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valentina_108 [34]
3 years ago
15

1. Find the zeros of the function.

Mathematics
1 answer:
Mama L [17]3 years ago
3 0
1. f(x) = 9x² + 6x - 8
f(x) = (3x - 2)(3x + 4)
When  (3x - 2) = 0, then x = 2/3
When (3x + 4) = 0, then x = -4/3

Answer: The zeros are two divided by three and negative four divided by three.

2. f(x) = 9x³ - 45x² + 36x
  f(x) = 9x(x² - 5x + 4)
        = 9x(x - 1)(x - 4)
  When 9x = 0, then x = 0
  When (x-1) = 0, then x = 1
  When (x-4) = 0, then x = 4

 Answer: 0, 1 and 4

3. f(x) = 4(x+7)²(x-7)³
 When (x+7)² = 0, then x = -7 (twice)
 When (x-7)³ = 0, then x = 7 (thrice)

 Answer: 7, multiplicity 2; -7 multiplicity 3

4. The zeros of f(x) are √5, -√5, -7
 The factors of f(x) are (x-√5)(x+√5)(x+7)
 Note that (x-√5)(x+√5) = x² - (√5)² = x² - 5
 f(x) = (x²-5)(x+7)
       = x³ + 7x² - 5x - 35

Answer: f(x) = x³ + 7x² - 5x - 35

5. Expand (2x + 4)³
 From Pascal's Triangle, the coefficients are 1 3 3 1
 Therefore
 (2x + 4)³ = 1(2x)³(4)⁰ + 3(2x)²(4)¹ + 3(2x)¹(4)² + 1(2x)⁰(4)³
                = 8x³ + 48x² + 96x + 64

 Answer: 8x³ + 48x² + 96x + 64
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<h3>What is geometric transformation?</h3>

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a two-dimensional figure shown in the picture on a coordinate plane.

From the graph the coordinate point or vertex of the point Z:

Z = (1, 2)

Dilating the above point by scale factor 2

Z' = (2×1, 2×2) = (2, 4)

Similarly, for point E:

E = (3, 5)

E' = (2×3, 2×5) = (6, 10)

Similarly, for point N:

N = (4, 5)

N' = (2×4, 2×5) = (8, 10)

Similarly, for point O:

O = (6, 2)

O' = (2×6, 2×2) = (12, 4)

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The angles below are supplementary. what is the value of x?
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If 2 liters of sea water contain 70 grams of salt, how much salt is in 32 liters of sea water?
OLga [1]

Answer:

1120 grams

Step-by-step explanation:

The amount of sea water is directly proportional to the amount of salt in the water.

Let the amount of sea water be W and the amount of salt be S.

This means that:

W α S

=> W = kS

where k = constant of proportionality

2 liters of sea water contain 70 grams of salt Therefore:

2 = k * 70

k = 2 / 70 = 1/35

Therefore, for 32 liters of sea water:

32 = 1/35 * S

S = 35 * 32

S = 1120 grams

There are 1120 grams of salt in 32 liters of water.

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3 years ago
Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?
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3 years ago
Car decreased in price by 3%. Original price is $45600. New Price= A x original price
Karo-lina-s [1.5K]

A decrease of 3% means the car is now valued at 97% of the original price. ( 100% -3% = 97%)


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