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3 years ago

Find the length of side x in simplest radical form with a rational denominator.

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

7 0

Answer: 5/2

Explanation:

According to 30-60-90 triangle rule:

The side opposite of 30 degree is equal to half of the hypotenuse and the hypotenuse here is 5 so therefore x = 5/2

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ivolga24 [154]

Answer:

117m

Step-by-step explanation:

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7 0

3 years ago

Find the missing side. Round to the nearest tenth. For all 4 pics

Firlakuza [10]

Answer:

1st pic) 17.8

2nd pic) 16.8

3rd pic) 9.1

4th pic) 13.5

Step-by-step explanation:

1st pic: $cos = \frac{adjacent}{hypothenuse}$

(write equation) Cos 27 (cos 27 = 0.89) = $\frac{x}{20}$

(new equation) 0. 89 = $\frac{x}{20}$

(multiply 20 on both sides) 0.89 x 20 = $\frac{x}{20}$ x 20

(solve) 17.8 = x

2nd pic: $tan = \frac{adjacentx}{hypothenuse}$

(write equation) tan 40 (tan 40 = 0.84) = $\frac{32}{x}$

(new equation) 0.84 = $\frac{32}{x}$

(multiply 32 on both sides) 0.84 x 20 = $\frac{32}{x}$ x 20

(solve) 16.8 = x

3rd pic: $cos = \frac{adjacent}{hypothenuse}$

(write equation) cos 55 (cos 55 = 0.57) = $\frac{16}{x}$

(new equation) 0.57 = $\frac{16}{x}$

(multiply 16 on both sides) 0.57 x 16 = $\frac{16}{x}$ x 16

(solve) 9.1 = x

4th pic: $tan = \frac{adjacentx}{hypothenuse}$

(write eqaution) tan 42 (tan 42 = 0.90) = $\frac{x}{15}$

(new equation) 0.90 = $\frac{x}{15}$

(multiply 15 on both sides) 0.90 x 15 = $\frac{x}{15}$ x 15

(solve) 13.5 = x

4 0

3 years ago

The set of points P(0, 3), Q(2, 0), R(4, -3) are collinear and the line has a slope of _____.

vampirchik [111]

Answer:

slope = -1.5

Step-by-step explanation:

A set of three or more points are said to be collinear if they all lie on the same straight line.

We have been given the following collinear set of points;

P(0, 3), Q(2, 0), R(4, -3)

This implies that P, Q, and R lie on the same line.

The slope of a line is defined as; (change in y)/(change in x)

Using the points P and Q, the slope of the line is calculated as;

(0-3)/(2-0) = -3/2 = -1.5

7 0

3 years ago

Read 2 more answers

Which shapes can be drawn with two opposite angles equal to 105°

sertanlavr [38]

Answer:

see the explanation

Step-by-step explanation:

we know that

A shape with two opposite angles equal to 105° could be a quadrilateral, a parallelogram, a rhombus or a trapezoid

Because

A quadrilateral: A quadrilateral is a four-sided polygon. The sum of the interior angles in any quadrilateral must be equal to 360 degrees

If the quadrilateral have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

$360^o-2(105^o)=150^o$

A parallelogram: A Parallelogram is a flat shape with opposite sides parallel and equal in length. Opposite angles are congruent and consecutive angles are supplementary

If the parallelogram have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

$180^o-105^o=75^o$

A rhombus: A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel. Opposite angles are congruent and consecutive angles are supplementary

If the Rhombus have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

$180^o-105^o=75^o$

A trapezoid: A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel

If the trapezoid have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

$360^o-2(105^o)=150^o$

4 0

3 years ago

Evaluate the expression described below if the number is –2. The quotient of three less than twice a number and the number squar

lozanna [386]

(2x-3)/x^2
if the number is –2
then
[2(-2) - 3] / (-2)^2
= (-4-3)/4
= -7/4

answer is
D. -7/4

4 0

3 years ago