Find the Inverse f(x) = 5x3+ 5 1-6 f(x) = 10x 3 - 6 f(x) = 3x - 11 (x) = 2+1 f(x) = log2 (x+1) - 3 $(1) 5x $(x) =5/*+1 f(x) =(x + 2)2-5

\(( {t + 8})^{3} = {t}^{3} + 3 \times ({t})^{2} \times( 8) + 3 \times (t) \times ( {8})^{2} + {8}^{3} \\ \)

So :

\( ({t + 8})^{3} = {t}^{3} + 24 {t}^{2} + 192t + 512\)

Answer:

your answer to this question is 35

The curve passes through the point (3, 3), so \(y=3\) when \(x=3\). Then

\(y = ax^2 + bx \implies 3 = 9a + 3b \implies 3a + b = 1\)

The tangent line to the curve at (3, 3) has gradient \(\frac{dy}{dx}\) at \(x=3\). Compute the derivative.

\(y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b\)

Then when \(x=3\), the gradient is 4, so

\(2ax + b = 4 \implies 6a+b=4\)

Solve for \(a\) and \(b\). Eliminating \(b\), we find

\((6a+b) - (3a+b) = 4-1 \implies 3a = 3 \implies \boxed{a=1}\)

and it follows that

\(3 + b = 1 \implies \boxed{b = -2}\)

Answer:

Below in bold

Step-by-step explanation:

-3(8x - 2) = 9 - 21x

~Divide -3 to everything

8x - 2 = -3 + 7x

~Add 3 to both sides

8x + 1 = 7x

~Subtract 8x to both sides

1 = -x

~Divide -1 to both sides

-1 = x

Note that this isn't the most used way to solve equations because you would typically use distribution to simplify the left side.

Best of Luck!

Below in bold

Step-by-step explanation:

-3(8x - 2) = 9 - 21x

~Divide -3 to everything

8x - 2 = -3 + 7x

~Add 3 to both sides

8x + 1 = 7x

~Subtract 8x to both sides

1 = -x

~Divide -1 to both sides

-1 = x

Note that this isn't the most used way to solve equations because you would typically use distribution to simplify the left side.

Best of Luck!

A p-value less than 0.05 is considered significant because it indicates strong evidence against the null hypothesis.

A p-value is a measure of the strength of evidence against a null hypothesis. It tells you the probability of getting a test statistic as extreme as the one you observed, assuming the null hypothesis is true.

Now, to answer your question, if a p-value is less than an alpha set at 0.05, it is considered significant. This means that there is less than a 5% chance that the observed effect is due to random chance or error.

In other words, the evidence is strong enough to reject the null hypothesis and support the alternative hypothesis.

To better understand this concept, let's consider an example. Suppose we want to test whether a new drug is effective in treating a certain condition.

The null hypothesis is that the drug has no effect, while the alternative hypothesis is that it does have an effect. We conduct a clinical trial with a sample size of 100 patients and find that 60 of them show improvement after taking the drug.

We calculate a p-value of 0.02, which is less than our alpha of 0.05. This means that there is strong evidence to reject the null hypothesis and conclude that the drug is indeed effective.

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Answer:

Infinite solutions

Step-by-step explanation:

4x + 8 = 4x +8

Both sides are exactly the same, so there are infinite solutions.

The radius of the circle with an area of 78.5 cm² is 5 cm.

To solve the equation A = πr² for r, we need to isolate the variable r on one side of the equation. Let's do the calculations:

A = πr²
78.5 = 3.14r²

To solve for r, we need to divide both sides of the equation by π:

78.5/3.14 = r²

Simplifying the left side of the equation gives us:

25 = r²

To find the value of r, we can take the square root of both sides of the equation:

√25 = √(r²)
5 = r

Therefore, the radius of the circle with an area of 78.5 cm² is 5 cm.

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Answer: \(75\ m\)

Step-by-step explanation:

Given

The tower is 45 m high and Clinometer is set at 1.3 m above the ground

From the figure, we can write

\(\Rightarrow \tan 32^{\circ}=\dfrac{43.7}{x}\\\\\Rightarrow x=\dfrac{43.7}{\tan 32^{\circ}}\\\\\Rightarrow x=69.93\ m\)

Similarly, for \(\triangle ACD\)

\(\Rightarrow \tan 47^{\circ}=\dfrac{43.7+y}{x}\\\\\Rightarrow 69.93\times \tan 47^{\circ}=43.7+y\\\\\Rightarrow 74.99=43.7+y\\\Rightarrow y=31.29\ m\)

Height of the tower is \(43.7+31.29\approx 75\ m\)

Answer:

  (m^8)/(2n^4)

Step-by-step explanation:

The relevant laws of indices are ...

__

Simplifying the given expression using these rules gives ...

  \(3\dfrac{112m^{11}n^{-2}}{672m^3n^2}=\dfrac{336}{672}m^{11-3}n^{-2-2}=\boxed{\dfrac{m^8}{2n^4}}\)

A scatterplot that shows the number of hours studied on the x-axis and the number of errors on the y-axis would best support the teacher's observation.

Error in math is an incorrect answer to a mathematical equation or problem. It can be caused by a variety of factors, such as inaccurate calculations, misreading instructions, or not understanding the problem. Error in math can be frustrating and can lead to poor grades, but it can also be an opportunity for learning and growth. With the proper guidance and understanding, students can learn from their mistakes and become better mathematicians.

The scatterplot would likely show a negative correlation, with the number of errors decreasing as the number of hours studied increases. This indicates that as students study more, their performance on multiplication tests improves. It could also show an outlier or two, which could indicate that some students are able to learn multiplication facts more quickly than others.

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Answer:

x = 5

Step-by-step explanation:

4x - 3 = 2x + 7

Add 3 to both sides.

4x = 2x + 10

Subract 2x from both sides.

2x = 10

Divide both by 2.

Final Answer: 5

If you wanted to check your answer, you can plug in 5 from the x's

4(5) - 3 = 2(5) + 7

17 = 17

Answer: X = 5

Step-by-step explanation: The target should be to reduce the equations to having either one term or polynomial on each side, starting with the right side. First, start with subtracting 2x from each side. Then, add three to both sides. Finally, divide both sides. You can also double-check the answer by substituting.

4x - 3 = 2x + 7

2x - 3 = 7 (Subtracted 2x)

2x = 10 (Added 3 to both sides)

10/2 (Divide both sides)

X = 5

4(5) - 3 = 2(5) + 7

17 = 17

Answer:

(2, 11)

Step-by-step explanation:

Answer:

(1, 6)

Step-by-step explanation:

A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Answer:

a)  5.9

b)  4.2

Step-by-step explanation:

Plot the data points on the number line (see attached).

Part (a)

\(\begin{aligned}\textsf{Distance between Ben and Kloee} & = \sf \left| Ben - Kloee \right|\\& = \sf \left|-2.65-3\frac{1}{4}\right|\\& = \sf \left|-2.65-3.25\right|\\& = \sf \left|-5.9\right|\\& = \sf 5.9\end{aligned}\)

Part (b)

\(\begin{aligned}\textsf{Distance between Middle school and Football field} & = \sf \left| Middle\:school-Football\:field\right|\\& = \sf \left| 1.5-5.7\right|\\& = \sf \left| -4.2 \right|\\& = \sf 4.2\end{aligned}\)

Resolviendo las sumas y restas de la expresión podemos ver que:

0.9-8.8+11+2.6 = 5.7

Tenemos un problema que involucra sumas y restas, tenemos que resolver la siguiente expresión:

0.9-8.8+11+2.6

Vamos a hacerlo de izquierda a derecha, lo primero que debemos resolver es:

0.9 - 8.8 = -7.9

reemplazar esto nos da:

-7.9+11+2.6

Lo siguiente que debemos resolver es:

-7.9 +11 = 3.1

Reemplazando eso obtenemos:

3.1 + 2.6 = 5.7

ese es el resultado de la expresion.

Entonces podemos concluir que:

0.9-8.8+11+2.6 = 5.7

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The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

Answer:

slope = 0.5

Step-by-step explanation:

\(slope=\frac{-5-1}{-6-6} =\frac{-6}{-12} =\frac{1}{2} =0.5\)

Hope this helps

The slope of the graph through points (6,1) and (-6,-5) is 0.5.

The slope formula can be expressed as:

\(Slope (m) = \frac{y_2 - y_1}{x_2 - x_1}\)

Given the coordinates of the points through which the graph passes through:

Point 1 ( 6,1 )

x₁ = 6

y₁ = 1

Point 2( -6,-5 )

x₂ = -6

y₂ = -5

Plug the coordinates into the slope formula and simplify.

\(Slope (m) = \frac{y_2 - y_1}{x_2 - x_1}\\\\Slope (m) = \frac{-5 - 1}{-6 - 6}\\\\Slope (m) = \frac{-6}{-12}\\\\Slope (m) = \frac{1}{2}\\\\Slope (m) = 0.5\)

Therefore, the slope of the line is 0.5.

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Interest accrued at the end of the month is $1.41.

Credit cards impose interest on any sums that you don't pay by the due date each month. Interest accrues everyday when you hold a balance from month to month based on the so-called Daily Periodic Rate (DPR). DPR is only another term for your daily interest charge.

Step 1: Make the initial payment of $882 ($1,032 - $150).

Step 2: $882 times 1.00938 is $890.27

Step 3: Pay $1,032 multiplied by 1.00938 ($1,041.68) at the conclusion.

Step 4. $1,041.68 - $150= $891.68

The interest for the first month is $1.41.

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the answer is b, 7/25

Answer:

I think its Fibonacci numbers.

Answer:

29

Step-by-step explanation:

1+3=4, 3+4=7, 7+11=18, so 18+11 = 29

Step-by-step explanation:

Hey there!

From the given figure;

Measure of angle V + measure of angle W = measure of angle VUF {exterior angle is equal to the sum of opposite interior angles}

Therefore, angle VUF= 94°.

Hope it helps!

Answer:

<V + <W = < VUF

94 = < VUF

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

<V + <W = < VUF

71+ 23 = < VUF

94 = < VUF

Answer:3,13

Step-by-step explanation:the price of the bowl is 10$ then you add 3 extra ingredients for a dollar each 10+3=13

Answer:

3,13

Step-by-step explanation:

The power series representation for f(x) = ln(x^4 + 1), centered at 0, is:

f(x) = x^4 - x^8/2 + x^12/3 - x^16/4 + ..

To find a power series representation for the function f(x) = ln(x^4 + 1), we can start by using the logarithmic identity ln(1 + u) = u - (u^2)/2 + (u^3)/3 - (u^4)/4 + ..., valid for |u| < 1.

In this case, have u = x^4, so we can substitute it into the logarithmic identity:

ln(x^4 + 1) = x^4 - (x^4)^2/2 + (x^4)^3/3 - (x^4)^4/4 + ...

Simplifying the terms, we get:

ln(x^4 + 1) = x^4 - x^8/2 + x^12/3 - x^16/4 + ...

Now, we have expressed ln(x^4 + 1) as a power series centered at 0. The coefficients of the series are the coefficients of the powers of x^4: 1, -1/2, 1/3, -1/4, and so on.

Therefore, the power series representation for f(x) = ln(x^4 + 1), centered at 0, is:

f(x) = x^4 - x^8/2 + x^12/3 - x^16/4 + ...

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Vertex Form of a quadratic equation

A quadratic equation has the vertex form:

Where (h,k) is the vertex of the parabola and a is the leading coefficient.

If a is positive, the parabola is concave up, if a is negative, the parabola is concave down.

We'll identify each graph with a number so we can relate them with their corresponding equation.

Graph 1. Has the vertex at (-5,7) and opens up. The equation of this parabola (for a=1) is:

Graph 2 has the vertex at (5,7) and opens up. The equation is:

Graph 3 has the vertex at (5,-7) and opens up. The equation is

Graph 4 has the vertex at (5,-7) and opens down. The equation is

Graph 5 has the vertex at (-5,-7) and opens up. The equation is

Finally, graph 6 has the same vertex as graph 5 and opens up also, but it grows much faster than that one. The difference is that the leading factor is greater than one. This corresponds to the equation

The image below shows the correspondence between the graphs and their equations labeled with numbers.

The probability that your cards are all face cards are,

We know that Total number of cars is 52 .

26 red and 26 is black.

13 are hearts ,

13 are diamonds,

13 are clubs,

13 are spades.

(​a) The first club you get is the third card dealt,

Probability P (first club get is the third card dealt) = P(Non-club x Non club x club)

So,

P = \(\frac{39}{52} * \frac{38}{51} * \frac{13}{50}\)

P = 0.145

(b) Your cards are all black,

\(P_{all are black}\) = \(\frac{26}{52} *\frac{25}{51} *\frac{24}{50}\)

\(P_{all are black}\) = 0.116

(c) You get no hearts,

\(P_{no heart}\) = \(\frac{39}{52} *\frac{38}{51} *\frac{37}{50}\)

\(P_{no heart}\) = 0.413

(d) You have at least one red card,

\(P_{at least one red}\) = 1 - \(P_{no red}\)

\(P_{no red}\) = \(\frac{26}{52} *\frac{25}{51} *\frac{24}{50}\)

\(P_{no red}\) = 0.116

\(P_{at least one red}\) = 1 - 0.116

\(P_{at least one red}\) = 0.884

Therefore,

The probability that your cards are all face cards are,

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Answer:

Step-by-step explanation:

Area of top and bottom faces:

Area of front and back faces:

Area of left and right faces:

Total surface area:

Correct choice is C

Answer:

a) h = 15

b) x = 4

Step-by-step explanation:

a) set up a proportion:

  5 = h

   8     24

cross-multiply:

8h = 120

h = 15

b) x + 5 = x + 5 + 15

   5x + 1    5x + 1 + 35

cross-multiply:

(x + 5)(5x + 36) = (5x + 1)(x + 20)

5\(x^{2}\) + 61x + 180 = 5\(x^{2}\) + 101x + 20

180 = 40x + 20

160 = 40x

x = 4

In this scenario, we have a uniformly charged thin rod extending along the x-axis from the origin (x = 0) to positive infinity (x = +∞).

The term "uniformly charged" means that the charge is distributed evenly throughout the entire length of the rod.

To analyze this situation, we can consider the following steps: 1. Determine the linear charge density (λ) of the rod. Since the rod is uniformly charged, λ remains constant along its entire length. λ is usually given in units of charge per length (e.g., coulombs per meter).

2. To find the electric field at a particular point along or outside the rod, we can break the rod into infinitesimally small segments (dx) and consider the contribution of the electric field (dE) from each of these segments.

3. Calculate the electric field (dE) produced by each segment at the desired point using Coulomb's equations , considering the linear charge density (λ) and distance between the segment and the point.

4. Integrate the electric field contributions (dE) from all segments along the entire length of the rod (from x = 0 to x = +∞) to find the total electric field (E) at the point of interest.

By following these steps, you can analyze the electric field and related properties of a uniformly charged thin rod extending along the x-axis from x = 0 to x = +∞.

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