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Maru [420]
3 years ago
15

The first play of a football game resulted in a loss of 12 yards. Then a penalty resulted in another loss of 5 yards. What is th

e total loss or gain?
Mathematics
1 answer:
WINSTONCH [101]3 years ago
8 0
You will have to sabtion it because u are taking it away an u would give u 17
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pLEASE HELP ME!!! this is due tonight! In a certain fraction, the denominator is 5 less than the number. If 3 is added to both t
jok3333 [9.3K]

Answer: 11/6

Step-by-step explanation: Since 14 is already 5 more than 9, all you need to do is subtract 3 from each, then you get 11/6

6 0
3 years ago
4(g+2 )+8g=56 show work
Bingel [31]
4g+8+8g=56
12g+8=56
12g+-8=-8
12g=48
DIVIDE 12 TO BOTH 
g=4
5 0
3 years ago
Read 2 more answers
If this function is differentials at x=1/2, what is a+b?
Svet_ta [14]
<h3>Answer: D) 28</h3>

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

Work Shown:

Let

g(x) = ax^3 + 2

h(x) = bx^2 + 1

Plug x = 1/2 into each function

g(x) = ax^3 + 2

g(1/2) = a(1/2)^3 + 2

g(1/2) = (1/8)a + 2

and

h(x) = bx^2 + 1

h(1/2) = b(1/2)^2 + 1

h(1/2) = (1/4)b + 1

In order for f(x) to be differentiable at x = 1/2, the function f(x) must be continuous at x = 1/2. If we had a jump discontinuity here, then there is no way the function is differentiable here.

f(x) is continuous at x = 1/2 when g(1/2) = h(1/2).

This means,

g(1/2) = h(1/2)

(1/8)a + 2 = (1/4)b + 1

8*[(1/8)a + 2] = 8*[(1/4)b + 1]

a+16 = 2b+8

a = 2b+8-16

a = 2b-8

We'll keep this in mind for later.

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

Now let's compute the derivatives

g(x) = ax^3 + 2

g ' (x) = 3ax^2

h(x) = bx^2 + 1

h ' (x) = 2bx

Now plug in x = 1/2

g ' (x) = 3ax^2

g ' (1/2) = 3a(1/2)^2

g ' (1/2) = (3/4)a

and

h ' (x) = 2bx

h ' (1/2) = 2b(1/2)

h ' (1/2) = b

Equate the two items. We do so because we want f(x) to be differentiable at x = 1/2, so that means g ' (1/2) = h ' (1/2)

So,

g ' (1/2) = h ' (1/2)

(3/4)a = b

3a = 4b

a = (4b)/3

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

Earlier we found a = 2b-8.

Since both a = 2b-8 and a = (4b)/3, this means we can equate the right hand sides to solve for b

2b-8 = (4b)/3

3*(2b-8) = 3*(4b)/3

6b-24 = 4b

6b-4b = 24

2b = 24

b = 24/2

b = 12

Which leads to

a = 4b/3

a = 4*12/3

a = 48/3

a = 16

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

The piecewise function

f(x) = \begin{cases}ax^3+2, \ \ x < \frac{1}{2}\\bx^2+1, \ \ x \ge \frac{1}{2}\end{cases}

will update to

f(x) = \begin{cases}16x^3+2, \ \ x < \frac{1}{2}\\12x^2+1, \ \ x \ge \frac{1}{2}\end{cases}

To verify f(x) is differentiable at x = 1/2, you should check to see if both pieces evaluate to the same output when you plug in x = 1/2. In other words, you should check to see if g(1/2) = h(1/2).

Also, you should check to see if g ' (1/2) = h ' (1/2) so that f(x) is fully differentiable here. I'll let you do the check portions.

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

After getting our a and b values, we can finally say that

a+b = 16+12 = 28

8 0
2 years ago
A company has decided to use 0−1 integer programming to help make some investment decisions. There are three possible investment
artcher [175]

Answer:

See explaination for the details

Step-by-step explanation:

See attachment please

3 0
3 years ago
4/5 of the senior class went to prom if 324 seniors went to prom how many are there in the senior class
Sedbober [7]

Answer:

405

Step-by-step explanation:

324 seniors is 4/5 of all seniors. To find how many 5/5 of the seniors is, we find 1/5 and multiply it by 5. Since 4/5 is 4 times 1/5, divide 324 by 4. The answer is 81, which is 1/5 of the seniors. Multiply 81 by 5 to get all 5/5. 81 * 5 is 405

5 0
2 years ago
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