The table describes the quadratic function p(x). x p(x) -4 24 -3 9 -20 -1 -3 0 2 0 What is the equation of p(x) in vertex form? Op(x) = 2(x - 1)² - 3 p(x) = 2(x + 1)² - 3 Op(x) = 3(x - 1)² – 3 p(x) = 3(x - 1)² – 3​

Answer:

55

Step-by-step explanation:

0* .4

28*.5

410*.1

Answer:

a) 192Km

b) 50

Step-by-step explanation:

The ladder will reach up the side of the house to a height of approximately 47.1 feet.

We can use the Pythagorean theorem to solve this problem. Let x be the distance between the base of the ladder and the house after Jevonte pulls the ladder 3 feet farther from the house. Then, we have a right triangle with legs x and 48 feet, and hypotenuse 52 feet (the length of the ladder).

Using the Pythagorean theorem, we have:

x² + 48² = 52²

Simplifying, we get:

x² + 2304 = 2704

x² = 400

x = 20

Therefore, Jevonte pulls the ladder 3 feet farther from the house, so the ladder is now 23 feet away from the house. The ladder will reach up the side of the house to a height of:

√(52² - 23²) = 47.1 feet (rounded to the nearest tenth)

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The solutions of the equation tan(3) + 1 = sec(3) in the interval [0, 2) are approximately:

3 ≈ 0.523599 radians or 30 degrees (in the first quadrant)

3 + π ≈ 3.66444 radians or 210 degrees (in the third quadrant)

The equation tan(3) + 1 = sec(3) can be rewritten as:

tan(3) + 1 = 1/cos(3)

Multiplying both sides by cos(3), we get:

sin(3) cos(3) + cos(3) = 1

Using the identity sin(2x) = 2sin(x)cos(x), we can rewrite the left-hand side as:

sin(2*3) + cos(3) = 1

Simplifying this expression, we get:

2sin(3)cos(3) + cos(3) = 1

Factorizing out cos(3), we get:

cos(3)(2sin(3) + 1) = 1

Dividing both sides by 2sin(3) + 1, we get:

cos(3) = 1/(2sin(3) + 1)

We know that sin^2(3) + cos^2(3) = 1, so we can substitute cos^2(3) = 1 - sin^2(3) into the above equation and simplify:

1/(2sin(3) + 1) = cos(3) = sqrt(1 - sin^2(3))

Squaring both sides and simplifying, we get:

(2sin(3) + 1)^2 = 1 - sin^2(3)

Expanding the left-hand side and simplifying, we get:

4sin^3(3) - 3sin^2(3) - 3sin(3) + 1 = 0

This is a cubic equation in sin(3), which can be solved using various methods, such as Cardano's formula or numerical methods. However, the solutions are quite complicated and involve complex numbers.

In the interval [0, 2), we can use a numerical method, such as Newton's method, to find an approximate solution. Starting with an initial guess of sin(3) = 0.5, we can iteratively apply the formula:

sin(3)_n+1 = sin(3)_n - f(sin(3)_n)/f'(sin(3)_n)

where f(sin(3)) = 4sin^3(3) - 3sin^2(3) - 3sin(3) + 1 and f'(sin(3)) = 12sin^2(3) - 6sin(3) - 3.

After several iterations, we find that sin(3) ≈ 0.464758. Substituting this into the equation cos(3) = 1/(2sin(3) + 1), we get cos(3) ≈ 0.885005.

Therefore, the solutions of the equation tan(3) + 1 = sec(3) in the interval [0, 2) are approximately:

3 ≈ 0.523599 radians or 30 degrees (in the first quadrant)

3 + π ≈ 3.66444 radians or 210 degrees (in the third quadrant)

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The equation of the ellipse  derived as is

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1.

The equation of foci is

F₁ = (h - √(a^2 - b^2), k) , F₂ = (h + √(a^2 - b^2), k)

An ellipse is  described as a set of points in a plane such that the sum of the distances from each point to two fixed points, called foci, is constant.

We can write the equation of an ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

where (h, k) = the center of the ellipse,

a = the semi-major axis,

and b = the semi-minor axis.

The foci of the ellipse are located along the major axis and are equidistant from the center, with a distance of : √(a^2 - b^2).

we know also the formula to find the foci of an ellipse is:

F₁ = (h - √(a^2 - b^2), k)

F₂ = (h + √(a^2 - b^2), k)

The sum of the distances from each point on the ellipse to the foci is constant. The equation can then be written as:

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

Simplifying, we then can write  the equation of the ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

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VZ is 92.5. WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.

what is midsegment  ?

A midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. It is also known as a midline. The midsegment of a triangle is parallel to the third side of the triangle, and its length is half the length of the third side.

In the given question,

Since WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.

Let's call the length of AX as L. Then, we have:

WY = 11t = 1/2 L

Multiplying both sides by 2, we get:

22t = L

Now, we can use this information to find VZ. Since WY is also parallel to VZ, we have:

WV = VZ

Substituting WV = L/2 and VZ = 5t + 51, we get:

L/2 = 5t + 51

Substituting L = 22t, we get:

22t/2 = 5t + 51

11t = 5t + 51

6t = 51

t = 8.5

Substituting t = 8.5 in the equation for VZ, we get:

VZ = 5t + 51 = 5(8.5) + 51 = 92.5

Therefore, VZ is 92.5.

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Answer: d. m = 2

Step-by-step explanation:

First, we will write a slope-intercept equation using the y-intercept given.

       y = mx + 4

Next, we will substitute the given point and solve for m, the slope.

       y = mx + 4

       (8) = m(2) + 4

       4 = 2m

       m = 2

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[tex]\boxed{\sf m=2}.[/tex]

In order to find the slope of any linear equation you need at least 2 points the line passes through. We're explicitly provided one, (2, 8), we just need to figure out the other one.

When the statement says that the line has a y-intercept of 4, it means that at a point with y=4 the function touches the y axis. The only way to touch the y-axis is if the x value is 0. Hence, another given point is (0, 4).

Formula: [tex]\sf m=\dfrac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

Naming the variables (can be done arbitrarily but always make sure the y's are actual y values from the ordered pairs and that x₁ goes with its corresponding y₁ value from the ordered pair):

[tex]x_{1} =2;\\x_{2} =0;\\y_{1} =8;\\y_{2} =4.[/tex]

Now substituting these values in the formula:

[tex]\sf m=\dfrac{(4)-(8) }{(0) -(2) }=\dfrac{-4}{-2} =\boxed{\sf 2}.[/tex]

Check out the attached image to see the graphed line.

Answer:

-13n + 5

Step-by-step explanation:

Give:

– 7n + –3 – 6n + 3 + 5

To Find:

simplify

Explanation:

– 7n + –3 – 6n + 3 + 5

= (-7n - 6n) + (-3 + 3 + 5)

=  - 13n + 0 + 5

= -13n + 5

Final Answer:

-13n + 5

From the given data, we have:

| x   | 2   | 3   | 4   | 5   | 6   |

| --- | --- | --- | --- | --- | --- |

| p(x) |    |    |    |    |    |

We need to find the value of p(x > 3).

We know that the sum of all the probabilities is equal to 1. So, we can find the missing probability by subtracting the sum of the probabilities we know from 1.

p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = 1

We don't know the value of p(x = 2), so we can't directly calculate p(x > 3). But we can find p(x ≤ 3) and subtract it from 1 to get p(x > 3).

p(x ≤ 3) = p(x = 2) + p(x = 3)

To find p(x = 2), we can use the fact that the sum of all the probabilities is 1:

p(x = 2) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6))

Now we can substitute this into the equation for p(x ≤ 3) and solve:

p(x ≤ 3) = p(x = 2) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6)) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 4) + p(x = 5) + p(x = 6))

Finally, we can subtract p(x ≤ 3) from 1 to get p(x > 3):

p(x > 3) = 1 - p(x ≤ 3)

p(x > 3) = 1 - (1 - (p(x = 4) + p(x = 5) + p(x = 6)))

p(x > 3) = p(x = 4) + p(x = 5) + p(x = 6)

Therefore, the value of p(x > 3) is the sum of the probabilities for x = 4, 5, and 6.

Answer:

6 out of 36 or 1 out of 6

Step-by-step explanation:

There are 36 possible ways two dice can roll, so the probability of the sum of seven is 6 out of 36, or 1/6.

[tex]\boxed{\sf 16.67\%}.[/tex]

So since we have a pair of dice, assuming they are standard 6 faced dices, the total amount of outcomes is given by just multiplying the number of faces or different numbers that the dices can present:

6 x 6 = 36 possible outcomes.

Now, here we need to count all the possible cases where the outcome of both dices will equal 7. And there are said cases:

1 + 6 = 7

Explanation. Here the first dice presented number 1 and the second presented number 6, adding up to 7.

Other cases that meet the requirement:

2 + 5 = 7

3 + 4 = 7

4 + 3 = 7

5 + 2 = 7

6 + 1 = 7

So the total amount of events that will meet the requirement is 6.

So if we have an event with 36 possible outcomes, and only 6 of those 36 outcomes will mean a success on the experiment. Then, to find the probability of those 6 events from happening all we need to do is divide the amount of events considered "success" which is the numbers adding up to 7 by the total amout of outcomes (36).

So, the probability of rolling a sum of 7 with 2 dices is:

[tex]\sf P(\dfrac{6}{36} )=\dfrac{1}{6} =\boxed{\sf 16.67\%}.[/tex]

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Answer:

25

Step-by-step explanation:

To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:

[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]

The constant term is 25.

Could I get Brainilest, please? I'm trying to get to the expert level

The cost of one T-shirt and one jacket is $12 and $13 respectively.

Let

cost of one t-shirt = x

cost of one jacket = y

8x + 3y = 135

7x + 5y = 149

Multiply (1) by 5 and (2) by 3

40x + 15y = 675

21x + 15y = 447

Subtract the equations to eliminate y

40x - 21x = 675 - 447

19x = 228

divide both sides by 19

x = 228/19

x = 12

Substitute x = 12 into (1)

8x + 3y = 135

8(12) + 3y = 135

96 + 3y = 135

3y = 135 - 96

3y = 39

y = 39/3

y = 13

Hence, a T-shirt and a Jacket cost $12 and $13 respectively.

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The p-value from the hypothesis is 0.0583 which is not significant at p<0.05

To determine the p-value of the hypothesis, we need to use the formula;

z = (x - a) / √(a(1 - a)/n)

x = 93 / 900 = 31/300 = 0.103

a = 12% = 12/100 = 0.12

n = 900

Substituting the values into the formula;

z = (0.103 - 0.12)/√(0.12(1 - 0.12)/900)

z = -0.017 / √0.0001173

z = -1.569

Using a standard normal distribution table;

p-value = 0.058324

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The answer to Monnor's problem is NOTA

For any quadratic equation of the form ax² + bx + c, the sum of roots is given by:

sum of roots = -b/a

In this case, x² - 7x + 5 = 0. Where a = 1 and b = -7. Thus:

sum of roots = -(-7)/1 = 7

Since Monnor must find the square of the sum of the roots of the equation, we have:

square of the sum of the roots = 7² = 49

Thus, the answer to Monnor's problem is NOTA

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Valid row operations are:

Invalid row operations are:

0R₁ → R₁ (this is equivalent to multiplying a row by zero, which is not a valid row operation)

R₃ ÷ 0 → R₃ (division by zero is undefined)

-2 ÷ R₁ → R₁ (division by a variable is not a valid row operation)

2R₁ + R₂ → R₂ (the row operation should be adding multiples of one row to another row, not a combination of multiple rows)

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The result of adding -4 (row 1) to row 3 is determined as (0  - 9   2)|12.

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  2  1] | -5

To multiply row by -4, we will multiply each entity by 4 as shown below;

= -4(1 2  1) | -5

= (-4  -8  - 4) |20

To add the result to 3;

(-4  -8  - 4)|20 + (4  - 1   6) | -8

= (0  - 9   2)|12

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.

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(9,21) is a solution of y=x+12

When is an ordered pair a solution?

To find if an ordered pair (x,y) is a solution to an equation, substitute the x-value and y-value from the ordered pair into the equation, evaluate both sides of the equation individually, and see if the equation is true.

Warning: A common mistake is to use the first coordinate (the x-coordinate, on the left of the ordered pair) as the value on the left side of the equation, and the second coordinate (the y-coordinate, on the right of the ordered pair), as the value for the right side of the equation.  Make sure to substitute the x-value for the "x" in the equation, and the y-value for the "y" in the equation.

Going through the choices:

Point A (24,12)

y = x+12

(12)  ??  (24) + 12

12  ≠  36

not equal -- not a solution

Point B (-12,-24)

y = x+12

(-24)  ??  (-12) + 12

-24  ≠  0

not equal -- not a solution

Point C (9,21)

y = x+12

(21)  ??  (9) + 12

21  =  21

equal -- (9,21) is a solution

Point D (0,-12)

y = x+12

(-12)  ??  (0) + 12

-12  ≠  12

not equal -- not a solution

The systems of linear equations can be classified as "consistent dependent," "consistent independent," or "inconsistent" as follows:

A. System A = Inconsistent (No solution)

B. System B = Consistent dependent (Indefinitely many solutions)

C. System C = Consistent independent (A unique solution)

To identify the systems of linear equations, you first need to note the meaning of the different systems of equations. First, the Consistent dependent has two equations that represent the same line, so they intersect at infinitely many points and any point on the line represents a solution to the system.

Next, the Consistent independent has the two equations represented by two distinct non-parallel lines, so they intersect at exactly one point, which is the unique solution to the system.

Finally, the Inconsistent has two equations that are represented by two distinct parallel lines, so they do not intersect, and there is no solution to the system.

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Step-by-step explanation:

You will have to know more....like the area or the perimeter or the diagonal measure to determine the base if you only have the height.

The events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.

To calculate the percentage of the student population being surveyed, you can use the formula:

Percentage = (Number of students surveyed / Total number of students) * 100

In this case, the number of students surveyed is 15 (girls' basketball team), and the total number of students is 1,000.

Percentage = (15 / 1,000) * 100 = 1.5%

So, the events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.

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The events committee wants to survey students about a school dance. The committee is

meeting in the gym, where the girls' basketball team is practicing. They survey the

players on the girls' basketball team.

If there are 1,000 students in the school, and the girls' basketball team has 15 players, what percentage of the student population is being surveyed by the events committee about the school dance?

Answer:

Phone dies in 6 hours

Step-by-step explanation:

Answer:

x = 45°

Because there are 180° in a triangle

The row operation is given as follows:

Division by 7 = multiplication by 1/7.

The matrix after the row operation is then given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

The element at row 1 and column 1 is given as follows:

7.

An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:

7/k = 1

k = 7.

The first row is given as follows:

7, -4 and 8.

Dividing every element of the first row by 7, the resulting matrix is then given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

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There are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

What is combinations?

Combinations are a mathematical concept used to count the number of ways that a certain number of items can be selected from a larger set of items without regard to the order in which they are selected.

We can use combinations to solve this problem. We need to choose 8 inquiries out of 16 for the first agent, and the remaining 8 inquiries will be handled by the second agent.

The number of ways to choose 8 inquiries out of 16 is:

C(16, 8) = 16! ÷ (8! * (16-8)!) = 12870

This is the number of ways the inquiries can be directed to one agent. Since there are two agents and each handles 8 inquiries, we need to divide this number by 2 to avoid counting each arrangement twice:

12870 ÷2 = 6435

Therefore, there are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

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Step-by-step explanation:

Answer

The price of 6 DVDs, including sales tax = $62.87

Sales tax = $2.99

Required:

The cost of one DVD.

Explanation:

Step 1: Price of 6 DVDs excluding sales tax.

The price of 6 DVDs excluding sales tax = $62.87 - $2.99 = $59.88

Step 2: Use the Unitary Method:

According to the question,

6 DVDs price = $59.88

1 DVD price excluding sales tax = $ 59.88/6

Open and clear communication is crucial when discussing estate planning and wills with family members to prevent misunderstandings and hurt feelings.

1. It is understandable that Brennan and Maureen feel shocked and disappointed with the reduced inheritance.

While it is not required for parents to disclose every detail of their estate planning to their children, it would have been helpful if they had discussed the impact of the gifts on their estate and their final inheritance.

Clear communication can prevent misunderstandings and hurt feelings in the future.

2. Brennan and Maureen have a responsibility to discuss the will with their parents. It is essential to have an open and honest conversation about their parents' wishes and intentions to avoid any confusion or disputes in the future.

While it can be uncomfortable to talk about death and inheritance, it is a crucial conversation to have.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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Answer:

90% of 300 = .90 × 300 = 270 high- definition televisions on order.

The function f(x) = (1/2)x^2 + 3x - 5 has a minimum value

To determine whether the function f(x) = (1/2)x^2 + 3x - 5 has a minimum or maximum value, we can use the fact that the vertex of a quadratic function represents the minimum or maximum point of the function.

To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.

In this case, a = 1/2 and b = 3, so we have:

x = -b/2a = -(3)/(2(1/2)) = -3

To find the corresponding y-coordinate, we can substitute x = -3 into the function:

f(-3) = (1/2)(-3)^2 + 3(-3) - 5 = -9.5

Since the coefficient of the quadratic term is positive, we know that the parabola opens upward and the vertex represents a minimum value.

Therefore, the minimum value of the function is -9.5, which occurs at x = -3.

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The two items that together cost 34% of her budget have a summed cost of $170

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

She has a budget of $500.

To calculate which two items together cost 34% of her budget, we use

Amount = 34% * Budget

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

Amount = 34% * 500

Evaluate

Amount = 170

Hence, the two items would have a summed cost of $170

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