Zach has a box with a volume of 48 cubic units. Which could be the dimensions of Zach's box?
Select all that apply.


A. 2 units wide, 3 units long, 8 units tall

B. 5 units wide, 8 units long, 1 unit tall

C. 4 units wide, 6 units long, 2 units tall

D. 3 units wide, 5 units long, 3 units tall

(a.) A slice parallel to the base would result in two rectangular prisms, as opposed to a cube now. These two rectangular prisms would be congruent to each other as it is a perfect slice through the middle.

(b) A slice that contains and AE and DH will make a slanted cube, meaning it will turn into a cubic pyramid.

(c.) A slice that will contain and vertex F will make the cut the figure in half going slanted. They will technically be congruent, although there is no name for this figure.

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:

0.40 cens

Step-by-step explanation:

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:

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:

3y+3

Step-by-step explanation:

I hope this works

Answer:

The answer is 240.6 feet

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

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

4.85 hours

Step-by-step explanation:

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

4.85 hours

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:

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]

the distance between the 2 points is 10

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:

(3, -4)

Step.

The coordinates of the point which lies on the equation is A ( 3 , -4 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

y + 4 = 4 ( x - 3 )   be equation (1)

when x = 3 and and y = -4

Substituting the values of x and y in the equation , we get

-4 + 4 = 4 ( 3 - 3 )

0 = 4 ( 0 )

0 = 0

Therefore , the point A ( 3 , -4 ) lies in the equation

Hence , the coordinates of the point is A ( 3 , -4 )

To learn more about equations click :

https://brainly.com/question/19297665

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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

Step-by-step explanation:

905÷5=5a÷5

there for a=181

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:

yes

Step-by-step explanation:

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:

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: 1.C 2.B 3.C

Step-by-step explanation:

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:

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

Step-by-step explanation:

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

Answer:

$32.85

Step-by-step explanation: 9.5% of 30 is 2.85

30 + 2.85 = 32.85

Answer:

1/49

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

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

Answer:

1 1/3

Step-by-step explanation:

4/3 = 1 1/3