What adds up to -11 but multiplies to 10?

Which logarithmic equation is equivalent to 3^c=257

vagabundo [1.1K]

Answer: $log_3(257) = c$

Step-by-step explanation:

5 0

2 years ago

The function y = x 2 - 10x + 31 has a ____

katrin [286]

Answer:

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

$f(x) = x^2-10x+31$

Taking first derivative

$f'(x) = 2x-10$

Now the first derivative has to be put equal to zero to find the critical value

$2x-10 = 0\\2x = 10\\x = \frac{10}{2} = 5$

The function has only one critical value which is 5.

Taking 2nd derivative

$f''(x) =2$

$f''(5) = 2$

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

$f(5) = (5)^2-10(5)+31\\=25-50+31\\=6$

Hence,

The function y = x 2 - 10x + 31 has a minimum value of 6

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

8 0

3 years ago

How to do this question plz answer

ANEK [815]

9514 1404 393

Answer:

more than half are being used

Step-by-step explanation:

Perhaps easiest to understand is the most straightforward: figure the total number of seats and the number of seats being used. Check to see if that is more than half.

The 1 first-class carriage has usage of ...

(3/8)(64 seats) = 24 seats.

The 6 standard carriages have usage of ...

(7/13)(6 · 78 seats) = 252 seats.

The total number of seats used is ...

24 + 252 = 276 . . . . seats used

__

The total number of seats on the train is ...

1·64 +6·78 = 532 . . . . seats on the train

Half of the seats on the train will be ...

532/2 = 266 seats . . . . half the seats

The 276 used seats are more than half of the total number. More than half the seats are being used.

_____

Alternate solution

Another way to look at this is to compare utilization to 1/2 in each carriage class.

In first class 1/2 -3/8 = 1/8 of 64 seats = 8 seats fewer than 1/2 the seats are being used.

In standard class, 7/13 -1/2 = 14/26 -13/26 = 1/26 of 78 seats = 3 seats more than 1/2 the seats are being used. There are 6 standard class carriages, so 6·3 = 18 more than half the seats in the standard-class carriages are being used.

This number is 10 more than the 8 under-utilized seats in first class, so more than half the train seats are being used.

8 0

2 years ago

What percentage is the fraction ‘2/4’ equal to ? A. 30% B. 20% C. 50% D. 40%

Solnce55 [7]

Answer: C.) 50%

Step-by-step explanation:

2/4 simplified = 1/2

1/2 = "one half"

= 50%

3 0

3 years ago

Read 2 more answers

I need help please this is confusing

kap26 [50]

Step-by-step explanation:

slope formula when it's perpendicular : m1 × m = -1

Now Differentiate the quadratic function given.

d/dx ( x^2 - x + 1 ) at an x value of -1 from the point "(-1 , 3 )"

= 2x - 1 .... plug in the x value

= 2 × -1 - 1 = -3.

Use this equation...

y - y1 = m(x - x1)

m = slope = derivative at x = -1

y1 = value found by subbing -1 into the original function

x1 = the x value often given.

y - 3 = 1/3 (x + 1)

= 1/3x + 1/3 + 3

y = 1/3x + 10/3.

not sure about this one - it probably intersects at the x & y intercepts of the equation of the normal line.

y = 0 + 10/3 = 10/3

1/3x = 0 - 10/3

x = -10/3 / 1/3 = -10

so the point .... (-10 , 10/3)

7 0

2 years ago