I need help with 4 and 5

Mathematics

2 answers:

zmey [24]3 years ago

8 0

4. where you have any repeated x values this is not a function
Answer is b

5. a has rate of change = -3, so has c,
b has rate of change (7-5)/(-1-(-2) = 2
d has rate of change (10-6)/(6-2) = 1

madreJ [45]3 years ago

6 0

4. Look at each set of points. If all x-coordinates are different, it is a function. If the same number shows up more than once as an x-coordinate, it is not a function.
Here are the x-coordinates for each choice:
a. 0, 1, 2, 3 All are different. This is a function.
b. 0, 0, 2, 2 There are two zeros and two twos. Not a function.
c. 0, 1, 2, 3 All are different. This is a function.
d. 0, -1, -2, -3 All are different. This is a function.

5. The rate of change is the slope.
a. slope is -3
b. slope = (9 - 7)/(0 - (-1)) = 2
c. 3y + 9x = 10
3y = -9x + 10
y = -3x + 10/3
slope = -3
d. slope = (14 - 10)/(10 - 6) = 4/4 = 1

The greatest slope is 2 in option b.

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This is the question i have.

Nimfa-mama [501]

S (-10,1)

T (-6,1)

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V (-6,9)

3 0

3 years ago

Part 1

svetlana [45]

Answer:

A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.

B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.

Step-by-step explanation:

f(x) = 12x^2 + 5x - 2.

Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).

To find the roots of f(x), set f(x) = 0. Therefore:

12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:

12x^2 + 8x - 3x - 2 = 0.

4x(3x + 2) -1(3x+2) = 0.

(4x-1)(3x+2) = 0.

4x-1 = 0 or 3x+2 = 0.

x = 1/4 or x = -2/3.

It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!

8 0

3 years ago

Find the equation of the tangent line. y=(9-x^2)^1/3 at (1,2)

Schach [20]

Get the derivative:

y = (9 - x²)¹ʹ³

dy/dx = 1/3 (9 - x²)⁻²ʹ³ d/dx [9 - x²]

dy/dx = 1/3 (9 - x²)⁻²ʹ³ (-2x)

dy/dx = -2/3 x (9 - x²)⁻²ʹ³

Evaluate it at x = 1 :

dy/dx (1) = -2/3 • 8⁻²ʹ³

Since 8 = 2³, we have