factors of 3x^2y^2+6x^2+12y^2+24

Final answer:

When solving math problems with rules of exponents, it is important to understand key concepts such as multiplication of exponentials, taking square roots of exponentials, and dividing exponentials.

Explanation:

When solving math problems with rules of exponents, there are several key concepts to keep in mind:

It is important to understand these rules and practice applying them to various problems in order to master solving math problems with rules of exponents.

Answer:

The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32

Step-by-step explanation:

The sequence is:

[tex]a_1=-1\\a_n=2*a_{n-1}[/tex]

So, for finding the first six terms of the sequence, we need to replace n by the numbers 1 to 6 and we get:

[tex]a_1=-1\\a_2=2*a_{2-1} =2*a_1\\a_3=2*a_{3-1} =2*a_2\\a_4=2*a_{4-1} =2*a_3\\a_5=2*a_{5-1} =2*a_4\\a_6=2*a_{6-1} =2*a_5\\[/tex]

That means that the term n is 2 times the last term. Then, replacing the values of [tex]a_1, a_2, a_3, a_4[/tex] and [tex]a_5[/tex], we get:

[tex]a_1=-1\\a_2=2*(-1)=-2\\a_3=2*(-2)=-4\\a_4=2*(-4)=-8\\a_5=2*(-8)=-16\\a_6=2*(-16)=-32\\[/tex]

So, The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32

Answer:

Step-by-step explanation:

Rational functions are functions that can be written as the ratio of two polynomial functions, while inverse variations are a type of rational function where the product of two varying quantities is a constant.

A rational function is any function that can be written as the ratio of two polynomial functions. Both the numerator and the denominator are polynomials. For example, f(x) = (2x^2 + 3)/(x - 5) is a rational function where 2x^2 + 3 and x - 5 are polynomial functions.

On the other hand, an inverse variation, or inverse proportion, is a specific type of rational function where the product of two varying quantities is a constant. It is in the form of y = k/x, where k is a nonzero constant. For example, if y varies inversely as x, then the product of x and y is constant, which means xy = k.

To summarize, all inverse variations are rational functions since they can be expressed as a ratio of two polynomials. However, not all rational functions are inverse variations since not all can be written in the form y = k/x.

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The correct answer to fill in the blank is:

“Cognitive flexibility”

Cognitive flexibility refers to a person’s ability to adapt the mental processing strategies to face new and unexpected situations or problems. In this case, some of the students who initially did not solve the problem transformed their way of solving the puzzle after the discussion thus getting it right the next time.

Answer:

Option C is correct.

The missing steps in this proof is; [tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex].

Explanation:         

Given ΔABC.

Prove that:  The sum of the interior angle measures of ΔABC is [tex]180^{\circ}[/tex]

Let A ,B and C forms a triangle    [Given]

Parallel lines are those two lines that are always the same distance apart and never touch.

then, by the definition of parallel lines and labeling angles

DE be the line passing through B, parallel to AC, with angles as labelled in the figure as shown below in the attachment.

Alternative Interior Angle theorem states that the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles also this theorem says that when the lines are parallel, then the alternate interior angles are equal.

Then,

[tex]\angle 1 \cong \angle 4[/tex] and                              

[tex]\angle 3 \cong \angle 5[/tex]        [By Alternative Interior angle theorem]            

Angles are always congruent if their measures in degrees are equal.

therefore,

[tex]m\angle 1 =m\angle 4[/tex] and

[tex]m\angle 3=m\angle 5[/tex]      [By Congruent Angle have equal measure]                                                                   ......[1]

Straight Angles states that angles on one side of a straight line always add to 180 degrees.

From the given figure;

By the addition angle and definition of straight angle we get;

[tex]m\angle 4 +m\angle 2 +m\angle 5 =180^{\circ}[/tex]      ......[2]

Substituting equation [1] in [2] we get;

[tex]m\angle 1 +m\angle 2 +m\angle 3 =180^{\circ}[/tex]  

Therefore, the sum of the interior angles measures of triangle ABC is [tex]180^{\circ}[/tex]

Answer:

its answer d

Step-by-step explanation:

add them together:

124 + 88 + 62 +137 +195 = $606 total

The solutions to the equation c² = 5c are c = 0 and c = 5.

We have,

To solve the equation c² = 5c by factoring,

we can rearrange it as:

c² - 5c = 0

Then we can factor out the common factor of c, giving:

c(c - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.

So we have:

c = 0 or c - 5 = 0

Solving for c in each case, we get:

c = 0 or c = 5

Therefore,

The solutions to the equation c² = 5c are c = 0 and c = 5.

Learn more about solutions to equations here:

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Simplified form of the expression 4m+5−3m:

m + 5

Expression : Degree of m is 1 , so the expression is linear.

Given , that expression: 4m+5−3m

Now to simplify the expression,

⇒ 4m + 5 − 3m

Combine like terms,

⇒ (4m - 3m) + 5

⇒ m + 5

Thus the simplified form is m + 5 .

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Answer:  Option 'd' is correct.

Step-by-step explanation:

Since we have given that

[tex]f(x) = x^2[/tex]

We need to shift the function f(x) 3 units to the right to obtain the graph of g(x).

As we  know that shifting right is the horizontal shift.

And f(x-h) = g(x) , here f shift right h units.

so, After shifting 3 units right, we get that

[tex]g(x)=(x-3)^2[/tex]

Hence, Option 'd' is correct.

In the given diagram, the points that are shown to be collinear are H and E.

Collinearity in geometry refers to the condition where three or more points lie on the same straight line. In this case, points H and E are collinear as they lie on the same straight line, which is represented by a vertical double-headed arrow passing through them.

The diagram consists of two parallelograms, labeled 'I M' and 'E P', with three points inside each. In the parallelogram 'I M', the points are labeled as I, H, and J from top to bottom. Similarly, in the parallelogram 'E P', the points are labeled as F, E, and G from top to bottom. Among these points, only H and E share the same straight line, making them collinear. The other points do not share this line and hence are not collinear with H and E. This concept is fundamental in understanding geometric relationships and properties.

Answer:

C is the answer.

Step-by-step explanation:

52.5 + 75 = x

x + 75 = 52.5

75 – 52.5 = x

x – 52.5 = 75

6^2 + 3^2 = x^2

36 + 9 = x^2

45=X^2

X= sqrt(45) = 3squareroot5

 answer is A