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3 years ago

. Which equation represents y = −x2 + 4x − 1 in vertex form?

Mathematics

1 answer:

Stels [109]3 years ago

6 0

Answer:

Rewrite in vertex form and use this form to find the vertex

(

)

(

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Step-by-step explanation:

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Are 1,2,3 right just in case

FromTheMoon [43]

Yes. youre right, but no2 you can kinda make it a little more 3d like their example just saying

4 0

3 years ago

At a concession stand, five hot dog(s) and two hamburger(s) cost $11.75; two hot dog(s) and five hamburger(s) cost $11.00. Find

serg [7]

Answer:

x:hot dogs

y: hamburger

5x + 2y = 11.75

2x + 5y = 11.00

10x + 4y = 23.50

-10x - 25y = -55.00

-21y = -31.50

y = $1.50 each hamburger

2x + 5(1.50)= 11.00

2x + 7.50 = 11.00

2x = $3.50

x = $1.75 each hot dog

8 0

4 years ago

PLEASE ANSWER ASAP FOR BRIANLEST DUE IN 3 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!

bezimeni [28]

Answer: 3rd one

Step-by-step explanation:

5 0

3 years ago

Find the imaginary part of\[(\cos12^\circ+i\sin12^\circ+\cos48^\circ+i\sin48^\circ)^6.\]

iren [92.7K]

Answer:

The imaginary part is 0

Step-by-step explanation:

The number given is:

$x=(\cos(12)+i\sin(12)+ \cos(48)+ i\sin(48))^6$

First, we can expand this power using the binomial theorem:

$(a+b)^k=\sum_{j=0}^{k}\binom{k}{j}a^{k-j}b^{j}$

After that, we can apply De Moivre's theorem to expand each summand: $(\cos(a)+i\sin(a))^k=\cos(ka)+i\sin(ka)$

The final step is to find the common factor of i in the last expansion. Now:

$x^6=((\cos(12)+i\sin(12))+(\cos(48)+ i\sin(48)))^6$

$=\binom{6}{0}(\cos(12)+i\sin(12))^6(\cos(48)+ i\sin(48))^0+\binom{6}{1}(\cos(12)+i\sin(12))^5(\cos(48)+ i\sin(48))^1+\binom{6}{2}(\cos(12)+i\sin(12))^4(\cos(48)+ i\sin(48))^2+\binom{6}{3}(\cos(12)+i\sin(12))^3(\cos(48)+ i\sin(48))^3+\binom{6}{4}(\cos(12)+i\sin(12))^2(\cos(48)+ i\sin(48))^4+\binom{6}{5}(\cos(12)+i\sin(12))^1(\cos(48)+ i\sin(48))^5+\binom{6}{6}(\cos(12)+i\sin(12))^0(\cos(48)+ i\sin(48))^6$

$=(\cos(72)+i\sin(72))+6(\cos(60)+i\sin(60))(\cos(48)+ i\sin(48))+15(\cos(48)+i\sin(48))(\cos(96)+ i\sin(96))+20(\cos(36)+i\sin(36))(\cos(144)+ i\sin(144))+15(\cos(24)+i\sin(24))(\cos(192)+ i\sin(192))+6(\cos(12)+i\sin(12))(\cos(240)+ i\sin(240))+(\cos(288)+ i\sin(288))$

The last part is to multiply these factors and extract the imaginary part. This computation gives:

$Re x^6=\cos 72+6cos 60\cos 48-6\sin 60\sin 48+15\cos 96\cos 48-15\sin 96\sin 48+20\cos 36\cos 144-20\sin 36\sin 144+15\cos 24\cos 192-15\sin 24\sin 192+6\cos 12\cos 240-6\sin 12\sin 240+\cos 288$

$Im x^6=\sin 72+6cos 60\sin 48+6\sin 60\cos 48+15\cos 96\sin 48+15\sin 96\cos 48+20\cos 36\sin 144+20\sin 36\cos 144+15\cos 24\sin 192+15\sin 24\cos 192+6\cos 12\sin 240+6\sin 12\cos 240+\sin 288$

(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)

A calculator simplifies the imaginary part Im(x⁶) to 0

4 0

3 years ago

21.6% of all registered doctors were female, if there were 45,200 females registered doctors that year, what was the total numbe

Marina86 [1]

Answer:

209259

Step-by-step explanation:

45200 / 21.6 = 209259.259259

209259.259259 rounded to nearest whole number = 209259

7 0

3 years ago