Answer:
<h2>
36 units</h2><h2>
</h2>
Step-by-step explanation:
perimeter of the given triangle = 16 + slant (10) + slant (10)
= 36 units
(see image below)
Absolute value is simply the distance from zero on a number line. -44 is 44 away from zero, so the absolute value of -44 is
44
Answer:
Step-by-step explanation:
Given the simultaneous equation 2p - 3q = 4 and 3p + 2q = 9, to get the value of p and q we will use elimination method.
2p - 3q = 4 ...................... 1 * 3
3p + 2q = 9 ..................... 2 * 2
Multiplying equation 1 by 3 and 3 by 2:
6p - 9q = 12
6p + 4q = 18
Subtracting both equation
-9q-4q = 12-18
-13q = -6
q = -6/-13
q = 6/13
Substituting q = 6/13 into equation 2
2p - 3(6/13) = 4
2p - 18/13 = 4
2p = 4+18/13
2p = (52+18)/13
2p = 70/13
p = 70/26
p = 35/13
<em>Hence p = 35/13 and q = 6/13</em>
<em></em>
<em>b) </em>If if 223ₓ = 87 find x
Using the number base system and converting 223ₓ to base 2 will give us;
223ₓ = 2*x² + 2*x¹ + 3*x⁰
223ₓ = 2x²+2x+3
Substituting back into the equation, 2x²+2x+3 = 87
2x²+2x+3-87 = 0
2x²+2x-84 = 0
x²+x-42 = 0
On factorizing:
(x²+6x)-(7x-42) = 0
x(x+6)-7(x+6) = 0
(x+6)(x-7) = 0
x+6 = 0 and x-7 = 0
x = -6 and 7
<em>Hence the value of x is 7 (neglecting the negative value)</em>
Answer:
principal (p)=$35000
time(t)=8years
rate ( r)=7%
Step-by-step explanation:
- compounded amount(c.a)=p((1+r/100)^t )=$35000((1+7/100)^8)=$60136.5
- compound interest gain=$60136.5-$35000=$25136.5
- Karl gain interest in 1 year=$35000((1+7/100)-1)=$2450
- gain % in 1 year=$2450/$25136.5×100%=9.74%
