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3 years ago

19x – y – 2z + x + 5y + 2z

1 answer:

7 0

$19x - y - 2z + x + 5y + 2z \\ \\ (19x + x) + (-y+5y) + (-2z + 2z) \ / \ gather \ like \ terms \\ \\ 20x + 4y \ / \ simplify \\ \\ Answer: \fbox {20x + 4y}$

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Gabe read a total of 21 books with his book club over 7 months. After belonging to the book club for 22 months, how many books w

cestrela7 [59]

Answer:

Step-by-step explanation:

6 0

2 years ago

Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?.

loris [4]

To solve the problem we must know the Basic Rules of Exponentiation.

<h2>Basic Rules of Exponentiation</h2>

$x^ax^b = x^{(a+b)}$
$\dfrac{x^a}{x^b} = x^{(a-b)}$
$(a^a)^b =x^{(a\times b)}$
$(xy)^a = x^ay^a$

$x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4$

The solution of the expression is $\dfrac{4x^4}{y^6}$ .

<h2>Explanation</h2>

Given to us

$(16x^8y^{12})^{\frac{1}{2}}$

Solution

We know that 16 can be reduced to $2^4$ ,

$=(2^4x^8y^{12})^{\frac{1}{2}}$

Using identity $(xy)^a = x^ay^a$ ,

$=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}$

Using identity $(a^a)^b =x^{(a\times b)}$ ,

$=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})$

Solving further

$=2^2x^4y^{-6}$

Using identity $\dfrac{x^a}{x^b} = x^{(a-b)}$ ,

$=\dfrac{2^2x^4}{y^6}$

$=\dfrac{4x^4}{y^6}$

Hence, the solution of the expression is $\dfrac{4x^4}{y^6}$ .

Learn more about Exponentiation:

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8 0

2 years ago

Suppose A is an invertible n×n matrix and v is an eigenvector of A with associated eigenvalue 4. Convince yourself that v is an

mote1985 [20]

The eigenvector of matrix A4 is 4096.

The eigenvalue of the matrix A-1 is 1/8.

(A+4I) has an eigenvalue of 12.

40 is the eigenvalue of 5Av.

The collection of scalar values known as the eigenvalues of a matrix are connected to the set of linear equations that are most likely contained within the matrix equations.

The eigenvectors are also known as the characteristic roots.

If the matrix A's eigen vector v is linked to an eigen value.

Av then equals lamda v.

The fact that v is an eigen vector of A with the value eight is assumed.

hence, Av = 8v.

We must determine the eigenvalue of A4.

A4*v equals A3(8v) = 84*v equals 4096v.

As a result, the eigenvalue of A4 is 4096.

Suppose A has an eigenvalue of 8. The eigenvalue of A-1 is thus 1/8.

It is calculated that the eigenvalue of (A+4I) is (A +4In)v = Av + 4v = 8v + 4v =12v.

(A+4I) has an eigenvalue of 12.

The value of 5Av's eigenvalue is 5Av = 5*8v = 40v.

40 is the eigenvalue of 5Av.

Learn more about the eigen vectors here:

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7 0

8 months ago

Complete the equation: x^2+8x + _=(_)^2

pentagon [3]

Answer:

x^2+8x+16=(x-4)^2

EXPLANATION:

(a+b)^2=a2+2.a.b+b2

we have to break the middle term in 2ab here a is x then 2xb=8x, => b=4, but value of a and b to get the required equation!

8 0

2 years ago

9 3/10 - 5 3/4 as a mixed number in simplest form

Artemon [7]

Answer:

3 1/20

Step-by-step explanation:

First, we will convert the mixed numbers into improper fractions...

9 3/10 (9*10=90+3=93) so the improper fraction is 93/10

5 3/4 (5*4=20+3=23) therefore the improper fraction is 23/4

We then want to make the denominator the same...

93/10 (*4) = 372/40

23/4 (*10) = 230/40

We then put it into the question...

372/40 - 230/40 = 142/40

Lastly, we now need to turn this into a mixed number...

142/40=3.55 so the answer is 3 2/40

3 2/40 in it's simplest form is 3 1/20

Hope this helps!

6 0

2 years ago

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