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3 years ago

What is the name given to this pair of angles?

Mathematics

1 answer:

poizon [28]3 years ago

3 0

They are corresponding angles.

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If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.

Lelechka [254]

Answer:

$\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }$

Step-by-step explanation:

Hello,

a and b are the zeros, we can say that

$f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)$

So we can say that

$a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}$

Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

for instance we can write

$(x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab$

and we can notice that

$a^2+b^2=(a+b)^2-2ab$ so

$(x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab$

it comes

$x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}$

multiply by 3

$3x^2-20x+2*16+5=3x^2-20x+37$

4 0

3 years ago

Ascending order 1/2 1/3 5/12 3/4

tekilochka [14]

Answer:

1/3, 5/12, 1/2, 3/4

Step-by-step explanation:

5 0

2 years ago

The dot plot shows the height, in feet, of a group of trees being studied. How many trees are being studied? Enter the answer in

suter [353]

Answer:13

Step-by-step explanation: I took the test in K12 and the answer is 13

3 0

3 years ago

How many liters are in 1 dekaliter?

shepuryov [24]

Answer:

nsdkbljcb;awjef

Step-by-step explanation:

jwaefjalfjwkhjefkuw

7 0

3 years ago

Is the relation a function? <br><br> {( 1, 12), (3, 14), (14, 3), (5, 12)}<br><br> yes or no

Iteru [2.4K]

Answer:

Yes.

Step-by-step explanation:

Yes because each value of x maps to a single value of y.

THere is a many-to-one relation with (1, 12) and (5, 12) but that is OK for a function. What would not be OK is if we had a one-to-many relation like (1, 12) and (1, 14) included in the ordered pairs - that is not a function.

6 0

3 years ago

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