This is a modulus inequality.
First part: when (6x + 2) is positive
6x + 2 < 10
6x < 10 - 2
6x < 8
x < 8/6
x < 4/3
Second part: when (6x + 2) is negative.
-(6x + 2) < 10 Divide both sides of inequality by -1 and change the sign.
(6x + 2) > -10
6x + 2 > -10
6x > -10 - 2
6x > -12 Divide both sides by 6.
x > -12/6
x > -2.
Combined solution: x < 4/3 and x > -2
-2 < x < 4/3.
Graph is a line on the number line between -2 and 4/3.
-2 and 4/3 are excluded from solution.
Amount of water after splash = 25(4/5) = 20L
Amount of water after Tina adds water = 20L + 7L = 27L
Answer:10 over 13 x
Step-by-step explanation: convert the decimal number into a fraction 800-5x divided by 13 over 2
to divided by a fraction , multiply by the reciprocal of that fraction 800-5x x2 over 13
factor out 5 from the expression 5(160-x x2over 13) use the commutative property to reorder the terms 5(160-2over 13x) factor out 1 over 13 from the expression 5x 1 over 13x(2080-2x)factor out 2 from the expression 5x 1 over13 x2(1040-x)use the commutative property to recorder the terms 5*2x 1 over 13x (1040x) calculate the product 10 over 13x(1040-x) solution 10 over 13x (1040-x)
for simplify expression: covert the decimal number into a fraction 800-5x divided by 13 over 2 to divide by a fraction , multiply by the reciprocal of that fraction 800-5x x2 over 13 calculate the product 800- 10 over 13x
solution: 800-10 over 13x so your answer would still be
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
Answer:
61.4
Step-by-step explanation:
64 minus 4.1 percent is 61.376. Rounded to the nearest tenth would be 61.4.