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liberstina [14]
3 years ago
11

Sum of 7 7/8 + 2 11/12

Mathematics
1 answer:
dlinn [17]3 years ago
4 0
Solutions 

1) <span>Add the whole numbers first ( 7 and 2 )

</span><span>9+<span>7/8</span>+<span>11/12

2) </span></span>Find the Least Common Denominator (LCD) of 

<span><span>7 / 8</span>,<span>11 / 12
</span></span>
Start by Listing Multiples

List out all multiples of each denominator, and find the first common one.

8 : <span><span>8,16,24</span>
</span>
12 : <span>12,24
</span>
Therefore, the LCD is <span>24 

</span>Method 2: By Prime Factors

List all prime factors of each denominator, and find the union of these primes.

8 : <span>2,2,2
</span>
12 : <span>2,2,3
</span>
Therefore, the LCD is <span>2×2×2×3=24

3) </span>Make the denominators the same as the LCD

<span>9+<span><span>7×3 / </span><span>8×3</span></span>+<span><span>11×2 / </span><span>12×2

</span></span></span>4) Simplify. Denominators are now the same

<span>9+<span>21 / 24</span>+<span>22 / 24

5) J</span></span>oin the denominators

<span>9+<span><span>21+22 / </span>24</span></span>
6) Simplify

<span>9+<span>43 / 24

7) </span></span>Convert 43 / 24 <span>to mixed fraction

</span><span>9+1 <span>19 / 24

8) </span></span>Simplify

<span><span>10 <span>19 / 24</span></span></span>
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Alex is 4 years younger than 2 times his sister's age. Write a rule that represents Alex's age x as a function of his sister's a
Vesna [10]

Answer:

y = 2x - 4; Alex is 18.

Step-by-step explanation:

Since Alex is 4 years younger than 2 times his sister's age, and his sister is y and Alex is x, the function of y to x must be y = 2x - 4.

According to the rule, if Alex's sister is 11, Alex is 2 times that minus four. If you calculate that, you get

11 * 2 = 22

22 - 4 = 18

So Alex is 18 if his sister is 11.

6 0
3 years ago
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If construction costs are $160,000 per kilometer, find the cost of building the new road in the figure
MAVERICK [17]

Answer:

$4,160,000

Step-by-step explanation:

First, find the length of the new road in km using Pythagorean Theorem.

According to Pythagorean Theorem:

c² = a² + b²,

Where, c is the longest leg, which is the hypotenuse, a and b are the 2 other legs of the ∆.

Since we are calculating the lenght in km, convert each lenght of the two legs of the ∆ into km.

1 km = 1,000 m

10,000 m = 10 km

24,000 m = 24 km

c² = 24² + 10²

c² = 576 + 100

c² = 676

c = √676

c = 26 km

Lenght of the new road = 26 km

If cost of construction is $160,000 per kilometer, therefore, cost of constructing 26 km road = 160,000*26 = $4,160,000

7 0
3 years ago
The sum of the arithmetic progression 4, ..., 76 is 1920. Find the number of terms and the common difference.​
valkas [14]

<u>Number of terms = 48</u>

<u>common difference = 1.5</u>

This question involves the concept of Arithmetic Progression.

  • The formula for sum of an arithmetic progression series with first and last term given is;

S_{n} = \frac{n}{2}(a + l)

where;

a = first term

l = last term

n = number of terms

  • From the given sequence, we see that;

first term; a = 4

last term; l = 76

Sum of A.P; S_{n} = 1920

  • Plugging in relevant values into the sum of an AP formula, we have;

1920 = \frac{n}{2}(4 + 76)

simplifying this gives;

1920 = 40n

n = 1920/40

n = 48

  • Formula for nth term of an AP is;

t_{n} = a_{1} + (n - 1)d

where;

a_{1} is first term

d is common difference

n is number of term

t_{n} is the nth term in question

the 48th term is 76

Thus;

76 = 4 + (48 - 1)d

76 - 4 = 47d

72 = 47d

d = 72/47

d ≈ 1.5

Thus;

Number of terms = 48

common difference = 1.5

Read more at; brainly.com/question/16935540

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What are the rate of change and the initial value of the function represented by the graph?
Norma-Jean [14]

Answer:D

Step-by-step explanation:

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Answer: (0,4)

Step-by-step explanation:

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