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Sveta_85 [38]
2 years ago
11

Function Q gives a puppy's weight in pounds as function of its age in months. What does each expression represent in this situat

ion. Q(18) Q(30) = 27.5
Mathematics
1 answer:
babymother [125]2 years ago
6 0

Answer:

Q(18) is a mathematical representation of the weight in pounds of a puppy after 18 months.

Q(30) = 27.5 ; This means that the weight of puppy after 30 months will be 27.5 pounds

Step-by-step explanation:

Given the expressions :

Q(18)

Q(30) = 27.5

Function Q gives a puppy's weight in pounds as function of its age in months

What does each expression represent in this situation?

A function is generally represented in the form a(x) ;

Hence, Q(18) is a mathematical representation of the weight in pounds of a puppy after 17 months

Q(30) = 27.5 ; This means that the weight of puppy after 30 months will be 27.5 pounds. 27.5 is the result of working out the function Q at 30.

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A percentage is a number out of 100.  So, 17.5% is really 17.5/100, or 0.175.

To find 17.5% of 1500, you multiply 1500 by 0.175

1500 x 0.175 = 262.5.

The commission is $262.50.
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Nicholas drew a triangle with 45, 35, and 100 degree angles. Is there another triangle with the same three angles but different
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Answer:

Yes, there are infinite triangles with the same three angles but different side lengths

Step-by-step explanation:

we know that

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Answer:

This is ezz lol.

Step-by-step explanation:

Your answer would be 1/5

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What would y=x^2 +x+ 2 be in vertex form
balu736 [363]

Answer:

y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

Step-by-step explanation:

y =  {x}^{2}  + x + 2

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

y = a(x - h)^{2}  + k

The following equation above is the vertex form of Quadratic Function.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Formula</u>

h =  -  \frac{b}{2a}  \\ k =  \frac{4ac -  {b}^{2} }{4a}

We substitute the value of these terms from the standard form.

y = a {x}^{2}  + bx + c

h =  -  \frac{1}{2(1)}  \\ h =  -  \frac{ 1}{2}

Our h is - 1/2

k =  \frac{4(1)(2) - ( {1})^{2} }{4(1)}  \\ k =  \frac{8 - 1}{4}  \\ k =  \frac{7}{4}

Our k is 7/4.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Calculus</u>

We can use differential or derivative to find the vertex as well.

f(x) = a {x}^{n}

Therefore our derivative of f(x) —

f'(x) = n \times a {x}^{n - 1}

From the standard form of the given equation.

y =  {x}^{2}  +  x + 2

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times  {x}^{1 - 1} ) + 0

Any constants that are differentiated will automatically become 0.

f'(x) = 2 {x}+ 1

Then we substitute f'(x) = 0

0 =2x + 1 \\ 2x + 1 = 0 \\ 2x =  - 1 \\x =  -  \frac{1}{2}

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

y =  {x}^{2}  + x + 2

y = ( -  \frac{1}{2} )^{2}  + ( -  \frac{1}{2} ) + 2 \\ y =  \frac{1}{4}  -  \frac{1}{2}  + 2 \\ y =  \frac{1}{4}  -  \frac{2}{4}  +  \frac{8}{4}  \\ y =  \frac{7}{4}

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

y = a {(x - h)}^{2}  + k \\ y = (x - ( -  \frac{1}{2} ))^{2}  +  \frac{7}{4}  \\ y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

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