|2x-3| < 9 solve for x

Answers

Answer 1

Answer: $|2x-3| < 9 \n \n2x-3 < 9 \ \ and \ \ 2x-3 > -9 \n \n 2x < 9 +3 \ \ and \ \ 2x > -9 +3 \n \n 2x < 12\ \ and \ \ 2x > -6 \n \n x < 6\ \ and \ \ x > - 3 \n \n x \in (-3,6)$

Answer 2

Answer: $|2x-3| < 9\iff2x-3 < 9\ \wedge\ 2x-3 > -9\n\n2x < 9+3\ \wedge\ 2x > -9+3\n\n2x < 12\ \wedge\ 2x > -6\n\nx < 6\ \wedge\ x > -3\n\n\nx\in(-3;\ 6)$

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The area of a square is 72. what is the longest straight line that can be drawn between any two points of the square

Answers

The longest straight line that can be drawn between any two points of a square is the one that includes the points on the opposite corners of the squares. To determine the length of this straight line, we must first determine the length of the square's side. Since the area of the square can be calculated by taking the square of the side, then

s^2 = 72
s = 6 sqrt(2)

Then, using the Pythagorean theorem, we will find c (the longest side of straight line of the square)

c^2 = a^2 + b^2

Upon substitution of the length of the square's side, we have
c^2 = (6 sqrt(2))^2 + (6 sqrt(2))^2
c^2 = 72+72
c = 72

The length of the longest line is 72.

The image of the point (1, -2) after a rotation of 180° about the origin is:

Answers

Answer:

$(-1,2)$

Step-by-step explanation:

We have been coordinates of a point $(1,-2)$ . We are asked to find the coordinates of the point after a rotation of 180° about the origin.

We know that after rotating a point 180° about the origin, the coordinates of point changes their signs to opposite. The rule of rotating a point 180° about the origin is $(x,y)\rightarrow (-x,-y)$ .

After rotating the point $(1,-2)$ 180° about the origin its coordinates would be:

$(1,-2)\rightarrow (-1,--2)$

$(1,-2)\rightarrow (-1,2)$

Therefore, the coordinates of the given point after a rotation of 180° about the origin would be $(-1,2)$ .

The answer is (-1,2)

In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.

Answers

Answer:

0.51 cm

Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

$\sin \angle P=\frac{\text{Opposite leg}}{\text{Hypotenuse}}=(MN)/(MP)\n \nMN=MP\sin \angle P\n \nMN=4\sin 21^(\circ)\approx 1.43\ cm$

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

$\cos \angle M=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}=(MH)/(MN)\n \nMH=MN\cos \angle M$

In the right triangle, two acute angles are always complementary, so

$m\angle M=90^(\circ)-m\angle P=90^(\circ)-21^(\circ)=69^(\circ)$

Thus,

$MH=1.43\cos 69^(\circ)\approx 0.51\ cm$

Are there any perfect squares that go into 380?

Answers

I belive the answer is no. Tell me if im doing this wrong, but the square root of 380 is a decimal number.

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Answers

B because tangent is Opposite/hypotenuse. = 6/8 = 0.75

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