What is the result when 3/8x + 2 1/5 - 3 1/2x

Dvinal [7]

Answer:

Step-by-step explanation:

The area of a regular polygon is

$A=\frac{1}{2}ap$ where a is the apothem and p is the perimeter. Perimeter is simple: just count the number of sides the polygon has and multiply it by 3 (the length of one side).

p = 3(9) is 27 inches for the perimeter.

We have what we need now to find the area:

$A=\frac{1}{2}(4.1)(27)$ and

$A=\frac{1}{2}( 110.7)$ so

A = 55.35 square inches

5 0

2 years ago

Given right triangle A w/a hypotenuse length of x+4 and a leg of x, and right triangle B, w/ a hypotense length of 3y and a leg

alex41 [277]

Answer:

Value is x=8 and y=4

Step-by-step explanation:

Given : A right triangle 'A' hypotenuse length of x+4 and a leg of x,

and right triangle 'B' hypotenuse length of 3y and a leg length of y+4

To find : For what values of x and y are the triangles congruent by HL?

Solution :

Triangle A,

Hypotenuse: x+4

Leg: x

Triangle B,

Hypotenuse: 3y

Leg: y+4

Since the triangle A and B are congruent so, the sides of triangles are equal.

$x+4=3y$ (Hypotenuse are equal) ..........[1]

and $x=y+4$ (Legs are equal) ..........[2]

Solving the equation of system,

Put the value of x from [2] in [1],

$x+4=3y$

$y+4+4=3y$

$8=2y$

$y=4$

Substitute y in [2],

$x=y+4$

$x=4+4$

$x=8$

Therefore, The value of x=8 and y=4

Verifying for the values of x and y:

Triangle A,

Hypotenuse: x+4=8+4=12

Leg: x=8

Triangle B,

Hypotenuse: 3y=3(4)=12

Leg: y+4=4+4=8

Both hypotenuses and both legs are equal hence they are congruent.

6 0

2 years ago

An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location i

Alexandra [31]

<h3>Answer: D) 1692 miles</h3>

============================================

Explanation:

A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram

Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.
Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.
Plot the points E and F, which are north and south of point B.
Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.

The diagram below shows all of this visually summarized. We have the segments

AB = 550 miles
BC = 483 miles
AC = x miles

And we have these angles

Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)
Angle ABC = 79 degrees (red)
Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)

Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.

------------------------------

Once the diagram is set up, we'll use the law of cosines to find x.

Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.

The interior angles of triangle ABC are

A = 46 degrees
B = 79 degrees
C = 55 degrees

The sides opposite the angles are

a = 483 (opposite angle A)
b = x (opposite angle B)
c = 550 (opposite angle C)

Now we can apply the law of cosines

b^2 = a^2 + c^2 - 2*a*c*cos(B)

x^2 = 483^2 + 550^2 - 2*483*550*cos(79)

x^2 = 434412.180756441

x = sqrt(434412.180756441)

x = 659.099522649229

x = 659

Side AC, or CA, is roughly 659 miles long.

------------

To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)

Distance Traveled = AB + BC + CA

Distance Traveled = 550 + 483 + 659

Distance Traveled = 1692 miles

3 0

2 years ago

Please help me out with this!! No joke answers!

Oxana [17]

Answer:

13 protons

14 neutrons

13 electrons

Step-by-step explanation:

protons and electrons are mostly always the same

7 0

3 years ago

renee saves 30% of every paycheck. his paycheck last week was $560 . how much did renee save last week

IRISSAK [1]

30% of 560.....turn percent to decimal..." of " means multiply
0.30(560) = 168..so last week, Renee saved $ 168

7 0

3 years ago

What is the result when 3/8x + 2 1/5 - 3 1/2x - 4 1/10