All categories

4 years ago

Factor the trinomial by grouping. - 13x + 6 + 6x^2

Mathematics

1 answer:

Grace [21]4 years ago

5 0

Answer:

(2x-3)(3x-2)

Step-by-step explanation:

$-13x+6+6x^2= \\\\6x^2-13x+6= \\\\6x^2-4x-9x+6= \\\\2x(3x-2)-3(3x-2)= \\\\(2x-3)(3x-2)$

Hope this helps!

You might be interested in

What is the percent increase when 7,200 increases by 1,800?

Vinvika [58]

Answer:

25%

Step-by-step explanation:

To find the percent increase, take the increase amount over the original amount

1800/7200

.25

Multiply by 100 to get a percent

25%

3 0

3 years ago

Find hcf and lcm of (1 - x + 2x^2 + x^3 + 4x^4)

blondinia [14]

Answer:

(x-1)

−3x+2=x

−2x−x+2

x(x−2)−1(x−2)=(x−2)(x−1)

Now

−4x+3=x

−3x−x+3

x(x−3)−1(x−3)=(x−3)(x−1)

6 0

3 years ago

Prove that:

Lorico [155]

A.)

$\csc^2(x) \tan^2 (x)- 1 = \tan^2(x)$

Use the identities $\csc x = 1 / \sin x$ and $\tan x = \sin x / \cos x$ on the left-hand side

$\begin{aligned}
\text{LHS} &= \csc^2(x) \tan^2 (x)- 1 \\
&= \frac{1}{\sin^2 (x)} \cdot \frac{\sin^2 (x)}{\cos^2 (x)} - 1 \\
&= \frac{1}{\cos^2 (x)} - 1
\end{aligned}$

Make 1 have a common denominator to allow for fraction subtraction
Multiply the numerator and denominator of 1 by cos^2 x

$\begin{aligned} \text{LHS} &= \frac{1}{\cos^2 (x)} - 1 \cdot \tfrac{\cos^2 (x)}{\cos^2 (x)} \\
&= \frac{1}{\cos^2 (x)} - \frac{\cos^2 (x)}{\cos^2 (x)} \\
&= \frac{1 - \cos^2 x}{\cos^2 (x)}
\end{aligned}$

Use Pythagorean identity for the numerator.

If $\sin^2 (x) + \cos^2(x) = 1$ then subtracting both sides by $\cos^2 (x)$ yields $\sin^2(x) = 1 - \cos^2(x)$ . We can substitute that into the numerator

$\begin{aligned} \text{LHS} &= \frac{1 - \cos^2 (x)}{\cos^2 (x)} \\
&= \frac{\sin^2 (x)}{\cos^2 (x)} \\
&= \tan^2 (x) && \text{Since } \tan x = \tfrac{\sin x }{\cos x} \\
&= \text{RHS}
\end{aligned}$

======

b.)

$\dfrac{\sec(x)}{\cos(x)} - \dfrac{\tan(x)}{\cot(x)} = 1$

For the left-hand side:
By definition, $\sec(x) = 1/\cos(x)$ and $\tan (x) = 1/\cot (x)$

$\begin{aligned}
\text{LHS} &= \dfrac{\sec(x)}{\cos(x)} - \dfrac{\tan(x)}{\cot(x)} \\
&= \dfrac{ \frac{1}{\cos(x)} }{\cos(x)} - \dfrac{\frac{1}{\cot(x)}}{\cot(x)} \\
&= \frac{1}{\cos^2 (x)} - \frac{1}{\cot^2(x)} 
\end{aligned}$

Since $\cot (x) = \cos (x) / \sin (x)$

$\begin{aligned} \text{LHS} &= \frac{1}{\cos^2 (x)} - \frac{1}{\frac{\cos^2(x)}{\sin^2(x)} } \\ &= \frac{1}{\cos^2 (x)} -\frac{\sin^2(x)}{\cos^2(x)} \\ &= \frac{1 - \sin^2(x)}{\cos^2 (x)} \end{aligned}$

Using Pythagorean identity, $\cos^2(x) = 1 - \sin^2(x)$ so

$\begin{aligned} \text{LHS} &= \frac{\cos^2(x)}{\cos^2 (x)} \\
&= 1 \\
&= \text{RHS}
\end{aligned}$

6 0

3 years ago

The list shows the thicknesses of several different types of art paper.

Naily [24]

Answer:

B. 0.210

Step-by-step explanation:

Range is the minimum value subtracted from the maximum value. In this case 0.004 is the smallest value and 0.214 is the largest.

Range = 0.214 - 0.004 = 0.210 = B

6 0

3 years ago

12. Volume of a cube is 648V3 cm³. Find its total surface<br>area.

AleksAgata [21]

Answer:

area= 449.2984 cm^2 if I understand correctly that the volume is 648 cm^3

Step-by-step explanation:

side length=the cube root of 648

side length=8.6535 cm

area=8.6536x8.6535x6=449.2984 cm^2

7 0

3 years ago