MATHEMATICS HIGH SCHOOL

A company is deciding which box to use for theirmerchandise. The first box measures 8 inches by 6.25 inches
by 10.5 inches. The second box measures 9 inches by 5.5
inches by 11.75 inches. Which box required more material to
make?

Answers

Answer 1
Answer: Total surface area of first box = 2(8 * 6.25) + 2(8 * 10.5) + 2(6.25 * 10.5) = 2(50) + 2(84) + 2(65.625) = 100 + 168 + 131.25 = 399.25 sq. ins

Total surface area of second box = 2(9 * 5.5) + 2(9 * 11.75) + 2(5.5 * 11.75) = 2(49.5) + 2(105.75) + 2(64.625) = 99 + 211.5 + 129.25 = 439.75 sq. ins

Hence, the second box requires more material to make.

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Write the expression as either the sine, cosine, or tangent of a single angle. sin(pi/2)cos(pi/7)+cos(pi/2)sin(pi/7)

Answers

I will use the sin (a + b) identity: 
sin (a + b) = sina cosb + cosa sinb and
here a = π/2 and b = π/7 

so sin (π/2 + π/7) 
= sin (9π / 14)

Answer:

\text{sin}((9\pi)/(14)).

Step-by-step explanation:

We have been given a trigonometric expression \text{sin}((\pi)/(2))\text{cos}((\pi)/(7))+\text{cos}((\pi)/(2))\text{sin}((\pi)/(7)). We are asked to write our given expression as either the sine, cosine, or tangent of a single angle.

Using identity \text{sin}(a)\text{cos}(b)+\text{cos}(a)\text{sin}(b)=\text{sin}(a+b), we can rewrite our given expression.

Let a=(\pi)/(2) and b=(\pi)/(7).

Upon substituting these values in above identity, we will get:

\text{sin}((\pi)/(2))\text{cos}((\pi)/(7))+\text{cos}((\pi)/(2))\text{sin}((\pi)/(7))=\text{sin}((\pi)/(2)+(\pi)/(7))

Upon simplifying right side of our equation, we will get:

\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((\pi*7)/(2*7)+(\pi*2)/(7*2))

\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((7\pi)/(14)+(2\pi)/(14))

\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((7\pi+2\pi)/(14))

\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((9\pi)/(14))

Therefore, our required expression would be \text{sin}((9\pi)/(14)).

Segment CD is given with vertices C(a,b) and D(2a,b). Find the length of segment C'D', the image of segment CD after a dilation with a scale factor of 2.

Answers

the dilation is a scale factor of 2, that is:

C'D' = 2(CD)

the length of CD is given by:
CD = √( (a - 2a)^2 + (b - b)^2 )

CD = √(a^2) = a

hence the new segment is 2a long.

At a school carnival, the diameter of the mat of a trampoline is 12 feet and the diameter of its metal frame is 14 feet. What is the length, in feet, of the metal frame that surrounds the trampoline? Use 3.14 for π and round your answer to the nearest tenth.37.7 feet
44.0 feet
75.4 feet
87.9 feet

Answers

we don't need to know the trampoline diameter, it's a trick

the legnth of the metal fram is the circumference
C=pid
d=14
c=14pi
pi=3.14
c=14*3.14
c=43.96
round
C=44

answer is 44 feet

your answer is 44.0 feet                                                                                                      

A measurement can be precise without being accurate.
a. True
b. False

Answers

The answer is B. false. Being precise in a measurement needs to be accurate and exact in details. without one factor of its doesn't prove that it would be relevant in information because the measurement is not exact and accurate

After 1 year, a bank account contains $7,746.90. After 2 years, the same account contains $7,901.84. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years? (Round money values to the nearest penny.)

Answers

These are the choice given. I'll just substitute x with 1 and 2 to see if the amount corresponds to the given amount.
A.    y = 7591.96(1.02)x
  y = 7,591.96(1.02)¹ = 7,743.80 
  y = 7,591.96(1.02)² = 7,898.68

B.    y = 7591.96(0.02)x
y = 7,591.96(0.02)¹ = 151.84
y =7,591.96(0.02)² = 3.04

C.    y = 7595(1.02)x    THIS IS THE CORRECT EQUATION.
y = 7,595(1.02)¹ = 7,746.90
y = 7,595(1.02)² = 7,901.84

D.    y = 7595(0.02)x
 

How do you subtract 9-3 7/8?

Answers

you take 9 times 8 which is 72out of 9 and subtract 3 which is 7 and 7/8 out of 7 is 6 and 1/8
Since 1-7/8=1/8, you have to also subtract 9-3=6. But since there is a fraction, you have to take away and extra one since if it was six it would be too big if you tried to add it back to 3&7/8. It would equal out to 10, so the answer is 5&1/8. If you add that up it equals 9.
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