Answer:
The three angles of the right-angled triangle are
a = 35°
b = 90°
c = 55°
Step-by-step explanation:
We are given the ratio of angles of a right-angled triangle
a:b:c = 7:18:11
Recall that the sum of interior angles in a right-angled triangle is always 180°
7x + 18x + 11x = 180
36x = 180
x = 180/36
x = 5
a:b:c = 7x:18x:11x
a:b:c = 7(5):18(5):11(5)
a:b:c = 35:90:55
a = 35°
b = 90°
c = 55°
Alternatively:
We are given that the smallest angle is 35°
a = 7x = 35
x = 35/7
x = 5
b = 18x
b = 18(5)
b = 90°
c = 11x
c = 11(5)
c = 55°
Answer:
h(x) = - 4x² + 5
Step-by-step explanation:
To find h(x) = g(2x² + 1), substitute x = 2x² + 1 into g(x)
h(x) = - 2(2x² + 1) + 7
= - 4x² - 2 + 7
= - 4x² + 5
The area of the composite figure is 54. (9 x 6)
Step-by-step explanation:
Write the prime factorization of each term:
9r⁵s = 3² × r⁵ × s
6r⁴s² = 2 × 3 × r⁴ × s²
12r²s = 2² × 3 × r² × s
The greatest common factor will have all the common factors raised to their lowest exponent.
So all three terms have 3, r, and s as factors. The lowest exponent of 3 is 1. The lowest exponent of r is 2. The lowest exponent of s is 1.
GCF = 3 × r² × s
GCF = 3r²s
Factor out the GCF:
9r⁵s + 6r⁴s² − 12r²s
3r²s (3r³ + 2r²s − 4)
Answer:
1/5
Step-by-step explanation:
