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Gekata [30.6K]
3 years ago
10

which shows one way to determine the factors of 12x^3 - 2x^2 + 18x - 3 by grouping? A) 2x^2(6x - 1) + 3(6x - 1) B) 2x^2(6x - 1)

- 3(6x - 1) C) 6x(2x^2 - 3) - 1(2x^2 - 3) D) 6x(2x^2 + 3) + 1(2x^2 + 3)
Mathematics
1 answer:
Eva8 [605]3 years ago
4 0

Answer:

2x^2(6x - 1) + 3(6x - 1)

Step-by-step explanation:

Given

12x^3 - 2x^2 + 18x - 3

Required

Factorize

To start with; we need to group the expression into two

(12x^3 - 2x^2) + (18x - 3)

Factorize each grouped expression, using their common factor

2x^2(6x - 1) + 3(6x - 1)

From the list of given options;

Option A is correct

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If the distance between opposite numbers on a number line is 10 units, what are the opposite numbers?
Margarita [4]

Answer:

  5 and -5

Step-by-step explanation:

Opposite numbers are the same distance from 0 on the number line. So, each of the numbers is a distance from zero that is half the distance between them.

The numbers are 10/2 = 5, and -5.

4 0
3 years ago
IF TWO ANGLES ARE CONSECUTIVE EXTERIOR ANGLES AND <1=59, WHAT IS THE MEASURE OF <2?
lutik1710 [3]

Answer:

<2 = 121

Step-by-step explanation:

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6 0
3 years ago
Thank you for anyone who knows this
katen-ka-za [31]

Answer:  

  • Part (a) Vertex = (-3, -1)
  • Part (b) Vertex = (4, 5)
  • Part (c) function 2; max value = 5

=====================================================

Explanations:

Part (a)

In this case, the vertex is the highest point, so the vertex of function 1 is (-3, -1)

If the parabola was flipped so that it opened upward, instead of downward, then the vertex would be the lowest point.

----------------------------

Part (b)

We could graph this function to see where the highest or lowest point is, but there's another way we could find the vertex using algebra.

The given equation is in the form y = ax^2 + bx + c where in this case

  • a = -2
  • b = 16
  • c = -27

The a and b values are plugged into the formula below to get

h = -b/(2a)

h = -16/(2*(-2))

h = -16/(-4)

h = 4

This is the x coordinate the vertex since the vertex is (h,k)

To find k, we plug that value of h into the original function to find its corresponding y value.

y = -2x^2 + 16x - 27

y = -2(4)^2 + 16(4) - 27

y = -2(16) + 16(4) - 27

y = -32 + 64 - 27

y = 5

We found that h = 4 leads to k = 5. The vertex is (h,k) = (4, 5)

----------------------------

Part (c)

We'll compare the y values of each vertex

  • Function 1 has a vertex of (-3, 1)
  • Function 2 has a vertex of (4, 5)

The vertex with the larger y value is the winner, so that would be function 2. This parabola reaches a higher peak compared to the other curve.

The max value here is y = 5. In other words, it's the maximum output the function can produce.

If you graphed functions 1 and 2 together on the same xy grid (see below), you'll see that the curve for function 2 reaches a higher peak.

7 0
2 years ago
A jewelry company prints a hidden logo watermark. The watermark is a chord that is 0.8 cm from the center of a circular ring tha
Sergeeva-Olga [200]

Answer:

length of chord is 6cm

Step-by-step explanation:

Here, we are to calculate the length of the chord.

It should be understood that the chord has a length of 0.8cm from the center of the circle of radius 3cm, thereby forming two right-angled triangles with the radius 3cm being the hypotenuse of each and 0.8cm being the height of each.

Now, the chord is divided into 2 by this height dropping from the center of the circle. To calculate the first half, we use Pythagoras’ theorem with 3cm being hypotenuse and 0.8cm being the other side.

mathematically;

3^2 = 0.8^2 + l^2

9 = 0.64 + l^2

l^2 = 9-0.64

l^2 = 8.36

l = √(8.36)

l = 2.89 approximately

The length of the chord would be 2l = 2 * 2.89 = 5.78 cm which is 6cm to the nearest length

5 0
3 years ago
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