Hi! Sorry, it would've taken too long to type out, so I wrote it and have the attachment. Good luck!
Step-by-step explanation:
x = one odd number
the second odd number is (x+2), as both are consecutive.
so,
x × (x + 2) = 195
x² + 2x = 195
x² + 2x - 195 = 0
the formula to solve this is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -195
x = (-2 ± sqrt(4 - 4×1×-195))/(2×1) =
= (-2 ± sqrt(4 + 4×195))/2 = (-2 ± sqrt(784))/2 =
= (-2 ± 28)/2 = -1 ± 14
x1 = -1 + 14 = 13
x2 = -1 - 14 = -15 which is invalid as the numbers are positive.
so, the two numbers are 13 and 15.
Nearest hundred thousand: 400,000
Nearest thousand: 422,000
hope this helps x
(3/4)x+(3/2)x=9/4
(3/4)x+(3.2/2.2)x=9/4
(3/4)x+(6/4)x=9/4
3x+6x=9
9x=9
x=1
<u>Let's consider the facts at hand</u>:
- By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
- ∠BEC = ∠DFC
- Sides BE = DF
<u>Based on the diagram, triangles BCE and triangles DCF are similar</u>
⇒ based on the Angle-Angle theorem
⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC
⇒ the two triangles are similar
Hope that helps!
<em>Definitions of Theorem I used:</em>
- <u><em>Vertical Angle Theorem: </em></u><em>opposite angles of two intersecting lines must be equal</em>
- <u><em>Angle-Angle Theorem:</em></u><em> if two angles of both triangles are equal, then the given triangles must be similar</em>
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