MATHEMATICS HIGH SCHOOL

1/3*h(-8) h(x)= x^2 - 5x +7

Answers

Answer 1
Answer:

Answer: 37

Step-by-step explanation:

    First, we need to find what h(-8) is. We can do this by substituting and simplifying the given function.

Given:

  h(x) = x² - 5x +7

Substitute:

  h(-8) = (-8)² - 5(-8) +7

Square and multiply:

  h(-8) = 64 + 40 +7

Add:

  h(-8) = 111

    Next, we can find one-third of this. To do this, we will multiply.

Multiply:

  (1/3) * 111 = 37

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James paddles upstream in a canoe at 2mph (relative to the shore), and when he paddles down-stream, he goes 9mph. Find the speed of the current and the speed James can paddle in still water and come up with an equation.
What fraction of 1 minute is 47 seconds
Please help with number 1 please ?

0.34343434..
is it rational or irrational

Answers

Rational. Since it’s reappearing multiple times in a pattern, and not random numbers bunched together

5 t-shirts and a hat costs £27.00 2 t-shirts and a hat costs £12.00.
How much does a t-shirt cost?
How much does a hat cost?

Answers

Answer:

£2

Step-by-step explanation:

Let T represent T-shirt and H represent hat

5T + H = £27.00

2T + H = £12.00 Subtract two equation

5T + H - 2T - H = £27 - £12 ➡ 3T = £15 and T = £5 this is the cost for a t-shirt

If a t-shirt costs £5 and 2 t-shirt + a hat costs £12 then a hat costs £2
Let say that t-shirt is X and hat is Y
We get: 5X+Y=27.00
2X+Y=12.00
solve for X in the first equation
5X+Y= 27
5X=27-Y
X=27-Y/5
Replace X= 27-Y/5 in equation 1 or 2
I use equation 2:
2*27-Y/5+Y=12
54-2Y/5+Y=12
make the denominator equal
54-2Y/5+5Y/5=12
54+3Y/5=12
Multiply 5 both side
54+3Y = 60
3Y = 60-54
3Y= 6
Y=6/3
Y=2
Replace Y= 2 in equation 1 or 2
I use 2:
2X+2=12
2X=10
X=5
Thus the answer is T-shirt cost : £5 and hat cost : £2

Comparative advantage Hours needed to produce one unit
Ukuleles surfboards
Jack 12. 4
Jill 25. 5

11. Is this an output problem or an input problem

12. What is Jacks opportunity cost of producing
1 ukulele? 3

13. What is Jacks opportunity cost of
producing 1 Surfboard?
.3

14. What is jills opportunity cost of producing
1 ukulele?
5

15. What is jills opportunity cost of
producing 1 surfboard?
.2

16. Who has the absolute advantage in
producing ukuleles?
Jill

17. Who has the absolute advantage in
producing surboards?
jack

18. Who has the comparative advantage in
producing ukuleles?
Jill

19. Who has the comparative advantage in
producing Surfboards ?jack

Answers

Answer:

11. This is an input problem. The hours needed to produce one unit represent the input required to produce each unit of ukuleles and surfboards.

12. Jack's opportunity cost of producing 1 ukulele is 3 surfboards. This means that if Jack decides to produce 1 ukulele, he foregoes the opportunity to produce 3 surfboards.

13. Jack's opportunity cost of producing 1 surfboard is 0.3 ukuleles. This means that if Jack decides to produce 1 surfboard, he foregoes the opportunity to produce 0.3 ukuleles.

14. Jill's opportunity cost of producing 1 ukulele is 5 surfboards. This means that if Jill decides to produce 1 ukulele, she foregoes the opportunity to produce 5 surfboards.

15. Jill's opportunity cost of producing 1 surfboard is 0.2 ukuleles. This means that if Jill decides to produce 1 surfboard, she foregoes the opportunity to produce 0.2 ukuleles.

16. Jill has the absolute advantage in producing ukuleles because she can produce 1 ukulele in 25 hours, while Jack requires 12 hours to produce 1 ukulele.

17. Jack has the absolute advantage in producing surfboards because he can produce 1 surfboard in 4 hours, while Jill requires 5 hours to produce 1 surfboard.

18. Jill has the comparative advantage in producing ukuleles because her opportunity cost of producing 1 ukulele (5 surfboards) is lower than Jack's opportunity cost of producing 1 ukulele (3 surfboards).

19. Jack has the comparative advantage in producing surfboards because his opportunity cost of producing 1 surfboard (0.3 ukuleles) is lower than Jill's opportunity cost of producing 1 surfboard (0.2 ukuleles).

Suppose you choose a marble from a bag containing 3 red marbles, 3 white marbles, and 5 blue marbles. You return the first marble to the bag and then choose again. Find P(red and blue).

Answers

The answer is 15/121.

Since we have red AND blue, that means that both of these events occur, so we will use the multiplication rule and multiply these two probabilities:

- A probability of choosing a red marble: 3/11. (because there are 3 marbles out of total 11 marbles)
- A probability of choosing a blue marble after the red one: 5/11. (because there are 3 marbles out of total 11 marbles; there are 11 in total again because the first marble has been returned)

So, P(red and blue) is 3/11 * 5/11 = (3*5)/(11*11) = 15/121

Solve 64x^3 +1 =0the back of the texts books gives me the answers -1/4 and 1 plus or minus i√3 all over 8
I understand where the -1/4 comes from . I just don't understand the second answer. I know they used the quadratic formula to get it but I always end up with something to totally different

Answers

Expand the expression using the formula:
a^3+b^3=(a+b)(a^2 - ab + b^2)

64x^3+1=0 \n(4x)^3+1^3=0 \n(4x+1)((4x)^2- 4x * 1+1^2)=0 \n(4x+1)(16x^2-4x+1)=0 \n4x+1=0 \ \lor \ 16x^2-4x+1=0

The first equation:
4x+1=0 \n 4x=-1 \n x=-(1)/(4)

The second equation:
16x^2-4x+1=0 \n \na=16 \n b=-4 \n c=1 \n b^2-4ac=(-4)^2-4 * 16 * 1=16-64=-48 \n√(b^2-4ac)=√(-48)=√(48) * √(-1)=√(16 * 3) * √(-1)=\pm 4√(3) i \n \nx=(-b \pm √(b^2-4ac))/(2a)=(-(-4) \pm 4√(3)i)/(2 * 16)=(4 \pm 4√(3)i)/(32)=(4(1 \pm √(3)i))/(4 * 8)=(1 \pm √(3)i)/(8) \nx=(1-√(3)i)/(8) \ \lor \ x=(1+√(3)i)/(8)

The final answer:
\boxed{x=-(1)/(4) \hbox{ or } x=(1-√(3)i)/(8) \hbox{ or } x=(1+√(3)i)/(8)}

Pls, help Which of the following is true?|−6| < 5
|−6| < |5|
|−5| < |−6|
|−5| < −6

Answers

Answer:

C

Step-by-step explanation:

Its not A because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its not B because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its C because The left side 5 is less than the right side 6, which means that the given statement is always true.

Its not D because The left side is 5 is not less than the right side 6, which means that the given statement is false.
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