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2 years ago

What are the coordinates of one of the vertices of a rectangle when two sides are given by the lines x - 3y = -8 and 3x + y = 6?

Mathematics

1 answer:

Aleonysh [2.5K]2 years ago

5 0

Answer:

(1, 3)

Step-by-step explanation:

x - 3y = -8

3x + y = 6

Isolate a variable in one of the equations:

y = 6 - 3x

Substitute the value of y into the other equation:

x - 3(6 - 3x) = -8

Use distributive property:

x - 18 + 9x = -8

Combine like terms:

10x - 18 = -8

Isolate the variable:

10x = 10

x = 1

Substitute the value of x into any equation:

3(1) + y = 6

3 + y = 6

Isolate the variable:

y = 3

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Elsa's magic wand can cast 53 spells. Her wand can cast 17fewer spells than her sister Anna's wand, which is a little bigger and

Mademuasel [1]

Answer:

Anna's wand can cast 70 spells

Step-by-step explanation:

Elsa's wand can cast 53 spells

her wand casts 17 fewer cells than her sister Anna's

Amount of spells cast by Anna's wand = ?

We write the question down in the form of an equation

$x - 17 = 53$

where $x$ is the amount of spells Anna's wand can cast.

we then proceed to solve by collecting like terms to different sides of the equation. We'll have

$x = 53 + 17$

which leaves us with

$x = 70$

This means that Anna's wand can cast 70 spells.

4 0

2 years ago

Find the determinant of A. A.29 B.2 C.-2 D.13

strojnjashka [21]

Answer:

Step-by-step explanation:

The determinant of a matrix is a special number that can be calculated from a square matrix.

...

To work out the determinant of a 3×3 matrix:

Multiply a by the determinant of the 2×2 matrix that is not in a's row or column.

Likewise for b, and for c.

Sum them up, but remember the minus in front of the b.

7 0

2 years ago

For which value of x is the equation 4x + 24 = 8x + 2x true?

Paha777 [63]

Answer:

x=4

Step-by-step explanation:

4x+24=8x+2x

4x+24=10x

-4x -4x

24=6x

/6 /6

x=4

3 0

2 years ago

The solution to -16 + x = -30 is -14. True False

11111nata11111 [884]

Answer:

false

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

A sample of size 6 will be drawn from a normal population with mean 61 and standard deviation 14. Use the TI-84 Plus calculator.

AVprozaik [17]

Answer:

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X} = 61$

$\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715$

So then is appropiate use the normal distribution to find the probabilities for $\bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is also normal and given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X} = 61$

$\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715$

So then is appropiate use the normal distribution to find the probabilities for $\bar X$

8 0

2 years ago