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3 years ago

F(x) = -2x² – 12x – 19

Mathematics

1 answer:

Oliga [24]3 years ago

6 0

Answer:

just figue out 2x2 then the answer subtract 12x then subtrct 191

Step-by-step explanation:

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The graphs of f(x) and g(x) are shown below:

rosijanka [135]

<h2>Answer:</h2>

Option: C is the correct answer.

C.) x = −3.8, 3

<h2>Step-by-step explanation:</h2>

The function f(x) is given by:

$f(x)=x^2-x-12$

and the function g(x) is given by:

$g(x)=-1.8x-0.6$

Now, we are asked to find the solution of the equation:

$f(x)=g(x)$

i.e. we have to find the value of x such that both the functions are equal i.e.

$x^2-x-12=-1.8x-0.6\\\\i.e.\\\\x^2-x+1.8x-12+0.6=0\\\\i.e.\\\\x^2+0.8x-11.4=0\\\\i.e.\\\\10x^2+8x-114=0\\\\i.e.\\\\5x^2+4x-57=0$

Now, on solving the equation using the quadratic formula i.e. the solution of the equation:

$ax^2+bx+c=0$

is given by:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here we have:

$a=5,\ b=4\ and\ c=-57$

Hence, the solution is given by:

$x=\dfrac{-4\pm \sqrt{4^2-4\times 5\times (-57)}}{2\times 5}\\\\i.e.\\\\x=\dfrac{-4\pm \sqrt{16+1140}}{10}\\\\i.e.\\\\x=-3.8\ and\ x=3$

6 0

3 years ago

The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a n

xz_007 [3.2K]

Answer:

(15,595, 16,805)

Step-by-step explanation:

We have to:

m = 16.2, sd = 3.75, n = 150

m is the mean, sd is the standard deviation and n is the sample size.

the degree of freedom would be:

n - 1 = 150 - 1 = 149

df = 149

at 95% confidence level the t is:

alpha = 1 - 95% = 1 - 0.95 = 0.05

alpha / 2 = 0.05 / 2 = 0.025

now well for t alpha / 2 (0.025) and df (149) = t = 1,976

the margin of error = E = t * sd / (n ^ (1/2))

replacing:

E = 1,976 * 3.75 / (150 ^ (1/2))

E = 0.605

The 95% confidence interval estimate of the popilation mean is:

m - E <u <m + E

16.2 - 0.605 <u <16.2 + 0.605

15,595 <u <16,805

(15,595, 16,805)

5 0

3 years ago

Find the equation of a line that contains the points (3,7) and (-6, 4). Write the equation in slope-intercept form, using

NikAS [45]

Answer:

$y=\frac{1}{3} x+6$

Step-by-step explanation:

$(3,7)(-6,4)$

Step 1. Find the slope (by using the slope-formula)

m = slope

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4-7}{-6-3}$

$m=\frac{-3}{-9}$

$m=\frac{3}{9}$

$m=\frac{1}{3}$

Step 2. Write the equation (using the slope and the points)

Here's how to do it:

Slope-intercept Formula $y=mx+b$ whrere m = slope and b = y-intercept

Plug in the slope into the Slope-intercept Formula

$y=\frac{1}{3} x+b$

Find the y-intercept (b) by using a point and substituting their x and y values

$y=\frac{1}{3} x+b$

Point: (3, 7)

$7=\frac{1}{3} (3)+b$

$7=1+b$

$b=7-1$

$b=6$

Step 3. Write the equation in Slope-intercept form

$y=mx+b$

$y=\frac{1}{3} x+6$

3 0

2 years ago

A cylinder’s volume must be 850 cubic feet while the radius of the cylinder cannot exceed 6 feet. What is the smallest possible

Neporo4naja [7]

I think it's B. not sure though u should wait. till someone else answer to see if I am right

6 0

3 years ago

1-cos^2 A / sec^2 A - tan^2 A

tiny-mole [99]

I hope this helps you

✔cos^2A+sin^2A=1

✔1-cos^2A=sin^2A

✔cos2A=cos^2A-sin^2A

✔sin2A=2.sinA.cosA

secA=1/cosA

tgA=sinA/cosA

sin^2A/1/cos^2A-sin^2A/cos^2A

sin^2A.cos^2A/cos2A

2.sin^2A.cos^2A/cos2A

sin2A.2.sin2A/cos2A

tg2A.2.sin2A

6 0

3 years ago