{1-0.25}\\SST =16[/tex]

correct answer choice is A