The width of a rectangle is 3 cm less than the length.The area of the rectangle is 10cm^2. Write an equation that models the situation

9514 1404 393

Answer:

  a) x = {-1, 3, 4}

  b) (0.472, 13.128)

  c) (3.528, -1.128)

  d) x < 0.472 U x > 3.528

  e) 0.472 < x < 3.528

Step-by-step explanation:

This is a cubic (odd degree) function with a positive leading coefficient, so it will be increasing until the first turning point, and after the last turning point. It will be decreasing between the turning points.

a) A graph shows the zeros to be x = -1, x = 3, x = 4.

b) A graph shows the local maximum to be approximately (0.472, 13.128). The x-coordinate of this point is exactly 2-√(7/3).

c) The local minimum is about (3.528, -1.128). Its x-coordinate is exactly 2+√(7/3).

d) As stated above, the increasing intervals are (-∞, 0.428) ∪ (3.528, ∞).

e) The decreasing interval is (0.428, 3.528).

_____

Additional comments

The sum of odd-degree term coefficients is the same as the sum of coefficients of even-degree terms, so you know one of the roots is -1. Factoring that out gives the quadratic x^2 -7x +12 = (x -3)(x -4), so the other two roots are 3 and 4.

The derivative is 3x^2 -12x +5 = 3(x -2)^2 -7, so its roots (turning points of f(x)) are 2±√(7/3).

I find a graphing calculator can show me the roots and turning points easily.

Answer:

11+x because the equation is reversabel.

Step-by-step explanation:

Answer:

the height is 15

Answer:

B) 15

Step-by-step explanation:

Volume of a cone formula:

V = πr²(h/3)

D/2 = r

10/2 = r

r = 5

393 = (3.14)5²(h/3)

393 = 78.5(h/3)

h = 15.02

h = 15

Answer:

Step-by-step explanation:

[tex]\text{here is the missing text:} \\ \\ \text{ Suppose a company issues an annual coupon bond with a maturity of 2 years,} \\ \\ \text{ price of $950 \ par \ value \ of $1,000, and coupon rate of 5\% They also issue an}[/tex]

[tex]\text{ annual zero-coupon bond with a maturity of 1 year, price of $900, \ and \ par \ value \ of \ $1,000.}[/tex]

[tex]\text{To determine the 1-year spot rate using the 1-year zero bond.} \\ \\ FV = PV \times (1 + S_1) \\ \\ 1+ S_1 = \dfrac{FV}{PV} \\ \\ 1 + S_1 = \dfrac{1000}{900} \\ \\ S_1 = 11.11\%[/tex]

[tex]\text{PV of the 2-year bond = 950} \\ \\ Annual coupon = 1000 \times 5\% = \$50 \\ \\ \\ 950 = \dfrac{50}{(1+S_1) }+ \dfrac{(50+1000)}{(1+S_2)^2} \\ \\ 950 = \dfrac{50}{1.1111}+ \dfrac{1050}{(1+S_2)^2} \\ \\ \dfrac{1050}{(1+S_2)^2}=950 -45\\ \\ \dfrac{1050}{(1+S_2)^2}=905 \\ \\ (1+S_2)^2 = \dfrac{1050}{905} \\ \\ 1 + S_2= \sqrt{(1.16022)} \\ \\ S_2 = 7.714\%[/tex]

[tex]\text{the arbitrage-free price of the 2-year bond}= \dfrac{1000}{(1+0.07714)^2} \\ \\ = \mathbf{\$861.90}[/tex]

Answer:

I’ve got the graphs for both equations below.

With y = 7/2x + 3

        y = -x-6

I used substitution with simultaneous equations and got x = -2 and y = -4 :)

Answer:

(7/8 - 4/5)^2 = 9/

1600

= 0.005625

Step-by-step explanation:

Subtract: 7/

8

- 4/

5

= 7 · 5/

8 · 5

- 4 · 8/

5 · 8

= 35/

40

- 32/

40

= 35 - 32/

40

= 3/

40

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(8, 5) = 40. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 5 = 40. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - seven eighths minus four fifths = three fortieths

the distance between the 2 points is 10

Answer:

$3 dollars

Step-by-step explanation:

mode is the one that appears the most frequently in a set and three bucks is shown multiple times the most

Answer:

b

Step-by-step explanation:

Answer:

1 1/3

Step-by-step explanation:

4/3 = 1 1/3

Answer:

1/49

hope it hepled:))))))))))

[tex]\frac{1}{7} *\frac{1}{7} =\frac{1*1}{7*7} =\frac{1}{49}[/tex]

Assuming that 6.8 means the area of the triangle, the height would be 1.94.

If this is incorrect, please, don't refrain to tell me. Thank you.

Answer:

0.40 cens

Step-by-step explanation:

Answer:Y< 5x2 - 5 because it will be squared making it an exponential function

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{Since the enrollment decreases every year this is exponential decay of the form}\\ \\ F=Ir^t\\ \\ F=12000(1-.05)^t\\ \\ S(n)=12000(0.95)^n[/tex]

Answer:

4.85 hours

Step-by-step explanation:

(1 hr 35 minutes) + (60 minutes) + (61 minutes) + (20 minutes) + (55 minutes) =

4.85 hours

Answer:

I think you might mean 5.784 and if that is the case it would be 5.8

Step-by-step explanation:

5.8 would be the answer because 8 is closer to 10 than 0 so 7 would be rounded up to 8

Answer:

1

Step-by-step explanation:

I really can't give you a step-by-step

Answer: Square, 24 square inches

Step-by-step explanation:

Given

Diameter of round pizza [tex]d=16\ in.[/tex]

Side of square pizza [tex]a=15\ in.[/tex]

Area of circle [tex]\pi r^2[/tex]

The area of a square is [tex]a^2[/tex]

[tex]\therefore \text{Area of round Pizza}=\pi \times (\frac{16}{2})^2\\\Rightarrow A_1=\pi \times 8^2=201.088\ in.^2[/tex]

The area of square pizza is

[tex]A_2=15^2=225\ in.^2[/tex]

Clearly, the area of square pizza is more and the difference in their area is

[tex]\Rightarrow A_2-A_1=225-201.088=23.91\approx\ 24\ in.^2[/tex]

Answer:

3y+3

Step-by-step explanation:

I hope this works

Step-by-step explanation:

905÷5=5a÷5

there for a=181

Answer:

a1=12

a6=12

a5=20

a3=20

a4=15

a2=15

as=94

Step-by-step explanation:

it is asking for each of the areas

I'm assuming As stands for areas summed

Answer:

a1=a6=lb=3×4=12

a5=a3=lb=5×3=15

a4=a2=lb=5×4=20

As=12×2+15×2+20×2=a1+a2+a3+a4+a5+a6=24+30+40= 94

Answer: 1.C 2.B 3.C

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

The angles inside a triangle always sum to 180°. We already have a 32° angle and a 90° - totalling 122° - and when we add x°, we'd like the sum to be 180°. So x must be 180 - 122 = 58.

Answer:

58

Step-by-step explanation:

The total should be 180 degrees. We know the the top angle is 32 degrees and the bottom left is 90 degrees because it has a square there. So 32+90=122. If we subtract 122 from 180 we are left with 58 degrees so x=58

Answer:

3.5

Step-by-step explanation:

14 wands

14/4=3.5

Answer:

30 wands in total

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

30 divided by 4 is 7.5

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

Your answer is [7.5 Wands]

Step-by-step explanation:

Answer:

1. 28

2. 53

Step-by-step explanation:

1. The angle CFD is a straight line, this means that the measure is 180. This means, using the angle addition postulate, you can set up the equation [tex]180=x+152[/tex]. Then, subtract 152 from both sides to get [tex]x=28[/tex].

2. The question states that the two angles are complementary. This means that they summate to 90 degrees. So using the angle addition postulate again, you can set up the equation, [tex]90=x+37[/tex]. Finally, subtract 37 from both sides to get [tex]x=53[/tex].

Answer: pretty sure lily is right

Step-by-step explanation:

Answer:

Louis is right

Step-by-step explanation:

it looks like she spent about 15$ on coffee one week

Answer:d

Step-by-step explanation: