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3 years ago

The amount of time, in hours, babies spent sleeping in two different nurseries is shown on the dot plots below.

Mathematics

2 answers:

zimovet [89]3 years ago

6 0

Answer:

the answer is B on edgen.

Step-by-step explanation:

azamat3 years ago

4 0

Answer:

The babies in Nursery 2 spent more time napping.

Step-by-step explanation:

i had took a test and got it right

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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.

Vertex — Formula

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

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.

Vertex — Calculus

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.

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

7 0

3 years ago

See the pic below please! AND SHOW WORK!

irinina [24]

Well I don't know !
Let's check out the choices:

A). 3a - 4b = 21, a=0, b=7

   3(0) - 4(7) = 21

   0 - 28 = 21 Nope. That's not true.

B). 3a - 4b = 21, a=-3, b=2

   3(-3) - 4(-2) = 21

   -9 + 8 = 21

   -1 = 21 Nope. That's not right.

C). 3a - 4b = 21, a=-2, b=-3

      3(-2) - 4(-3) = 21

   -6 + 12 = 21

   6 = 21 Nope. That's not it.

Only one choice left.
This one had better be it:

D). 3a - 4b = 21, a=7, b=0

   3(7) - 4(0) = 21

   21 - 0 = 21

   21 = 21 Yay ! That's it !

7 0

3 years ago

Read 2 more answers

Which of the following represents the total surface area?

arsen [322]

Answer:

Step-by-step explanation:

It is the 2nd one.

2nd one. makes more scence

8 0

3 years ago

Read 2 more answers