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Gnesinka [82]
2 years ago
8

Which of the following is a linear function?

Mathematics
1 answer:
djyliett [7]2 years ago
3 0
It should be the last option. With linear functions, you should be graphing a straight line.
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At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other
Juli2301 [7.4K]
Let’s call the speed of the slower car S, then the speed of the other is S+10mph.
At 5pm they have been travelling for 3 hours. The slower car travels a distance 3S and the faster one 3(S+10).
But the two distances must add up to 240 miles so 3S+3(S+10)=240, 3S+3S+30=240, 6S=210, S=35 mph. The faster car’s speed is 45mph. We can see that 3S is the same distance as 3x, so x=S=35 mph, and the distance the faster car travels is 3×45=135 miles.
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3 years ago
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X2+11x+30 what does x2 mean
Alexxandr [17]

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3 years ago
It costs $859.32 to have a school dance (tickets $8)
djverab [1.8K]

A) 859.32/8= 107.415=108 tickets

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Match each series with the equivalent series written in sigma notation
PIT_PIT [208]

Answer:

3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n

4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n

2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n

3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

3 + 12 + 48 + 192 + 768

The expression can be written as:

3 \to 3*4^{0 --- 0

12 \to 3 * 4^{1 ---- 1

48 \to 3 * 4^{2 --- 2

192 \to 3 * 4^{3 ---- 3

768 \to 3 * 4^{4 ---- 4

For the nth term, the expression is:

Term = 3 * 4^{n ---- n

So, the summation is:

3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n

Solving (b):

4 + 32 + 256 + 2048 + 16384

The expression can be written as:

4 \to 4 * 8^0 --- 0

32 \to 4 * 8^1 ---- 1

256 \to 4 * 8^2 --- 2

2048 \to 4 * 8^3 ---- 3

16384 \to 4 * 8^4 ---- 4

For the nth term, the expression is:

Term \to 4 * 8^n ---- n

So, the summation is:

4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n

Solving (c):

2 + 6 + 18 + 54 + 162

The expression can be written as:

2 \to 2 * 3^0 --- 0

6 \to 2 * 3^1 ---- 1

18 \to 2 * 3^2 --- 2

54 \to 2 * 3^3 ---- 3

162 \to 2 * 3^4 ---- 4

For the nth term, the expression is:

Term \to 2 * 3^n ---- n

So, the summation is:

2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n

Solving (d):

3 + 15 + 75 + 375 + 1875

The expression can be written as:

3 \to 3 * 5^0 --- 0

15 \to 3 * 5^1 ---- 1

75 \to 3 * 5^2 --- 2

375 \to 3 * 5^3 ---- 3

1875 \to 3 * 5^4 ---- 4

For the nth term, the expression is:

Term \to 3 * 5^n ---- n

So, the summation is:

3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n

5 0
2 years ago
Find y if the distance between
Helen [10]

Answer:

y = 6

Step-by-step explanation:

\sqrt{(10-3)^2 + (y+18)^2} = 25 \\ 49 + y^2 + 324 + 36y = 625 \\

y^2 + 36y - 252 = 0

(y-6)(y+42) = 0

y = 6 (accettable)

y = -42 (not accettable)

5 0
2 years ago
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