Ana dives into a pool off of a springboard high dive.
Her height (in meters above the water), seconds after diving, is modeled by

h(x)=−5(x+1)(x−3)h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 3, right parenthesis
How many seconds after diving will Ana hit the water?

From the knowledge of vertical angle theorem, angle TXS is equal to angle RXU which is equal to

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

When two lines intersect at a point, they form four angles around that point, and the vertical angles are the pair of opposite angles, which are across from each other and not adjacent.

Vertical angel theorem have it that Vertical angles are congruent, which means that they have the same measure or size. This theorem helps us in providing a correct answer for the problem

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Carly will need to buy 27.05 gallons of gas for the trip, which will cost her $7.28.

To calculate the total cost of the road trip, we need to find out how many gallons of gas Carly will need and then multiply that by the cost per gallon.

First, we need to convert the distance from miles to gallons, using the truck's fuel efficiency of 21 miles per gallon

568 miles ÷ 21 miles per gallon = 27.05 gallons

So Carly will need approximately 27.05 gallons of gas for the trip.

Next, we need to convert the cost of gas from liters to gallons. There are 3.79 liters in 1 gallon, so the cost of gas is:

$1.02 per liter ÷ 3.79 liters per gallon = $0.269 per gallon

Finally, we can calculate the total cost of the road trip by multiplying the number of gallons of gas by the cost per gallon

27.05 gallons × $0.269 per gallon = $7.28

Therefore, the road trip will cost Carly approximately $7.28.

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Alex will pay 13.8 for her lunch after adding a 15% tip.

We will calculate the amount she paid for her lunch by calculating the tip she paid and adding it to the original price of the lunch(i.e. 12).

[tex]\implies{\sf{15 \% \ of \ 12 \ = \ 12 \times \dfrac{\cancel{15}}{\cancel{100}} }}[/tex]

[tex]\implies{\sf{Tip = \cancel{12} \times \dfrac{3}{\cancel{20}}}}[/tex]

[tex]\implies{\sf{Tip = 3 \times \dfrac{3}{5}}}[/tex]

[tex]\implies{\sf{Tip = \dfrac{9}{5}}}[/tex]

[tex]\implies{\sf{ Tip = 1.8}}[/tex]

Now, add the amount of lunch and tip

[tex]\implies{\bf{ Total \ amount = 12 + 1.8}} \\ \implies{\bf{Total \ amount = 13.8}[/tex]

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Answer:

14

Step-by-step explanation:

28 mm is the diameter of the button, so we have to find the radius, which is half of the diameter.

28/2=14

So, the radius of this button is 14 mm

Thus, 3290 persons in total have entered the contest. We calculated the sum using the following arithmetic series formula: [tex]S = (n/2) * [2a + (n-1)d][/tex]

The phrase "arithmetic progression" (AP) describes a series of numbers in which every term—aside from the first—is derived by multiplying the previous term by a set value. The common difference is a constant number. The following equation can be used to symbolise an arithmetic progression: a n = a 1 + (n-1)d where d is the clear differentiation, a n is the n - th term, a 1 represents the initial term, and n is the total number of terms. For instance, an arithmetic progression with 5 terms and a common difference of 3 starting at 1 would be: 1, 4, 7, 10, 13

given

The formula for the sum of an arithmetic series can be used to determine the total number of contestants:

[tex]S = (n/2) * [2a + (n-1)d][/tex]

Here are the facts:

a = 23 (the first phrase) (the first term)

d = 7 (the usual difference, since each day 7 more participants enter the contest) (the common difference, since each day 7 more people enter the contest)

n = 28 (the number of terms, since the contest lasts 28 days) (the number of terms, since the contest lasts 28 days)

With these values entered into the formula, we obtain:

S = (28/2) * [2(23) + (28-1)(7)]

S = 14 * [46 + 189]

S = 14 * 235

S = 3290

Thus, 3290 persons in total have entered the contest. We calculated the sum using the following arithmetic series formula: S = (n/2) * [2a + (n-1)d].

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Answer:

x=9,-2

Step-by-step explanation:

in this case [tex]x^{2} -7x-18[/tex]

you can chose if you want the -7x and -18 to be a or b because [tex]x^{2}[/tex] would be c.

a. The Hamiltonian is given by:

H = T + V = (p² / 2I) + 0 = p² / 2I

b. Since the commutator is zero, we can conclude that the Hamiltonian and L commute.

c. The energy eigenfunctions are given by:

ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) × [tex]e^{(inφ)[/tex] × P[tex]_{n}[/tex](cosθ)

When time is not explicitly included in the function, it is used to characterize a dynamic system (such as the motion of a particle) in terms of momentum components and coordinates of space and time, and it is equal to the total energy of the system.

(a) The Hamiltonian is given by:

H = T + V = (p² / 2I) + 0 = p² / 2I

where T is the kinetic energy and V is the potential energy. Since the rotator is constrained to rotate in the x-y plane, there is no potential energy.

b. To show that the Hamiltonian and L commute, we need to calculate their commutator:

[H, L] = HL - LH

where L is the angular momentum operator given by L = r x p, where r is the position vector and p is the momentum operator.

HL = (p² / 2I) × (r × p) - (r × p) × (p² / 2I)

  = (1/2I) × (p² × r × p - r × p × p²)

  = (1/2I) × [p², r x p]

LH = (r x p) × (p² / 2I) - (p² / 2I) × (r x p)

  = (1/2I) × (r × p × p² - p² × r x p)

  = -(1/2I) × [p², r x p]

Therefore, [H, L] = [p², r x p] / 2I - [p², r x p] / 2I = 0.

Since the commutator is zero, we can conclude that the Hamiltonian and L commute.

c. The allowed energies of the rigid rotator are given by:

E[tex]_{n}[/tex]= (n² × h²) / (8I)

where n is a positive integer and h is Planck's constant. The energy levels are quantized and spaced equally apart, with the energy increasing as n increases.

The energy eigenfunctions are given by:

ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) * [tex]e^{(inφ)[/tex] * P[tex]_{n}[/tex](cosθ)

where θ is the polar angle and φ is the azimuthal angle, and P_n(x) is the n-th order Legendre polynomial. The eigenfunctions are normalized and orthogonal, with each energy level having a unique set of eigenfunctions.

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Answer:

We can start by calculating the total amount of money earned per week:

$12.50/hour x 25 hours/week = $312.50/week

To find out how many weeks it will take to earn $3,437.50, we can set up a proportion:

Total amount earned / Amount earned per week = Number of weeks

$3,437.50 / $312.50/week = 11 weeks

Therefore, it will take 11 weeks to earn $3,437.50 working 25 hours per week at a rate of $12.50 per hour.

The possible number of pounds of candy that Linda will buy can be shown as p > 5 .

Let's use algebra to solve the problem. We know that Linda will spend more than $30 on candy, so we can write:

6p > 30

Dividing both sides by 6, we get :

p > 5

This means that Linda must buy more than 5 pounds of candy in order to spend more than $30. And this can be shown by the expression, p > 5.

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One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:

$4a^5 - 3a^4 + 2a^3 - 7a^2$

A polynomial expression is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. The term "polynomial" comes from the fact that the expression can be thought of as a sum of many terms, each of which is a product of one or more variables raised to a non-negative integer power.

For example, the expression 3x^2 + 4x - 1 is a polynomial in one variable, x, with three terms. The first term is 3x^2, the second term is 4x, and the third term is -1. The highest power of the variable in this expression is 2, which makes it a polynomial of degree 2.

Polynomial expressions can be written in standard form, where the terms are arranged in descending order of degree and the coefficients are written with the highest power of the variable first. For example, the expression above could be written in standard form as 3x^2 + 4x - 1.

One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:

$4a^5 - 3a^4 + 2a^3 - 7a^2$

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Answer: 3. is 13

4. is 36

5. is 21

6. is 15

7. is 21

8. is 2

9. is 6

10. is 45

Step-by-step explanation:

the letters are there to just confuse you. i promise its all right <-- the answers

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Answer:

true

Step-by-step explanation:

because there's less humidity

Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.

In mathematics, rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

Let's represent the number of books sold as "x". Then, the total amount of money that Mrs. Dundee will make from the first publisher is:

Total from first publisher = $80,000 + ($3 x x) = $3x + $80,000

Similarly, the total amount of money that she will make from the second publisher is:

Total from second publisher = $30,000 + ($5 x x) = $5x + $30,000

We want to find the range of values of x for which the total amount from the second publisher is greater than the total amount from the first publisher. In other words, we want to find the range of values of x for which,

$5x + $30,000 > $3x + $80,000

Simplifying this inequality, we get:

$2x > $50,000

x > $25,000

Therefore, Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.

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Answer: The formula for the volume of a cone is V=1/3hπr²

Step-by-step explanation: The volume or capacity of a cone is one-third of its corresponding cylinder. This means that when a cone and a cylinder have the same base dimension and height, the volume of the cone is one-third of the volume of the cylinder.

Answer:

x=4 y=3

Step-by-step explanation:

because y=3 and x=4

Answer:

1.6

Step-by-step explanation:

0.8×2=1.6

double radius to find diameter

Answer:

1.6ft

Step-by-step explanation:

We did a similar problem, except we had to go from diameter to radius.

Remember, to go from diameter to radius we divided by 2.  Now, we do the inverse as we are going from radius to diameter.

We multiply 0.8 x 2 to get 1.6 ft

So the diameter of this object is 1.6ft

ans. (c) 1/2

given line,

y = 1/2 x -2

we know that the slope form of the line is given by

y =mx+c

comparing both equations we get

m= 1/2

hence, the slope is 1/2

The sums that prove that the wooden boards can create a triangular outline according to triangle inequality rule are:

The triangle inequality rule states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Testing each combination of sides, we get:

Case 1:

Let 5 feet be the third side

Then,

2.5 + 4 > 5

6.5 > 5

Case 2:

Let 2.5 feet be the third side

Then,

4 + 5 > 2.5

9 > 2.5

Case 3:

Let 4 feet be the third side

Then,

5 + 2.5 > 4

7.5 > 4

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1) Note that the rates of change (slope) are 4 and 30 respectively over (0,3).  This mean that the slope of y=1+4^x is much higher. This is also evidenced in the graph.

It is crucial to compare the slopes of linear equations because it can disclose vital information about how the dependent variable varies in relation to the independent variable.

It may also be used to find patterns or trends in data and forecast future behavior.

Note that to get the y values of each function, we just plugged in the value of x into the equation to solve. See the attached sheet showing the formula .

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Answer:

b + 17

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 3(6 + b) - (2b + 1)

Let's simplify the expression,

→ 3(6 + b) - (2b + 1)

Applying Distributive property:

→ 3(6) + 3(b) - (2b) - (1)

→ 18 + 3b - 2b - 1

Combining the like terms:

→ (3b - 2b) + (18 - 1)

→ (1b) + (17)

→ b + 17

Hence, the answer is b + 17.

Answer:

5 and 1/6 hours

Step By Step Explanation:

Answer: 6(x - (23/2))² = 14x + 1044

Step-by-step explanation:

First, we need to move all the terms to one side of the equation:

6x² - 46x - 312 - 14x = 0

Next, we need to factor out the coefficient of the x² term:

6(x² - (46/6)x) - 312 - 14x = 0

Simplifying:

6(x² - 23x) - 312 - 14x = 0

To complete the square, we need to add and subtract the square of half the coefficient of the x-term inside the parentheses:

6[(x - (23/2))² - (23/2)²] - 312 - 14x = 0

Simplifying:

6(x - (23/2))² - 6(23/2)² - 312 - 14x = 0

Expanding the square term:

6(x - (23/2))² - 1044 - 14x = 0

Finally, adding 1044 to both sides and simplifying:

6(x - (23/2))² = 14x + 1044

The intermediate step after completing the square is:

6(x - (23/2))² = 14x + 1044

the amount of paint required is dependent on the size of the area that needs to be painted.

In an equation or algebraic expression, an uncertain amount is denoted by a symbol in algebra, which is often a letter. A variable is, in the simplest terms, a quantity that can change and is not fixed. The two primary categories of variables are categorical and numerical. Then, for both categorical and numerical variables, discrete or continuous subcategories are created for each category. In this section, a summary of several categories is provided. a measure that can take many different forms. Something that can alter; the sign of a variable; a variable in a scientific experiment.

Because it is the variable which the homeowner may alter or control, the area of the house that needs to be painted in this scenario is the independent variable. Because it depends on the portion of the home that needs to be painted, the overall quantity of paints that need to be obtained is a variable that is dependent. To put it a different way, the amount of paint required depends on the size of the area that needs to be painted.

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Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

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The surface area of the cube is  3 6/16 cm²

To determine the value of the surface area of the cube, we need too know the formula

The formula for calculating the surface area of a cube is represented as;

Surface area = 6a²

Such that the variable 'a' is the length of the side of the cube

From the information given, we have that;

a = 3/4

Substitute the value, we get;

Surface area = 6 (3/4)²

find the squares

Surface area = 6(9/16)

Multiply the values

Surface area = 3 6/16 cm²

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The second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

An expression is a grouping of figures, symbols, and algebra (such as addition, reduction, multiply, and division) that expresses a value. Variables, that are symbols for unknowable values, are symbols that can be included in expressions. The statement can be evaluated to give a specific value after the contents of the variables are assigned. An expression using a variable x, for instance, is 3x + 5. When we give x a number of 2, the expression is evaluated to: 3(2) + 5 = 6 + 5 = 11 . As a result, the expression's value at x = 2 is 11.

given

a. Assume that "S" represents the number of field goals Suzy scores each minute and "J" represents the number of field goals Joshua scores each minute.

The calculation for the total number of field goals Suzy and Joshua score in their 30-minute workout is as follows:

[tex]Field goals total = (9 + 10 S) + (20 (S + J)[/tex]

The first term (9 + 10S) denotes Suzy's total number of field goals in the first 10 minutes, while the second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

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They should mix 16 pounds of City Roast Columbian coffee with 4 pounds of French Roast Columbian coffee to make their blend.

Let x be the number of pounds of City Roast Columbian coffee.

Let y be the number of pounds of French Roast Columbian coffee.

The total cost of the blend is 7.80x + 8.10y

The total weight is x + y = 20.

We can write an equation for the cost per pound:

(7.80x + 8.10y) / 20 = 7.86.

We will multiply both sides by 20 which gives:

7.80x + 8.10y = 157.20.

We can use this equation along with the total weight equation to solve for x and y:

x + y = 20

y = 20 - x (subtract x from both sides)

7.80x + 8.10(20 - x) = 157.20 (substitute y = 20 - x into the cost equation)

7.80x + 162 - 8.10x = 157.20 (distribute)

-0.30x = -4.80

x = 16

Solve for the equation (x + y = 20):

y = 20 - x

y = 20 - 16

y = 4.

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The main advantage of an independent measures design is that it reduces the risk of order or practice effects and minimizes the influence of individual differences between participant

An independent measures design, also known as a between-subjects design, is a type of research study in which different groups of participants are used for each condition being tested.

In other words, each participant is only exposed to one condition, and the data from each group is analyzed and compared to determine if there are any significant differences between the groups.

The main characteristics of an independent measures design are:

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Answer:

f(x) C= x+50 x=17.50$/h

Step-by-step explanation:

I might not be sure about it, but it might be a function that is f(x) C= x + 50 dollars

x=17.50 dollars /hour

so that means if it is 1 hour, then 17.50$ +50$ which is 67.50$, if it's 2 hours then 17.50$/h = n$/2h so n=17.50$ *2 = 35$ + 50$ = 85$