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garik1379 [7]
1 year ago
13

Evaluate the expression shown below and write your answer as a fraction in simplest form 3/20 + 7/16 ​

Mathematics
1 answer:
slavikrds [6]1 year ago
3 0

Answer:

Add

3 over 20

3

20

+ 7 over 16

7

16

= 47 over 80

47

80

Step 1 of 2: Add, sub-step a: Find the common denominator.

Find common denominator

3 over 20

3

20

+ 7 over 16

7

16

= ( 3 × 4 ) over ( 20 × 4 )

3 × 4

20 × 4

+ ( 7 × 5 ) over ( 16 × 5 )

7 × 5

16 × 5

= 12 over 80

12

80

+ 35 over 80

35

80

80 is the least common multiple of denominators 20 and 16. Use it to convert to equivalent fractions with this common denominator.

Add

12 over 80

12

80

+ 35 over 80

35

80

= ( 12 + 35 ) over 80

12 + 35

80

= 47 over 80

47

80

Step 1 of 2: Add.Hide

Step 2 of 2: Simplify.

Simplify

47 over 80

47

80

Step 2 of 2: Simplify, sub-step a: Reduce the fraction to the lowest terms.

Reduce the fraction to lowest terms

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The temperature falls from 10°F to -15° F. What is the difference in these<br> temperatures?
nadya68 [22]

Answer:

the difference is 25

Step-by-step explanation:

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10+15 = 25

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3 years ago
An object is launched from a launching pad 144 ft. above the ground at a velocity of 128ft/sec. what is the maximum height reach
ollegr [7]

Answer:

18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144

b. The maximum height = 400 feet

c. Attached graph

19) The rocket will reach the maximum height after 4 seconds

20) The rocket hits the ground after 9 seconds

Step-by-step explanation:

* Lets study the rule of motion for an object with constant acceleration

# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time

  and a is the acceleration of gravity

# The vertical distances h in x second is h(x) - h(0), where h(0)

   is the initial height of the object above the ground

∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial

  velocity, a is the acceleration of gravity (32 feet/second²) and x

  is the time

18)a.

∵ The value of a = -32 ft/sec² ⇒ negative because the direction

   of the motion

  is upward

∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16

∴ h(x) = vx - 16x² + h(0)

∴ h(x) = -16x² + vx + h(0) ⇒ proved

* Find the height of the object after x seconds from the ground

∵ h(0) = 144 and v = 128 ft/sec

∴ h(x) = -16x² + 128x + 144

b.

* At the maximum height h'(x) = 0

∵ h'(x) = -32x + 128

∴ -32x + 128 = 0 ⇒ subtract 128 from both sides

∴ -32x = -128 ⇒ ÷ -32

∴ x = 4 seconds

- The time for the maximum height = 4 seconds

- Substitute this value of x in the equation of h(x)

∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet

c. Attached graph

19)

- The object will reach the maximum height after 4 seconds

20)

- When the rocket hits the ground h(x) = 0

∵ h(x) = -16x² + 128x + 144

∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16

∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x

∵ x² - 8x - 9 = 0

∴ (x - 9)( x + 1) = 0

∴ x - 9 = 0 OR x + 1 = 0

∴ x = 9 OR x = -1

- We will rejected -1 because there is no -ve value for the time

* The time for the object to hit the ground is 9 seconds

8 0
3 years ago
Rearrange w=3(2a+b)-4 to make a the subject
garik1379 [7]

Answer:

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Step-by-step explanation:

To get the answer you have to first open the bracket which will give you w=6a+6b-4.You then take 6b-4 to the other side to meet w after this divide all by 6 to make a the subject of the formula.

4 0
3 years ago
Select all of the following tables which represent y as a function of and are one-to-<br> one.
zvonat [6]

Answer:

Option 3

Step-by-step explanation:

Each value of x maps onto one value of y and vice versa.

5 0
2 years ago
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