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NeTakaya
3 years ago
12

Help pls. I have been stuck on this for 15 minutes now.​

Mathematics
2 answers:
Setler [38]3 years ago
7 0

Answer:

y= 0.35x+18.99

m= 0.35

18.99= 0.35(0)+b

18.99= 0+b

18.99=b

zlopas [31]3 years ago
6 0

Answer:

Y=0.35x+18.99

Step-by-step explanation:

Y = total cost

X = number of letters

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Pls Help!!! Worth 99 Pts!!
Alenkasestr [34]
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)

To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0   x=-4   x=2

So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)

And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5 
3 gets us 21

So now you know end behavior, zeroes, and signs of intervals

Hope this helps<span />
6 0
3 years ago
Read 2 more answers
Factorize x^2/16+xy+4y^2​
lisov135 [29]

Answer:

\frac{x^2}{16} +xy+4y^2 can be factored out as: (\frac{x}{4} +2\,y)^2

Step-by-step explanation:

Recall the formula for the perfect square of a binomial :

(a+b)^2=a^2+2ab+b^2

Now, let's try to identify the values of a and b in the given trinomial.

Notice that the first term and the last term are perfect squares:

\frac{x^2}{16} = (\frac{x}{4} )^2\\4y^2=(2y)^2

so, we can investigate what the middle term would be considering our a=\frac{x}{4}, and b=2y:

2\,a\,b=2\,(\frac{x}{4}) \,(2\,y)=x\,y

Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:

(\frac{x}{4} +2\,y)^2

4 0
3 years ago
Prove or disprove (from i=0 to n) sum([2i]^4) &lt;= (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
Need help asap with b and c!!! plz help for a cookie :)
Debora [2.8K]
You can think of this question like the photo attached above.

Hi!

I think for b, the answer would be:

You can construct an angle that is one fourth the measure of angle JKL, by dividing angle either angle MKL or JKM in half.
This is because one-fourth is also equal to one quarter (1/4). If you split angle JKL into 4 equal angles, you would have an angle that is one-fourth the measure (original angle) of angle JKL.

I think for c, the answer would be:

You can construct a 15 degree angle from a given 60 degree angle, by dividing the 60 degree angle into 4 equal angles.
This would work, because each of the 4 angles would be 15 degrees.

Hope this helps! Best of luck!



4 0
3 years ago
Find the gradient of the line segment between the points N(-1,2) and M(-6,3)​
siniylev [52]

Answer:

1/5

Step-by-step explanation:

Gradient is another word for slope. To find the gradient, we have to use a formula.

8 0
3 years ago
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