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Sonja [21]
3 years ago
8

HELP ME ASAP

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
7 0
The distance between said towns would be 70 miles apart
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Mrs. Donelly drew the triangle above on the chalkboard and asked her students to write down possible side lengths for a, b, and
GenaCL600 [577]

Answer:

a=2;b=4;c=6.

Louis wrote the correct answer.

4 0
2 years ago
If p is a polynomial show that lim x→ap(x)=p(a
Lostsunrise [7]

Let p(x) be a polynomial, and suppose that a is any real number. Prove that

lim x→a p(x) = p(a) .

 

Solution. Notice that

 

2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .

 

So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x – 2.

 

Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| < 1, so −2 < x < 0. In particular |x| < 2. So

 

|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|

= 2|x|^3 + 5|x|^2 + |x| + 2

< 2(2)^3 + 5(2)^2 + (2) + 2

= 40

 

Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2 + x − 2| < ε/40 · 40 = ε.

3 0
3 years ago
Write a compound interest function to model each situation. Then find the balance after the given number of years.
andriy [413]

Answer:

See explanation

Step-by-step explanation:

The standard compound interest formula is A = P(1+\frac{r}{n})^{nt} where:

P is the principal amount

r is the interest rate (typically as a percentage)

t is the time

n is the times compounded per unit of time

So,

1)  A = 50000(1+\frac{0.03}{12})^{(12)(6)} =59847.42

2) A = 43000(1+\frac{0.05}{1})^{(1)(3)} =49777.88

3) A = 65000(1+\frac{0.06}{4})^{(4)(12)} =132826.08

You should check my answers though, I may have mixed up some terms.

3 0
3 years ago
What is the solution to this system of equations?
Anit [1.1K]

Answer:

the correct answer is b (4,2)

7 0
3 years ago
What are the solutions to the equation 3x2 + 15x = 18?
jok3333 [9.3K]

3x {}^{2}  + 15x = 18

<h2>Divide the entire thing by 3</h2>

x {}^{2}  + 5x = 6

x {}^{2}  + 5x - 6 = 0

<h2>You can find the roots by using the quadratic formula or by using the form x²-Sx+P</h2>

let \:  \alpha \:  and \: \beta  \: be \: the \: roots

<h2>Two numbers whose sum is -5 and product is -6</h2><h2>-6 and +1</h2>

<h2>Your answer is B</h2>

6 0
2 years ago
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