Factorise 3x squared-13x-10

Write the expression in standard form. (6f-5+3g)-(-6g+3)

andreev551 [17]

(6f-5+3g)-(-6g+3) = 6f-5+3g-(-6g)-3) = 6f-8+3g+6g = 6f+9g-8.

6 0

3 years ago

8 ABC please trig assignment

Papessa [141]

Using equivalent angles, the solutions are given as follows:

a) $x = \frac{15\pi}{23}$ .

b) $x = \frac{9\pi}{62}, x = \frac{53\pi}{62}$ .

c) $x = \frac{3\pi}{8}, \frac{11\pi}{8}$

<h3>What are equivalent angles?</h3>

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.

Hence:

$\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}$

Hence $x = \frac{15\pi}{23}$ .

For item b, if two angles are complementary, the sine of one is the cosine of the other.

Complementary angles add to 90º = 0.5pi, hence:

$x + \frac{11\pi}{31} = \frac{\pi}{2}$

$x = \frac{31\pi}{62} - \frac{22\pi}{62}$

$x = \frac{9\pi}{62}$

The equivalent angle on the second quadrant is:

$\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}$

Hence the solutions are:

$x = \frac{9\pi}{62}, x = \frac{53\pi}{62}$

For item c, the angles are also complementary, hence:

$x + \frac{\pi}{8} = \frac{\pi}{2}$

$x = \frac{4\pi}{8} - \frac{\pi}{8}$

$x = \frac{3\pi}{8}$

The tangent is also positive on the third quadrant, hence the equivalent angle is:

$x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}$

Hence the solutions are:

$x = \frac{3\pi}{8}, \frac{11\pi}{8}$

More can be learned about equivalent angles at brainly.com/question/28163477

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6 0

1 year ago

Simplify 3x^2x 4x^5 please help

Firdavs [7]

Answer:

$12x^7$

Step-by-step explanation:

$3x^2 \times 4x^5$

$3 \times x^2 \times 4 \times x^5$

$3 \times 4 \times x^{2+5}$

$12 \times x^7$

8 0

3 years ago

* A helicopter's altitude changes by – 28 ft in 3 s.

strojnjashka [21]

Answer:

-9.33 ft per second

Step-by-step explanation:

To calculate this, you just have to divide -28 by 3. When doing this, it will give the change per second or for every 1 second.

-28/3 = -9.33

Therefore, the average change in the helicopter's altitude each second is -9.33 ft.

6 0

3 years ago

A rectangular piece of land whose length is twice its width has a diagonal distance of 90 yards. How many yards, to the nearest

dezoksy [38]

Answer:

A person saves 30.7 yards

Step-by-step explanation:

the path a person walks diagonally creates a right triangle with the lenght and the width of the rectangular piece of land. The diagonal is 90 yards which becomes the hypotenuse.

let w be the width, then l becomes the length, which is twice the width. Therefore, leg l=2a and leg w=a.

By the Pythagorean Theorem:

$c^{2}=l^{2}+w^{2}$

Replacing the values:

$90^{2}=(2a)^{2}+a^{2}\\90^{2}=4a^{2}+a^{2}\\90^{2}=5a^{2}\\\\a=\sqrt{\frac{90^{2}}{5} } } =\frac{90}{\sqrt{5} }$

But that a is the value for the width, if a person walks the width and the length, it becomes:

the length plus the width=2a+a=3a.

So:

$a=\frac{90}{\sqrt{5} } \\\\3a=\frac{3(90)}{\sqrt{5} }$

Now, the difference between walking across the land and surrounding it, is:

$d=\frac{3(90)}{\sqrt{5} }-90=30.7476\\\\d=30.7$

We can conclude, a person saves 30.7 yards if walking across the land.

8 0

3 years ago