All categories

1 year ago

Please help :) Thanks!

Mathematics

2 answers:

Nady [450]1 year ago

8 0

The slope is positive so you can use 3/1 witch means the slope of the graph is 3.

LiRa [457]1 year ago

4 0

Answer:

Hi there!!

Since this is a positive slope, so we can use 3/1=3

The slope is 3

You might be interested in

6 + 2x = 24

Nutka1998 [239]

6 + 2x = 24
2x = 18
x = 9
answer
9
----------
3x – 5 ≥ 7
3x ≥ 12
x ≥ 4
answer
{4, 5, 6}

--------------
4x – 3 ≥ 5
4x ≥ 8
x ≥ 2
answer
{2, 3, 4}

-----------------

3r ≤ 4r – 6
r ≥ 6
answer
{6, 7, 8, 9,10}

6 0

3 years ago

Find the x- and y-intercept of, y = 1/2x - 7

Arturiano [62]

Y-intercept is (0,-7) x-intercept is (14,0)

7 0

2 years ago

Which is a correct first step in solving the inequality-4(2x - 1) > 5 - 3x?

prisoha [69]

The answer is distribute -4 to get -8x+4>5-3x

3 0

2 years ago

Read 2 more answers

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 $n \geq 0$ ,

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

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

3 years ago

Danielle earns a 8.25% commission on everything she sells at the electronics store where she works. She also earns a base salary

Mariulka [41]

Answer: her sales last week was $4300.

Step-by-step explanation:

Let x represent her her sales in a week.

Danielle earns a 8.25% commission on everything she sells at the electronics store where she works. This means that the commission she gets if she makes sales of $x is 0.0825x

She also earns a base salary of $675 per week. The expression for the total earnings for a week in which she made sales of $x would be

0.0825x + 675

if her total earnings for last week were $1,029.75, it means that

0.0825x + 675 = 1029.75

0.0825x = 1029.75 - 675

0.0825x = 354.75

x = 354.75/0.0825

x = $4300

3 0

3 years ago