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3 years ago

Let x^2+10x=6.

Mathematics

2 answers:

wariber [46]3 years ago

8 0

Answer:

x^2 + 10x + 25 = 31

Step-by-step explanation:

x^2 + 10x + (10/2)^2 = 6 + 25

x^2 + 10x + 25 = 6 + 25

x^2 + 10x + 25 = 31

The first step requires a bit of explanation. The way to complete the square is to take 1/2 the linear term (10x) and square it

1/2 10 = 5

5 squared = 25

That number must be added to the right side to maintain equality.

Alex17521 [72]3 years ago

7 0

Answer:

x² + 10x + 25 = 31

Step-by-step explanation:

To complete the square use half the x coefficent (10/2 = 5)

and square it (5² = 25)

Then add it to both sides

x² + 10x + 25 = 6 + 25

x² + 10x + 25 = 31

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Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates

nika2105 [10]

We would need to figure out the gradient of each "pair", as provided in the image.

The equation of the gradient is found by,

m = $\frac{ y_{2 } - y_{1 } }{ x_{2 } - x_{1 } }$

Parallel lines mean they have the same gradient
Perpendicular lines will follow the formula $m_{1 } * m_{2 } = -1$
"None" will apply to those that do not follow either.

Now we calculate the gradient of the pairs given to us by substituting the x and y values.

RS = $\frac{2-5}{8-(-1) }$
= $-\frac{1}{3}$

TU = $\frac{-2 - 5}{-4 -5}$
= $\frac{7}{9}$

Therefore, the "pair" RS and TU will be NONE.

ST = $\frac{5 - 2}{5-8}$
= -1

RU = $\frac{-2 -5}{-4 -(-1) }$
= $\frac{7}{3}$

Therefore, the "pair" ST and RU is also NONE.

Hope this helped! Feel free to ask me if there's any part of the working you don't understand :)

8 0

4 years ago

Read 2 more answers

A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The

Feliz [49]

Answer:

$\frac{11}{12}\pi r^{2}h\ units^{3}$

Step-by-step explanation:

we know that

Te volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2}h$

we have

$r=(r/2)\ units$

substitute

$V=\frac{1}{3}\pi (r/2)^{2}h$

$V=\frac{1}{12}\pi r^{2}h$

Te volume of the cylinder is equal to

$V=\pi r^{2}h$

we know that

To find the volume of the space remaining in the cylinder after the cone is placed inside it, subtract the volume of the cone from the volume of cylinder

$\pi r^{2}h-\frac{1}{12}\pi r^{2}h=\frac{11}{12}\pi r^{2}h\ units^{3}$

5 0

3 years ago

Use substitution to solve the following system of equations. -2x + 4y = -18 AND x = y + 3

loris [4]

Answer:

x = -3 ; y = -6

Step-by-step explanation:

x = y + 3

-2x + 4y = -18

-2(y+3) + 4y = -18

-2y -6 + 4y = -18

2y = -12

y = -6

x = -6+3

x = -3

4 0

3 years ago

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kobusy [5.1K]

Choosing blue or red: 3 blue + 4 red = 7 marbles
3 blue + 2 green + 4 red + 1 yellow = 10 marbles

Probability blue or red marble: 7/10

Choosing a marble that isn't blue or red: 2 green + 1 yellow = 3 marbles
Total marbles: 3 blue + 2 green + 4 red + 1 yellow = 10 marbles

Probability non-blue or red marble: 3/10

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3 years ago

How to convert improper fractions to a mixed numeral

Deffense [45]

Say for example, you have the improper fraction 18/7
The first step is to find out how many times 7 fits into 18
This looks like flipping the fraction, 7/18 = 2 whole times with 4 parts left over
The 4 left over gets put in front of the original number (7) to give 2 4/7

To check if you have done it correctly, multiply the whole number (2) by the denominator ( 7 ) and then add the numerator.
2 x 7 = 14 + 4 = 18

Hope this helps

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3 years ago

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Let ​x^2+10x=6.

Let x^2+10x=6.