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3 years ago

What is the factored form of b2 – 4b – 32?

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

7 0

Answer:

(b – 8)(b + 4)

Step-by-step explanation:

The signs of the binomial constants must be different in order for their product to be -32.

The one with the larger magnitude must be negative in order for their sum to be -4. The only viable choice is (b -8)(b +4).

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|4b-4|+|3-b^3|+2b^3;b=2

Katen [24]

|4b - 4| + |3 - b³| + 2b³

subtitute b = 2 to the expression

|4·2 - 4| + |3 - 2³| + 2·2³ = |8 - 4| + |3 - 8| + 2·8 = |4| + |-5| + 16 = 4 + 5 + 16 = 25

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

|4b - 4| + |3 - b²| + 2b³

|4·2 - 4| + |3 - 2²| + 2·2³ = |8 - 4| + |3 - 4| + 2·8 = |4| + |-1| + 16 = 4 + 1 + 16 = 21

5 0

4 years ago

What is the area, in square centimeters, of the shape below?

Karolina [17]

Answer:

21.46 cm squared

Step-by-step explanation:

3.8x5.8=21.46

8 0

3 years ago

A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken

baherus [9]

Answer:

The correct set of hypotheses is

$H_{0}$ : d=80 degrees

$H_{0}$ : d>80 degrees

Step-by-step explanation:

The weatherman claims that the average temperature during July in Chattanooga is 80 degrees or less. To test this claim, following hypotheses need to be taken:

Let d be the the average temperature during July in Chattanooga, then

$H_{0}$ : d=80 degrees

$H_{0}$ : d>80 degrees

7 0

3 years ago

The standard form of a quadratic equation is given as y=ax^2+bx+c and vertex form is given as y=a(x−h)^2+k. Write a formula that

Tju [1.3M]

Answers:

$h = -\frac{b}{2a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

where 'a' cannot be zero.

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

Explanation:

The vertex is (h,k)

The x coordinate of the vertex is h which is found through this formula

$x = -\frac{b}{2a}$

For example, if we had the quadratic $y = 3x^2-6x+5$ , then we'll plug in a = 3 and b = -6 to get: $h = -\frac{b}{2a} = -\frac{-6}{2*3} = 1$

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To find the value of k, we plug that h value into the original standard form of the quadratic and simplify.

$y = ax^2+bx+c\\\\k = ah^2+bh+c\\\\k = a\left(\frac{-b}{2a}\right)^2+b\left(\frac{-b}{2a}\right)+c\\\\k = a*\frac{b^2}{4a^2}+\frac{-b^2}{2a}+c\\\\k = \frac{b^2}{4a}+\frac{-b^2}{2a}+c\\\\$

$k = \frac{b^2}{4a}+\frac{-b^2}{2a}*\frac{2}{2}+c*\frac{4a}{4a}\\\\k = \frac{b^2}{4a}+\frac{-2b^2}{4a}+\frac{4ac}{4a}\\\\k = \frac{b^2-2b^2+4ac}{4a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

It's interesting how we end up with the numerator of $-b^2+4ac$ which is similar to $b^2-4ac$ found under the square root in the quadratic formula. There are other ways to express that formula above. We need $a \ne 0$ to avoid dividing by zero. The values of b and c are allowed to be zero.