All categories

3 years ago

Plz help i dont want to fail plzzzzzz

Mathematics

2 answers:

Anika [276]3 years ago

7 0

3p + 4c = 40 ⇒ 15p + 20c = 200
5p + 2c = 34 ⇒ 15p + 6c = 102
14c = 98
14 14
c = 7
5p + 2(7) = 34
5p + 14 = 34
- 14 - 14
5p = 20
5 5
p = 4
(p, c) = (4, 7)

Serjik [45]3 years ago

4 0

Answer:

c= 7 p=4

Step-by-step explanation:

3p + 4c = $40

therefore

15p + 20c = 200

5p + 2c = 34

therefore

15p + 6c = 102

14c = 98

98/14=7

c = 7

5p + 2(7) = 34

5p + 14 = 34

- 14 - 14

5p = 2020/5= 4

p = 4

You might be interested in

St 2

Lubov Fominskaja [6]

Answer:

$5.5

Step-by-step explanation:

6 * N (notebook) + 3 * P (pen) = 27

n = 1.5 +P

6 * (1.5 + P) + 3 * P = 27

9 +6p +3p = 27

9p = 18

p (pen): $2

N (notebook): $3.5

combined cost of 1 pen and 1 notebook: $2 + $ 3.5 = $ 5.5

3 0

3 years ago

Earl runs 75 meters in 30 seconds. How many meters does Earl run per seconds?

nikdorinn [45]

75 metres 30 sec
5/2 metres a sec
2.5 metres a sec

3 0

3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$