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Ipatiy [6.2K]
3 years ago
14

The area of a rectangular piece of cardboard is represented by

Mathematics
1 answer:
Liula [17]3 years ago
5 0

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

A = wl

w(2w + 3) = 9

From this, we get that:

l = 2w + 3, A = 9

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

In this question:

w(2w+3) = 9

2w^2 + 3w - 9 = 0

Thus a quadratic equation with a = 2, b = 3, c = -9

Then

\Delta = 3^2 - 4(2)(-9) = 81

w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5

w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

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Write the equation of the trigonometric graph.
prisoha [69]

Answer:

f(x)= \sin(6x)+3

Step-by-step explanation:

The parent function of this graph is:  y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

f(x) = \sf A \sin (B(x + C)) + D

  • A = amplitude (height from the mid-line to the peak)
  • 2π/B = period (horizontal distance between consecutive peaks)
  • C = phase shift (horizontal shift - positive is to the left)
  • D = vertical shift

The parent function y = sin(x) has the following:

  • Amplitude (A) = 1
  • Period = 2π
  • Phase shift (C) = 0
  • Vertical shift (D) = 0
  • Mid-line:  y = 0

From inspection of the given graph:

  • Amplitude (A) = 1
  • \sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}
  • Phase shift (C) = 0
  • Vertical shift (D) = +3  (as mid-line is y = 3)

\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6

Substituting the values into the standard form:

\implies f(x) =1 \sin (6(x + 0)) + 3

\implies f(x) = \sin (6x) + 3

Therefore, the equation of the given trigonometric graph is:

f(x)= \sin(6x)+3

6 0
2 years ago
50 points! Due in 20 minutes! So hurry ! no random answers please. Will mark brainliest:)
olga2289 [7]
The new coordinates are (3, 1)
5 0
3 years ago
An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the i
Natasha_Volkova [10]

Answer:

The amount invested in the mutual fund that earned 5% was $1,000

The amount invested in the mutual fund that earned 3% was $1,800

Step-by-step explanation:

Let

x ----> the amount invested in the mutual fund that earned 5%

y ----> the amount invested in the mutual fund that earned 3%

we know that

x+y=2,800 ----> y=2,800-x ----> equation A

5\%=5/100=0.05

3\%=3/100=0.03

0.05x+0.03y=104 ----> equation B

Solve the system by substitution

substitute equation A in equation B

0.05x+0.03(2,800-x)=104

Solve for x

0.05x+84-0.03x=104

0.05x-0.03x=104-84

0.02x=20

x=\$1,000

<em>Find the value of y</em>

y=2,800-x

y=2,800-1,000=\$1,800

therefore

The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800

5 0
3 years ago
Help number 5 15 pointsss
r-ruslan [8.4K]

Answer:

x=101

Step-by-step explanation:


8 0
3 years ago
Read 2 more answers
3x - 5y = -9<br> x + 2y = 8
Rus_ich [418]

Answer: 3x-5y=-9 is simplified to y=3/5x+9/5

x+2y=8 is simplified to y=-1/2x+4

3 0
3 years ago
Read 2 more answers
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