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jenyasd209 [6]
3 years ago
5

99 POINTS

Mathematics
2 answers:
Allisa [31]3 years ago
7 0
1. slope is -6/2 which simplifies to -3
4. it will travel 275 miles
3. the slope of the line is .15, each pencil costs 15 cents
thats all ik
STALIN [3.7K]3 years ago
6 0
1) y2-y1/x2-x1 = -5-1/4-2 = -6/2 = -3

2) The triangles are proportional to each other because, the bigger triangles AB(base) to BC(height) ratio is 8:4, which if simplified would be 4:2, and the smaller triangles is 4:2, which is the same. In other words, both of the triangles are the same. 

3) y=0.15x, so the slope is 0.15, and each pencil costs 15 cents, or 0.15 dollar.

4) y=55x, where x=5, so y=55(5)=275.
The bus will travel 275 miles in 5 hours.

5) Slope-intercept form : y=mx+b, where m=slope, and b=y-int.
So, C = 15t+4 is the equation.

6) Yes, this graph does show a proportional relationship, because it costs $1 for every 10 photos, and this ratio is same for every amount of photos.

7) y-y1 = m(x-x1)
y-6 = 4(x-4)
y-6 = 4x - 16
y = 4x - 10

8) Olivia: y=2x
    Matt: y=3x
Matt travels at a faster rate, and I know this because Matt walks at 3 miles per hour, while Olivia walks 2 miles per hour, and obviously 3 mph is faster than 2 mph.
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Correct answers only please!
marishachu [46]

Answer:

A = $ 7,299.92

A = P + I where

P (principal) = $ 6,000.00

I (interest) = $ 1,299.92

Step-by-step explanation:

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

7 0
4 years ago
If you have 1 1/2 gallons of soup how many 1 cup servings can you make?
irinina [24]
1 ½ gallons is equal to 24 cups. 
So your answer is 24 cups can be served with 1 ½ gallons of soup.
7 0
4 years ago
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Calculate simple interest earned on a deposit of $500 at a rate of 5% for 5 years.
Ilya [14]

Answer:

A = $625.00

(I = A - P = $125.00)

Equation:

A = P(1 + rt)

Step-by-step explanation:

7 0
3 years ago
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Find the nth term of the sequence 7,25,51,85,127​
olya-2409 [2.1K]

Let <em>a </em>(<em>n</em>) denote the <em>n</em>-th term of the given sequence.

Check the forward differences, and denote the <em>n</em>-th difference by <em>b </em>(<em>n</em>). That is,

<em>b </em>(<em>n</em>) = <em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>)

These so-called first differences are

<em>b</em> (1) = <em>a</em> (2) - <em>a</em> (1) = 25 - 7 = 18

<em>b</em> (2) = <em>a</em> (3) - <em>a</em> (2) = 51 - 25 = 26

<em>b </em>(3) = <em>a</em> (4) - <em>a</em> (3) = 85 - 51 = 34

<em>b</em> (4) = <em>a </em>(5) - <em>a</em> (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence <em>b</em> is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means <em>b</em> is an arithmetic sequence, and in particular follows the rule

<em>b</em> (<em>n</em>) = 18 + 8 (<em>n</em> - 1) = 8<em>n</em> + 10

for <em>n</em> ≥ 1.

So we have

<em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>) = 8<em>n</em> + 10

or, replacing <em>n</em> + 1 with <em>n</em>,

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8 (<em>n</em> - 1) + 10

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8<em>n</em> + 2

We can solve for <em>a</em> (<em>n</em>) by iteratively substituting:

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 2) + 8 (<em>n</em> - 1) + 2] + 8<em>n</em> + 2

<em>a</em> (<em>n</em>) = <em>a </em>(<em>n</em> - 2) + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> - 2) + 2] + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2)) + 3×2

and so on. The pattern should be clear; we end up with

<em>a</em> (<em>n</em>) = <em>a</em> (1) + 8 (<em>n</em> + (<em>n</em> - 1) + … + 3 + 2) + (<em>n</em> - 1)×2

The middle group is the sum,

\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8

so that

<em>a</em> (<em>n</em>) = <em>a</em> (1) + (4<em>n</em> ² + 4<em>n</em> - 8) + 2 (<em>n</em> - 1)

<em>a</em> (<em>n</em>) = 4<em>n</em> ² + 6<em>n</em> - 3

4 0
3 years ago
Mason used 3/4 of the nails in a box. He has 12 nails left. How many did he use?
Karolina [17]
If he has 12 nails left, he used 36 nails.
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