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4 years ago

Which equation can pair with x-y=-2 to create a consistent and dependent system?

Mathematics

1 answer:

MrRissso [65]4 years ago

3 0

See the explanation

<h2>Explanation:</h2>

A system that has one or infinitely many solutions is called <em>consistent. </em>If an equation in a system tells us no new information then the equations of the system are <em>dependent. </em>In other words, to find an equation that creates a consistent and dependent system with the given equation we have to get the same line:

The given line is:

$x-y=-2$

If we multiply both sides of the equation by a constant we will have the same line when plotting, therefore let's multiply by 3:

$3(x-y)=3(-2) \\ \\ 3x-3y=-6$

So a system of two linear equation that is consistent and dependent is:

$\left \{ {{x-y=-2} \atop {3x-3y=-6}} \right.$

<h2>Learn more:</h2>

Graph of lines: brainly.com/question/14434483#

#LearnWithBrainly

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Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.

DaniilM [7]

(a) Data with the eight day's measurement.

Raw data: [60,58,64,64,68,50,57,82],

Sorted data: [50,57,58,60,64,64,68,82]

Sample size = 8 (even)

mean = 62.875

median = (60+64)/2 = 62

1st quartile = (57+58)/2 = 57.5

3rd quartile = (64+68)/2 = 66

IQR = 66 - 57.5 = 8.5

(b) Data without the eight day's measurement.

Raw data: [60,58,64,64,68,50,57]

Sorted data: [50,57,58,60,64,64,68]

Sample size = 7 (odd)

mean = 60.143

median = 60

1st quartile = 57

3rd quartile = 64

IQR = 64 -57 = 7

Answers:

1. The average is the same with or without the 8th day's data. FALSE

2. The median is the same with or without the 8th day's data. FALSE

3. The IQR decreases when the 8th day is included. FALSE

4. The IQR increases when the 8th day is included. TRUE

5. The median is higher when the 8th day is included. TRUE

6 0

3 years ago

An architectural engineer is designing a parabola dome that will be 200 feet in diameter with a max height of 50 feet. find the

il63 [147K]

Answer:

y = -0.005x² + 50

Step-by-step explanation:

The diameter is 200 feet, so the parabola has roots at (-100, 0) and (100, 0). The maximum height is 50, so the vertex of the parabola is at (0, 50).

Using vertex form of a parabola:

y = a (x − h)² + k

y = a (x − 0)² + 50

y = ax² + 50

Plugging in either root:

0 = a (100)² + 50

a = -0.005

y = -0.005x² + 50

5 0

3 years ago

PLEASE HELP ME If 0 < z ≤ 90 and sin(9z − 1) = cos(6z + 1), what is the value of z? z = 3 z = 4 z = 5 z = 6

Burka [1]

Answer:

z = 6

Step-by-step explanation:

We know that ...

sin(x) = cos(90 -x)

Substituting (9z-1) for x, this is ...

sin(9z -1) = cos(90 -(9z -1))

But we also are given ...

sin(9z -1) = cos(6z +1)

Equating the arguments of the cosine function, we have ...

90 -(9z -1) = 6z +1

90 = 15z . . . . . . . . . add (9z-1) to both sides

6 = z . . . . . . . . . . . . divide by 15

_____

<em>Comment on the graph</em>

The attached graph shows 5 solutions in the domain of interest. These come from the fact that the relation we used is actually ...

sin(x) = cos(90 +360k -x) . . . . . for any integer k

Then the above equation becomes ...

90 +360k = 15z

6 +24k = z . . . . . . . . . for any integer k

The sine and cosine functions also enjoy the relation ...

sin(x) = cos(x -90)

sin(9z -1) = cos(9z -1 -90) = cos(6z +1)

3z = 92 . . . . . equating arguments of cos( ) and adding 91-6z

z = 30 2/3

6 0

3 years ago

You charged 1,000 on your credit card for Christmas presents. Your credit card company charges you 26% annual interest, compound

Grace [21]

Answer:

94 months

Step-by-step explanation:

You can use the amortization formula for this.

A = P(r/12)/(1 -(1 +r/12)^(-n))

A is the monthly payment; P is the principal amount; r is the annual interest rate, and n is the number of months.

Filling in the numbers, we can solve for n:

25 = 1000(0.26/12)/(1 -(1+0.26/12)^-n)

Multiplying by the denominator and dividing by 25, we have ...

1 -(1+0.26/12)^-n = 1000(0.26)/(12(25)) = 13/15

Subtracting 13/15 and adding (1+0.26/12)^-n gives ...

2/15 = (1+0.26/12)^-n

Taking logs turns this into a linear equation:

log(2/15) = -n·log(1+0.26/12)

n = log(15/2)/log(1+0.26/12) = 93.999

It would take 94 months, or 7 years 10 months, to pay off the balance.

_____

Your total of payments would be $2,350.

3 0

3 years ago

10x+2/2=4x+.25 help please

d1i1m1o1n [39]

Answer:

x= 0.125

Step-by-step explanation:

4 0

3 years ago