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2 years ago

Write as a product 60 + 6ab - 30b - 12a

Mathematics

1 answer:

Delvig [45]2 years ago

4 0

Answer:

6(a - 5)(b - 2)

Step-by-step explanation:

60 + 6ab - 30b - 12a

Factor out the common term 6:

= 6(10 + ab - 5b - 2a)

Rearrange:

= 6(ab - 2a - 5b + 10)

Factor:

= 6(a - 5)(b - 2)

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A sphere rolls up an inclined plane of inclination angle 30 degree. At the bottom of the incline the center of mass of the spher

Zigmanuir [339]

Answer: The sphere is 0.002548 cm travel up the plane.

Step-by-step explanation:

Since we have given that

Inclination angle = 30°

Translational speed = 0.25 m/s

As we know that

$KE=0.5\times lw^2=PE$

and

Length of solid sphere is given by

$l=\dfrac{2Mr^2}{5}$

So, it becomes,

$KE=0.5\times \dfrac{2Mr^2}{5}w^2=Mgd\sin \theta$

And $0.25\ m/sv=rw$

So, it becomes,

$1\times (0.25)^2=5\times d\times 9.81\times \sin 30^\circ\\\\0.0625=49.05d\times \dfrac{1}{2}\\\\\dfrac{0.125}{49.05}=d\\\\d=0.002548$

Hence, the sphere is 0.002548 cm travel up the plane.

5 0

4 years ago

The population is______________.

Ipatiy [6.2K]

Answer:

(A) Incoming students at a particular university.

Step-by-step explanation:

In Mathematics, population is defined as a discrete group of people, animals or things that can be identified by at least one common characteristics for the purpose of data collection and analysis.

In this question incoming students are classified as a population as they share common characteristic of being new to this particular university.

3 0

3 years ago

Which formula can be used to describe the sequence below 27,9,3

Ierofanga [76]

Answer:

$a_n=27 \cdot (\frac{1}{3})^{n-1}$ .

Step-by-step explanation:

This is a geometric sequence that means there is a common ratio. That means there is a number you can multiply over and over to get the next term.

The first term is 27.

The second term is (1/3)(27)=9.

The third term is (1/3)(9)=3.

So the common ratio is 1/3.

That means you can keep multiplying by 1/3 to find the next term in the sequence.

The explicit form for a geometric sequence is $a_n=a_1 \cdot r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio.

We are given $a_1=27$ and $r=\frac{1}{3}$ .

So the explicit form for the given sequence is $a_n=27 \cdot (\frac{1}{3})^{n-1}$ .

3 0

3 years ago

Which of the following equations is the result of completing the square on x^2 - 6x - 9 = 0?

azamat

Answer:

x = 3 +- √18

Step-by-step explanation:

By completing the square method

3 0

2 years ago

How does the number of solutions of a system depend on ranks of the coefficient matrix and the augmented matrix?

fenix001 [56]

Answer:

The number of solutions of a system is given by the number of different variables in the system, this number has to be the same as the number of independent equations. The coefficients and the augmented matrix of the system show these values in a matrix form. A system has a unique solution when the rank of both matrixes and the number o variables in the system are the same.

Step-by-step explanation:

For example, the following system has 2 different variables, x and y.

$x+y=1\\x+2y=5$

In order to find a unique solution to the system, the number of independent equations and variables in the system must be the same In the previous example, you have 2 independent equations and 2 variables, then the solution of the system is unique.

The rank of a matrix is the dimension of the vector generated by the columns, in other words, the rank is the number of independent columns of the matrix.

According to Rouché-Capelli Theorem, a system of equations is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. The inconsistency of the system is because you can't find a combination of the variables that will solve the system.

6 0

3 years ago