Which of the following statements demonstrates the associative property of multiplication?

Factorise the following. 49g^2 - 36h^2 - 28g - 24h

vagabundo [1.1K]

Answer: -4(7g - 6h)(7g + 6h)

Step-by-step explanation:

Separate the 4 terms into two groups of 2 terms. Then factor out the GCF of each group. You should end up with a common factor in each group - that is one of the factors. The other factor is what you factored out from each term.

49g² - 36h² - 28g - 24h

(7g - 6h)(7g + 6h) -4(7g + 6h)

They both have a common factor of (7g + 6h)

The terms factored out are (7g - 6h) and -4

So, the factorization is: -4(7g - 6h)(7g + 6h)

7 0

3 years ago

Answer this...: ab=?

Andrej [43]

Answer:

I don't know

thanks for points

Step-by-step explanation:

a = Apple

nd

b=ball

4 0

3 years ago

Determine whether the given signal is a solution to the difference equation. Then find the general solution to the difference eq

Ulleksa [173]

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

The given equation is:

$y_{k + 2} + 8y_{k +1} - 9y_{k} = 20k + 12..(1)$

put,

$y_k = k^2\\\\y_{k+2}=(k+2)^2\\\\y_{k+1}=(k+1)^2\\\\$

$(k+2)^2+8(K+1)^2-9k^2 = 20k+12\\\\=20k+12= 20K+12\\\\$

hence y_k=k^2 is its solution.

Now,

$\to y_{k+2}+ 8y_k + 1 - 9y_k = 20k + 12$

the symbol form is:

$(E^2+8E-9)_{yk}=20k+12$

$\to m^2+8m-9=0\\\\\to m^2+(9-1)m-9=0\\\\\to m^2+9m-m-9=0\\\\\to m(m+9)-(m+9)=0\\\\\to (m+9)(m-1)=0\\\\\to m=-9 \ \ \ \ \ \ \ m=1\\$

The general solution is:

$y_k = c_1(-9)^k + c_2(`1)^k\\\\y_k =c_1(-9)^k+c_2$

The complete solution is:

$y_k=(y_k)_c+(y_k)_y\\\\y_k= c_1(-9)^k+c_2+k^2$

The answer is option b: $y_k = k^2 + c_1(-9)^k + c_2$

After solve the complete solution is:

$\bold{y_1=c_1(-9)^k+c_2+k^2.....}$

5 0

3 years ago

during a bike challenge, riders have to collect various colored ribbons. each 1/2 mile they collect a red ribbon, each 1/8 mile

Natali [406]

The correct answer is: 
green and blue.

Explanation: 
We want to see which fractions $\frac{3}{4}$ is a multiple of. We know that $\frac{3}{4}$ is a multiple of $\frac{1}{4}$ , because $\frac{1}{4}$ *3= $\frac{3}{4}$ .

We can divide fractions to determine if $\frac{3}{4}$ is a multiple of $\frac{1}{2}$ :
$\frac{ \frac{3}{4}}{ \frac{1}{2}}$ ;

in order to divide fractions, flip the second one and multiply:
$\frac{3}{4}$ )* $\frac{2}{1}$ = $\frac{6}{4}$ =1 $\frac{1}{2}$ .
This did not divide evenly, so $\frac{3}{4}$ is not a multiple of 1/2.

Checking to see if $\frac{3}{4}$ is a multiple of $\frac{1}{8}$ , $\frac{ \frac{3}{4}}{ \frac{1}{8}}$ ;

flip the second one and multiply:
$\frac{3}{4}$ * $\frac{8}{1}$ = $\frac{24}{4}$ =6.
This divided evenly, so $\frac{3}{4}$ is a multiple of $\frac{1}{8}$ .

6 0

3 years ago

Read 2 more answers

What is the absolute value of a number ?

stepladder [879]

Answer:

Step-by-step explanation:

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

7 0

2 years ago

Read 2 more answers