Answer:
27/ (4 x^6 y^8)
Step-by-step explanation:
4(3x^2y^4)^3/(2x^3y^5)^4
expand
4 (3^3 x^2^4 y^4^3) / (2^4 x^3^4 y^5^4)
power of the power rule , exponents to the power are multiplied
4 (3^3 x^(2*4) y^(4*3) / (2^4 x^(3*4) y^(5*4))
4 (27 x^(8) y^(12) / (16 x^(12) y^(20))
put like terms over each other
4 * (27/16) * x^8/x*16 * y^12/y^20
when dividing exponents , we subtract the powers
27 * 4/16 * x^ (8-14) * y^ (12-20)
27* 1/4 * x^(-6) * y^ (-8)
27/4 * x^(-6)(y)^ (-8)
negative terms go to the denominator
27/ (4 x^6 y^8)
<span>A-2b=2
A-b=6
</span>
<span>A-2b=2
-2(A-b=6)
-2A+2b= -12
A-2b=2
-2A+2b = -12
-------------------
-A = -10
-A/-1 = -10/-1
A = 10
a-b=6
10 - b = 6
10-10-b = 6 -10
-b = -4
-b/-1 = 14/-1
b= 4
Check
a - 2b =2
10 - 2(4) =2
10 - 8 = 2
2=2
</span>
Answer:Partial quotients Paloma should show in her work are B) 30,10,1.
Step-by-step explanation:
Given : Paloma dividing 1292 (dividend) by 31 (divisor) using partial quotients.
so the easy multiples of 31 are as 31×2=62 ,31×3=93,31×10=310....so on
if she uses 30 as her first partial quotient then 31×30=930, so after subtracting 930 from 1292 we get 362 as new dividend then 31×10=310 is the easiest multiple of 31 so that 362-310=52 as new dividend ,then 31×1=31 subtracting this from 52 gives 52-31=21 which is the remainder.
Therefore, Partial quotients Paloma should show in her work are 30,10 and 1.
3 RIGHT TRIANGLES
1 big right triangle is divided into 2 smaller ones. Medium
and small.
<span> a.How far is the spot on the beach from the parking lot? </span>
Medium triangle: long leg = 32 m ; short leg = x
Small triangle: long leg = x ; short leg = 18m
32/x = x/18
32*18 = x*x
576 = x²
√576 = √x²
24 = x
Parking lot to the beach is 24 meters.
<span>b. How far will he have to walk from the parking lot to get to the refreshment stand?</span>
Use Pythagorean theorem:
Medium triangle: long leg = 32 m ; short leg = 24 m ;
hypotenuse = ?
32²+ 24² = c²
1024 + 576 = c²
1600 = c²
√1600 = √c²
40 m = c
Parking lot to refreshment stand is 40 meters.
Answer:
x=
Step-by-step explanation:
47(218 x+12 ) =−2(17 −528 x)
Simplify 47(218 x+12 ) : 327(21x+4) 327(21x+4) =−2(17 −528 x)
Multiply both sides by 7(21x+4)
327(21x+4) · 7(21x+4)=−2(17 −528 x)· 7(21x+4)
Simplify, 32=−14(17 −528 x)(21x+4)
Solve 32=−14(17 −528 x)(21x+4): x=32+4√589105 , x=32−4√589105 x=32+4√589105 , x=32−4√589105
