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Brilliant_brown [7]
3 years ago
9

Jacques needs to convert the function f(x) = x2 − 6x + 14 to vertex form, f(x) = (x − h)2 + k, in order to find the minimum.

Mathematics
2 answers:
Olenka [21]3 years ago
6 0

Answer:

C. 5

Step-by-step explanation:

Given function is,

f(x) = x^2 - 6x + 14

Here, the coefficient of x = 6,

Thus, We need to add and subtract the square of half of 6 in the given equation for getting the vertex form,

By adding and subtracting 9,

f(x) = x^2 - 6x + 9 + 14 - 9

f(x) = (x-3)^2 + 5   ( Because, a² - 2ab + b² = (a-b)²  )

Which is the required vertex form he will get,

By comparing it with f(x) = (x+h)^2+k

We get, k = 5,

⇒ Option C is correct.

Anarel [89]3 years ago
5 0

k = 5

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Since the coefficient of the x² term is 1 then

add/ subtract (half the coefficient of the x-term )² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 + 14 = (x - 3)² + 5 → k = 5


   

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Help I will be marking brainliest!!!
Keith_Richards [23]
<h3>Answer:  A.  18*sqrt(3)</h3>

=============================================

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

----------------------

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

4 0
2 years ago
Ibrahim has some building blocks that are all cubes of the same size. He uses three of the blocks to make a pile with a height o
MArishka [77]

Answer:

72.5

Step-by-step explanation:

one block = 43.5 / 3 = 14.5

five blocks = 5 * 14.5 = 72.5 (ans)

4 0
3 years ago
Suppose you want to build a small walkway around your garden so that there is someplace to walk around and work on your vegetabl
wolverine [178]

Answer:

Approximately 3.5 feet - Option B

Step-by-step explanation:

Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.

( 30 + 2x ) * ( 20 + 2x ) = 1000 - Expand "( 30 + 2x ) * ( 20 + 2x )"

600 + 100x + 4x^2 = 1000 - Subtract 1000 on either side, making on side = 0

4x^2 + 100x - 400 = 0 - Take the "quadratic equation formula"  

( Quadratic Equation is as follows ) - x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a},

x=\frac{-100+\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad \frac{5\left(\sqrt{41}-5\right)}{2},

x=\frac{-100-\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad -\frac{5\left(5+\sqrt{41}\right)}{2}

There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) \frac{5\left(\sqrt{41}-5\right)}{2}. The approximated value however is 3.5081...or approximately 3.5 feet.

4 0
3 years ago
What is thirty-four and twelve hindredths in expanded form?
strojnjashka [21]
The answer is two hundred thirty four.
6 0
3 years ago
The O'Brien family is ordering food for a family reunion. The family orders 16 pounds of potato salad. If 20 people attend the r
sukhopar [10]

Answer:

Each person would receive maximum 0.8 pounds of potato.

Step-by-step explanation:

Given:

Total Amount of Potato = 16 pounds.

Number of people attend reunion = 20

We need to find the largest amount of potato each person would receive.

Solution:

largest amount of potato each person would receive can be calculated by dividing Total Amount of Potato with Number of people attend the reunion.

framing in equation form we get;

largest amount of potato each person would receive = \frac{16}{20} =0.8\ pounds

Hence Each person would receive maximum 0.8 pounds of potato.

5 0
3 years ago
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