1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wolverine [178]
3 years ago
6

1. if the sum of the square of the number and 4 time the number is 21 what is the number?

Mathematics
1 answer:
Vika [28.1K]3 years ago
7 0

Answer:

Step-by-step explanation:

1. Let the number be x

x^2 + 4x = 21

x^2 + 4x - 21 = 0

Solve the quadratic equation using factorization method

x^2 - 3x + 7x - 21 = 0

x(x - 3) + 7(x - 3) = 0

(x - 3)(x+7) = 0

x - 3 = 0 x + 7 = 0

x = 3 x = -7

The number is either 3 or -7

2. Same solution as number 1

3. Let

Width = x

Length = 2x - 3

Area of the rectangle = 9 square ft

Area of a rectangle = length × width

9 = (2x - 3) (x)

9 = 2x^2 - 3x

2x^2 - 3x - 9 = 0

Solve using quadratic formula

a = 2

b = -3

c = -9

x = -b +or- √b^2 - 4ac / 2a

= -(-3) +or- √(-3)^2 - 4(2)(-9) / 2(2)

= 3 +or- √ 9 - (-72) / 4

= 3 +or- √9 + 72 / 4

= 3 +or- √81 / 4

= 3 +or- 9 / 4

x = (3 + 9)/4 or (3 - 9) / 4

= 12 / 4 or -6 / 4

x = 3 or -3/2

Width can not be a negative value

So,

Width = x = 3 ft

Length = 2x - 3

= 2(3) - 3

= 6 - 3

= 3ft

2.if the sum of the square of the number and 4 time that number is 21 the what is the number?

3. the length of the rectangle is 3 less than twice the width. if the area is 9 square ft, the length and width of the rectangle.

4.given the figure below. find the area of the shaded part of the rectangle if the area of the big but angle is 6 times the area of the unshaded rectangle ​

Unshaded area

Length = 2x

Width = x

Shaded area

Length = (2x+3)

Width = (x+3)

Area of the shaded area = 6 × the unshaded area

(2x) (x) = 6(2x + 3)(x+3)

2x^2 = 6(2x^2 + 6x + 3x + 9)

2x^2 = 12x^2 + 36x + 9x + 54

2x^2 = 12x^2 + 45x + 54

12x^2 + 45x + 54 - 2x^2 = 0

10x^2 + 45x + 54 = 0

You might be interested in
Write the equation in slope-intercept form of the line that has a slope of 2 and contains
mina [271]

Equation in slope-intercept form is y = 2x - 6

Step-by-step explanation:

  • Step 1: Given slope of the line, m = 2. Form an equation y = mx + b

⇒ y = 2x + b ---- (1)

  • Step 2: The line passes through the point (4,2). So it will satisfy the equation. Find b by substituting x = 4 and y = 2.

⇒ 2 = 2 × 4 + b = 8 + b

⇒ b = -6

  • Step 3: Form the slope-intercept equation.

⇒ y = 2x - 6

8 0
3 years ago
(7x-12)+(13-2x)<br><img src="https://tex.z-dn.net/?f=%287x%20-%2012%29%20%2B%20%2813%20-%202x%29" id="TexFormula1" title="(7x -
Julli [10]
The answer is : 5x+1
5 0
3 years ago
Find the solution for the following equation using the algebraic method: 3x^2+10x=8
likoan [24]
The answer should be 0.875.
6 0
3 years ago
How many solutions does the equation -6y+13+9y=8y-3
Lina20 [59]

Answer:

Single Solution of 3.2 (16/5)

Step-by-step explanation:

3x = 8x -16 <--- I combine like terms.

-5x = -16

-16/-5 = x

x = 3.2

BTW Negative times a Negative equals a positive.

3 0
2 years ago
Which is greater 3/5, 33/50, 303/500, 3,003/5,000, 30,003/50,000
ad-work [718]

33/50 because it is biggest

5 0
3 years ago
Read 2 more answers
Other questions:
  • What is 74 multiply by 65?
    14·1 answer
  • On September 4, Nita Darmati signed a $5,350 promissory note to purchase furniture for her home office. The note had a simple in
    5·1 answer
  • Help this homework is due by tomorrow
    9·2 answers
  • I have a box of chocolates with white,milk and dark chocolate in. The ratio of white to not white is 3:4. The ratio of not dark
    9·1 answer
  • Mark the statements that are true.
    5·1 answer
  • a store has a 20% off sale on pants with this discount, the price of one pair of pants before tax is $15.20. what was the origin
    11·1 answer
  • What number needs to be added to 4 and 7 so that the ratio of
    11·2 answers
  • What is the measure of angle A?
    5·1 answer
  • The triangles shown are similar. Which angle corresponds to angle E
    5·1 answer
  • Matt washed 3 cars in 50 minutes, what is his hourly rate of cars washed?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!