First to answer and is correct gets brainliest

Why is -a² is always negative (a ≠ 0) and why is (-a)² is always positive?

hjlf

$-a^2=(-1)\cdot a\cdot a$

Regardless of the sign of $a$ , we have $a\cdot a=a^2\ge0$ (never negative). But multiplying by -1 makes it negative.

On the other hand,

$(-a)^2=((-1)\cdot a)^2=(-1)^2\cdot a^2=1\cdot a^2=a^2$

which can never be negative for real $a$ .

6 0

3 years ago

Solve the system using substitution: y + 8x = 10 and 2y - 4x = 40

exis [7]

Answer:

Hence x = -1 and y = 18

Step-by-step explanation:

Given the system of equations

y + 8x = 10... 1

2y - 4x = 40 ... 2

From 1; y = 10-8x

Substitute into 2;

2(10-8x) - 4x = 40

20 - 16x - 4x = 40

20 - 20x = 40

-20x = 40 - 20

-20x = 20

x = -1

Recall that y = 10-8x

y = 10 - 8(-1)

y = 10 + 8

y = 18

Hence x = -1 and y = 18

4 0

3 years ago

At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A

NeTakaya

Answer:

Part A

The most correct option is;

b. y = 128(0.989)x + 72

Part B

Ella can drink the tea after 7:22

Step-by-step explanation:

Here we have the temperature variation with time given in an exponential equation as follows;

Let the temperature at time x (in minutes) = y

Therefore, y = a × mˣ + b

Where:

b = Shift of the curve or the limit value of the decreasing exponential function as x → ∞

When y = 200, x = 0

Therefore. 200 = a × m⁰ + c = a + c

We note that c is the shift of the graph, the value upon which temperature increases = final temperature = 72°F

Hence a = 200 - 72 = 128°F

When y = 197, x = 2 minutes

Therefore, 197 = 128·m² + 72 =

m² = (197 - 72)/128 = 125/128

m = √(125/128) = 0.98821

Hence the exponential equation of cooling is presented in the following equation;

y = 128 × (0.98821)ˣ + 72

Therefore, the most correct option is b. y = 128(0.989)x + 72

Part B

When the temperature is 172°F we have;

172 = 128 × (0.989)ˣ + 72

∴ (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32

log(0.989)ˣ = log(25/32)

x·log(0.989) = log(25/32)

x = log(25/32)/log(0.989) = 22.32 minutes

Hence Ella can drink the tea after 7:22.

6 0

3 years ago

-8xc = 1 solve for x

Nastasia [14]

Answer:

[-8c]⁻¹ = x

Step-by-step explanation:

-8xc = 1

____ ___

-8c -8c

$x = - \frac{1}{8c} \\ \\ or \\ \\ x = ({ -8c})^{-1}$

This, according to the Negative Exponential Rule [Reverse], is how you write this as a rational exponent. You bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM POSITIVE TO NEGATIVE:

b⁻ⁿ = 1\bⁿ

I am joyous to assist you anytime.

3 0

3 years ago

How to simplify this

algol [13]

To simplify this, you would have to turn b^-2 into a positive exponent.
To do this, we have to flip b^-2, which would get rid of the negate from the exponent: -2

3a^4 b^-2 c^3 / b^-2

Then we get the answer:

3a^4 c^3
------------
b^-2

I have a picture to clarify!
I hope this helped, let me know if you don't understand! ^.^

6 0

3 years ago