Given: <span>9=(1/27)^(a+3)
[Note: Please review rules of PEMDAS.
The question posted as is means
</span><span>9=[(1/27)^a]+3 which is probably not what you mean. It has been interpreted with (a+3) as the exponent, please check.]
</span><span>
Need to find value of a that satisfies above.
We will first isolate a in order to solve for its value.
</span>9=(1/27)^(a+3)
Switch unknown to the left
(1/27)^(a+3) = 9
Since both 27 and 9 are powers of 3, we can take log to base 3.
take log (base 3) on both sides, applying rule of logarithm of exponents.
(a+3)log_3(1/27)=log_3(9)
(a+3)log_3(3^(-3))=log_3(3^2)
Apply definition of logarithm [log_a(a^k)=k]
(a+3)(-3)=2
(a+3)=-2/3
a=-3 2/3=-11/3
Check: (1/27)^(-11/3+3)=(1/27)^(-2/3)=(3^(-3))^(-2/3)=3^(-3(-2/3))=3^2=9 ok
Answer: a=-11/3 or a=-3.667 (approx.)
Answer:
angle BCD=58 degree
angle ACD=32 degree
angle DAC=58 degree
angle CDB=90 degree
Step-by-step explanation:
Hope it helps you!!
Answer: 15m
Step-by-step explanation:
Since 1cm is to 5m, just multiply 3 by 5 and you will get 15.
If it is ....
The coefficient of x² is (( 3 ))
& the coefficient of x is (( -2 ))
_________________________________
If it is .....
The coefficient of x² is (( zero 0 ))
& the coefficient of x is (( 1 ))
<u>vertex</u>
y = 3(x - 2)² - 4
y = 3((x - 2)(x - 2)) - 4
y = 3(x² - 2x - 2x + 4) - 4
y = 3(x² - 4x + 4) - 4
y = 3(x²) - 3(4x) + 3(4) - 4
y = 3x² - 12x + 12 - 4
y = 3x² - 12x + 8
3x² - 12x + 8 = 0
x = <u>-(-12) +/- √((-12)² - 4(3)(8))</u>
2(3)
x = <u>12 +/- √(144 - 96)</u>
6
x = <u>12 +/- √(48)
</u> <u> </u> 6<u>
</u>x =<u> 12 +/- 6.93</u>
<u /> 6
x = 2 +/- 1.155
x = 2 + 1.155 x = 2 - 1.155
x = 3.155 x = 0.845
y = 3x² - 12x + 8
y = 3(3.155)² - 12(3.155) + 8
y = 3(1.334025) - 3.786 + 8
y = 4.002075 - 3.786 + 8
y = 0.216075 + 8
y = 8.216075
(x, y) = (3.155, 8.216075)
or
y = 3x² - 12x + 8
y = 3(0.845)² - 12(0.845) + 8
y = 3(0.714025) - 10.14 + 8
y = 2.142075 - 10.14 + 8
y = -7.857925 + 8
y = 0.142675
(x, y) = (0.845, 0.142675)
<u>y-intercept</u>
y = 3x² - 12x + 8
y = 3(0)² - 12(0) + 8
y = 3(0) - 0 + 8
y = 0 - 0 + 8
y = 0 + 8
0 = -y + 8
y = 8
(x, y) = (0, 8)
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<u>vertex</u>
y = 4(x - 5)² = 1
y = 4(x - 5)² - 1
y = 4((x - 5)(x - 5)) - 1
y = 4(x² - 5x - 5x + 25) - 1
y = 4(x² - 10x + 25) - 1
y = 4(x²) - 4(10x) + 4(25) - 1
y = 4x² - 40x + 100 - 1
y = 4x² - 40x + 99
4x² - 40x + 99 = 0
x = <u>-(-40) +/- √((-40)² - 4(4)(99))</u>
2(4)
x = <u>40 +/- √(1600 - 1584)</u>
8
x = <u>40 +/- √(16)</u>
8
x = <u>40 +/- 4</u>
8
x = 5 +/- 1/2
x = 5 + 1/2 x = 5 - 1/2
x = 5 1/2 x = 4 1/2
y = 4x² - 40x + 99
y = 4(5 1/2)² - 40(5 1/2) + 99
y = 4(30 1/4) - 220 + 99
y = 121 - 220 + 99
y = -99 + 99
y = 0
(x, y) = (5 1/2, 0)
or
y = 4x² - 40x + 99
y = 4(4 1/2)² - 40(4 1/2) + 99
y = 4(20 1/4) - 180 + 99
y = 81 - 180 + 99
y = -99 + 99
y = 0
(x, y) = (4 1/2, 0)
<u>y-intercept</u>
y = 4x² - 40x + 99
y = 4(0)² - 40(0) + 99
y = 4(0) - 0 + 99
y = 0 - 0 + 99
y = 0 + 99
y = 99
(x, y) = (0, 99)
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<u>vertex</u>
y = (x - 1)² = 2
y = (x - 1)² - 2
y = ((x - 1)(x - 1)) - 2
y = (x² - x - x + 1) - 2
y = x² - 2x + 1 - 2
y = x² - 2x - 1
x² - 2x - 1 = 0
x = <u>-(-2) +/- √((-2)² - 4(1)(-1))</u>
2(1)
x = <u>2 +/- √(4 + 4)</u>
2
x = <u>2 +/- √(8)</u>
2
x = <u>2 +/- 2.83</u>
2
x = 1 +/- 1.415
x = 1 + 1.415 x = 1 - 1.415
x = 2.415 x = 0.415
y = x² - 2x - 1
y = (2.145)² - 2(2.145) - 1
y = 4.60125 - 4.029 - 1
y = 0.57225 - 1
y = 0.42775
(x, y) = (2.415, 0.42775)
or
y = x² - 2x - 1
y = (0.415)² - 2(0.415) - 1
y = 0.172225 - 0.83 - 1
y = -0.657775 - 1
y = -1.657775
(x, y) = (0.415, -1.657775)
<u>y-intercept</u>
y = x² - 2x - 1
y = (0)² - 2(0) - 1
y = 0 - 0 - 1
y = 0 - 1
y = -1
(x, y) = (0, -1)