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4 years ago

Find the axis of symmetry y= -2x^2 -8x -15

1 answer:

4 0

The squared variable is the "x", therefore is a vertical parabola so its axis of symmetry will come from the vertex's x-coordinate.

now, let's find the vertex of it.

$\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
y=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{-8}x\stackrel{\stackrel{c}{\downarrow }}{-15}
\qquad \qquad 
\left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left( -\cfrac{-8}{2(-2)}~~,~~\qquad \quad \right)\implies \left( -2~~,~~\qquad \right)
\\\\\\
\stackrel{\textit{axis of symmetry}}{x=-2}$

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Marat540 [252]

Answer:

3x+5=17

x=4

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3 years ago

Solve for x. 1/4+1/2+x=−3/4<br><br> Please Hurry!

seraphim [82]

Answer:

If you want it solved to exact form which im assuming you do the answer is x= -3/2

But if you want decimal form it is x= -1.5 and the mixed number form is x= -1 1/2

Tip for the future if you have questions like this use Math-way its a website. Its an algebra calculator and it works wonders. :)

Step-by-step explanation:

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3 years ago

A small military base housing 1,000 troops, each of whom is susceptible to a certain virus infection. Assuming that during the c

slava [35]

Answer:

$I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}$

Step-by-step explanation:

The rate of infection is jointly proportional to the number of infected troopers and the number of non-infected ones. It can be expressed as follows:

$\frac{dI}{dt}=a*I*(1000-I)$

Rearranging and integrating

$\frac{dI}{dt}=a*I*(1000-I)\\\\\frac{dI}{I*(1000-I)}=a*dt\\\\\int\frac{dI}{I*(1000-I)}=\int a*dt\\\\-\frac{ln(1000/I-1)}{1000}+C=a*t$

At the initial breakout (t=0) there was one trooper infected (I=1)

$-\frac{ln(1000/1-1)}{1000}+C=0\\\\-0,006906755+C=0\\\\C=0,006906755$

In two days (t=2) there were 5 troopers infected

$-\frac{ln(1000/5-1)}{1000}+0,006906755=a*2\\\\-0,005293305+0,006906755=2*a\\a = 0,00161345 / 2 = 0,000806725$

Rearranging, we can model the number of infected troops (I) as

$-\frac{ln(1000/I-1)}{1000}+0,006906755=0,000806725*t\\\\-\frac{ln(1000/I-1)}{1000}=0,000806725*t-0,006906755\\-ln(1000/I-1)=0,806725*t-0.6906755\\\\\frac{1000}{I}-1=exp^{0,806725*t-0.6906755} \\\\\frac{1000}{I}=exp^{0,806725*t-0.6906755}+1\\\\I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}$

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3 years ago

The Michigan veteran population in 1990 was 14.2% and in 2000 was 12.4%.

Mandarinka [93]

Let x- intercept represents time

Let y-intercept represents population

Let 1990 represent initial year

Points are (0,14.2)(10,12.4)

slope m= $\frac{y2-y1}{x2-x1}$

= $\frac{12.4-14.2}{10-0} =\frac{-1.8}{10} = -0.08$

General linear equation

y= mx+b --------------(i)

here m is slope and b is intercept

plug the 1st point in equation

14.2= -0.018(0) + b

b=14.2

y= 0.018x + 14.2

replace y with p(t) and x with t

p(t) = -0.018t + 14.2

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3 years ago

Factor x2 – 8x + 15.<br> Which pair of numbers has a product of ac and a sum of b?

Troyanec [42]

-5 and -3 are your numbers.

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3 years ago