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Kryger [21]
3 years ago
8

Simplify completely ((x2-4x+4)/(x2+10x+25)) x ((x+5)/(x2+3x-10)) ...?

Mathematics
1 answer:
Ne4ueva [31]3 years ago
3 0
First of all you'll have to 
Factor x^2-4x+4 = (x-2)^2
Factor x^2+10x+25 = (x+5)^2
Factor x^2+3x-10 = (x+5)(x-2)

So you'll have (x-2)^2/(x+5)^2 X (x+5)/(x+5)(x-2)
Then cancel the (x-2) and (x+5) on both sides

Thus getting the answer of x-2/(x+5)^2
or x-2/x+10+25
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What is the unit rate of four pounds of apples that cost $1.96
forsale [732]
\frac{1.96}{4}=0.49

Solution: 0.49 pounds
4 0
3 years ago
Read 2 more answers
Laquita had 5 7/9 yards of fabric. She used 3 2/3 to make a blouse.Write and slove an expresstion to find how much fabric has be
enyata [817]

Answer: \frac{11}{3}\ yards

Step-by-step explanation:

Given

Laquita has 5 \frac{7}{9}\ yards of fabric i.e.

\Rightarrow \dfrac{5\times9+7}{9}=\dfrac{45+7}{9}=\dfrac{52}{9}\ yards

She used  3\ \frac{2}{3} yards to make a blouse i.e.

\Rightarrow \dfrac{3\times 3+2}{3}=\dfrac{11}{3}\ yards

Left fabric

\Rightarrow \frac{52}{9}-\frac{11}{3}=\frac{52-33}{9}\\\\\Rightarrow \frac{19}{9}\ yards

8 0
3 years ago
Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (
galben [10]

Answer:

(a) Yes, λ_{A}+λ_{B}

(b) Yes, λ_{A}λ_{B}

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation λ_{A} to denote Lambda(A) sign.

v is an eigenvector of matrix A with eigenvalue λ_{A}

v is also eigenvector of matrix B with eigenvalue λ_{B}

So we can write this in equation form as

Av=λ_{A}v

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector  that is in the same direction as of Av, then this v  is called the eigenvector of A. Av is λ_{A} times the original v. The number λ_{A} is the eigenvalue of A.

λ_{A} this number is very important and tells us what is happening when we multiply Av. Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of Av by using the following equation:

det(A-λI)=0

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that v is an eigenvector of A + B and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)

so,  (A+B)(v)=(λ_{A}+λ_{B})(v)

which means that v is also an eigenvector of A+B and the associated eigenvalues are λ_{A}+λ_{B}

(b) Show that v is an eigenvector of AB and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)

so,  

(AB)(v)=λ_{A}λ_{B}(v)

which means that v is also an eigenvector of AB and the associated eigenvalues are λ_{A}λ_{B}

5 0
3 years ago
A credit card company uses your average daily balance to compute your finance charge. You charge $100 on May 2 and $200 on May 2
liraira [26]

Answer:

<h2>$5.56</h2>

Step-by-step explanation:

On may 2, charge = $100

On may 20, charge = $200

To get the average daily balance, we will use the concept of calculating slope;

let d be day of the month and c be the amount charged

when d1 = 2, c1 = 100

when d2 = 20, c2 = 200

average daily balance = c2-c1/d2-d1

average daily balance = 200-100/20-2

average daily balance = 100/18

average daily balance ≈ 5.56

Hence your average daily balance is approximately $5.56

4 0
2 years ago
Justin has a credit card with a limit of $1,000 and an introductory APR of 0% for six months. After that the, APR for purchases
yuradex [85]
Given:
APR for first six months = 0%
APR for purchases after the 1st six months = 22.9%
APR for cash advances = 24.9%
APR for penalties = 29.4%

Obtaining $350 from an ATM using his credit card is a form of Cash Advances. So, the APR for this transaction is 24.9% Choice A.
4 0
3 years ago
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