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viktelen [127]
3 years ago
6

Find a quadratic equation whose roots are the reciprocals of the roots of 3x^2+5x-2=0.

Mathematics
1 answer:
mel-nik [20]3 years ago
6 0
3x^2 + 5x - 2 = 0
3x^2 + 6x - x - 2 = 0
(3x^2 + 6x) + (-x - 2) = 0
3x(x + 2) - 1(x + 2) = 0
(3x - 1)(x + 2) = 0
3x - 1 = 0 or x + 2 = 0
3x = 1 or x = -2
x = 1/3 or x = -2

Reciprocals are 3 and -1/2
Equation with roots at 3 and -1/2 is (x - 3)(x + 1/2) = x^2 - 5/2 x - 3/2 = 2x^2 - 5x - 3
Therefore, required equation is y = 2x^2 - 5x - 3
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You invested money in two funds. Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you receiv
Angelina_Jolie [31]

You invested 11000 in in 2st fund and 9000 in 2nd fund

<h3><u>Solution:</u></h3>

Given that, You invested money in two funds.  

Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.  

This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500.

Let the amount in Fund I be $x and amount in Fund II be $ y

Then, for last year ⇒ 0.08x+0.05y=1330 ----- eqn (1)  

And for this year ⇒ 0.12x+0.02y=1500 ------- eqn (2)  

Multiply (1) by 2 ⇒ 0.16 x + 0.1 y = 2660  

Multiply (2) by 5 ⇒ 0.6 x + 0.1 y = 7500

Subtract the two equations  

(2) ⇒ 0.6x + 0.1y = 7500

(1) ⇒ 0.16x + 0.1y = 2660

(-) --------------------------------

0.44x + 0 = 4840

x = 11000

Now, from eqn (2)  

0.12(11000) + 0.02y = 1500  

0.02y = 1500 – 1320  

0.02y = 180  

y = 9000

Hence, he invested 11000 in in 2st fund and 9000 in 2nd fund

5 0
3 years ago
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. Whe
svp [43]

Answer:

Step-by-step explanation:

This is exponential, of the form

y=a(b)^x where a is the initial amount and b is the growth/decay rate. If Ginny begins the study with 1200 frogs in the population, our a value is 1200.

If the population is decreasing 3% per year, it is decreasing 100% - 3% = 97% which, as a decimal, is .97. Our exponential function, then, is

y=1200(.97)^x

6 0
3 years ago
Look at the picture below
Lelu [443]

Answer: Phillip is correct. The triangles are <u>not </u>congruent.

How do we know this? Because triangle ABC has the 15 inch side between the two angles 50 and 60 degrees. The other triangle must have the same set up (just with different letters XYZ). This isn't the case. The 15 inch side for triangle XYZ is between the 50 and 70 degree angle.

This mismatch means we cannot use the "S" in the ASA or AAS simply because we don't have a proper corresponding pair of sides. If we knew AB, BC, XZ or YZ, then we might be able to use ASA or AAS.

At this point, there isn't enough information. So that means John and Mary are incorrect, leaving Phillip to be correct by default.

Note: Phillip may be wrong and the triangles could be congruent, but again, we don't have enough info. If there was an answer choice simply saying "there isn't enough info to say either if the triangles are congruent or not", then this would be the best answer. Unfortunately, it looks like this answer is missing. So what I bolded above is the next best thing.

7 0
3 years ago
Read 2 more answers
How do work this out
BabaBlast [244]
We can factor this by using grouping. Take the leading coefficient and multiply it by the constant. In this case we get 5*-7 = -35. 

Now we need 2 numbers that add to 2 and multiply to be -35. The numbers are -5 and 7.

So split the 2r into these two terms and group.

(5r^2 - 5r) + (7r - 7)

Factor both groups.

5r(r-1) + 7(r-1)

The factors of (r-1) can be added together to get the answer.

(r-1)(5r+7)
6 0
3 years ago
Y = -2 x - 5 what is the answer help
blondinia [14]

Answer:

x = -5/2

Step-by-step explanation:

0 = -2x - 5

2x = -5

Divide^

x = -5/2

Hope this helped

Brainliest is appreicated./

7 0
2 years ago
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