What is the vertex form of f(x)?
What is the minimum value of f(x)?

f(x)=x^2-6x+16

Answer:

Box A: 4

Box B: 6

Box C: 20

Step-by-step explanation:

Because 4+2 = 6

4 x 5 = 20

The solution is: The retail price is $6.50.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Here, we have,

given that,

The total price of an article is $7.02, including tax.

If the tax rate is 8%

Lets price of article = x

Tax  is 8%  of article = 0.08x

so, we get,

x+0.08x=7.02

1.08x=7.02

x=7.02/1.08

x=6.5

The retail price is $6.50.

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The volume of the cube after drilling hole is 538.24 cu.m, the correct option is D.

A three dimensional figure that has all faces of a square, it has total 6 faces of equal length, height and width.

The Side of the cube is 9 cm.

The volume of the metal = Volume of the cube -  Volume of cone

Volume of the cube = a³

Volume of cone = πr²h/3

Volume of metal = (9)³ - πr²h/3

The radius of the cone is half of the side length = 9/2 =4.5 cm

The height of the cone is 9 cm

Volume of metal = (9)³ - 3.14 * 4.5 ² * 9 /3

Volume of metal = 538.24 cu. cm

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Hi

The answer : the percent of decrease  is 29%

The model to represent the balance in an account from an initial deposit of $200 at an annual interest of 4.2% is given by the formula A = 200(1.042)^x. Here A is the amount accrued after x years.

The subject of the given problem is related to exponential growth as it involves the growth of a principal amount in a bank account accruing annual interest. The model to represent the balance in the account after x years can be described by the formula A = P(1 + r/n)^(nt). Where, A represents the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, t is the time the money is invested for in years.

In this case, P = $200, r = 4.2/100 = 0.042 (converted percentage to decimal), n = 1 (since it is compounded annually), and t = x (number of years). Substituting these values into the formula, we obtain the model: A = 200 (1 + 0.042) ^ (1*x) simplified to, A = 200(1.042)^x. Which is used to represent the balance in the account after x years.

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We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.

We have been given an angle 425 degrees.

From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.

Let us check each of the options one by one.

(A) The angle being subtracted is [tex]1000n[/tex]. Therefore, we have [tex]\frac{1000n}{360}=2.77n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(B)

The angle being subtracted is [tex]840n[/tex]. Therefore, we have [tex]\frac{840n}{360}=2.33n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(C)

The angle being added is [tex]960n[/tex]. Therefore, we have [tex]\frac{960n}{360}=2.67n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(D)

The angle being added is [tex]1440n[/tex]. Therefore, we have [tex]\frac{1440n}{360}=4n[/tex], which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.

Hence, correct answer is option (D).

The height of the giraffe whose shadow is 5 feet 9 inches at the same time will be 10 feet and 6.5 inches.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

The next stop on the road trip is the zoo.

Jacob goes to find his favorite animal, the giraffe.

Jacob wonders how tall the tallest giraffe at the zoo is.

If Jacob is 5 feet 6 inches and his shadow at the time is 3 feet long.

Then the height of the giraffe whose shadow is 5 feet 9 inches at the same time will be

Let x be the hieght of the giraffe. Then we have

The ratio will remain constant.

x / 5.75 = 5.5 / 3

x = 10.54

x = 10 feet 6.5 inches

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Final answer:

To triple the volume of a square-based Egyptian pyramid, you must multiply every dimension of the pyramid by 3. This is because volume is proportional to all three dimensions of the shape, and changing just one dimension won't achieve the desired effect.

Explanation:

The question asks which action would triple the volume of a square-based Egyptian pyramid. The volume (V) of a pyramid is calculated using the formula V = (1/3) × base area × height. To triple the volume, you would need to triple the factor of each dimension because volume is a three-dimensional measurement, and changing one dimension alone would not be sufficient.

Option A suggests multiplying only the height by 3, but this would not triple the volume as the base area remains the same. Option B suggests adding 3 to each dimension, but adding a constant to linear dimensions does not maintain a proportional relationship to volume.

Option D suggests adding 3 to the slant height, which does not directly correlate to the volume. Therefore, option C is correct: Multiplying every dimension of the Pyramid by 3 would indeed triple the volume because changing each dimension equally maintains the proportion. This is similar to how if a block's dimensions were doubled (2L × 2L × 2L), the new volume would be 8 times the original (8L³).

Answer:

-5

Step-by-step explanation:

The leading term in a polynomial consist on the highest degree term.  To get the highest degree term, we need to reorder the polynomial from left to right, starting with the highest degree term.

In this case:

[tex]f(x)=\frac{1}{2} x^{2} +8-5x^{3} -19x[/tex]

reordering

[tex]f(x)=-5x^{3} +\frac{1}{2}x^{2}  -19x+8[/tex]

So, the leading coefficient is the one with the leading term:

[tex]-5x^{3}[/tex]

So, it is -5

Quadratic equations can be solved using several methods; one of them, is by using quadratic formula

The solution to [tex]5x^2 - 8x + 5 = 0[/tex] is: [tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]

The equation is given as:

[tex]5x^2 - 8x + 5 = 0[/tex]

The quadratic formula is:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

In the given equation;

[tex]a = 5\\b = -8\\c = 5[/tex]

So:

[tex]x = \frac{-(-8) \± \sqrt{(-8)^2 - 4 \times 5 \times 5}}{2 \times 5}[/tex]

[tex]x = \frac{8 \± \sqrt{-36}}{10}[/tex]

Expand

[tex]x = \frac{8 \± \sqrt{36} \times \sqrt{-1}}{10}[/tex]

[tex]x = \frac{8 \± 6 \times \sqrt{-1}}{10}[/tex]

In complex numbers;

[tex]i = \sqrt{-1}[/tex]

So, we have:

[tex]x = \frac{8 \± 6 \times i}{10}[/tex]

[tex]x = \frac{8 \± 6i}{10}[/tex]

Simplify

[tex]x = \frac{4 \± 3i}{5}[/tex]

Split

[tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]

Hence, the solution to [tex]5x^2 - 8x + 5 = 0[/tex] is: [tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]

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Answer:

(x+9)^2

Step-by-step explanation:

An equation of a line that is the perpendicular bisector line segment AB is y=-x+10.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, line segment AB is defined by the endpoints A(4,2) and B(8,6).

Midpoint of line AB is (x, y) =[(x₂+x₁)/2, (y₂+y₁)/2]

= [(8+4)/2, (6+2)/2]

= (6, 4)

Slope of line AB is (y₂-y₁)/(x₂-x₁)

= (6-2)/(8-4)

= 4/4

= 1

The slope of a line perpendicular to given line is m1=-1/m2

So, the slope of a line is -1

Now, substitute m=-1 and (x, y)=(6, 4) in y=mx+c, we get

4=-1(6)+c

c=10

Substitute m=-1 and c=10 in y=mx+c, we get

y=-x+10

Therefore, an equation of a line that is the perpendicular bisector line segment AB is y=-x+10.

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Answer:

The answer is 3

Step-by-step explanation:

The value of x is 3.

The correct option is B.

Use one of your formulas from the figure we can write

x(x+21) = (x+1)(x+1+14)

Now, solving for x we get

x² + 21x = (x+1)(x+15)

x² + 21x = x² + 15x + x + 15

x² + 21x= x² + 16x+ 15

21x = 16x+ 15

21x - 16x = 15

5x= 15

x= 15/5

x= 3

Thus, the value x is 3.

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The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.

To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.

The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:

[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]

For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:

[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]

So, the ball reaches its maximum height at t = 1  second.

To find the maximum height, we substitute t = 1 into the function h(t) :

[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]

Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.

To find the value of y in the given isosceles trapezoid ABCD, we can set up an equation AB = CD and solve for y.

To find the value of y in the given isosceles trapezoid ABCD, we can set up the equation AB = CD and solve for y.

Given that AB = 6y + 5 and CD = 2y + 1, we have the equation 6y + 5 = 2y + 1.

Simplifying this equation, we can subtract 2y from both sides to get 4y + 5 = 1.

Finally, subtracting 5 from both sides gives us 4y = -4.

Dividing both sides of the equation by 4, we find that y = -1.

To find the value of y in an isosceles trapezoid ABCD with given side lengths in terms of y, we set the equations for the congruent legs, AB = 6y + 5 and CD = 2y + 1, equal to each other and solve for y, arriving at y = -1.

To find the value of y in an isosceles trapezoid where the lengths of the sides are given in terms of y, we can utilize the properties of an isosceles trapezoid. In an isosceles trapezoid, the legs (non-parallel sides) are congruent. Given that AB = 6y + 5 and CD = 2y + 1, and these lengths must be equal for ABCD to be an isosceles trapezoid, we can set up the following equation:

6y + 5 = 2y + 1

Solving for y, we subtract 2y from both sides to get:

4y + 5 = 1

Now, subtract 5 from both sides:

4y = -4

And finally, divide by 4 to find y:

y = -1

Thus, the value of y is -1.

The polynomial x(5x-8)-2(5x-8) is factored by identifying the common factor (5x-8) and simplifying to get (5x-8)(x-2), which corresponds to option C.

The question asks to factor the polynomial: x(5x-8)-2(5x-8). To factor this polynomial, observe that the term (5x-8) is common in both parts of the expression. This allows us to apply the factorization method by taking out the common factor. The steps are as follows:

Identify the common factor in both terms, which is (5x-8).

Factor out the common factor: (5x-8)(x-2).

This simplification shows that the polynomial can be written as the product of (5x-8) and (x-2), matching option C: (5x-8)(x-2).

Answer:

$50

Step-by-step explanation:

because I know :p

Have a good day!

Answer:

To find the height, you would do the area divided by the base, or in this case,187.5 / 25 which equals 7.5 inches

Step-by-step explanation: