Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.

The completed statement based on two-dimensional motion in the x-y plane can be presented as follows;

The two-dimensional motion in the x-y plane, the x part of the motion and the y part of the motion are independent, whether or not there is an acceleration in any direction. The correct option is therefore;

D) Whether or not there is an acceleration in any direction

Two-dimensional motion in the x-y plane can be analyzed by separating them into its horizontal (x) and vertical (y) components, and analyze each component using the one dimensional equations of motion.

The meaning of the motion on the x-y plane is that the x-direction motion of an object exclusive or excludes the effect of the motion of the object in the y-direction, vis a vis, the y-direction motion.

The horizontal and vertical components of the motion can be analyzes individually or by themselves, by making use of the equations of motion for a one-dimensional motion, whether or not there is an acceleration in any direction as the acceleration are also evaluated using one dimensional equations.

The possible options in the question from a similar question on the internet are;

A) When there is no acceleration in any direction

B) When there is no acceleration in one direction

C) Only when an acceleration is present in both directions

D) Whether or not there is an acceleration in either direction

E) Only when the acceleration is in the y-direction

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Answer:

Cupcake

Step-by-step explanation:

Because the sale price is bigger

Answer:

2^4

Step-by-step explanation:

2^2 = 2 * 2 = 4

4^4 = 4*4*4*4 = 256

2^4 = 4*4 = 16

8^2 = 8*8 = 64

2^8 = 2*2*2*2*2*2*2*2 = 256

Hence, 16 can be written as 2^4

Thus, Answer is [C] 2^4

[RevyBreeze]

Answer:

wow sounds good and cheap im gonna go get salad now thanks alot

Step-by-step explanation:

The cost of 8 pounds of salad with a container is $7.05.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, At a salad bar, the cost per ounce is $0.85,

Assuming the total cost to be C and no. of ounces to be x.

∴ C(x) = 0.85x + 0.25 which represents the cost of any no. of ounces.

The cost of 8 ounces of salad will cost,

C(8) = 0.85×8 + 0.25.

C(8) = 6.8 + 0.25.

C(8) = 7.05.

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About 1.60% of all samples of 28 women in their 20s today have mean heights of at least 65.61 inches.

In order to solve this problem,

We have to use the central limit theorem,

which states that the sample means of a sufficiently large sample size from any population will be normally distributed.

We are given that the mean height of women in their 20s in the past was 64.4 inches, and we want to know what percentage of samples of 28 women today have a mean height of at least 65.61 inches.

We have to calculate the z-score for a mean height of 65.61 inches,

⇒ z = (65.61 - 64.4) / (2.29 / √(28))

⇒ z = 2.17

We can use a standard normal table or calculator to find the percentage of samples with a z-score of 2.17 or greater.

This turns out to be about 1.60%.

Therefore,

Today's samples of 28 women in their 20s had mean heights of at least 65.61 inches in roughly 1.60% of all cases.

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The frequency distribution table can be used to analyze the distribution of companies based on their per unit sales, and can help identify trends and patterns in the data.

To construct a frequency distribution of companies based on per unit sales, we need to gather data on the sales figures of each company and then categorize them into intervals of per unit sales.

Here is an example frequency distribution table based on per unit sales ($ millions):

Per unit sales ($ millions) Frequency
0.0 up to 0.5             2
0.5 up to 1                 4
1 up to 1.5                  6
1.5 up to 2                 8
2 up to 2.5                5
2.5 up to 3                3
3 up to 3.5                2
3.5 up to 4                1

In this table, we have eight intervals of per unit sales, ranging from 0.0 up to 4.0 million dollars. For each interval, we count the number of companies that fall within that range, and record the frequency. For example, we have 2 companies with sales figures between 0.0 and 0.5 million dollars, 4 companies with sales figures between 0.5 and 1 million dollars, and so on.

This frequency distribution table can be used to analyze the distribution of companies based on their per unit sales, and can help identify trends and patterns in the data.

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Answer:

2/7 ÷ 3/4 = 8/21

Step-by-step explanation:

Answer:

Hey there!

g(x) is 4x-1

f(g(x) is f(4x-1)

f(4x-1)=2(4x-1)-5

f(4x-1)=8x-2-5

f(4x-1)=8x-7

The answer is 8x-7

Let me know if this helps :)

The possible widths of the play area are 5 feet and 4 feet.

Given that Vanessa has 180 feet of fencing to build a rectangular play area for her dog and she wants the play area to enclose at least 1800 square feet.

Let's assume the width of the play area is x feet, then the length of the play area will be given by the formula L = (180 - 2x)/2 or L = 90 - x. So, the area of the play area can be given by the formula of the rectangle i.e. A = Length × Width.

Therefore, A = x(90 - x) = 90x - x². According to the problem, the area of the play area should be at least 1800 square feet. Hence, 90x - x² ≥ 1800.

Rearranging this inequality, we get x² - 90x + 1800 ≤ 0. Dividing each term by 90, we get x² - x + 20 ≤ 0.

Solving the inequality using the quadratic formula, we get x = [-(-1) ± √((-1)² - 4(1)(20))] / (2 × 1) or x = [1 ± √(81)] / 2.

So, the possible widths of the play area are x = (1 + √81)/2 = 5 feet and x = (1 - √81)/2 = 4 feet.

When x = 5 feet, L = 90 - 5 = 85 feet. The area of the play area = 5 × 85 = 425 square feet.

When x = 4 feet, L = 90 - 4 = 86 feet. The area of the play area = 4 × 86 = 344 square feet.

Hence, the possible widths of the play area are 5 feet and 4 feet.

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a. The factor of intersection is \($$(\sqrt{a}(1 + \sqrt{2}) \sqrt{a}(1 - \sqrt{2}))$$\) b. The vital is \($$\int_{0}^{\sqrt{a}(1 + \sqrt{2})} (\sqrt{x} - \sqrt{a}) - (\sqrt{a} - x) dx$$\). c. The location of the shaded location is \(7a + 4\sqrt{2}a\) square devices.

(a) To find the factors of the intersection of the two curves, we need to resolve the equation\($$\sqrt{x} - \sqrt{a} = \sqrt{a} - x$$\)

Squaring both facets, we get \($$x - 2\sqrt{a}x + a = a - 2\sqrt{a}x + x^2$$\)

Simplifying, we get \($$x^2 - 4\sqrt{a}x + 2a = 0$$\)

Using the quadratic components, we get\($$x = \frac{4\sqrt{a} \pm \sqrt{16a - 8a}}{2} = \frac{4\sqrt{a} \pm 2\sqrt{2}\sqrt{a}}{2} = \sqrt{a}(1 \pm \sqrt{2})$$\)

Since\($$x \geq 0$$\), we handiest take the tremendous root, so \($$x = \sqrt{a}(1 + \sqrt{2})$$\)

Plugging this into either equation, we get \($$y = \sqrt{a}(1 - \sqrt{2})$$\)

So the factor of intersection is \($$(\sqrt{a}(1 + \sqrt{2}), \sqrt{a}(1 - \sqrt{2}))$$\)

(b) To shape the integral that represents the vicinity of the shaded vicinity, we need to find the distinction among the top and decrease features and integrate over the interval of intersection.

The upper feature is \($$y = \sqrt{x} - \sqrt{a}$$\) and the lower function is \($$y = \sqrt{a} - x$$\). The c language of intersection is \($$[0, \sqrt{a}(1 + \sqrt{2})]$$\). So the vital is \($$\int_{0}^{\sqrt{a}(1 + \sqrt{2})} (\sqrt{x} - \sqrt{a}) - (\sqrt{a} - x) dx$$\)

(c) To find the place of the shaded area, we need to assess the indispensable. Using the electricity rule and the substitution rule, we get

\($$\begin{aligned}\int_{0}^{\sqrt{a}(1 + \sqrt{2})} (\sqrt{x} - \sqrt{a}) - (\sqrt{a} - x) dx &= \left[\frac{x^{3/2}}{\frac32} - x\sqrt{a}\right]_{0}^{\sqrt{a}(1 + \sqrt{2})} - \left[x\sqrt{a} - \frac{x^2}{2}\right]_{0}^{\sqrt{a}(1 + \sqrt{2})}\end{aligned}$$\)

\($$\begin{aligned}&= \left[\frac23 a(1 + \sqrt{2})^{3/2} - a(1 + \sqrt{2})^{3/2}\right] - 0\end{aligned}$$\)

\($$\begin{aligned}- \left[a(1 + \sqrt{2})^{3/2} - a(1 + \sqrt{2})^2\right] + 0\\&= a(1 + \sqrt{2})^{3/2}\left(\frac23 - 1 - 1\right) + a(1 + \sqrt{2})^2\\&= a(1 + 4\sqrt{2} + 6)\\&= 7a + 4\sqrt{2}a\end{aligned}$$\)

So the location of the shaded location is \(7a + 4\sqrt{2}a\) square devices.

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Answer:

1    $16.50

2    $28.50

3    $40.50

$4.50 + $12c

$100.50

Step-by-step explanation:

Please find attached the complete question

Total cost in dollars = fixed cost + (variable cost x number of CDs bought)

fixed cost = $4.50

variable cost = $12

number of cds bought = c

total cost in dollars = $4.50 + $12c

total cost in dollars when 1 cd is bought = $4.50 + $12(1) = $16.50

total cost in dollars when 2 cds are bought = $4.50 + $12(2) = $28.50

total cost in dollars when 3 cds are bought = $4.50 + $12(3) = $40.50

total cost in dollars when 8 cds are bought = $4.50 + $12(8) = $100.50

The solution for given inequality is - 30 and 18. So the answer is option c. x < −30 and x < 18.

In mathematics, an inequality is an unequal comparison between 2 algebraic terms or algebraic expressions. The signs we used in inequality are Lessthan (<), greater than (>) or Less than or equal to(≤), greater than or equal to (≥).  

To solve an inequality we can add or subtract the same integer on both sides or we can multiply or divide the same integer on both sides. which doesn't change the condition of inequality.

Here we have an inequality that is

The inequality is three-fourths times the absolute value of the quantity third times x plus 2 end quantity is less than 6.  

The above statement can be converted as follows

=> \(\frac{3}{4} | \frac{x}{3} +2| < 6\)    

The equation can be solved as follows

=> \(3 | \frac{x}{3} +2| < 24\)    [  Multiplied by 4 on both sides ]

=> \(3 | \frac{x+6}{3} | < 24\)    

=> \(| x+6 | < 24\)    

=> \(x+6 < \pm24\)    

Take \(x+6 < 24\)  

=> x + 6 - 6 < 24 - 6     [ Subtract - 6 on both sides ]

=> x < 18

Take x + 6 < - 24

=> x + 6 - 6 < - 24 - 6   [ Subtract - 6 on both sides ]

=> x < - 30  

Therefore,

The solution for given inequality is - 30 and 18. So the answer is option c. x < −30 and x < 18.

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The factored form of 2x^3 + 11x + 15 is:

(2x + 1)(x^2 + 5) + 15

To factor 2x^3 + 11x + 15, we need to find two binomials that multiply to give us the expression.

One way to approach this is to use a method called grouping. We can first group the first two terms and the last two terms:

2x^3 + 11x + 15 = (2x^3 + 10x) + (x + 15)

Notice that we factored out a common factor of 2x from the first two terms, and a common factor of 1 from the last two terms.

Next, we can factor each group separately:

2x^3 + 10x = 2x(x^2 + 5)

x + 15 = 1(x + 15)

Putting these factors together, we get:

2x^3 + 11x + 15 = 2x(x^2 + 5) + 1(x + 15)

Therefore, the factored form of 2x^3 + 11x + 15 is:

(2x + 1)(x^2 + 5) + 15

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To find the vertical asymptotes of a rational function, we need to set the denominator equal to zero and solve for x.

To find the vertical asymptotes of a rational function, you need to determine the values of x that make the denominator of the function equal to zero.

Let's check the limit of our example function as x approaches each of the vertical asymptotes:

As x approaches 1 from the left side: f(x) approaches negative infinity

As x approaches 1 from the right side: f(x) approaches positive infinity

Therefore, x = 1 is a valid vertical asymptote.

As x approaches 3 from the left side: f(x) approaches positive infinity

As x approaches 3 from the right side: f(x) approaches negative infinity

Therefore, x = 3 is also a valid vertical asymptote.

The values of x that make the denominator zero are the vertical asymptotes of the function.

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Answer:

x = -7 and x = 4

Step-by-step explanation:

Note, I am taking the polynomial equation as
\(x^2 - 28 = -3x\)

Otherwise it does not become a polynomial of one variable and cannot be solved

Zeros of a polynomial are the values of x where the polynomial value itself is 0

Standard equation for a polynomial of degree 2 is ax² + bx + c = 0 where a, b and c are constants

Degree is the highest exponent. Here the highest exponent is 2 so the polynomial has degree 2. Such a polynomial is called a quadratic polynomial

So we first have to convert
x² - 28 = - 3x into  this form ax² + bx + c

1. Add 3x to both sides
x² - 28 + 3x = -3x + 3x =0

==> x² + 3x - 28  = 0
With a = 1, b = 3 and c = -28

2. Factor x² + 3x - 28  = 0

Here a = 1, b = 3 and c = -28

Factoring means find two expressions x+a and x +b such that (x + a) (x + b) = x² + 3x - 28  = 0

Then we can state that
x + a = 0           ==> x = -a as one solution
x + b = 0           ==> x = -b as the other solution

To factor, find two numbers m and n(could be negative) such that mn = c and m + n = b

28 has factors 7 and 4 so that is a good start

-28 = -7 x 4 or could also be 7 x -4

How do we choose?
Add both and see what gives you +3

-7 +  4 = -3  Nope
7 + -4 = 7-4 = 3 YES

So the factors are 7 and -4

(x + m) = (x + 7)
(x + n)  = (x -4)

So the original quadratic polynomial becomes

(x + 7)(x -4) =

This means

x + 7 = 0 ==> x = -7

x -  4 = 0 ==> x = 4

So the solutions(also called roots) of x² + 3x - 28  = 0 are:

x = -7 and x = 4

Both the above values satisfy the quadratic equation

Answer:

q = 4

Step-by-step explanation:

given p and q vary inversely then the equation relating them is

p = \(\frac{k}{q}\) ← k is the constant of variation

to find k use the condition p = 8 when q = 6 , that is

8 = \(\frac{k}{6}\) ( multiply both sides by 6 )

48 = k

p = \(\frac{48}{q}\) ← equation of variation

when p = 12 , then

12 = \(\frac{48}{q}\) ( multiply both sides by q )

12q = 48 ( divide both sides by 12 )

q = 4

Answer:

4

Step-by-step explanation:

-

Answer: 89c^3

Step-by-step explanation:

3

The answer is I think now sure 33.2

Answer:

He will need 8 boxes.

Step-by-step explanation:

380/48 = 7.196 You would need to round up to the next box.

Helping in the name of Jesus.

Sam will need 8 boxes of programs for the school play on Thursday.

To determine how many boxes of programs Sam will need for the school play, given that each box contains 48 programs and he needs 380 programs, you can follow these steps:

1. Divide the total number of programs needed (380) by the number of programs in each box (48).
2. If the result is a whole number, that's the number of boxes needed. If the result is not a whole number, round up to the nearest whole number to ensure enough programs.

Now, let's calculate:

380 programs ÷ 48 programs per box = 7.9167

Since this is not a whole number, round up to the nearest whole number, which is 8.

So, Sam will need 8 boxes of programs for the school play on Thursday.

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Answer:

x = 9

Step-by-step explanation:

divide both sides by 14

Answer: x = 9.

Step-by-step explanation: Step 1: Flip the equation.

14x=126

Step 2: Divide both sides by 14.

14x /14

=

126 /14

x=9

Answer:

Step-by-step explanation:

The slope intercept form of a line is y=mx+b where m=slope and b=y intercept so we can solve for y from what you were given.

-2y=-16x+8

y=8x-4

So the slope is 8 and the y intercept is -4.

Answer:

1. h = 12/b

2. h = 8 in

Step-by-step explanation:

Part 1

Use the formula for the area of a parallelogram:  

A = bh, where b- length, h - height

Since the area is constant, 12 in², the formula for the height is:  

bh = 12

h = 12/b

Part 2

If b = 1.5 in, the height is:

h = 12/1.5 = 8 in

The height is too much compared to the base, this is because the area is fixed and the height gets greater if the base gets smaller.

The height and base are inversely proportional.

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The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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The size of an exterior angle of a regular hexagon is 60 degrees.

In a regular hexagon, all the interior angles are equal and are given by the formula:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

For a hexagon, n = 6, so the interior angle is:

Interior angle = (6-2) x 180 / 6 = 120 degrees

An exterior angle is the supplement of an interior angle, which means it is the angle that when added to the interior angle, will equal 180 degrees.

So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.

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Answer:

above sea level

Step-by-step explanation:

Answer:

C

\(y=(5x+2)(x+3)\)

\(\implies x=-\dfrac25,\ \ x=-3\)

Step-by-step explanation:

Factor  \(y=5x^2+17x+6\)

Multiply the coefficient of \(x^2\) and the constant:  

⇒ 5 x 6 = 30

Find factors of 30 that add together to make the coefficient of \(x\):  

⇒ 2 and 15

Rewrite 17x as 15x + 2x:

\(\implies y=5x^2+15x+2x+6\)

Group:

\(\implies y=(5x^2+15x)+(2x+6)\)

Factor brackets:

\(\implies y=5x(x+3)+2(x+3)\)

Factor out common term \((x + 3)\):

\(\implies y=(5x+2)(x+3)\)

To find the zeroes, set y to zero and solve for x:

\(\implies (5x+2)(x+3)=0\)

\(\implies 5x+2=0 \ \ \textsf{and} \ \ x+3=0\)

\(\implies x=-\dfrac25,\ \ x=-3\)

ac is 5(6)=30

So the zeros are

Option C is correct

Answer:

the three vertices are (1, 1), (2, 0), (-1, -3).

The vertices of the triangles are the coordinates of the point of

intersection of the graph of the equation of the three lines.

Correct response:

The coordinates of the three vertices of the triangles are;

E. \(\underline{(2, 0), \ (1, -1), \ and \ (-1, -3)}\)

The equation of the given lines are;

y = -x + 2, y = 2·x - 1, y = x - 2

The point of the intersection of the two lines, gives the vertices, and are

the solution of the two linear equations of the lines.

At the points where the lines intersect, we have;

-x + 2 = 2·x - 1

Which gives;

3·x = 3

x = 1

y = -1 + 2 = -1

A vertex is at the point (1, -1)

The coordinate of the second vertex is given as follows;

2·x - 1 = x - 2

2·x - x = -2 + 1 = -1

x = -1

y = -1 - 2 = -3

The second vertex is; (-1, -3)

The coordinates of the third vertex is given as follows;

-x + 2 = x - 2

2·x = 4

x = 2

y = 2 - 2 = 0

Which gives the point; (2, 0)

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Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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