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3 years ago

Six less than a number is negative two? In a equation

Mathematics

1 answer:

Zina [86]3 years ago

3 0

Answer:

$x-6=-2$

Step-by-step explanation:

Let $x$ , be "a number".

6 less, would be $x-6$ . "Is" means equals ( = )

You then can put that together to get your equation.

<em>Hope this helps!!!</em>

You might be interested in

Determine if this is a linearly dependent or independent set: (V, V, V ) where syon V = (1,2,2,-1), V = (4,9,9,-4), v = (5,8,9,-

marishachu [46]

Answer:

This is a linearly independent set.

Step-by-step explanation:

We have these following vectors:

$V_{1} = (1,2,2,-1)$

$V_{2} = (4,9,9,-4)$

$V_{3} = (5,8,9,-5)$

In a set of 3 vectors, if one of these vectors can be written as a linear combination of the 2 other vectors, they are linearly dependent. Otherwise, they are linearly independent.

We can verify this by solving the following system:

$xV_{1} + yV_{2} + zV_{3} = (0,0,0,0)$

If the only solution is $(x,y,z) = (0,0,0)$ , they are L.I. Otherwise, they are L.D.

Solution:

$xV_{1} + yV_{2} + zV_{3} = (0,0,0,0)$

$x(1,2,2,-1) + y(4,9,9,-4) + z (5,8,9,-5) = (0,0,0,0)$

We have the following system of equations:

$x + 4y + 5z = 0$

$2x + 9y + 8z = 0$

$2x + 9y + 9z = 0$

$-x -4y - 5z = 0$

I am going to solve this by the row-reduction of the augmented matrix.

This system has the following augmented matrix:

$\left[\begin{array}{cccc}1&4&5&0\\2&9&8&0\\2&9&9&0\\-1&-4&-5&0\end{array}\right]$

To reduce the first row, i am going to make these following operations:

$L_{2} = L_{2} - 2L_{1}$

$L_{3} = L_{3} - 3L_{1}$

$L_{4} = L_{4} + L_{1}$

So the augmented matrix now is:

$\left[\begin{array}{cccc}1&4&5&0\\0&1&-2&0\\0&1&-1&0\\0&0&0&0\end{array}\right]$

Now I reduce the second row, doing:

$L_{3} = L_{3} - L_{2}$

So the matrix is:

$\left[\begin{array}{cccc}1&4&5&0\\0&1&-2&0\\0&0&1&0\\0&0&0&0\end{array}\right]$

Now we can solve the system:

From the third line, we have that

$z = 0$

From the second line:

$y - 2z = 0$

$y - 2(0) = 0$

$y = 0$

From the first line

$x + 4y + 5z = 0$

$x + 4(0) + 5(0) = 0$

$x = 0$

The only solution for this system is $(x,y,z) = (0,0,0)$ . This means that we have a linearly independent set.

3 0

3 years ago

20 Points! Which ordered pair is the best estimate for the solution of the system of equations?

yan [13]

Answer:

The best estimate for the solution is the ordered pair $(-6.5,-3.5)$

Step-by-step explanation:

we have

$y=\frac{3}{2}x+6$ ------> equation A

$y=\frac{1}{4}x-2$ ------> equation B

we know that

using a graphing tool, the solution of the system of equations is the intersection point both graphs

The intersection point is $(-6.4,-3.6)$

therefore

The best estimate for the solution is the ordered pair $(-6.5,-3.5)$

3 0

3 years ago

In a sale a gameboys are reduced by two fifths. what is the sale price if the original price was 50

vladimir1956 [14]

Answer:

The sale price would be $30.

Step-by-step explanation:

2/5 is like saying 20/50. If you take 50 and subtract 20 from that, you will be left with 30.

4 0

3 years ago

A hot air balloons height varies directly as the balloons ascents the time in minutes. A hot air balloon rises at 350 feet in fi

SVEN [57.7K]

Answer:

h α t

h = kt

k = h/t

350 = k5

350/5 = k

k = 70

Step-by-step explanation:

Given that :

Ballon height varies directly as the Ascent time in minutes

Height of hot air Ballon rises 350 feets in 5 seconds

Expressing as a direct variation :

Let height of Ballon = h

Time it takes to rise = t

h α t

h = kt

k = h/t

350 = k5

350/5 = k

k = 70

8 0

4 years ago

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation o

GREYUIT [131]

Answer:

And then we can conclude that the middle 75% values of her lap times are from a=126.835 to b=132.585

Step-by-step explanation:

1) 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".

2) Solution to the problem

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

$X \sim N(129.71,2.5)$

Where $\mu=129.71$ and $\sigma=2.5$

Since we want the middle 75% values then on tha tails we need 1-0.75 =0.25 or 25% of the data and since the distribution is symmetric we need 12.5 % of the values on each tail.

For this part we want to find a value a and b, such that we satisfy this condition:

$P(X>b)=0.125$ (a)

$P(X$ (b)

We can use the z score formula in order to find the value a and b given by:

$z=\frac{x-\mu}{\sigma}$

As we can see on the figure attached the z value that satisfy the condition (b) with 0.125 of the area on the left and 0.875 of the area on the right it's z=-1.15. On this case P(Z<-1.15)=0.125 and P(z>-1.15)=0.875

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-1.15$

And if we solve for a we got

$a=129.71 -1.15*2.5=126.835$

So the value of height that separates the bottom 12.5% of data from the top 87.5% is 126.835.

As we can see on the figure attached the z value that satisfy the condition (b) with 0.875 of the area on the left and 0.125 of the area on the right it's z=1.15. On this case P(Z<1.15)=0.875 and P(Z>1.15)=0.125

If we use condition (b) from previous we have this:

$P(X>b)=P(\frac{X-\mu}{\sigma}>\frac{b-\mu}{\sigma})=0.125$