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Elenna [48]
3 years ago
11

A curve has equation y=x^3_6x+1.at the point where x=2

Mathematics
1 answer:
lisov135 [29]3 years ago
6 0

Answer:2^3=8

6.2=12

Y=8-12+1= -3

Step-by-step explanation:

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If j and k are nonzero integers, which pair of points must lie in the same quadrant?
Marizza181 [45]
<h3>Answer:  Choice D.   (3j, 3k)  and (3/j, 3/k)</h3>

The slash indicates a fraction.

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

Proof:

We'll need to consider 4 different cases.

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

Case (1): j > 0 and k > 0

If j > 0, then 3j > 0 and 3/j > 0

If k > 0, then 3k > 0 and 3/k > 0

The two points (3j, 3k) and (3/j, 3/k) are both in quadrant 1.

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

Case (2): j > 0 and k < 0

If j > 0, then 3j > 0 and 3/j > 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are both in quadrant 4.

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

Case (3): j < 0 and k > 0

If j < 0, then 3j < 0 and 3/j < 0

If k > 0, then 3k > 0 and 3/k > 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 3.

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

Case (4): j < 0 and k < 0

If j < 0, then 3j < 0 and 3/j < 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 4.

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

For nonzero integers j and k, we've shown that Points (3j, 3k) and (3/j, 3/k) are in the same quadrant. This concludes the proof.

8 0
2 years ago
Read 2 more answers
Identify the​ vertex, the axis of​ symmetry, the maximum or minimum​ value, and the range of the parabola for y=x^2+6x+13
charle [14.2K]

Answer:


Step-by-step explanation:

First we can determine the x value of our vertex via the equation:

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

Note that in general a quadratic equation is such that:

ax^2+bx+c

In this case a,b and c are the coefficients and so a=1, b=6 and c=13.

Therefore we can determine the x component of the vertex by plugging in the values known and so:

x=\frac{-b}{2a}=\frac{-6}{2(1)}=\frac{-6}{2}=-3

Now we can determine the y-component of our vertex by plugging in the x-component to the equation and so:

f(x)=x^2+6x+13\\\\f(-3)=(-3)^2+6(-3)+13\\\\f(-3)=4

Therefore our vertex is (-3,4).  Now in vertex our x component determines is the axis of symmetry so the equation for axis of symmetry is:

x=-3

Similarly, the y-component of our vertex is the minimum or maximum.  In this case it is the minimum you can determine this because a is positive meaning that the parabola will point up, and so the equation for the  minimum is:

y=4

The range of the formula is the smallest y-value meaning the minimum y=4 and all real numbers that are more than 4, mathematically:

Range = All real numbers greater than or equal to 4.

4 0
3 years ago
The sum of two numbers is 56. One number is 2 more than the other. What is the smaller number?
grin007 [14]

Answer:

27

Step-by-step explanation:

27 plus 29 is 56

6 0
2 years ago
WHAT IS THE ANSWER:19.393x738.3803=
solniwko [45]
19.393x738.3803= 14319.409
7 0
2 years ago
Read 2 more answers
Burt's grandparents started a savings account for him when he was born. They invested
SashulF [63]

Answer:

4594.76 USD will be in the account on Burt's 18th birthday.

Step-by-step explanation:

Since interest rate is constant in time, we can use the definition of composite interest to determine how much money will be on Burt's 18th birthday, that is:

C = C_{o}\cdot \left(1+\frac{r}{100} \right)^{t} (1)

Where:

C_{o} - Initial amount, measured in US dollars.

C - Current amount, measured in US dollars.

r - Annual interest rate, measured in percentage.

t - Time, measured in years.

If we know that C_{o} = 1250\,USD, r = 7.5 and t = 18, then the money in the savings account on Burt's 18th birthday is:

C = (1250\,USD)\cdot \left(1+\frac{7.5}{100} \right)^{18}

C = 4594.76\,USD

4594.76 USD will be in the account on Burt's 18th birthday.

5 0
3 years ago
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