Answer : 23.77
Pythagoras theorem states that in any right angled triangle , the sum of squares of base and perpendicular is equal to the square of hypotenuse .
- Here in the given figure , hypotenuse is 30.5 and perpendicular is 19.1 .
![\sf\longrightarrow (base)^2+(perpendicular)^2=hypotenuse^2\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%28base%29%5E2%2B%28perpendicular%29%5E2%3Dhypotenuse%5E2%5C%5C)
- Substituting the respective values,
![\sf\longrightarrow x^2 +(19.1)^2 = (30.5)^2 \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%2B%2819.1%29%5E2%20%3D%20%2830.5%29%5E2%20%5C%5C)
![\sf\longrightarrow x^2 + 364.81 = 930.25 \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%2B%20364.81%20%3D%20930.25%20%5C%5C)
![\sf\longrightarrow x^2 = 930.25 -364.81\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%3D%20930.25%20-364.81%5C%5C)
![\sf\longrightarrow x^2 = 565.44\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%3D%20565.44%5C%5C)
![\sf\longrightarrow x=\sqrt{565.44} \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%3D%5Csqrt%7B565.44%7D%20%5C%5C)
![\sf\longrightarrow \underline{\boxed{\bf base (x) = 23.77 }} \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%5Cunderline%7B%5Cboxed%7B%5Cbf%20base%20%28x%29%20%3D%2023.77%20%7D%7D%20%5C%5C)
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Factorise 4b² + 16b ⇒ 4b(b+4)
expand (a-1)(a-2) ⇒ a(a-2) - 1(a-2) ⇒ a² - 2a - 1a + 2 ⇒a² - 3a + 2
factorise x² + 8x + 7 ⇒(x + 1) (x + 7)
evaluate y⁶ / y² ⇒ y * y * y * y * y * y / y * y = y⁴
if x = -1 and y = 5, find z when z = x² + 2y² ;
z = -1² + 2(5²) ⇒ 1 + 2(25) ⇒1 + 50 = 51
Make x the subject: y = 4x - 3
y = 4x - 3
<u>+3 +3</u>
3 + y = 4x
<u>÷4 ÷4 </u>
(3+y)/4 = x
Answer:
x=75
Step-by-step explanation:
if the polygons are similar
40 30
------- = --------
100 x
using cross products
40x = 30*100
40x =3000
divide by 40
40x/40 = 3000/40
x =75
D. 8
you cross multiply. so 14x4=56
then divide 56 by 7 to get 8