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xz_007 [3.2K]
3 years ago
7

A quadratic equation is shown below: 3x2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the

radicand. Show your work. (5 points) Part B: Solve 3x2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Mathematics
1 answer:
Triss [41]3 years ago
6 0

Answer:

\text{The roots of }3x^2+5x-8=0\text{ are }x=1,\frac{-8}{3}

Step-by-step explanation:

\text{Part A: Given a quadratic equation }3x^2-15x+20=0  

\text{Comparing above equation with }ax^2+bx+c=0  

a=3, b=-15, c=20

Discriminant can be calculated as

D=b^2-4ac

D=(-15)^2-4(3)(20)=225-240=-15

The roots are imaginary

The solution is

x=\frac{-b\pm\sqrt{D}}{2a}

x=\frac{-(-15)\pm \sqrt{-15}}{2(3)}=\frac{15\pm\sqrt{15}i}{6}

The roots are not real i.e these are imaginary    

\text{Part B: Given a quadratic equation }3x^2+5x-8=0  

\text{Comparing above equation with }ax^2+bx+c=0  

a=3, b=5, c=-8

Discriminant can be calculated as

D=b^2-4ac

D=(5)^2-4(3)(-8)=25+96=121>0

The roots are real

By quadratic formula method

The solution is

x=\frac{-b\pm\sqrt{D}}{2a}

x=\frac{-5)\pm \sqrt{121}}{2(3)}=\frac{-5\pm 11}{6}

x=1,\frac{-8}{3}

which are required roots.

I choose this method because I can get the solutions directly by substituting the values in formula, and I don't have to guess the possible solutions.

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Pls help I need a good grade
choli [55]

Answer:

-8

Step-by-step explanation:

-40/5=-8

6 0
3 years ago
9/10-3/14_____<br><br> Simplest form
Lera25 [3.4K]
10=2×5 and 14=2×7 so least common denominator will be 2×5×7=70
9/10=63/70
3/14=15/70
So 63/70-15/70=48/70=24/35
3 0
4 years ago
Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (round your answers to the nea
creativ13 [48]
Given a table below which gives the years in A.D. for an archaeological excavation site using the method of tree ring dating:

\begin{tabular}&#10;{|c|c|c|c|c|c|c|c|c|}&#10;1229&1292&1187&1257&1268&1316&1275& 1317&1275&#10;\end{tabular}

Part A:

The sample mean is given by:

\bar{x}= \frac{1229+1292+1187+1257+1268+1316+1275+ 1317+1275}{9} \\  \\  = \frac{11416}{9} =1268

Therefore, the sample mean is 1268.



Part B:

We calculate the sample standard deviation as follows:

s= \frac{1}{9-1} \left(\sqrt{(1229-1268)^2+(1292-1268)^2+(1187-1268)^2+(1257-1268)^2+(1268-1268)^2+(1316-1268)^2+(1275-1268)^2+(1317-1268)^2+(1275-1268)^2}\right)\\ \\ = \frac{1}{8}\left(\sqrt{(-39)^2+24^2+(-81)^2+(-11)^2+0^2+48^2+7^2+49^2+7^2}\right)\\ \\ = \frac{1}{8}\left(\sqrt{1521+576+6561+121+2304+49+2401+49}\right)\\ \\ = \frac{1}{8}\left(\sqrt{13,582}\right)\\ \\ = \frac{1}{8}(116.54)=14.57\approx15



Part C:

The 90% confidence interval is given by:

90\% \ C. \ I.=1268\pm1.65\left(\frac{15}{\sqrt{9}}\right) \\  \\ =1268\pm\left(\frac{15}{3}\right)=1268\pm5 \\  \\ =(1268-5, \ 1268+5)=(1263, \ 1273)
8 0
3 years ago
Find an obtuse angle whose sine is<br> a) 0.25<br> b) 0.75<br> c) 0.875<br> d) 0.3465
swat32

Answer:

a) 165.52 degrees.

b)  131.41 degrees.

c)  118.96 degrees.

d)  159.73 degrees.

Step-by-step explanation:

The sine of an obtuse angle is positive as it is in the second quadrant.

a) Using a calculate the angle whose sine ( arcsin) is 0.25  = 14.478 degrees

so the obtuse angle  = 180 - 14.478 = 165.52 degrees to nearest hundredth

b) c) and d) are calculated in the same way.

7 0
3 years ago
Jane is using a carpenter’s square at eye level to determine the height of the tree, as shown in the figure. She is standing 9 f
larisa [96]

Applying the trigonometry ratio, TOA, the measurement that is closest to the height of the tree in feet is: D. 21

Recall:

Trigonometry ratios can be applied to solve any right triangle for missing side lengths or angles. They are denoted with the acronym, SOH CAH TOA.

Using trigonometry ratio, TOA, find the length of the side of the tree in the bigger triangle as follows:

tan 60 = x/9

x = tan 60 × 9

x = 15.6 ft

Height of the tree = 15.6 + 5.2 = 20.8 ft.

  • In conclusion, applying the trigonometry ratio, TOA, the measurement that is closest to the height of the tree in feet is: D. 21

Learn more about trigonometry ratio on:

brainly.com/question/10417664

8 0
3 years ago
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