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3 years ago

What is the vertex of (x) = –16x² + 64x + 80.

Mathematics

1 answer:

cricket20 [7]3 years ago

7 0

Answer:

Step-by-step explanation:

f(x) = a(x - h)² + k - the vertex form of the equation of the parabola with vertex (h, k)

$f(x) = -16x^2+ 64x + 80\\\\f(x) = -16(x^2- 4x) + 80\\\\f(x) = -16(\underline {x^2-2\cdot2x\cdot2+2^2}-2^2) + 80\\\\f(x) = -16\big[(x-2)^2-4\big] + 80\\\\f(x) = -16(x-2)^2+64 + 80\\\\\bold{f(x)=-16(x-2)^2+124\quad\implies\quad h=2\,,\quad k=124}$

The vertex is (2, 124)

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3 years ago

9(2.3n+6)+10.45>43.7

kifflom [539]

Answer:

Step-by-step explanation:

9(2.3n+6)+10.45>43.7

(9*2.3n)+(9*6)+10.45>43.7

20.7n+54+10.45>43.7

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3 years ago

A triangle has side lengths of (2b+c)(2b+c) centimeters, (7b+4d)(7b+4d) centimeters, and (6d+2c)(6d+2c) centimeters. Which expre

Gnoma [55]

Answer:

(9b + 3c + 10d)cm

Step-by-step explanation:

Given the sides of a triangle expressed as (2b+c), (7b + 4d) and (6d+2c). The perimeter of the triangle is the sum of all the sides of the triangles.

Perimeter of the triangle = 2b+c + 7b+4d + 6d+2c

Perimeter of the triangle = 2b + 7b + c + 2c + 4d + 6d

Perimeter of the triangle = 9b + 3c + 10d

Hence the perimeter of the triangle is (9b + 3c + 10d)cm

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3 years ago

Read 2 more answers

Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can

lesya [120]

Answer:

The set A={(1,2),(2,2),(3,2),(4,2),(5,2),(6,2),(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(1,(2,6),(3,6),(4,6),(5,6),(6,6)}

B={(2,2),(4,2),(6,2),(2,4),(2,6),(1,3),(1,5),(1,1),(3,1),(3,3),(3,5),(4,4),(4,6),(5,1),(5,3),(5,5),(6,4),(6,6)}

C={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,5),(3,3),(3,5),(3,4),(3,6),(4,1),(4,3),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,3),(6,5)}.

A∩B:{(2,2),(4,2),(6,2),(2,4),(2,6),(4,4),(4,6),(6,4),(6,6)}

A∪B={(1,2),(2,2),(4,2),(6,2),(2,4),(2,6),(4,4),(4,6),(6,4),(6,6),(3,2),(5,2),(1,4),(3,4),(5,4),(1,6),(3,6),(5,6),(1,3),(1,5),(1,1)(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)}

A∩C={(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)}

Step-by-step explanation:

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3 years ago

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Guess the rule and add the next number in the sequence. 7, 10, 16, 25, 37,

Delvig [45]

Answer:

Step-by-step explanation:

Let us first closely examine the sequence for any mathematical correlation between the terms of sequence.

It is visualized that the series is progressing with addition of increasing even numbers starting with +6 ( +6, +8, +10, +12, +14, +16, +18 …) in the previous term to obtain next terms of the series. This logic continues for entire series.

The given series is:

1 ,7 ,15 ,25 ,37

Starting with first number of the series

1 + 6 = 7

7 + 8 = 15

15 + 10 = 25

25 + 12 = 37

37 + 14 = 51

51 + 16 = 67

67 + 18 = 85

The extended series is

1, 7, 15, 25, 37, 51, 67, 85

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