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Stels [109]
3 years ago
11

Find the solution using the Quadratic Formula. (show work) 2x + 8x+ 5 = 0 a. 47 ſ6 b. -27 56 c. -2± √3​

Mathematics
1 answer:
Nookie1986 [14]3 years ago
8 0

Answer:

The roots of the equation for the given quadratic equation is               -2\pm \frac{\sqrt{6}}{2} .

Step-by-step explanation:

Given quadratic equation as :

2 x² + 8 x + 5 = 0

The roots of the quadratic equation  ax² + bx + c = 0 as can be find as :

x = \frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}

x = \frac{-8\pm \sqrt{8^{2}-4\times 2\times 5}}{2\times 2}

or, x = \frac{-8\pm \sqrt{64-40}}{4}

Or, x = \frac{-8\pm \sqrt{24}}{4}

Or, x = \frac{-8\pm 2\sqrt{6}}{4}

∴ x = -2\pm \frac{\sqrt{6}}{2}

Hence The roots of the equation for the given quadratic equation is -2\pm \frac{\sqrt{6}}{2} . Answer

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Hannah has a bowl containing 54 goldfish crackers. She is eating crackers at a rate of 9 crackers every two minutes. What is the
taurus [48]
<span>The line would first have to have a negative slope, since she is consuming the crackers, leading to fewer crackers left in the bowl every minute. Since she is eating 9 crackers every two minutes, this would be a slope of (-9/2) to describe the number left in the bowl.</span>
3 0
3 years ago
Find the solution to the following system using substitution or elimination: y = 3x + 2 y = -2x - 8 O A. (-5,-) OB. (-2,-4) O C.
mr Goodwill [35]

Answer:

B. (-2,-4)

Explanation

Given equations:

   y = 3x + 2

   y = -2x - 8

Solving both equations will yield the values of x and y;

Solution:

   y = 3x + 2    ----- (i)

   y = -2x - 8   ------ (ii)

Using substitution method, input equation i, into ii

    3x + 2 = -2x - 8

Collect like terms and solve;

     3x + 2x = -8 -2

         5x  = -10

            x  = -2

Then put x = -2 into i, to find y

      y = (-2 x 3) + 2

       y = -6 + 2 = -4

So, the solution of the equation is B. (-2,-4)

6 0
3 years ago
two brothers marco and fernando are training for a marathon marco runs at a rate of 6miles per hor. Fernando funs at at a rate o
satela [25.4K]
We know that
speed=distance/time
solve for time
time=distance/speed

in this problem
<span>Marco runs at a rate of 6 miles per hour. 
</span><span>Fernando funs at a rate of 7.2 miles per hour
Difference=7.2-6=1.2 miles/hour
so
speed=1.2 miles/hour
distance=0.3 miles
time=?
</span>time=distance/speed-----> 0.3/1.2-----> 0.25 hour-----> 0.25*60=15 minutes
<span>
the answer is
0.25 hour (15 minutes)

Alternative Method
Let 
x---------> Fernando's distance when Marco is 0.3 miles apart

</span>Fernando funs at a rate of 7.2 miles per hour
<span>for distance =x
time=x/7.2------> equation 1

</span>Marco runs at a rate of 6 miles per hour. 
for distance=x-0.30
time=(x-0.30)/6------> equation 2

equate equation 1 and equation 2
 7.2*(x-0.3)=6x-----> 7.2x-2.16=6x
7.2x-6x=2.16------> x=2.16/1.2-------> x=1.8 miles

time=x/7.2-----1.8/7.2=0.25 hour
6 0
3 years ago
Jewan is setting up a monthly budget. His gross monthly income is $3125, but 20% is deducted for taxes. How much money is deduct
romanna [79]

Answer:

$625

$2500

Step-by-step explanation:

tax = percent of tax x income

0.2 x 3125 = 625

amount remaining = income - tax

3125 - 625

4 0
3 years ago
When 258 college students are randomly selected and surveyed, it is found that 106 own a car. Find a 99% confidence interval for
juin [17]

Answer: 0.332 < p < 0.490

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

, where n= sample size

\hat{p} = sample proportion

z* = critical z-value.

As per given , we have

n= 258

Sample proportion of college students who own a car = \hat{p}=\dfrac{106}{258}\approx0.411

Critical z-value for 99% confidence interval is 2.576. (By z-table)

Therefore , the  99% confidence interval for the true proportion(p) of all college students who own a car will be :0.411\pm (2.576)\sqrt{\dfrac{0.411(1-0.411)}{258}}\\\\=0.411\pm (2.576)\sqrt{0.00093829}\\\\= 0.411\pm (2.576)(0.0306315197142)\\\\=0.411\pm 0.0789=(0.411-0.0789,\ 0.411+0.0789)\\\\=(0.3321,\ 0.4899)\approx(0.332,\ 0.490)

Hence, a 99% confidence interval for the true proportion of all college students who own a car : 0.332 < p < 0.490

3 0
3 years ago
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