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cestrela7 [59]
2 years ago
14

The quadratic equation x^2 + 3x + 50 = 0 has roots r and s. Find a quadratic equation whose roots are r^2 and s^2.

Mathematics
1 answer:
Stolb23 [73]2 years ago
7 0

Answer:

x^2 + 91x + 2500

-----------------------------------------------------------------------------

x^2 + 3x + 50

(x-r)(x-s)

-> x^2-(r+s)x+rs

rs = 50, r + s = -3

-> (rs)^2 = 2500

(r+s)^2 = 9

-> r^2 + 2rs + s^2 = 9

-> r^2 + 2(50) + s^2 = 9

-> r^2 + s^2 + 100 = 9

-> r^2 + s^2 = -91

(x-r^2)(x-s^2)

-> x^2-(r^2+s^2)x+(rs)^2

-> x^2 - (-91)x + 2500

x^2 + 91x + 2500

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A man is five times as old as his son. Four years ago the man was thirteen times as old as his son.
skad [1K]

Answer:

Age of son = 6 years

Age of man = 5×6 = 30 years

Step-by-step explanation:

<u>GIVEN :-</u>

  • A man is 5 times as old as his son. (In Present)
  • 4 years ago , the man was 13 times as old as his son

<u>TO FIND :-</u>

  • The present ages of the man & his son.

<u>SOLUTION :-</u>

Let the present age of son be 'x'.

⇒ Present age of man = 5x

4 years ago ,

Age of son = (Present age of son) - 4 = x - 4

Age of man = (Present age of man) - 4 = 5x - 4

The man was thirteen times as old as his son. So,

=> 5x - 4 = 13(x - 4)

Now , solve the equation.

  • Open the brackets in R.H.S.

=> 5x - 4 = 13x - 52

  • Take 5x to R.H.S. and -52 to L.H.S. Also , take care of their signs because they are getting displaced from L.H.S. to R.H.S. or vice-versa.

=> 13x - 5x = 52 - 4

=> 8x = 48

  • Divide both the sides by 8

=> \frac{8x}{8} = \frac{48}{8}

=> x = 6

<u>CONCLUSION :-</u>

Age of son = 6 years

Age of man = 5×6 = 30 years

8 0
2 years ago
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Tanzania [10]

Answer:

B. 8

Step-by-step explanation:

6, 15, 7, 5, 11, 11, 8

5, 6, 7, 8, 11, 11, 15

The middle number is 8.

4 0
3 years ago
Read 2 more answers
Is X-13=x+1 true or false
Black_prince [1.1K]

Answer: FALSE.

Step-by-step explanation:

Given the following equation provided in the exercise:

x-13=x+1

You need to solve for the variable "x".

In order to solve for "x" you can folllow the steps shown below:

1. You must apply the Addition property of equality and add 13 to both sides of the equation. Then:

x-13+(13)=x+1+(13)\\\\x=x+14

2. Finally you need to apply the Subtraction property of equality and subtract "x" from both sides of the equation. So you get:

x-(x)=x+14-(x)\\\\0=14\ (FALSE)

Therefore, as you can observe, the given equation has no solutions.

3 0
3 years ago
Any sort of help is appreciated, ty
Semenov [28]
The answer would be 1952 because the display of flag makes a right triangle so we will use Pythagorean theorem in order to find the sides and the sides total is 244 according to theorem, so we multiply by 8 to get the 8 flag display.  <span />
8 0
3 years ago
Which system of inequalities represents reglon Z?<br> 6
yKpoI14uk [10]

Answer:

The system of inequalities is

y\geq 3x-2

y<-(1/5)x+2

Step-by-step explanation:

step 1

Find the equation of the solid blue line

Let

A(0,-2), B(1,1)

Find the slope of AB

m=(1+2)/(1-0)=3

The equation of the line into slope intercept form is equal to

y=mx+b

we have

m=3

b=-2 - ----> the point A is the y-intercept

substitute

y=3x-2 - -----> equation of the solid blue line

The solution of the inequality is the shaded area above the solid line

therefore

The first inequality is

y\geq 3x-2

C(0,2), D(5,1)

step 2

Find the equation of the dashed red line

Let

Find the slope of CD

m=(1-2)/(5-0)=-1/5

The equation of the line into slope intercept form is equal to

y=mx+b

we have

m=-1/5

b=2 ----> the point C is the y-intercept

substitute

y=-(1/5)x+2  -----> equation of the dashed red line

The solution of the inequality is the shaded area below the dashed line

therefore

The second inequality is

y<-(1/5)x+2

The system of inequalities is

y\geq 3x-2

y<-(1/5)x+2

3 0
3 years ago
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