Answers:
x = 25 in
y = 16.3°
z = 73.7°
Explanation:
Part (a): getting the value of x:
Since the given triangle is a right-angled triangle, we can get the value of x which is the hypotenuse of the triangle using the Pythagorean theorem as follows:
(hypotenuse)² = (side1)² + (side2)²
x² = (24)² + (7)²
x² = 625
x = √625
either x = 25 in ..........> accepted
or x = -25 in .........> rejected as side length cannot be negative.
Based on the above:
x = 25 in
Part (b): getting the value of y:
Since the given triangle is a right-angled triangle, therefore, special trigonometric functions can be applied.
These functions are as follows:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
In the given, we have:
θ = y
opposite side = 7 in
adjacent side = 24 in
Apply in the tan formula:
tan y = 7/24
y = 16.3° to the nearest tenth
Part (c): getting the value of z:
This can be solved in two ways:
Solution 1: Using angles
Sum on internal angles in a triangle is 180
90 + 16.3 + z = 180
z = 73.7°
Solution 2: Using special trig functions:
We have θ = z
opposite side = 24 in
adjacent side = 7 in
tan z = 24/7
z = 73.7° to the nearest tenth
Hope this helps :)
Answer:
18/5
Step-by-step explanation:
4−
2
5
=
4
1
−
2
5
=
4
1
+
−2
5
=
20
5
+
−2
5
=
20+−2
5
=
18
5
(Decimal: 3.6)
I am assuming that your function is

due to the fact you did not write x-1
the domain is the numbers you can use for x without getting wierd results
wierd results happen when you divide by 0 or take the square root of a negative number
the arean't any division signs so no division by 0
but there is a square root sign
so the part under the square root must be greater than or equal to 0
find where it is equal to 0
0=x+6
minus 6
-6=x
when x is smaller than -6, we get undefined because we get square root of a negative
so the domain (numbers you can use for x) is D={x|x≥-6} or basically x≥-6
f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. FYI: Different textbooks have different interpretations of the reference "standard form" of a quadratic function.
The standard form of a parabola is y=ax2++bx+c , where a≠0 . The vertex is the minimum or maximum point of a parabola. If a>0 , the vertex is the minimum point and the parabola opens upward. If a<0 , the vertex is the maximum point and the parabola opens downward.