The function g(x) is a transfomation of the function f(x). If g(x) = 2(x – 3) 2
f(x) = 2(x + 4) then what translation describes the change from f (x) to g(x)?
2
1

\(y = -2x^2 + 8x + 3\)

The equation of a quadratic function of vertex (h,k) is given by:

\(y = a(x - h)^2 + k\)

The vertex is the maximum point, which is (2,11), hence \(h = 2, k = 11\). Then:

\(y = a(x - 2)^2 + 11\)

The initial height is of 3 feet, then when \(x = 0, y = 3\), and this is used to find a.

\(y = a(x - 2)^2 + 11\)

\(3 = 4a + 11\)

\(4a = -8\)

\(a = -\frac{8}{4}\)

\(a = -2\)

Then:

\(y = -2(x - 2)^2 + 11\)

In standard format, the model is:

\(y = -2x^2 + 8x - 8 + 11\)

\(y = -2x^2 + 8x + 3\)

It hits the ground when \(y = 0\), so:

\(-2x^2 + 8x + 3 = 0\)

\(2x^2 - 8x - 3 = 0\)

Which has coefficients \(a = 2, b = -8, c = -3\). So

\(\Delta = b^2 - 4ac = (-8)^2 - 4(2)(-3) = 88\)

\(x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + sqrt{88}}{4} = 4.35\)

\(x_1 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - sqrt{88}}{4} = -0.35\)

Time is positive, so it lands on the ground after 4.35 seconds.

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Answer:

Step-by-step explanation:

Answer:

X=4

Step-by-step explanation:

Given mean =8,

Total number given including X is 5

5×8= 40

40-(Given number)

40-6-7-13-10=4

x=4 Is the final answer

To maximize Z = X1 - X2 subject to the given constraints, the solution involves finding the feasible region, calculating the objective function at each corner point, and selecting the point that yields the maximum value.

To minimize Z = 5X1 + 4X2 subject to the given constraints, the solution involves finding the feasible region, calculating the objective function at each corner point, and selecting the point that yields the minimum value for Z.

(e) To maximize Z = X1 - X2, subject to the constraints -X1 + 2X2 ≤ 13, -X1 + X2 ≤ 23, and X1 + X2 ≤ 11, we first plot the feasible region determined by the intersection of the constraint lines. Then we calculate the objective function at each corner point of the feasible region and select the point that gives the maximum value for Z.

(f) To minimize Z = 5X1 + 4X2, subject to the constraints -4X1 + 3X2 ≤ 2, 8X1 - 10X2 ≤ 80, and X1, X2 ≥ 0, we again plot the feasible region determined by the intersection of the constraint lines. Then we calculate the objective function at each corner point of the feasible region and select the point that gives the minimum value for Z.

The steps involved in finding the corner points and calculating the objective function at each point are not provided in the question, so the specific solution and correct answer cannot be determined without additional information.

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Answer:  x > 0   x = (0, ∞)

Step-by-step explanation:

The domain (x-values) are the number of ounces the package weighs.

The package must weigh greater than 0 but there doesn't appear to be a maximum weight. Therefore, x > 0

The domain is the set of values for which the given function is defined. The domain of the given relation is (0,∞).

The domain is the set of values for which the given function is defined.

The range is the set of all values which the given function can output.

Given the postal service charges $2 to ship packages up to 5 ounces in weight and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce. Therefore, the independent variable in this relationship is the weight of the postal.

Since the weight of the postal can be anything greater than 0.

Therefore, the domain of the relation is (0,∞).

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Answer:

what grade are you in so i can help

Step-by-step explanation:

The total distance Renaldo could travel on his trip when he starts from Atlanta goes to London and  Newyork city, and return to Atlanta is 15502 miles.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The distance between Atlanta and London = 4281 miles,

The distance between London to Newyork city  = 3470 miles,

Write the trip blue plan as shown below,

Renaldo start from Atlanta → London → Newyork city →  London → Atlanta

Calculate the total distance as shown below,

The total distance = 4281 + 3470 + 3470 + 4281

The total distance = 2 (4281 + 3470)

The total distance = 2 × 7751

The total distance = 15502 miles

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Okay, here we have this:

Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:

Then we will use the following formula:

A= πrL + πr^2

Replacing:

A= π(4 m)(10 m) + π(4 m)^2

A= 40π m^2 + 16π m^2

A= 56π m^2

A≈175,9 m^2

Finally we obtain that the surface area of the cone is approximately 175,9 m^2.

Answer:

y=-30x+450

if she reads 30 pages every day it will take 15 days

The equation is formed and solved below.

What is an equation?

A mathematical equation is a calculation that uses the matching sign to represent the similarity of two expressions. A polynomial equation is the most prevalent kind of equation. An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance.

Lane ate = x marshmallows (let)

Chad ate = x + 5 marshmallows

Jeff ate = (x + 5) + 7 = x + 12 marshmallows

Then, the equation formed is

x + x + 5 + x + 12 = 254

The equation is solved as

3x + 17 = 254

or, 3x = 254 - 17

or, x = 237/3 = 79

Jeff ate = 79 + 12 = 91 marshmallows

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Step-by-step explanation:

8x-2=46

collect like terms

8x=46+2

8x=48

Divide both sides by 8

8x÷8=48÷8

x=6

Answer:

The variable is "y"

The like terms are "2y" and "6y"

The exponent is the 3 in "y^3"

The constant is "-4"

Step-by-step explanation:

Answer:

try your best

Step-by-step explanation:

don't give up

The equation 2x + cos(x) = 0 has exactly one real root. This can be shown by considering the behavior of the function f(x) = 2x + cos(x) and using the intermediate value theorem.

To prove that the equation 2x + cos(x) = 0 has exactly one real root, we need to demonstrate the existence and uniqueness of the root.

Existence of a real root: By considering the behavior of the function f(x) = 2x + cos(x), we can observe that f(x) is continuous for all real numbers. As x approaches negative infinity, the value of f(x) becomes more negative, and as x approaches positive infinity, the value of f(x) becomes more positive. Since f(x) is continuous and changes sign as x varies, the intermediate value theorem guarantees the existence of at least one real root.

Uniqueness of the real root: To prove uniqueness, we consider the derivative of f(x), which is f'(x) = 2 - sin(x). Since the derivative f'(x) is always positive, it indicates that the function f(x) is strictly increasing. As a result, f(x) = 0 can have at most one real root since there are no significant changes in f(x) after the initial root.

Therefore, the equation 2x + cos(x) = 0 has exactly one real root.

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Answer: Let us call the centers of the four circles C1, C3, C5, and C7, respectively, where the subscript refers to the radius of the circle. Without loss of generality, we can assume that the tangent point A lies to the right of all the centers, as shown in the diagram below:

                 C7

          o-----------o

       C5 /             \ C3

         /               \

        o-----------------o

                C1

                |

                |

                | l

                |

                A

Let us first find the coordinates of the centers C1, C3, C5, and C7. Since all the circles are tangent to line l at point A, the centers must lie on the perpendicular bisector of the line segment joining A to the centers. Let us denote the distance from A to the center Cn by dn. Then, the coordinates of Cn are given by (an, dn), where an is the x-coordinate of point A.

Using the Pythagorean theorem, we can write the following equations relating the distances dn:

d1 = sqrt((d3 - 2)^2 - 1)

d3 = sqrt((d5 - 4)^2 - 9)

d5 = sqrt((d7 - 6)^2 - 25)

We can solve these equations to obtain:

d1 = sqrt(16 - (d7 - 6)^2)

d3 = sqrt(4 - (d7 - 6)^2)

d5 = sqrt(1 - (d7 - 6)^2)

Now, let us consider the region S that lies inside exactly one of the four circles. This region is bounded by the circle of radius 1 centered at C1, the circle of radius 3 centered at C3, the circle of radius 5 centered at C5, and the circle of radius 7 centered at C7. Since the circles are all tangent to line l at point A, the boundary of region S must pass through point A.

The maximum possible area of region S occurs when the boundary passes through the centers of the two largest circles, C5 and C7. To see why, imagine sliding the circle of radius 1 along line l until it is tangent to the circle of radius 3 at point B. This increases the area of region S, since it adds more points to the interior of the circle of radius 1 without removing any points from the interior of the other circles. Similarly, sliding the circle of radius 5 along line l until it is tangent to the circle of radius 7 at point C also increases the area of region S. Therefore, the boundary of region S must pass through points B and C.

Using the coordinates we obtained earlier, we can find the x-coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (d7 - 6)^2)

x_C = a + 6 + sqrt(9 - (d7 - 6)^2)

To maximize the area of region S, we want to maximize the distance BC. Using the distance formula, we have:

BC^2 = (x_C - x_B)^2 + (d5 - d3)^2

Substituting the expressions we derived earlier for d3 and d5, we get:

BC^2 = 32 - 2(d7 - 6)sqrt(9 - (d7 - 6)^2)

To maximize BC^2, we need to maximize the expression inside the square root. Let y = d7 - 6. Then, we want to maximize:

f(y) = 9y^2 - y^4

Taking the derivative of f(y) with respect to y and setting it equal to zero, we get:

f'(y) = 18y - 4y^3 = 0

This equation has three solutions: y = 0, y = sqrt(6)/2, and y = -sqrt(6)/2. The only solution that gives a maximum value of BC^2 is y = sqrt(6)/2, which corresponds to d7 = 6 + sqrt(6)/2.

Substituting this value of d7 into our expressions for d1, d3, and d5, we obtain:

d1 = sqrt(16 - (sqrt(6)/2)^2) = sqrt(55/2)

d3 = sqrt(4 - (sqrt(6)/2)^2) = sqrt(19/2)

d5 = sqrt(1 - (sqrt(6)/2)^2) = sqrt(5/2)

Using these values, we can compute the coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (sqrt(6)/2)^2) = a - 2 - sqrt(55)/2

x_C = a + 6 + sqrt(9 - (sqrt(6)/2)^2) = a + 6 + sqrt(55)/2

The distance between points B and C is then:

BC = |x_C - x_B| = 8 + sqrt(55)

Finally, the area of region S is given by:

Area(S) = Area(circle of radius 5 centered at C5) - Area(circle of radius 7 centered at C7)

= pi(5^2) - pi(7^2)

= 25pi - 49pi

= -24pi

Since the area of region S cannot be negative, the maximum possible area is zero. This means that there is no point that lies inside exactly one of the four circles. In other words, any point that lies inside one of the circles must also lie inside at least one of the other circles.

Step-by-step explanation:

Answer:

0.965925826

0.258819045

Step-by-step explanation:

→If you were to calculate \(sin(75)\), you would have a total of:

0.965925826

→If you were to calculate \(cos(-75)\), you would have a total of:

0.258819045

The values of x and y that make RAPT a parallelogram are;

x = 15 and y = 25

Angle T and angle P are supplementary angles by parallel lines. Thus they sum up to 180 degrees and we have;

3x + 10 + 8x + 5 = 180

11x + 15 = 180

11x = 165

x = 15

T = 55°

P = 125°

Likewise R and T are supplementary angles by parallel lines and so we have;

55 + 5y = 180

5y = 180 -55

5y = 125

y = 25

R = 125°

A must be 55° since the angles add up to 360°.

R + A + P + T =

125 + 55 + 125 + 55 = 360°

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The lightbulb should be placed at the co-ordinate F(0,1)

The general equation of a parabola is as y²=4ax for a parabola opening towards the positive x-axis.

Here a represents the point on the x-axis where the focal point lies and through which the directrix passes.

For the given question,

Equation of Parabola: x²=4y

Comparing the given equation to standard parabolic equation for parabola on y-axis( x²= 4ay)

Then,  x²=4y: x²=4ay

thus value of a=1

Hence, the focal point of the parabola will be (0,1)

Since the lightbulb is to be placed on the focal point of the parabolic mirror, the lightbulb would be placed at a unit distance away from the vertex of the parabola

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The correct answer is (b) SSE can never be smaller than SST.

SSE (Sum of Squared Errors) and SST (Total Sum of Squares) are terms used in statistics, specifically in the context of regression analysis.

In regression analysis, the total variation in the dependent variable (Y) can be decomposed into two parts: the variation explained by the independent variable(s) (X) and the variation that is not explained by the independent variable(s). SST represents the total variation in Y, while SSE represents the unexplained variation in Y.

a. larger than SST: This is not possible, as SSE represents only the unexplained variation in Y, while SST represents the total variation in Y. Therefore, SSE must always be less than or equal to SST.

b. smaller than SST: This is true, as explained above. SSE represents the unexplained variation in Y, which is always less than or equal to the total variation in Y represented by SST.

c. equal to 1: This is not possible, as SSE and SST are measures of variation in Y and are not constrained to a particular range or value.

d. equal to zero: This is also not possible, as SSE represents the unexplained variation in Y, and there will almost always be some unexplained variation in real-world data. If SSE were equal to zero, it would indicate a perfect fit of the regression model, which is unlikely to occur in practice.

Therefore, the correct answer is (b) SSE can never be smaller than SST.

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SSE can't exceed SST, can be smaller than SST, can equal to 1 when data is standardized, and can equal to zero if the model fits the data perfectly.

SSE (Sum of Squared Errors) and SST (Total Sum of Squares) are statistical measures used in regression analysis. They provide information about the variability of data points around a fitted value. The SSE is never larger than SST as it accounts for the variance that the model doesn't explain, whereas SST accounts for total variance in the data. SSE can be equal to zero if the model perfectly fits the data. It cannot be equal to 1 unless the data is standardized and the model perfectly fits the data. Therefore, the answer can be summarized as:

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The missing fractions in the number line are

1. 1/7 2/7 3/7 4/7 5/7 6/7

2. 1/6 2/6 3/6 4/6 5/6

3. 2/8 5/8 7/8

Number lines are visual representations of numbers placed in a horizontal line, they are used to represent and compare real numbers and are commonly used in mathematics to help students develop an understanding of number relationships and operations.

the number line consists of evenly spaced points each of which is assigned a number

The missing fractions are filled by division.

In the division the number of spaces to fill plus the last forms the denominator (zero not inclusive). the numerator is the particular number counted

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a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%.

Human blood is categorized into four types which are A, B, AB, and O. The percentages of Americans who have each of the four types are given below:

O - 43% A - 40% B - 12% AB - 5%

To calculate probabilities for various scenarios, we can use these percentages as follows.

a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%. The combined percentage of O and AB blood types is 48%. We can therefore say that the probability of an American having O or AB blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%. The percentage of Americans who don't have type O blood is the sum of percentages of A, B, and AB blood types, which is  Hence, the probability of not having O blood is lower than 57%. Therefore, the probability of a randomly selected American not having type O blood is 57%.

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Answer:

Option 2

 x     y

−3     0

−1      3

 0     4

 3     0

4 3

Step-by-step explanation:

For a relation x →  y to be a function, there can be one and only one value of y for a value of x

Looking at the tables we see that option 1 is out since all x values are 2 andthere are multiple values of y

The last option is out because for x = 0 there are two values of y=-2 and y = 2

Correct choice is the second option which has a unique y value for each value of x

Answer:

option 2 im doing it rn

Step-by-step explanation:

Answer:

R92.463

Step-by-step explanation:

100% - 20% = 80% = 0.8

0.8 times 124.95 = R99.96

7.5% = 0.075

99.96 - (99.96 x 0.075) = R92.463

So, Maria pay R92.463 for the swimming costume.

The product in descending order with respect to the power c is cn³ + cp³ - cpn² - cp²n

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By multiplying the variables, we have the following:

c(n - p)²(n + p)

c(n - p)(n - p)(n + p)

c(n² - pn - pn + p²)(n + p)

c(n² - 2pn + p²)(n + p)

c(n³ + pn² - 2pn² - 2p²n + p²n + p³)

c(n³ - pn² - p²n + p³)

cn³ - cpn² - cp²n + cp³

cn³ + cp³ - cpn² - cp²n

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The pairs of vectors that satisfy the given conditions are (a, c) and (b, d).

To find the pairs of vectors that are perpendicular, we need to calculate the dot product of the vectors. The dot product of two vectors is equal to the sum of the products of their corresponding components. If the dot product of two vectors is zero, then the vectors are perpendicular.

The dot product of vectors a and c is:

a ∙ c = (i − 4 j − k) ∙ (−3 i − j + k) = (1)(−3) + (−4)(−1) + (−1)(1) = 0

The dot product of vectors b and d is:

b ∙ d = (i + j + 2k) ∙ (− i − j + k) = (1)(−1) + (1)(−1) + (2)(1) = 0

Therefore, the pairs of vectors that are perpendicular are (a, c) and (b, d).

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The domain of the graph is (d) all set of real values

The graph represents the given parameter

This graph represents a function

Say the graph represents the function f(x)

The x values represent the domain

i.e domain = Set of all x values

On the graph, we can see that the graph extends across the x-axis till infinity on both sides

This means that

Domain = All set of real values

Hence, the domain of the relation is (d) all set of real values

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Answer:

-3

Step-by-step explanation:

You cant count the spaces up (9) and over (-3) between the two points and do up/over so it would be 9/-3 and simplified that is -3/1 or 3

The best way for Abdulbaasit to buy the car would be to opt for the bank loan with the cash discount, as it offers a lower monthly payment and immediate cost savings.

To determine the best way to buy a car, we need to compare the financing options provided by the dealership and the bank. Let's evaluate both scenarios:

1. Financing at the dealership:

- Car price: $30,000

- Interest rate: 2.4% per year, compounded monthly

- Loan term: 5 years (60 months)

Using the provided interest rate and loan term, we can calculate the monthly payment using the formula for monthly loan payments:

Monthly interest rate = \((1 + 0.024)^(1/12)\) - 1 = 0.001979

Loan amount = Car price = $30,000

Monthly payment = Loan amount * (Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Loan term))

Plugging in the values:

Monthly payment = $30,000 * 0.001979 /\((1 - (1 + 0.001979)^(-60)) =\)$535.01 (approximately)

2. Bank loan with a cash discount:

- Car price with the $3,000 cash discount: $30,000 - $3,000 = $27,000

- Interest rate: 5.4% per year, compounded monthly

- Loan term: 5 years (60 months)

Using the provided interest rate and loan term, we can calculate the monthly payment using the same formula as above:

Monthly interest rate = (1 + 0.054)^(1/12) - 1 = 0.004373

Loan amount = Car price with cash discount = $27,000

Monthly payment = $27,000 * 0.004373 / (1 - (1 + 0.004373)^(-60)) = $514.10 (approximately)

Comparing the two options, we can see that the bank loan with the cash discount offers a lower monthly payment of approximately $514.10, compared to the dealership financing with a monthly payment of approximately $535.01. Additionally, with the bank loan option, Abdulbaasit can pay immediately in cash and save $3,000 on the car purchase.

Therefore, the best way for Abdulbaasit to buy the car would be to opt for the bank loan with the cash discount, as it offers a lower monthly payment and immediate cost savings.

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Answer:

a. -5 + 3x = -41

3x = -36

x = -12

b. 7x - 4 = -2x + 11

9x = 15

x = 15/9 = 1 and 2/3

c. (-4x) / 5 = 8

-4x = 40

x = -10

d. x / 3 - 1/2 = 1/4

4x - 6 = 3 (multiply by lcm of 3, 2 and 4 which is 12)

4x = 9

x = 9/4 = 2 and 1 / 4

e. -4(6x + 1) + 3 = 11 + 2(x + 2)

-24x - 4 + 3 = 11 + 2x + 4

-24x - 1 = 2x + 15

-26x = 16

x = -8/13

The exact solutions of the given equation 2sin(x) + √2 = 0 are 5π/4 and 7π/4. These are the solutions in the interval (-π,π).

We need to solve the equation 2sin(x) + √2 = 0. We have 2sin(x) = -√2.

Dividing both sides by 2, we get sin(x) = -√2/2.Now, let us find the solutions of sin(x) = -√2/2. Since the values of sin(x) are -1, -1/2, 0, 1/2, and 1,

we find that sin(5π/4) = sin(7π/4) = -√2/2 are the solutions in the interval (-π,π).Therefore, the solutions of the given equation in the interval (-π,π) are 5π/4 and 7π/4.  

To solve the given equation 2sin(x) + √2 = 0, we have to isolate the sine term. We start by subtracting √2 from both sides. This gives 2sin(x) = -√2.

Next, we divide both sides by 2. This yields sin(x) = -√2/2. We need to find the solutions of sin(x) = -√2/2. The sine function is negative in the second and third quadrants.

Also, the sine function is equal to -√2/2 at two points in the interval (-π,π). We use the unit circle to find these points. The angle between the positive x-axis and the point (-1, -√2/2) is 5π/4.

Similarly, the angle between the positive x-axis and the point (1, -√2/2) is 7π/4. Therefore, the solutions of the given equation in the interval (-π,π) are 5π/4 and 7π/4.

The exact solutions of the given equation 2sin(x) + √2 = 0 are 5π/4 and 7π/4. These are the solutions in the interval (-π,π).

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Answer:

Step-by-step explanation:

You want to know how much of each kind of trail mix a grocer uses to make 15 lb of mix costing $2.50 per pound from mixes costing $3.00 and $1.50 per pound.

Let x represent the number of pounds of $3.00 mix. Then (15 -x) is the number of pounds of $1.50 mix. The total cost of the 15 pounds of mix is ...

  3.00x +1.50(15 -x) = 2.50(15)

  1.50x +22.50 = 37.50 . . . . . . . . . simplify

  1.50x = 15.00 . . . . . . . . . . subtract 22.50

  x = 10 . . . . . . . . . . . . . divide by 1.50

The grocer uses 10 lb of $3.00 mix and 5 lb of $1.50 mix.

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