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3 years ago

14

If 5n - 3 = 7n – 5, then n= A -4 BO o D 6

1 answer:

ch4aika [34]3 years ago

6 0

Answer:

The value of n is 1

Step-by-step explanation:

Given the expression $5n-3= 7n-5$

In other to solve for n we have to perform a series of step wise operations as follows

collecting like terms we have

$5n-7n= -5+3$

$-2n= -2\\$

The negative signs will council out on both sides we have

$2n= 2\\$

Dividing both sides by 2 we have

n= $\frac{2}{2}$

$n=1$

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I don't understand the question. Help please?<br><br>Find the value of X<br><br>Find the value of Y

slava [35]

Let's start with x... Since angle AOE is a 90 degree angle, then we know the supplementary angle EOB is also 90 degrees. The 2 angles that make up angle EOB are given to us as expressions. Added together the must equal 90 degrees...

(x+8) + (2x-8) = 90
3x = 90
x = 30

Now if we look at y, we see it is an opposite angle from angle DOB. Because it is opposite, it is also congruent... so it has to be equal to angle DOB... and since angle DOB is 2x - 8, we can substitute x with the answer we found in the last step, 30, to find the angle.

2x - 8= y
2(30) - 8 = y
60 - 8 = y
y = 52 degrees

Since angle DOB equals 52 degrees, then y = 52 degrees

x = 30 degrees
y = 52 degrees

*Note, you can also find the value of angles GOF and EOD by plugging x (30) into the expressions.

4 0

4 years ago

Given the set points K+1:(-1,8),(1,0) and (2,5), find the quadratic polynomial interpolate

Sauron [17]

Answer:

The interpolating polynomial is $p(x) = 1-4x+3x^2$ .

Step-by-step explanation:

We want to find a quadratic polynomial $p(x)$ such that $p(-1)=8$ , $p(1)=0$ and $p(2)=5$ . In order to do this let us write $p(x) = a_0+a_1x+a_3x^2$ .

Now, evaluating the polynomial in the points -1, 1 and 2 we get

$\begin{cases} 8 = p(-1) &= a_0-a_1+a_2\\ 0 = p(1) &= a_0+a_1+a_2\\ 5 = p(2) &= a_0+2a_1+4a_2\end{cases}$

This relations give us a linear system of equations:

$\begin{cases} 8 &= a_0-a_1+a_2\\ 0 &= a_0+a_1+a_2\\ 5&= a_0+2a_1+4a_2\end{cases}$

where the $a_0$ , $a_1$ and $a_2$ are the unknowns.

The augmented matrix of the system is

$\begin{pmatrix}1 & -1 & 1 & 8\\ 1 & 1 & 1 & 0\\ 1 & 2 & 4 & 5\end{pmatrix}$

In this matrix it is easy to eliminate the 1's of the first column and get

$\begin{pmatrix} 1 & -1 & 1 & 8\\ 0 & 2 & 0 & -8\\ 0 & 3 & 3 & -3\end{pmatrix}$

From this matrix we can find the values of each unknown. Notice that the second row gives us $2a_2=-8$ that yields $a_1=-4$ .

Then, the third row means $3a_1+3a_2=-3$ that gives $-12+3a_2=-3$ . So, $a_2=3$ .

Finally, the first row is $a_0-a_1+a_2=8$ and substituting is $a_0+7=8$ that yields $a_0=1$ .

Therefore, the interpolating polynomial is

$p(x) = 1-4x+3x^2$ .

8 0

3 years ago

Nolan has 4 times as many pens as Fiona, and Fiona has 6 times as many pencils as

denis-greek [22]

Answer:

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5 0

3 years ago

Find the slope of the line containing the pair of points.<br> (-10,6) and (-11,7)

denis-greek [22]

Answer:

Step-by-step explanation:

(-10,6)(-11,7)

Slope is -1

6 0

3 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

levacccp [35]

From given picture we can see that X is mid point of line PQ

So PQ=2PX

From given picture we can see that Y is mid point of line PR

So PR=2PY

Now consider triangles PRQ and PYX

Sides PQ and PX has same ratio as of sides PR and PY (as calculated above)

angle XPY= angle QPR (common angle)

Hence triangles PRQ and PYX are similar.

We know that ratio of the sides of similar triangles is always equal so we can write:

$\frac{PQ}{PX} = \frac{QR}{XY}$

Plug the given values QR=8 and PQ=2PX

$\frac{2PX}{PX} = \frac{8}{XY}$

$\frac{2}{1} = \frac{8}{XY}$

$2 = \frac{8}{XY}$

$XY = \frac{8}{2}$

$XY = 4$

Hence final answer is XY = 4 units.

7 0

4 years ago

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