MATHEMATICS HIGH SCHOOL

If 12 cows produce 70 gallons of milk, how many gallons of milk would 42 cows produce?A. 20
B. 245
C. 512
D. 840

Answers

Answer 1
Answer: This is a proportions question
  12        42
------  =  -------
  70          ?

Cross multiply

70x42=2940
12x?=2940
294/12=245

42 cows can produce 245 gallons of milk.
So the answer is B.

Hope I helped!
Answer 2
Answer:

Answer: 245 gallons

Step-by-step explanation: Set up a ratio,  cows/gallons  =  12/70  =  42/x, then cross multiply to get 12x = 70*42. Divide to get 245 gallons.

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Can someone help me with this? PLs i'm so confused!

Answers

1. E. sine\ A = (a)/(c) = (opposite)/(hypotenuse) = (BC)/(AB) = (5)/(13)

2. L. cos\ A = (b)/(c) = (adjacent)/(hypotenuse) = (AC)/(AB) = (12)/(13)

3. tan\ A = (a)/(b) = (opposite)/(adjacent) = (BC)/(AC) = (5)/(12)

4. Y. sin\ B = (a)/(c) = (opposite)/(hypotenuse) = (BC)/(AB) = (5)/(13)

5. W. cos\ B = (b)/(c) = (adjacent)/(hypotenuse) = (AC)/(AB) = (12)/(13)

6. tan\ B = (b)/(a) = (adjacent)/(opposite) = (AC)/(BC) = (12)/(5) = 2(2)/(5)

7. sin\ A = (a)/(c) = (opposite)/(hypotenuse) = (BC)/(AB) = (1)/(2)

8. W. cos\ A = (b)/(c) = (adjacent)/(hypotenuse) = (AC)/(AB) = (√(3))/(2)

9. I. tan\ A = (a)/(b) = (opposite)/(adjacent) = (BC)/(AC) = (1)/(√(3)) = (1)/(√(3)) * (√(3))/(√(3)) = (√(3))/(3)

10. sin\ B = (a)/(c) = (opposite)/(hypotenuse) = (BC)/(AB) = (1)/(2)

11. E. cos\ B = (b)/(c) = (adjacent)/(hypotenuse) = (AC)/(AB) = (√(3))/(1) = √(3)

12. I. tan\ B = (a)/(b) = (opposite)/(adjacent) = (BC)/(AC) = (1)/(√(3)) = (1)/(√(3)) * (√(3))/(√(3)) = (√(3))/(3)

13. U. sin\ A = (a)/(c) = (hypotenuse)/(opposite) = (BC)/(AB) = (12)/(15) = (4)/(5)

14. I. cos\A = (b)/(c) = (adjacent)/(hypotenuse) = (AC)/(AB) = (9)/(15) = (3)/(5)

15. tan\ A = (a)/(b) = (opposite)/(adjacent) = (BC)/(AC) = (12)/(9) = (4)/(3) = 1(1)/(3)

16. R. sin\ B = (a)/(c) = (opposite)/(hypotenuse) = (BC)/(AB) = (4)/(√(65)) = (4)/(√(65)) * (√(65))/(√(65)) = (4√(65))/(65)

17. M. cos\ B = (b)/(c) = (adjacent)/(hypotenuse) = (AC)/(AB) = (7)/(4) = 1(3)/(4)

18. N. tan\ B = (a)/(b) = (opposite)/(adjacent) = (BC)/(AC) = (4)/(7)

19. L. sin\ A = (a)/(c) = (opposite)/(hypotenuse) = (BC)/(AB) = (16)/(34) = (8)/(17)

20. H. cos\ B = (b)/(c) = (adjacent)/(hypotenuse) = \fac{AC}{AB} = (30)/(34) = (15)/(17)

21. tan\ B = (a)/(b) = (opposite)/(adjacent) = (BC)/(AC) = (16)/(30) = (8)/(15)

22. O. sin\ A = (a)/(c) = (opposite)/(hypotenuse) = (BC)/(AB) = (1)/(√(2)) = (1)/(√(2)) * (√(2))/(√(2)) = (√(2))/(2)

23. O. cos\ A = (b)/(c) = (adjacent)/(hypotenuse) = (AC)/(AB) = (1)/(√(2)) = (1)/(√(2)) * (√(2))/(√(2)) = (√(2))/(2)

24. N. tan\ A = (a)/(b) = (opposite)/(adjacent) = (BC)/(AC) = (1)/(1) = 1

If the area of a rectangle is 16s2t and the length is 8st2, what would be the width of the rectangle, given that width is found by dividing area by length? Simplify the answer.

Answers

so than divide area by length 

16s^2t         2s
----------- = --------  so from this result the width of rectangle will be equal 2s/t
8st^2             t

Mrs. Laser is building a new space for her chickens. She has 80 feet of fencing. What is the greatest fencing area she could create using fencing?

Answers

Answer:

400 ft^2

Step-by-step explanation:

It can be shown that a square area is the most efficient way in which to use fencing.  If the area is not square, the area will inevitably be smaller.  

Calculus is the tool most often used in higher math to solve optimization problems.  

But the same goal can be achieved in this problem by working with constraints:  

If x and y are the length and width respectively, then

2x + 2y = 80 ft, or x + y = 40, or x = 40 - y.  This is one constraint.  

The other constraint involves the area:  A = x*y, or A = (40 - y)*y.  To maximize this, we need to rewrite (40 - y)*y in standard form:

A = 40y - y^2, or, finally, A = -y^2 + 40 y.  The coefficients of this quadratic are -1, 40 and 0; the axis of symmetry is thus

x = -b/ [2a], or, in this case, x = -40/[2*(-1)], or x = 20.

Thus, If x = 20, y = 20 also, proving that the shape of the enclosed yard is that of a square.

Then Mrs. L' 80 feet of fencing is sufficient to construct a 20 ft by 20 ft space, which comes out to a maximum area of 400 ft^2.

40 -

400ft hope this helps you out

What is an equation in point-slope form of the line that passes through the point (4, −1) and has slope 6?

Answers

Answer:

y + 1 = 6(x - 4)

Answer: y + 1 = 6(x - 4)

3. What is the simplest way to write3a + 2b - 3a + b? Briefly show or explain your
reasoning.

Answers

Answer:

3b is the answer

3a+2b-3a+b

3a-3a+2b+b

2b+b

Step-by-step explanation:

The first step I did is switch up the equation so that the like terms are next to each other. So the a’s are next to each other and the b’s are next to each other. Then I subtracted 3a-3a and got 0 and in the last step I added the 2b + b and got 3b.

9a^2- 4b^2

First, Apply the distributive property 3a(3a)+3a(−2b)+2b(3a)+2b(−2b)

Second Simplify the term. 3a(3a)+2b(−2b)

Third, Simplify Each term.

3⋅3a2+2b(−2b)

9a2+2b(−2b)

9a2+2⋅−2b2

= 9a2−4b2

Find the surface area of the prism

Answers

surface area of one face = 9x9 = 81
total no. of faces = 6
total surface area of prism = 81 x 6 = 486in.
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