The point C(3, –1) is translated to the left 4 units and up 1 unit. a. Write the rule for this translation. b. What are the coordinates of the image point? A. (x, y) right arrow (x + 4, y +1); (7, –2) B. (x, y) right arrow (x – 4, y – 1); (–1, 0) C. (x, y) right arrow (x + 4, y – 1); (7, 0) D. (x, y) right arrow (x – 4, y + 1); (–1, 0)

The zeros and their multiplicities of the function are 1/(\(\sqrt{3}\),-1/\(\sqrt{3}\),-3,3 and 1,1,1,1.

The value which satisfy the polynomial. that is on substituting the value in the polynomial will give 0.

To find the zeros of the function, we need to solve the equation f(x) = 0. We can do this by factoring the polynomial using the difference of squares formula:

\(\begin{aligned} f(x)&=9 x^{4}-82 x^{2}+9 \ &= (3x^2 - 1)(3x^2 - 9) \ &= 3(x-\frac{1}{\sqrt{3}})(x+\frac{1}{\sqrt{3}})(x-3)(x+3) \end{aligned}\)

From this factorization, we can see that the zeros of the function are:

x = 1/(\(\sqrt{3}\),-1/\(\sqrt{3}\),-3,3

Therefore, the zero of f is (1/3, -1/3, 3, -3). To determine the multiplicities of each zero, we can look at the degree of each factor.

For the factors (x - 3) and (x + 3), we have a degree of 1, which means that each of these zeros has multiplicity 1.

For the factor (x - 1/√3), we have a degree of 1 as well, which means that this zero also has multiplicity 1.

For the factor (x + 1/√3), we have a degree of 1, which means that this zero also has multiplicity 1.

Therefore, the zeros and their multiplicities of the function are 1/(\(\sqrt{3}\),-1/\(\sqrt{3}\),-3,3 and 1,1,1,1.

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Answer:

yes

Step-by-step explanation:

Answer: no I don’t believe so

The volume of the solid obtained by rotating the region in the first quadrant bounded by the curve 4 - (x - 10)^2 about the y-axis is (2560π/3) cubic units.

To find the volume of the solid, we can use the method of cylindrical shells. The curve 4 - (x - 10)^2 represents a parabola with its vertex at (10, 4) and opening downwards.

1. First, let's determine the limits of integration. Since the region is in the first quadrant, it is bounded by the x-axis and the curve. To find the x-values where the curve intersects the x-axis, we set 4 - (x - 10)^2 = 0 and solve for x:

  (x - 10)^2 = 4

  x - 10 = ±2

  x = 8, 12

  So the limits of integration are x = 8 to x = 12.

2. Next, let's consider a small strip or "shell" of width Δx at a distance x from the y-axis. The height of this shell is given by the equation 4 - (x - 10)^2.

3. The circumference of the shell is given by 2πx, as it is being rotated about the y-axis.

4. The volume of the shell is calculated by multiplying the height, circumference, and width together: ΔV = (4 - (x - 10)^2) * 2πx * Δx.

5. To find the total volume, we integrate the expression ΔV from x = 8 to x = 12:

  V = ∫[8,12] (4 - (x - 10)^2) * 2πx dx.

6. Evaluating the integral, we obtain:

  V = 2π ∫[8,12] (4x - (x - 10)^2x) dx

    = 2π ∫[8,12] (4x^2 - x^3 - 20x + 100) dx

    = 2π [4/3 x^3 - 1/4 x^4 - 10x^2 + 100x] |[8,12]

    = 2π [(4/3 * 12^3 - 1/4 * 12^4 - 10 * 12^2 + 100 * 12) - (4/3 * 8^3 - 1/4 * 8^4 - 10 * 8^2 + 100 * 8)]

7. Simplifying the expression, we find:

  V = 2π [(4/3 * 12^3 - 1/4 * 12^4 - 10 * 12^2 + 100 * 12) - (4/3 * 8^3 - 1/4 * 8^4 - 10 * 8^2 + 100 * 8)]

    ≈ (2560π/3).

Therefore, the volume of the solid obtained by rotating the region in the first quadrant bounded by the curve 4 - (x - 10)^2 about the y-axis is approximately (2560π/3) cubic units.

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Step-by-step explanation:

\(y _{1} - y = m (x_{1} - x) \\ y - 2 = - 2 \div 5(x - + 5) \\ y - 2 = - 0.4(x - 5) \\ y = - 0.4x + 2 + 2 \\ y = - 0.4x + 4\)

Answer:

4(5 + 16)

Step-by-step explanation:

Answer:

7.8

Step-by-step explanation:

myjnhdgfb bgfb

Answer:

Letter A is your answer

Step-by-step explanation:

mark me brainliest

Answer:

3.14159265358

Step-by-step explanation:

Answer:

3.141592653589

Step-by-step explanation:

pi = 3.14159265358979323846264338327950288419716939937510...

Answer: 3.141592653589

Answer:

x=-1

Step-by-step explanation:

just like 8/8 is 1 the same concept only you add a negative

Answer:

x = -64

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Multiply 8 to both sides:

(x/8)8 = (-8)8

x = -8 * 8

x = -64

-64 is your solution for x.

~

The value of the slope is 5/7 while the y-intercept is 1.

Given that the graph passes through points (-7, 4) and (7, 6). These are the points we are going to consider on the graph.

Slope can be defined as the change in y divided by the change in x. Mathematically:

slope = y2 - y1 / x2 - x1

Using our points:

Point 1 is (-7, -4). Therefore: x1 = -7 and y1 = -4

Point 2 is (7, 6). Therefore: x2 = 7 and y2 = 6

Thus:

slope = 6 - (-4) / 7- (-7)

        = 6+4  /  7+7

        = 10/14 = 5/7

The y-intercept is where the line touches the y-axis. And looking at the graph,  the line touches the y-axis at 1. So y-intercept = 1

Since the slope is 5/7 and the y-intercept is 1. Therefore, option B is the correct answer.

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Answer:

D) triangle

Step-by-step answer:

A pyramid is a three-dimensional figure with a plane that is parallel to its base.

A three dimensional figure is a figure with a length, width and height. 3D shapes have faces, edges, and vertices.

Rectangle, square and triangle are two dimensional shapes while pyramid is a three dimensional shape.

A pyramid is a three-dimensional figure with a plane that is parallel to its base.

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The solution to the equation is -1.5 or -3/2.

We have the equation:

x² + 3-2x= 1+ x² +5

Combine Terms and subtract x² from both sides:

x² - x² + 3 -2x = 1 + 5 + x² - x²

3 -2x = 1 + 5

Add:

3 -2x = 6

Combine Terms and subtract 3 from both sides:

-2x + 3 -3 = 6 - 3

-2x = 3

Dividing by -2 we get:

x = 3/(-2)

x = -3/2

x = -1.5

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Answer of a)(0.01 * 2t)/(\((1+t^{2})^{2}\))  

b) e^((0.02 + 0.01/(1+\(t^2\))) * t) - 1

c)2 * [(1 + (0.02 + 0.01/\((1+(0.5t)^2)))^(2t) - 1]\) by susbstituting

(a) Instantaneous Interest Rate Curve:

The instantaneous interest rate is the derivative of the continuously compounded zero rate with respect to time. Taking the derivative of r_c(0,t), we get:

r_i(0,t) = d(r_c(0,t))/dt = (0.01 * 2t)/(\((1+t^{2})^{2}\))

(b) Annually Compounded Zero Rate Curve:

To compute the annually compounded zero rate, we use the relationship between continuously compounded rates and annually compounded rates. The annually compounded zero rate, denoted as r_a(0,t), can be calculated as:

r_a(0,t) = e^(r_c(0,t) * t) - 1

Substituting the expression for r_c(0,t) into the equation above, we have:

r_a(0,t) = e^((0.02 + 0.01/(1+\(t^2\))) * t) - 1

(c) Semiannually Compounded Zero Rate Curve:

Similar to the annually compounded zero rate, the semiannually compounded zero rate, denoted as r_s(0,t), can be calculated using the relationship:

r_s(0,t) = 2 * [(1 + r_c\((0,0.5t))^(2t)\) - 1]

Substituting the expression for r_c(0,t) into the equation above, we have:

r_s(0,t) = 2 * [(1 + (0.02 + 0.01/\((1+(0.5t)^2)))^(2t) - 1]\)

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Answer:

y= 11

Step-by-step explanation:

\(\boxed{slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

Substituting the coordinates and value of slope:

\( \frac{y - ( - 3)}{3 - ( - 4)} = 2\)

\( \frac{y + 3}{3 + 4} = 2\)

\( \frac{y + 3}{7} = 2\)

Multiply both sides by 7:

y +3= 2(7)

y +3= 14

Subtract 3 from both sides:

y= 14 -3

y= 11

A measure of goodness of fit for the estimated regression equation is the residual standard error (RSE)

It is a measure of goodness of fit for the estimated regression equation. It measures the average amount that the response variable (y) deviates from the estimated regression line, in the units of the response variable.

The RSE is calculated as the square root of the sum of squared residuals divided by the degrees of freedom. A smaller RSE indicates a better fit of the regression line to the data.

It represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the model. The value of R-squared ranges from 0 to 1, with higher values indicating a better fit of the model to the data.

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Answer: 28 and just positive 28

Step-by-step explanation: same signs add different signs subtract -28+28=0

Answer:

The answer is +28

Step-by-step explanation:

Just trust me! :)

Your welcome in advanced!!!

best of luck soldier

Answer: 15 m

Step-by-step explanation:

Given

Total volume of the combined pyramid is \(V=2700\ mm^3\)

Height of top and bottom pyramid is

\(h_t=16\ mm\)

\(h_b=20\ mm\)

If the base has a side length of x, its area must be \(x^2\)

Volume of square prism is given by

\(\Rightarrow V=\dfrac{1}{3}Bh\quad [\text{B=base area}]\\\\\text{Total volume will be the sum of the two pyramids}\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times 16+\dfrac{1}{3}\times x^2\times 20\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times (16+20)\\\\\Rightarrow x^2=225\\\Rightarrow x=15\ mm\)

Thus, the value of \(x\) is 15 m.

Answer:It is irrational since it will never stop going on

Step-by-step explanation:

Triangles are shapes with three sides and angles

The value of B is 16.3 degrees

The given parameters are:

a = 64

b = 18

c = 63

Next, we apply the following cosine formula

\(b^2 = a^2 + c^2 - 2ac\ cos(B)\)

So, we have:

\(18^2 = 64^2 + 63^2 - 2 * 64 * 63 \ cos(B)\)

Evaluate the exponents

\(324 = 8065 - 8064\ cos(B)\)

Collect like terms

\(324 - 8065 = - 8064\ cos(B)\)

\(-7741 = - 8064\ cos(B)\)

Solve for cos (B)

\(\cos(B) =0.9599\)

Take the arccos of both sides

\(B =cos^{-1}(0.9599)\)\(B = 16.3\)

Hence, the value of B is 16.3 degrees

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer:

Step-by-step explanation:

You see that 't' is the 'argument' or 'input' to h:  h(t).  It is always safe to assume that t is the independent variable and h is the depend

\(\huge\pmb{Hello!}\)

The answer is -10.

Remember the rule:

A positive times a positive is a positive

A negative times a positive is a negative

A negative times a negative is a positive

Thus, the answer is -10.

Hope it helps! Enjoy your day!

~Just a determined gal

\(\bf{erutaN\:tneliS\)

Answer:

A' (-5, 5)

B' (20, 0)

C' (5, -15)

Step-by-step explanation:

Multiply each coordinate by 5, and your result is given above.

Answer:

Step-by-step explanation:

Answer:

cups =15.99994. according to the holy bible.

Step-by-step explanation:

Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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Answer:

x = 6

Step-by-step explanation:

Equation

(1 + 5 + 10 + x)/4 = 5.5                    Multiply both sides by 4

Solution

4* (1 + 5 + 10 + x ) /4 = 5.5 * 4

16 + x = 22                                     Subtract 16 from both sides

16-16+x = 22- 16

x = 6

a) Probability model

P(40) = 1/6

P(0) = 5/36

P(-10) = 25/36

b)  E(X) = -5/18

standard deviation  = 18.331

c) standard deviation  = 91.65

d) Probability = 0.560

From the question, we have

a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:

P(40) = 1/6

P(0) = (5/6)(1/6) = 5/36

P(-10) = 1 - 1/6 - 5/36 = 25/36

b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9

Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324

standard deviation = sqrt [Var X] = 119043 / 6494 =18.331

c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

5 * E(X)  =  - 25/18

standard deviation = 5 * 18.331 = 91.65

d) Probability :

P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

Complete question:

From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?

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Average There are 120 ways to choose the three positions so that at least one freshman and one sophomore is chosen.

There are a total of 4 possible combinations of freshman and sophomore for the three positions, with at least one of each:

1. Freshman President, Sophomore Vice-President, Sophomore Treasurer

2. Sophomore President, Freshman Vice-President, Sophomore Treasurer

3. Freshman President, Sophomore Vice-President, Freshman Treasurer

4. Sophomore President, Freshman Vice-President, Freshman Treasurer

For each of the four combinations, there are 10 possible ways to choose the specific freshmen and sophomores for the positions (5 freshmen and 5 sophomores). That means there are 40 possible ways to choose the three positions with at least one freshman and one sophomore. Multiplying this by the 3 possible orders of the positions (President-Vice-President-Treasurer, President-Treasurer-Vice-President, Vice-President-President-Treasurer) gives us a total of 120 possible ways to choose the three positions so that at least one freshman and one sophomore is chosen.

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Answer:

288 good ways

Step-by-step explanation:

:)

Answer:

The answer to Y/X is 4/1

Answer:

true for all x  or AllRealNumbers

Step-by-step explanation: