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DanielleElmas [232]

2 years ago

8

Luis and Victor were both trying to solve the equation 5x = 20. Luis multiplied both sides of the equation by the reciprocal of

5. Victor divided both sides of the equation by 5. Who solved the equation correctly?
A.
Only Luis

B.
Only Victor

C.
Both Luis and Victor

D.
Neither Luis or Victor

1 answer:

Kamila [148]2 years ago

7 0

Answer: B

Step-by-step explanation:

20 divided by 5 =4 and 5x4=20

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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

5 0

3 years ago

Once each day, Erika tracks the depth of the water in her local creek. Her first nine measurements, in inches, are: 16, 15, 13,

solniwko [45]

Answer:

Median = 13

Step-by-step explanation:

We are given the following data:

16, 15, 13, 12, 17, 14, 11, 9, 11

Formula:

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: 9, 11, 11, 12, 13, 14, 15, 16, 17

Median =

$=\dfrac{9+1}{2}^{th} = 5^{th}\text{ term} = 13$

Thus, the median of the given data is 13.

4 0

3 years ago

Which addition property is demonstrated by this problem?<br><br> 23 + (4 + 3) = (23 + 4) + 3

makvit [3.9K]

Answer;
Commutative Property

It is considered commutative when changing the order of the operands does not change the result.

(a brainliest would be appreciated)

8 0

3 years ago

Identify an equation in point-slope form for the line perpendicular to

Zigmanuir [339]

Answer:

perp. : 1/3= m

y + 8 = 1/3(x -4): answer is c

y + 24/3 = (1/3)x - 4/3

y = (1/3)x - 28/3

Step-by-step explanation:

answer is c

8 0

3 years ago

1. Define a variable and write each phrase as an algebraic expression.

katen-ka-za [31]

Answer:

6x=6c?

30-=ml

Step-by-step explanation:

I'm sorry if i got this wrong

7 0

3 years ago