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3 years ago

What is the slope indicated in the table below?* X. 8 6 4 2 Y. 2 4 6 8

Mathematics

1 answer:

amm18123 years ago

5 0

Answer:

-1

Step-by-step explanation:

in order to find the slope you need to look at the change in x over the change in y. x is decreasing by 2 every time, and y is increasing by 2. you now have -2/2 simplify and you get -1

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Describe the set 3 ≤ x ≤ 10

SSSSS [86.1K]

Answer:

The answer is B, [3,10].

Step-by-step explanation:

5 0

2 years ago

What is 4n - 3 = -2n + 9 if n = 2

Schach [20]

4n-3=5=-2n+9=5 if n=2

6 0

4 years ago

Read 2 more answers

The ratio of the lengths of a triangle are 4:6:9 and its perimeter is 57cm. Find the length of the shortest side.

sergeinik [125]

Answer:12cm

Step-by-step explanation:

The ratio are:

4:6:9

Perimeter=57cm

Let a be the unknown value.

The triangle has three sides: 4a, 6a, 9a

Perimeter=The sum of three sides

57=4a + 6a +9a

57=19a

Divide both side by 19

a=57/19

a=3

Therefore

4a:6a:9a

4×3:6×3:9×3

12:18:27

So the shortest side is 12cm

5 0

4 years ago

The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs

S_A_V [24]

For problems involving algebra, you have to formulate algebraic equations to be able to solve the problem. Algebraic equations are mathematical terms which include variables to denote the unknown numbers.

For this problem, you are to find the total cost which consists of cost for the gun rent and cost for the paintballs. Hence, your equationmust consist of two terms. The equation must be:

Total cost = 100x + 1000

The term x denotes the number of guns. Hence, it must be multiplied with 100 to determine the cost. On the otherhand, the constant 1000 is for the paintballs. Since it was given that each team must have 2000 paintballs, then it follows that they must pay 1000 Php.

4 0

4 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 $n \geq 0$ ,

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