All categories

3 years ago

A line has a slope of 2 and passes (5,3). Find a coordinate of another point this line will pass through. Plz show work.

Mathematics

2 answers:

Snowcat [4.5K]3 years ago

4 0

Answer:

(6,5)

Step-by-step explanation:

The slope means y travels 2 while x travels 1. So 5+1 would be x and 3+2 would be y.

alexgriva [62]3 years ago

4 0

Answer: (0,-7)

Step-by-step explanation:

Use the slope intercept formula y = mx+b to solve for b

Substitute your given values: slope of 2 for m, use the point given (5,3) where 5 is the x value, and 3 is the y value, then solve for b.

3=2*5 +b

3=10+b

b= -7

Since b is the y intercept its x coordinate is 0. So the point is (0,-7)

You might be interested in

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

Brianna's teacher asks her if these two expressions 3r +5 and 4r are equivalent.

sukhopar [10]

Answer:

If Brianna's (I'll call her Bri in this situation) teacher says 3r + 5 and 4r are equal, you should definatly start by adding the 'r' value to the 3, which would be 8 afterwards. Bri is then incorrect because 4+5=9, and 9 is greater than 8, so Bri is wrong :'(...

Have a good day fellow lad,

AshlynnXOXO

4 0

2 years ago

How do I do A, B, and C on #2?<br> How do I do #3?<br><br><br> PLEASE, I REALLY NEED HELP. PLEASE.

kodGreya [7K]

Answer:

Dude the picture is really blurry

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

…………………………………………………………………

horrorfan [7]

do you sell genius brain

7 0

2 years ago

20 POINTS: solve for x.

lara [203]

Answer:x=7

Step-by-step explanation:

Here AD=6

AB=6 (tangents drawn from external point to a circle are equal)

Then BC=13-6=7

Now, CE=BC=7(tangents drawn from external point to a circle are equal)

EF=14-7=7

EF=FG=x=7(tangents drawn from external point to a circle are equal)

3 0

3 years ago