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2 years ago

Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x2 + 4x) + 7 y = 3(x2 + 4x +4) + 7 -

Mathematics

2 answers:

Vikki [24]2 years ago

8 1

Answer:

A. 12

B. 3

C. -2

D. -5

Step-by-step explanation:

hichkok12 [17]2 years ago

3 0

Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x2 + 4x) + 7 y = 3(x2 + 4x +4) + 7

$y=3x^{2} +12x+7$

Step 1: Let us try to make coefficient of $x^{2}$

So let us take 3 common from first two terms

y=3( $x^{2}$ +4x)+7

Now, To complete the square let us add and subtract square of half of coefficient of x

So, $(\frac{4}{2} )^{2}$

So, we get 2^2 or 4

y=3( $x^{2}$ +4x+4-4)+7

y=3( $x^{2}$ +4x+4)-3*4+7

y=3( $x^{2}$ +4x+4)-12+7

Now, factoring ( $x^{2}$ +4x+4) we get,

y=3( $x^{2}$ +2x+2x+4)-5

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

y=3 $(x+2)^{2}$ -5

So, y=3 $(x+2)^{2}$ -5 is in vertex form y=a $(x-h)^{2}$ +k

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Alex17521 [72]

since the triangles are similar

angle DEC = 60 degrees

3 angles inside a triangle equal 180 degrees

BAC = DCE = 64

CBA = EDC = 56

DEC = 180 -56 -64 = 60 degrees

used angle-angle theorem

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2 years ago

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A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

marishachu [46]

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

$V = s^2h = 5324$

$h = 5324 / s^2$

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top $s^2$

Side area 4sh

Total surface area $A = s^2 + 4sh$

We can substitute $h = 5324 / s^2$

$A = s^2 + 4s\frac{5324}{s^2}$

$A = s^2 + 21296/s$

To find the minimum of this function, we can take the first derivative, and set it to 0

$A' = 2s - 21296/s^2 = 0$

$2s = 21296/s^2$

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2 years ago

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. x2 + y2 = 25 (a) Fin

Artemon [7]

Answer:

(a) $\frac{dy}{dt}=-3\frac{3}{4}$

(b) $\frac{dx}{dt}=3\frac{3}{4}$

Step-by-step explanation:

$x^{2} +y^{2}=25$

Take $\frac{d}{dt}$ of of each term.

$\frac{d}{dt}(x^{2})+\frac{d}{dt}(y^{2})=\frac{d}{dt}(25)\\\\(\frac{d}{dx}(x^{2})*\frac{dx}{dt}) +(\frac{d}{dy}(y^{2})*\frac{dy}{dt})=\frac{d}{dt}(25)\\\\2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\\\$

For Question a

$2y\frac{dy}{dt}=-2x\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{-2x\frac{dx}{dt}}{2y} \\\\\frac{dy}{dt}=-\frac{x}{y}\frac{dx}{dt}$

Given that x = 3, y = 4, and dx/dt = 5.

$\frac{dy}{dt}=-\frac{3}{4}*5=-\frac{15}{4}\\ \\\frac{dy}{dt}=-3\frac{3}{4}$

For Question b

$2x\frac{dx}{dt}=-2y\frac{dy}{dt}\\\\\frac{dx}{dt}=\frac{-2y\frac{dy}{dt}}{2x} \\\\\frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}$

Given that x = 4, y = 3, and dx/dt = -5.

$\frac{dx}{dt}=-\frac{3}{4}*-5=\frac{15}{4}\\ \\\frac{dx}{dt}=3\frac{3}{4}$

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2 years ago

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 10.410.410, point, 4 years; th

kati45 [8]

Answer:

99.85%

Step-by-step explanation:

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 10.4 years; the standard deviation is 1.9 years.

Use the empirical rule (68-95-99.7%) to estimate the probability of a meerkat living less than 16.1 years.

Solution:

The empirical rule states that for a normal distribution most of the data fall within three standard deviations (σ) of the mean (µ). That is 68% of the data falls within the first standard deviation (µ ± σ), 95% falls within the first two standard deviations (µ ± 2σ), and 99.7% falls within the first three standard deviations (µ ± 3σ).

Therefore:

68% falls within (10.4 ± 1.9). 68% falls within 8.5 years to 12.3 years

95% falls within (10.4 ± 2*1.9). 95% falls within 6.6 years to 14.2 years

99.7% falls within (10.4 ± 3*1.9). 68% falls within 4.7 years to 16.1 years

Probability of a meerkat living less than 16.1 years = 100% - (100% - 99.7%)/2 = 100% - 0.15% = 99.85%

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alexandr1967 [171]

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2 years ago

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