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When 21 is subtracted from the square of a number, the result is 4 times the number. Find the positive solution.

wel

Let x = your number.

x^2 - 21 = 4x. Subtract 4x from both sides.

x^2 - 4x - 21 = 0. Factor.

(x - 7) (x + 3) = 0. Set each term to 0.

x + 3 = 0. Subtract 3 from both sides.

x = -3. This is the negative solution.

Set the other term equal to zero.

x - 7 = 0. Add 7 to each side.

x = 7. This is the positive solution.

7 0

3 years ago

Lines Line D E and Line A B are parallel. Lines D E and A B are parallel. Angles B and D are alternate interior angles. Which an

valina [46]

Answer:

a. angles A and C

b. angles B and D

Step-by-step explanation:

When two lines are parallel, it implies the value of the angle between them is $180^{0}$ . Thus the lines can not meet when extended continuously.

Alternate angles are two equal angles that lie on opposite sides of the transversal line. Alternate Interior Angles are a pair of equal angles on the inner side of two parallel lines.

Since lines DE and AB are parallel with alternate interior angles at B and D, then angles A and C with angles B and D are alternate interior angles.

i.e < A = < C (alternate interior angle property)

<B = < D (alternate interior angle property)

8 0

2 years ago

Read 2 more answers

A car rental company charges a base fee of $30 per day to rent a car, along with an additional $0.18 per mile driven. If George

sladkih [1.3K]

George's cost per day is

... c = 30 + 0.18m

We want c < 55, so we can write

... 30 + 0.18m < 55 . . . . . your inequality

_____

Here is the solution to the inequality

... 0.18m < 25

... m < 25/0.18

... m < 138.9

George must drive less than 138.9 miles that day.

3 0

3 years ago

Read 2 more answers

the units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than the ori

Anton [14]

Answer:

36

Step-by-step explanation:

Here is the correct and complete question: The units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than twice the original number. What is the original number?

Lets assume the original number be"10y+x". (x is unit digit and y is 10th digit)

∴ if number is reversed then resulting number be "10x+y".

As given: x= 2y

and $10x+y= 2(10y+x)-9$