What we know about prime and common factors help us to find the ___________ of two or more numbers.

Answer:

[tex](w+6)^2[/tex] is the factored form of the given expression.

Step-by-step explanation:

The given expression is:

[tex]w^2+12w+36[/tex]

Simplifying the above given expression, we get

[tex]w^2+6w+6w+36[/tex]

[tex]w(w+6)+6(w+6)[/tex]

[tex](w+6)(w+6)[/tex]

[tex](w+6)^2[/tex]

Which is the required factored form of the given expression.

Answer:

The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]

Step-by-step explanation:

Given: Polynomial [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]

We have to place the indicated product in the proper location o the grid.

Consider the given product [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]

Using distributive property, Multiply each term of first bracket with each term of last bracket, we have,

[tex]=3a\cdot \:9a^2+3a\left(-6ac\right)+3a\cdot \:4c^2+2c\cdot \:9a^2+2c\left(-6ac\right)+2c\cdot \:4c^2[/tex]

Apply plus-minus rule [tex]+\left(-a\right)=-a[/tex] , we have,

[tex]=3\cdot \:9a^2a-3\cdot \:6aac+3\cdot \:4ac^2+2\cdot \:9a^2c-2\cdot \:6acc+2\cdot \:4c^2c[/tex]

Simplify, we have,

[tex]=27a^3-18a^2c+12ac^2+18a^2c-12ac^2+8c^3[/tex]

Adding similar terms, we have,

[tex]=8c^3+27a^3[/tex]

Thus, The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]

Location on grid is as shown below

Answer: m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.

Step-by-step explanation:  We are given to find the measures of ∠1, ∠2 and ∠3 in the figure.

As shown in the attached figure, ABCD is a rhombus, where m∠A = 128°.

We know that, in a rhombus, all the sides are congruent,  the opposite angles are congruent and the adjacent angles are supplementary.

So, from rhombus ABCD, we have

[tex]m\angle A=m\angle C~~~~~\textup{[opposite angles]}\\\\\Rightarrow m\angle 1=128^\circ.[/tex]

Also, in ΔBCD, we have

[tex]BC=CD~~\textup{[all the sides are congruent]}\\\\\Rightarrow m\angle 3=m\angle 2~~\textup{[angles opposite to congruent sides care congruent]}.[/tex]

Now, since the sum of three angles of a triangle is 180°, we have from  ΔBCD that

[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ\\\\\Rightarrow 128^\circ+m\angle 2+m\angle 2=180^\circ\\\\\Rightarrow 2\times m\angle 2=180^\circ-128^\circ\\\\\Rightarrow 2\times m\angle 2=52^\circ\\\\\Rightarrow m\angle 2=26^\circ.[/tex]

Therefore, m∠3 = 26°.

Thus, m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.

The printing job that uses 1 3/4 packages of printer paper requires 875 sheets.

To determine how many sheets of paper are used in a printing job that uses 1 3/4 packages of paper, follow these steps:

Therefore, the printing job uses 875 sheets of paper.

It is given sinx=0.9 .We need to find cosx.

We use the identity :

[tex] sin^{2} x + cos^{2} x =1 [/tex]

Substituting sinx=0.9

[tex] (0.9)^{2} +cos^{2} x =1 [/tex]

[tex] 0.81+cos^{2} x=1 [/tex]

Substracting 0.81 both sides:

[tex] cos^{2} x =1-0.81 [/tex]

[tex] cos^{2} x=0.19 [/tex]

Taking root of both sides cosx=0.435

Rounding to nearest hundredth

cosx=0.44.

Answer:

The answer is 2,800 (B)

Good Luck :)

Answer:

Step-by-step explanation:

Polynomial :  

An expression that can have constants (like 4), variables (like x or y) and exponents (like the 2 in [tex]y^{2}[/tex]), that can be combined using addition, subtraction, multiplication and division, but:

no division by a variable.

a variable's exponents can only be 0,1,2,3,... etc.

it can't have an infinite number of terms.

Thus according to definition all are polynomials

A.20x² + y

B.20x2+y12

C.20x2y

D.20x²

The correct answer is option a. 0.37.

Given that [tex]cos(2\theta) = 0.73[/tex], find a possible value of sin(theta).

It is known that:

[tex]cos(2\theta) = 1-2sin^2(\theta)[/tex].

Substituting the given value:

[tex]0.73 = 1-2sin^2(\theta)[/tex]

Rearrange to solve for sin²(theta):

[tex]2sin^2(\theta)=1-0.73[/tex]

[tex]2sin^2(\theta)=0.27[/tex]

[tex]sin^2(\theta)=0.135[/tex]

So, [tex]sin(\theta) = \sqrt{0.135}\ or\ sin(\theta) = -\sqrt{0.135}[/tex].

Since we are looking for a possible value, we take the positive root:

[tex]sin(\theta) \approx 0.367[/tex]

Considering the options given, the closest possible value is 0.37.

Answer: f(x) = (x+7)^2 -9

Step-by-step explanation:

I know that this is late but hopefully it will help someone else.

Answer:

1. f(x)=4 sin (2 x-π)-1

 =4 sin [-(π-2 x)] -1

 = -4 sin 2 x -1

-1 ≤ sin 2 x ≤1

f(x) is minimum, when, sin 2 x=1

= -4 × 1 -1

= -5→Minimum value of f(x).

2. Minimum y value of g(x) by looking at the table is ,

g(x)=-3→Minimum

3. h(x)=(x-2)²+4

As, (x-2)², will yield always a positive value.

So, minimum of h(x), will be at , x=2

h(2)=(2-2)²+4=4→Minimum

Among the three function given, f(x) has minimum y -value,equal to -5.

Option A: f(x)

The total area of the figure is 8 square units.

Remember that the area of a triangle is equal to its height times its base over 2.

In the image we can see 3 triangles, the larger one has a height of 3 units and a base of 4 units, so its area is:

A = 3*4/2 = 6 square units.

The bottom left triangle has a base of 1 unit and a height of 1 unit, so its area is:

A' = 1*1/2 = 0.5 square units.

The bottom right triangle has a base of 3 units, and a height of 1 unit, so its area is:

A'' = 1*3/2 = 1.5 square units.

The total area is:

A + A' + A'' = (6 + 0.5 + 1.5) square units = 8 square units.

If you want to learn more about area, you can read:

https://brainly.com/question/24487155

Answer:

B

Step-by-step explanation:

Got it right on the test

Hope this helps :)

Answer:

B. Linear decreasing

Step-by-step explanation:

We are given that,

The graph of the function is passing through the points (0,3) and (1.5,0).

Then, the rate of change is [tex]m=\frac{0-3}{1.5-0}=\frac{-3}{1.5}=-2[/tex]

So, the function is represented by a straight line with constant rate of change -2.

Moreover, as the value of x is increasing, we see that the value of y is decreasing.

Hence, option B is correct.