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sergiy2304 [10]
3 years ago
6

Sophia 4/8 yards of string. She used 1/6 of the string for a school project how many yards of string did she use for her project

.
A. 5/6
B. 1/3
C. 1/12
D. 2/3
Mathematics
2 answers:
MariettaO [177]3 years ago
7 0
We will start off by simplifying 4/8 to 1/2

then we will multiply the fractions because it says "of"

1/2 × 1/6=1/12

therefore the answer is C. 1/12
KiRa [710]3 years ago
5 0
4/8(1/6)= 4/48= 1/12
Sophia used 1/12 yards of string for her project. 
Hope this helps!
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Use differentiation rules to find the values of a and b that make the function f(x) = ( x 2 if x ≤ 2, ax3 + bx if x > 2 diffe
Maurinko [17]

Answer:

The values of a and b are  a=\frac{1}{4} and b = 1

Step-by-step explanation:

* <em>Lets explain how to solve the equation</em>

  f(x) =  {x²                x  ≤ 2

            {ax³ + bx     x > 2  

* We need to find the values of a , b that make the function

 differentiable at x = 2

- <em>At first for f(x) to be continuous at x = 2, substitute x by two in the</em>

<em>  the two expressions and equate them</em>

∵ f(x) = x² at x ≤ 2 and f(x) = ax³ + bx at x > 2

∴ f(2) = (2)² = 4 ⇒ (1)

∴ f(2) = a(2)³ + b(2)

∴ f(2) = 8a + 2b ⇒ (2)

- Equate (1) and (2)

∴ 8a + 2b = 4 ⇒ (3)

* <em>For f(x) to be differentiable when x = 2, the function must be </em>

<em>  continuous when x = 2 and the one-sided derivatives must be </em>

<em>  equal when x = 2</em>

# <u>Remember</u>: If f(x)=ax^{b} , then f'(x)=abx^{b-1}

 If f(x)=ax , then f'(x)=a

 If f(x)=a , then f'(x)=0

∵ f(x) = x²

∴ f'(x) = 2x

- Substitute x by 2

∴ f'(2) = 2(2) = 4

∴ f'(2) = 4 ⇒ (4)

∵ f(x) = ax³ + bx

∴ f'(x) = 3ax² + b

- substitute x by 2

∴ f'(2) = 3a(2)² + b

∴ f'(2) = 12a + b ⇒ (5)

- Equate (4) and (5)

∴ 12a + b = 4 ⇒ (6)

* Now we have system of equations

 8a + 2b = 4 ⇒ (3)

 12a + b = 4 ⇒ (6)

- Multiply equation (6) by -2 to eliminate b

∴ -24 a - 2b = -8 ⇒ (7)

- Add equations (3) and (7)

∴ -16a = -4

- Divide both sides by -16

∴ a = \frac{1}{4}

- substitute the value of a in equation (6)

∴ 12(\frac{1}{4})+b=4

∴ 3 + b = 4

- Subtract 3 from both sides

∴ b = 1

* The values of a and b are  a=\frac{1}{4} and b = 1

5 0
3 years ago
If f(x) = 5^x2 - 3 and g(x) = x2 - 4x - 8, find (f - g)(x).
kkurt [141]

Answer:

4x² + 4x + 5

Step-by-step explanation:

Note that (f - g)(x) = f(x) - g(x), thus

f(x) - g(x)

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= 5x² - 3 - x² + 4x + 8 ← collect like terms

= 4x² + 4x + 5

3 0
3 years ago
Please help I asked this question earlier and nobody answered! :(​
tatiyna

Answer:

B

Step-by-step explanation:

One way to tell is to put both equations into slope-intercept form.  That form is usually written y=mx+b where  <em>m</em>  is the slope and  <em>b</em>  is the y-intercept.

Solve the first equation for y.

6x+2y=5 \\ 2y=-6x+5 \\ y=-3x+5/2

The slope of this line is -3, and its y-intercept is 5/2.

Solve the second equation for y.

y+3x=2\\y=-3x+2

The slope of this line is -3 and its y-intercept is 2.

The lines are parallel because they have the same slope and <u>different</u> y-intercepts.  There is no solution to the system.

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AnnZ [28]

Answer:

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Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
I need to get this done
Allushta [10]

Answer:

x = 17 and y = 8

Step-by-step explanation:

Since (6x + 3) and (8x - 31) are alternate interior angles, they are congruent.

Therefore, you can set them equal to each other and solve for x.

8x - 31 = 6x + 3

Combine like terms

2x = 34

Divide both sides by two

x = 17

Since (5y + 35) and (6x + 3) are consecutive interior angles, they add up to 180. Plug in 17 for x.

(5y + 35) + (6(17) + 3) = 180

Add like terms

5y + 140 = 180

5y = 40

y = 8

7 0
2 years ago
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