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Ksenya-84 [330]
3 years ago
8

Find the vertex: -4x² + 16x - 7​

Mathematics
1 answer:
guapka [62]3 years ago
7 0

Find the vertex: -4x^2 + 16x - 7​

Vertex = ( x, f(x)).

x = -b/2a

x = -16/2(-4)

x = -16/-8

x = 2

f(x) = -4x^2 + 16x - 7

Let x = 2

f(2) = -4(2)^2 + 16(2) - 7

f(2) = -4(4) + 32 - 7

f(2) = -16 + 32 - 7

f(2) = 16 - 7

f(2) = 9

Vertex = (2, 9)

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If U = {x: X € N, 1 < × < 15)
Inessa05 [86]

Answer:

Step-by-step explanation:

Given:

U = {x: X € N, 1 < × < 15) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A = {2,4,6,8,10,12,14}

B = {3,6,9,12,15}

C = {5,10,15}

(a) Verify A(BnB)=(AUB)(AUB)

A U (B n B)

=  {2,4,6,8,10,12,14} U (  {3,6,9,12,15} n  {3,6,9,12,15} )

=  {2,4,6,8,10,12,14} U {3,6,9,12,15}

=  {2,3,4,6,8,9,10,12,14,15}

( A U B) n (A U B)

= {2,3,4,6,8,9,10,12,14,15} n {2,3,4,6,8,9,10,12,14,15}

= {2,3,4,6,8,9,10,12,14,15}

Therefore

A U (B n B)  =  ( A U B) n (A U B)

verifies

(b) Verify An(BUC)=(AnB)u(AnC)

A n ( B U C)

=  {2,4,6,8,10,12,14} n ( {3,6,9,12,15} U {5,10,15} )

=  {2,4,6,8,10,12,14} n {3,5,6,9,10,12,15}

= {6,10,12}

( A n B ) U ( A n C )

= ( {2,4,6,8,10,12,14} n {3,6,9,12,15} ) U ( {2,4,6,8,10,12,14} n {5,10,15} )

= {6,12} U {10}

= {6,10,12}

Therefore

A n ( B U C) = ( A n B ) U ( A n C )

verifies

(c) Verify AU(BUC)=(AUB)U(AUC)​

AU(BUC)

=  {2,4,6,8,10,12,14}U{3,6,9,12,15}U{5,10,15}

= {2,3,4,5,6,8,9,10,12,14,15}

(AUB)U(AUC)​

=  ({2,4,6,8,10,12,14}{3,6,9,12,15})U({2,4,6,8,10,12,14}U{5,10,15})

= {2,3,4,6,8,9,10,12,14,15}U{2,4,5,6,8,10,12,14,15}

= {2,3,4,5,6,8,9,10,12,14,15}

Therefore

AU(BUC)=(AUB)U(AUC)​

verifies

5 0
3 years ago
Santa and his elves had a workshop that allowed them to produce 22{,}912{,}546{,}99222,912,546,99222, comma, 912, comma, 546, co
zvonat [6]

Answer: 180 times

Step-by-step explanation:

Given the following :

Production capacity of old workshop :22,912,546,992 toys per year

Production capacity of new workshop:

4,134,232,638,937 toys

Approximately how many times as many toys can the new workshop produce each year compared to the old workshop?

Production capacity of new workshop / production capacity of old workshop

= 4,134,232,638,937 / 22,912,546,992

= 180.435

= 180 ( nearest whole number)

3 0
3 years ago
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kvasek [131]

Answer:

10.26 in²

Step-by-step explanation:

The area (A) of the sector is

A = area of circle × fraction of circle

  = πr² × \frac{\frac{5\pi }{6} }{2\pi }

  = π × 2.8² × \frac{5}{12} ≈ 10.26 in²

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3 years ago
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Marina86 [1]

The simplified answer is 27m^2

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The system of equations has no solution:<br> y=2/3x-5<br> 4x - 6y = 30<br> true or false?
Serjik [45]

1. y = 2/3x - 5

2. 4x - 6y = 30

Divide 2. by 2

3. 2x - 3y = 15

Substitute 1. into 3.

4. 2x - 3(2/3x - 5) = 15

5. 2x - 2x + 15 = 15

6. 15 = 15

False. There are an infinite number of solutions.

3 0
2 years ago
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