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Pavlova-9 [17]
2 years ago
10

10. Factor Please help me I will mark as brainliest

Mathematics
1 answer:
suter [353]2 years ago
6 0

Answer:

<u>(3w + 7)² or (3w + 7)(3w + 7)</u>

Step-by-step explanation:

<u>Identity</u>

  • a² + 2ab + b² = (a + b)² = (a + b)(a + b)

<u>Solving</u>

  • 9w² + 42w + 49
  • (3w)² + 2(3w)(7)  + (7)²
  • <u>(3w + 7)² or (3w + 7)(3w + 7)</u>
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A deep sea diver started at sea level (0 feet) and dove at a rate of 5.6 feet per minute. If the diver dove for ½ hour, what rat
Leona [35]

Given:

A deep sea diver started at sea level (0 feet).

Rate of diving = 5.6 feet per minute.

Time = \dfrac{1}{2} hour

To find:

The rational number that represents his position relative to sea level.

Solution:

We know that,

1 hour = 60 minutes

\dfrac{1}{2} hour = 30 minutes

A deep sea diver, dove at a rate of 5.6 feet per minute.

Distance covered in 1 minute = 5.6 feet

Distance covered in 30 minute = 30 × 5.6 feet

                                                    = 168 feet

The diver dove 168 feet in \dfrac{1}{2} hour. Since it is below the sea level, therefore it should be negative.

So, the rational number that represents his position relative to sea level is -168 feet.

Therefore, the correct option is D.

5 0
3 years ago
F(x) = x2 − x − ln(x) (a) find the interval on which f is increasing. (enter your answer using interval notation.) find the inte
Mekhanik [1.2K]

Answer:

(a) Decreasing on (0, 1) and increasing on (1, ∞)

(b) Local minimum at (1, 0)

(c) No inflection point; concave up on (0, ∞)

Step-by-step explanation:

ƒ(x) = x² - x – lnx

(a) Intervals in which ƒ(x) is increasing and decreasing.

Step 1. Find the zeros of the first derivative of the function

ƒ'(x) = 2x – 1 - 1/x = 0

           2x² - x  -1 = 0

     ( x - 1) (2x + 1) = 0

         x = 1 or x = -½

We reject the negative root, because the argument of lnx cannot be negative.

There is one zero at (1, 0). This is your critical point.

Step 2. Apply the first derivative test.

Test all intervals to the left and to the right of the critical value to determine if the derivative is positive or negative.

(1) x = ½

ƒ'(½) = 2(½) - 1 - 1/(½) = 1 - 1 - 2 = -1

ƒ'(x) < 0 so the function is decreasing on (0, 1).

(2) x = 2

ƒ'(0) = 2(2) -1 – 1/2 = 4 - 1 – ½  = ⁵/₂

ƒ'(x) > 0 so the function is increasing on (1, ∞).

(b) Local extremum

ƒ(x) is decreasing when x < 1 and increasing when x >1.

Thus, (1, 0) is a local minimum, and ƒ(x) = 0 when x = 1.

(c) Inflection point

(1) Set the second derivative equal to zero

ƒ''(x) = 2 + 2/x² = 0

             x² + 2 = 0

                   x² = -2

There is no inflection point.

(2). Concavity

Apply the second derivative test on either side of the extremum.

\begin{array}{lccc}\text{Test} & x < 1 & x = 1 & x > 1\\\text{Sign of f''} & + & 0 & +\\\text{Concavity} & \text{up} & &\text{up}\\\end{array}

The function is concave up on (0, ∞).

6 0
3 years ago
Please help. Thank you
madam [21]

Answer:

c

Step-by-step explanation:

Pythagoras theroem

\sqrt{(( {32}^{2})  + {12}^{2} ) }

= 4√73

8 0
2 years ago
2x-10=5x-100 what is the value of x?
Leni [432]

Answer:

Step-by-step explanation: I did a formula to get the answer

2x-10=5x-100

2x=5x-90

I subtracted 100-10 and then got 90

3x=90

3x/3x=90/3

x=30

7 0
3 years ago
Evaluate the following: (½)(10) −(−12) −25
mr Goodwill [35]

Answer:

-8

Step-by-step explanation:

1/2 times 10 is 5. and a negative times a negative is a positive, so you have a positive 12, which becomes 5+12-25, which is -8

7 0
3 years ago
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