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mojhsa [17]
2 years ago
10

Theresa rolled a number cube, number 1 through 6, two times

Mathematics
2 answers:
AleksandrR [38]2 years ago
5 0
The answer is C i believe
Deffense [45]2 years ago
3 0

Answer:

B

Step-by-step explanation:

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Sin C =<br><br> Whats the answer ?!?
hichkok12 [17]

The answer would b "C" 15/17 because Sin is Opposite over Hypotenuse

Step-by-step explanation:

7 0
3 years ago
Karen wants to know how fast her sunflower will grow. Right now, her sunflower is 3 3/8
serg [7]

Answer:

Karen must ask the manager

Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
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 &gt; 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
The drama club spent $35 on decorations and $8.50 per person on food for a cast party. The total cost of the food
jenyasd209 [6]

Answer:

Option C) 27 people

Step-by-step explanation:

Let

x ----> the number of people

we know that

The cost of decorations ($35) plus the number of people (x) multiplied by the cost per person on food ($8.50) must be equal to $264.50

so

The linear equation that represent this situation is

35+8.50x=264.50

solve for x

Subtract 35 both sides

8.50x=264.50-35

8.50x=229.50

Divide by 8.50 both sides

x=229.50/8.50

x=27\ people

5 0
2 years ago
The rabbit population in a certain area is 500% of last years population. There are 900 rabbits this year. How many were there t
12345 [234]

Answer:

180 rabbits

Step-by-step explanation:

<u><em>The correct question is</em></u>

The rabbit population in a certain area is 500% of last years population. There are 900 rabbits this year. How many were there last year?

we know that

900 rabbits represent 500% of last year population

Last year population represent 100%

so

using proportion

Find out how many rabbits represent a percentage of 100%

\frac{900}{500\%}=\frac{x}{100\%}\\\\x=900(100)/500\\\\x=180\ rabbits

7 0
3 years ago
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