solve for x in the diagram

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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In 58 seconds after starting its descent, the aircraft will touch down.

The plane will land when its altitude y is zero.

So we can set y = 0 in the equation:

0 = 464 - 8x

Solving for x:

8x = 464

x = 58

Therefore, the plane will land 58 seconds after it begins its descent.

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Answer:

The second scatterplot does not suggest a linear relationship between x and y.

The number that take (a) both PE is 6 girls (b) Gymnastic but not acrobat is 7 girls (c)  At least one PE is 18 girls

How to determine the numbers?

Recall that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects.

From the given parameters,

(a)  The number that play both PE is given as

13 - x + x + 17 - x + 1 = 25

Solving the equation to get the value of x

13+17-x = 25

⇒ 31 -x =25

Collecting like terms we have

-x = 25 - 31

- x = -6

Dividing by a minus we have

x = 6

This means that 5 girls play both PE

(b)  Number that play gymnastic but not acrobat is given as

Gymnastic only that is

13 - x

13 - 6 = 7 girls

(c)  Number that play at least one game is calculated thus:

n(G) ∪ n(A)

That is (13 - x )  + (17 - x)

= 13-6 + 17 -6

7 + 11 = 18 girls

The smallest positive integer a that satisfies the conditions of the problem is a = 2.

The Intermediate Value Theorem states that if a function f(x) is continuous on the interval [a, b] and takes on values f(a) and f(b) at the endpoints a and b, respectively, then for any value c between f(a) and f(b), there exists at least one value x in the interval [a, b] such that f(x) = c.

In this problem, we are asked to find the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a for the polynomial f(x) = 3x³ - 4x² - 3x - 1.

To find this value of a, we need to evaluate f(0) and f(a) and look for a value of a such that f(0) and f(a) have opposite signs. This will guarantee the existence of a root of f(x) between 0 and a.

Evaluating f(0), we get:

f(0) = 3(0)³ - 4(0)² - 3(0) - 1 = -1

To find f(a), we need to solve for a using the equation f(a) = 0. We can use a numerical method, such as the Newton-Raphson method or the bisection method, to find the root of f(x) = 0. Using a calculator or a computer program, we find that f(a) = 0 for a ≈ 1.353.

Since f(0) = -1 and f(a) = 0 have opposite signs, the Intermediate Value Theorem guarantees the existence of at least one zero of f(x) between 0 and a = 1.353. Therefore, the smallest positive integer a that satisfies the conditions of the problem is a = 2.

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The time will take the car to reach it's destination is 0.005 hours

The first step is to convert 528 feet to miles

1 foot= 0.000189394 miles

528= x

cross multiply

= 528 × 0.000189394

= 0.1

Time= distance/speed

distance= 0.1 miles

speed= 20

Time= 0.1/20

= 0.005 hours

Hence it will take the car 0.005 hours to reach its destination

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The area of the decagon with side length 10 is 769.42 square units

From the question, we have the following parameters that can be used in our computation:

side length, l = 10

The area of the decagon is calculated as

Area = 5/2l² * √[5 + 2√5]

Where

l = 10

Substitute the known values in the above equation, so, we have the following representation

Area = 5/2 * 10² * √[5 + 2√5]

Evaluate

Area = 769.42

Hence, the area is 769.42

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The value of the expression is 16x(x+1) / 10x² -14x -12

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The given expression is

16/(x-2)  ÷ 4/(x+1) + 6/x

Simplify this to have

16 / (x-2) ÷ (10x + 6) / (x+1)(x)

this implies that 16/(x-2) * (x+1)(x)/(10x +6)

16(x² + x)/(x-2)(10x+6)

Therefore the value of the expression is

16x(x+1) / 10x² -14x -12

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The equation of the line of best fit for the set of data is given as follows:

y = 4.24773x - 0.32726

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

From the table in this problem, the points are given as follows:

(0.9, 3.51), (1.7, 6.61), (3, 12.27), (0.1, 0.15), (2.3, 9.59), (1.3, 5.35), (0.5, 1.65), (2.1, 8.8).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 4.24773x - 0.32726

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The equation for the translated function is the one in option D:

G(x) = (x - 6)² - 4

We start with the parent quadratic function:

F(x) = x²

We apply two translations, one of 6 units to the right which can be written as:

G(x) = F(x - 6)

And a translation of 4 units down, which is written as:

G(x) = F(x - 6) - 4

Replacing F(x) we will get:

G(x) = (x - 6)² - 4

The correct option is D.

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Answer:

Step-by-step explanation:

6v-19=3v-4

subtract 3v from both sides

3v-19=-4

add 19 to both sides

3v=15

divide both sides by 3

v=5

Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

Answer:

The pattern of association between time and distance is positive and linear.

The population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The problem is incomplete, hence the procedure to obtain the mean of a data-set, in this case the population, is presented.

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84 adult tickets were consequently sold on that day.

Let's fix this issue using a set of equations. Let x represent how many adult tickets were sold, and y represent how many kid tickets were sold.

We learn the following from the issue:

Total number of tickets sold = x + y

Total sales equal 9.9x + 5.5y = 1216.6.

To find y, we can utilize the first equation:

y = 146 - x

We obtain the following by substituting this into the second equation: 9.9x + 5.5(146 - x) = 1216.6

The result of simplifying and finding x is: 4.4x = 369.6 x = 84

Therefore, 84 adult tickets were consequently sold on that day.

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The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

Answer: The cost of a large pizza with 2 toppings depends on the pizza place. Let's say the cost is $15 per pizza, and each additional topping costs $2.

Let t be the number of toppings Anna has on her pizza. Then, the total cost of her pizza can be expressed as:

Total cost = $15 + $2t

Since Anna has 2 toppings on her pizza, we can substitute t = 2:

Total cost = $15 + $2(2)

Total cost = $15 + $4

Total cost = $19

Therefore, the total cost of Anna's pizza with 2 toppings is $19.

When the y-value starts to decrease and the x-value remains constant over time, Y decreases and X increases to a consistent slope.

A consistent slope represents a constant rate of change between two variables, typically represented by the ratio of the change in y to the change in x.

When the y-value starts to decrease and the x-value remains the same over time, the consistent slope represents a negative correlation between y and x.

This means that as the value of y decreases, the value of x remains the same or may increase, depending on the context of the problem.

Therefore, the answer is option B: Y decreases and X increases.

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The required graph shows the x-intercepts and the minimum value.

To find the x-intercepts of the function y = 3x² - 12x + 9, we set y = 0 and solve for x:

3x² - 12x + 9 = 0

Dividing both sides by 3 gives:

x² - 4x + 3 = 0

(x - 1)(x - 3) = 0

So, the x-intercepts are x = 1 and x = 3.

To find the minimum value of the function, we can use the formula:

x = -b / 2a

Here a = 3 and b = -12.

Substitute these values gives:

x = -(-12) / 2(3) = 2

So the minimum value occurs at x = 2.

To find the corresponding y-value, we can plug in x = 2 into the original function:

y = 3(2)² - 12(2) + 9 = -3

So the minimum value is y = -3.

Here is a graph showing the x-intercepts and the minimum value.

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The requried, there is only 1 possible lineup of 6 songs from a list of 6 songs.

To determine how many different lineups are possible, we can use the formula for combinations, which is:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items being selected, and the exclamation mark denotes the factorial function.

In this case, we have n = 6 (the total number of songs) and k = 6 (the number of songs to be selected). So we can plug these values into the formula:

6C6 = 6! / (6!(6-6)!) = 6! / (6!0!) = 1

Therefore, there is only 1 possible lineup of 6 songs from a list of 6 songs.

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The concept Pythagoras theorem is used here to determine the length of the hypotenuse. It is an important theorem which explains the relation between the sides of a right angled triangle. The length of hypotenuse is

According to Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. The sides of this triangle have been named perpendicular base and hypotenuse.

Hypotenuse² = Perpendicular² + Base²

9² + 4² = 97

√97 = 9.84 cm

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Your question is incomplete most probably your full question was:

What is the length of the hypotenuse of the triangle when x=9 now and other side y = 4.

The perimeter of the square with side of 5 cm is 20 cm.

The perimeter of the square with side length of 15 cm is 60 cm.

The area of each square is calculated as follows;

Let the dimension of first square = x

Let the dimension of second square = y

x² + y² = 250 ---- (1)

4(x + y) = 80 ----- (2)

x + y = 80/4

x + y = 20

x = 20 - y

Substitute x in equation (1)

(20 - y)² + y² = 250

400 - 40y + y² + y² = 250

2y² - 40y + 150 = 0

y² - 20y + 75 = 0

solve for y, using formula method;

y = 15 or 5

Solve for x;

x = 20 -15 = 5 or

x = 20 - 5 = 15

The perimeter of first = 4x = 4 x 5 = 20 cm

The perimeter of the second = 4y = 4 x 15 = 60 cm

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The angle in radians in simplest form is 7π/4 radians.

In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = rθ

Where:

By substituting the given parameters into the arc length formula, we have the following;

7π/2 = 2 × θ

θ = 7π/4 radians.

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The 3 : 5 ratio of the number of cups of sparkling water to the number of cups of apple juice indicates;

7. a) 12 cups of sparkling water

b) 15 cups of apple juice

c) Please find attached the required graph of the pairs of measurements, which are plotted as points using MS Excel

A ratio expresses the quantitative relationship between two quantities, and it is obtained by dividing the quantity of one by the other.

7. The ratio of the number of cups of sparkling water to the number of cups of apple juice = 3 to 5

a) Where the number of cups of apple juice = 20, we get;

20 = 4 × 5

Therefore, the number of cups of apple juice in the current mixture is 4 times the amount that is mixed with 3 cups of sparkling water

b) 9 cups of sparkling water is 3 times the amount required per 5 cups of apple juice

c) The plot of the points can be presented as follows;

(3, 5), (9, 15), (12, 20)

Please find attached the graph showing the pairs of measurements, plotted as points, created with MS Excel

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The number of non-working light bulbs that would be expected in the group of 1,000 light bulbs is: 50 bulbs

In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.

We are told that a sample of 40 bulbs were picked from a box of 1000 bulbs and it was discovered that 2 of the bulbs were not working. Thus:

Fraction of bulbs not working = 2/40 = 0.05

Thus, number of bulbs not working in a sample of 1000 bulbs is:

0.05 * 1000 = 50 bulbs

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The set of integers that will be in A but not B and C will be 24, 32, 40,

The multiples of 8 comprise a set of {8, 16, 24, 32, 40, ...}, while the multiples of 4 correspond to {4, 8, 12, 16, 20, ...} and  those of 2 are documented as {2, 4, 6, 8, 10, …}. The intersection of these two sets, B and C (B ∩ C = {4, 8, 12, 16, 20, ...}) remains unchanged.

It should be noted that to obtain the number of integers found in the multples of 8 that aren’t multiples either of 4 or 2, the intersection needs to be excluded from set A. This will yield {24, 32, 40, ...} - thus it is concluded that the integer set of multiples of 8, but not of 4 or 2, is {24, 32, 40, ...}

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Answer:

The smaller the coefficient (the number in front of the x), the wider the parabola

Step-by-step explanation:

The amount of soil to fill the garden box is V = 1,134 inches³

Given data ,

Let the volume of the first rectangular box be V₁

Let the volume of the second rectangular box be V₂

where Volume of Rectangle = Length x Width x Height

So , V₁ = 21 x 7 x 2

V₁ = 294 inches³

And , V₂ = 12 x 10 x ( 7 )

V₂ = 120 x 7

V₂ = 840 inches³

And , the total soil in the garden box = V₁ + V₂

Amount of soil in garden box = 1,134 inches³

Hence , the volume is V = 1,134 inches³

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Answer:

the answer is b

Step-by-step explanation:

The relationship between the mean and variance of the exponential distribution is (c) variance is the square of the mean.

In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.

The exponential distribution is widely used in various fields such as

For example, it can be used to model the time between machine failures or the time between arrivals of customers at a service facility.

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