Answer:
x = 23 degrees
Step-by-step explanation:
Supplementary angles add up to 180 degrees. Thus, 3x - 17 degrees plus al 5x + 21 deg must equal 180 degrees.
Combining like terms, we get 8x - 4 = 180, or 8x = 184.
Dividing both sides by 8 yields x = 184/8 = 23 = x (measured in degrees)
Part A)<span>In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
we know that
</span>cos 45°=√2/2
[he length of the hypotenuse]=11/cos 45-----------> 11/(√2/2)----> (11*2)/√2
=22/√2-------> 11√2 in
the answer Part A) is 11√2 in
Part B) <span>What is the exact value of sin 45° ?
</span>
we know that
sin 45°=11/(11√2)-------> 1/√2---------> (1/√2)*(√2/√2)-----> √2/2
the answer part b) is √2/2
Part C)
<span>What is the area of a regular hexagon with a side length of 4 m?
we know that
</span>In case of a regular hexagon <span> each of the six triangles that are formed by connecting its center with all six vertices is an equilateral triangle with a side equaled to 4 m.
The area of this hexagon is six times greater than the area of such a triangle
</span>
In an equilateral triangle with a side d<span>
the altitude </span>h can be calculate from the Pythagorean Theorem as
h²=d²−(d/2)²=(3/4)d²
<span>Therefore,
</span><span>h=d<span>√3/2
</span></span><span>Area of such a triangle is
</span>A=d*h/2------------> d²*√3/4
From this the area of the regular hexagon with a side d<span> is
</span>S=6*A----------> d²3√3/2
for d=4 m
S=4²3√3/2------> 24√3 m²------------> 41.57 m²
the answer Part C) is 41.57 m²
Part D) <span>In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
</span>[he length of the hypotenuse]=5/sin 30--------> 5/(1/2)---------> 10 cm
the answer part D) is 10 cm
To multiply whole numbers and fractions, multiply the numerator by the whole number. Example: 1/3×4= 4/3=1 1/3
The number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is 924, 000 ways
<h3>How to determine the combination</h3>
Note that the formula for combination is given as;
Combination = 
From the information we have that;
There are 28 questions in the pool
The test should have a total of 10 questions;
6 difficult , 10 average and 12 easy questions
We are asked to determine the combination of;
3 difficult questions
4 average questions
3 easy questions
6C3 = 
6C3 = 
6C3 = 20
10C4 = 
10C4 = 
10C4 = 210
12C4 = 
12C4 = 220
The number of ways of constructing the questions is
= 20 × 210 × 220
= 924, 000 ways
Thus, the number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is 924, 000 ways
Learn more about combination here:
brainly.com/question/4658834
#SPJ1
Answer:
<h2>A. y = 5</h2>
Step-by-step explanation:
A horizontal line has an equation: y = a (a - any real number).
Each point on a horizontal line y = a, has coordinates (x, a) (x - any real number).
We have the point (-7, 5) → y = 5
