A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the volume of the delivery box to be 224 cubic inches. If the width of the delivery box is 3 inches longer than the length and the height is 4 inches longer than the length, what must the length of the delivery box be?

3 inches
7 inches
8 inches
4 inches

Answers

Answer 1

Answer:

4 inches.

Step-by-step explanation:

Let l = length, w = width, and h = height

    The formula for the volume of a rectangular solid would be V = lwh. We are tasked with finding the length of the delivery box. In order to find the length, we need to change the variables so that l is the only variable in the equation.

    The prompt tells us that the width of the box is 3 inches longer than the length. That means that w = l + 3. Likewise, the prompt also informs us that the height is 4 inches longer than the length. Therefore, h = l + 4.

    Now that the variables have been changed so that l is the only variable, we can finally solve for l.

[tex]V=lwh\\\\224=l(l+3)(l+4)\\\\224=l^3+7l^2+12l\\\\0=l^3+7l^2+12l-224\\\\0=(l-4)(l^2+11l+56)[/tex]

    After factoring, we are left with (l - 4)(l² + 11l + 56) = 0. Ultimately, by using the quadratic formula, l² + 11l + 56 = 0 will have imaginary number solutions. However, l - 4 = 0 gives us l = 4. Therefore, the length of the delivery box is 4 inches.

Answer 2

Answer:

4 inches

Step-by-step explanation:

just took test


Related Questions

1 - 3/10 Write the answer as a fraction​

Answers

Answer:

7/10

Step-by-step explanation:

Get a common denominator

1 - 3/10

10/10 - 3/10

7/10

Ms. Davis writes an equation on the board.
(-6) + 6 = 0
Which scenario could represent this equation?

Answers

There are many answers we could go with here. One such answer could be the following:

You are 6 meters below the ocean surface doing a deep sea dive. This is represented by -6. Then going up 6 meters means you'll add on 6 to say (-6)+6 = 0, showing that you are at the 0 meter height, aka sea level.

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

Another possible answer could be this:

You are 6 dollars in debt. Debt is represented with negative numbers. You then somehow get 6 dollars in which you use to pay off that debt. Your balance is now (-6) + 6 = 0 dollars.

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

Another possible answer could be this:

Walking to the left is defined as moving in a negative direction. So -6 could mean we've moved 6 feet to the left. On the flip side, +6 means we move 6 feet to the right. The two cancel each other out (-6)+6 = 0 which says at the end of the day, we haven't moved anywhere. In other words, our displacement is 0 feet.

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

I'm sure there are other more creative ways to answer this question, but those three ideas above are good possible starting points.

Find the value of x.
B
10-X
3
D
х
2.
A
С
x = [?]

Answers

Answer:

3/(10-x) = 5/(10-x+x)

3/(10-x) = 1/2

6 = 10-x

x = 4

Hope this helps!

Find the measure of the third angle of a triangle if the measures of the other two angles are given.
35.5 and 82.6
A. 66.8
B. 58.4
C. 61.9
D. 31.9

Answers

9514 1404 393

Answer:

  C.  61.9°

Step-by-step explanation:

The sum of angles in a triangle is 180°, so the third angle is ...

  180° -35.5° -82.6° = 61.9°

For the Parabola y = (x - 7)^2 – 3. the equation for the Line Of Symmetry is

Answers

Answer:

x+=(y)=x

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

y = (x - 7)^2 – 3

This equation is in vertex form

y = a(x-h)^2 +k  where (h,k) is the vertex.  For a vertical parabola, the axis of symmetry is x=h

x = 7

(2 x 100) + (7 x 1) + (2 x 1/10) + (9 x 1/100) + (4 x 1/1000) as a decimal number

Answers

Answer:

207.294

Step-by-step explanation:

(2 x 100) + (7 x 1) + (2 x 1/10) + (9 x 1/100) + (4 x 1/1000)

(200) + (7) + (1/5) + (9/100) + (1/250)

= 207.294

The decimal number for the given expression is 207.294.

The given expression is (2 x 100) + (7 x 1) + (2 x 1/10) + (9 x 1/100) + (4 x 1/1000).

We need to write the decimal number for the given expression.

How to convert expanded form to standard form?

To convert the expanded form of a number to the standard form, simply add the values in the expanded form together.

Now, 200+7+0.2+0.09+0.004=207.294

Therefore, the decimal number for the given expression is 207.294.

To learn more about decimal numbers visit:

https://brainly.com/question/4708407.

#SPJ2

חן
d
60°
30°
e
The product of sin 30° and sin 60° is same as the product of
and

Answers

Answer:

Step-by-step explanation:

This is a fascinating question. It turns out to be true because of the relationship between a 30 degree angle and a 60 degree angle

The answer is that the product of sin30*sin60 = cos(30)*cos(60). This happens because sin(60) = cos(90-60) = cos(30)

Other angles will do the same thing sin36 * sin54 = cos(54)*cos(36)

CHO A (0,2) B(-2,0) C(2,-1) chứng minh A B C thẳng hàng

Answers

Step-by-step explanation:

language mujhe samajh mein nahin a rahi hai

31. Which choice describes the value of m when -5(m + 1) = 23?
А
B.
m 2-3
ms-
6 m2
D.ms-

Answers

Answer:

The correct choice is Option A. m ≥ -28/5

Step-by-step explanation:

PLZ ANSWER QUICK

Forest has a box of 12 candies. The Venn diagram below shows how many candies contain chocolate, coconut, both, or neither. Complete the following two-way frequency table.

Answers

Answer: Answer is in the image below.

Step-by-step explanation:

Find the sentence distance between the points (-2,2) and (-1,1). Round to two decimal places if necessary.

Someone help me

Answers

Answer:

1.41

Step-by-step explanation:

Coordinates of point 1 are:

(-2,2)

Coordinates of point 2 are:

(-1,1)

[tex]Distance \: between \: two \: points \\ = \sqrt{ {(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} } \\ = \sqrt{ { (- 1 - - 2)}^{2} + {(1 - 2)}^{2} } \\ = \sqrt{ { (1)}^{2} + {( - 1)}^{2} } \\ = \sqrt{ 1 + 1 } \\ = \sqrt{2} \\ = 1.41 [/tex]

Is pi + 1 rational or irrational

Answers

Answer:  Irrational

==========================================================

Explanation:

Let's assume that pi+1 is rational

If so, then pi+1 = m/n where m and n are integers and n is not zero.

Let's isolate pi

pi+1 = m/n

pi = (m/n) - 1

pi = (m/n) - (n/n)

pi = (m - n)/n

This says that pi is rational, as it's in the form integer/integer. But in reality, pi is irrational. The decimal form of pi goes on forever without any known pattern.

So going back to the assumption where we said "pi+1 is rational", that assumption can't be true. If it were true, then it leads to a contradiction. Therefore, pi+1 is irrational.

[tex]\huge\text{Hey there!}[/tex]

[tex]\boxed{\huge\text{\boxed{\mathsf{\pi + 1}}}}\\\boxed{\boxed{\huge\text{\boxed{= \mathsf{3.141593 + 1}}}}}\\\\\boxed{\boxed{\huge\text{\boxed{= \bf 4.141593}}}}\\\\\boxed{\huge\text{\boxed{\pi \approx \bold{3.14}\ \& \ 3.14 + 1\ is \approx \bf \underline{\underline{4.14}}}}}[/tex]

[tex]\huge\bullet\huge\text{ Pi \boxed{\pi} is an irrational number so any}\\\huge\text{real numbers (0 \& up) cannot be}\\\huge\text{indicated (expressed) by the clearer}\\\huge\text{(simple) fraction\bf (s)}[/tex]

[tex]\boxed{\boxed{\huge\text{To \underline{ANSWER} Your question it is: \bf \underline{\underline{irrational}}}}}\huge\checkmark[/tex][tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]~[tex]\boxed{\huge\text{\boxed{\frak {Amphitrite1040:)}}}}[/tex]

Please help me answer this

Answers

Answer:

77

Step-by-step explanation:

Use Pythagorean to solve this:

FH² = FG² - GH²GH² = EG² - EH²

Substitute values:

FH² = 85² - (45² - 27²)FH² = 5929FH = √5929FH = 77

Answer:

FH = 77

Step-by-step explanation:

Using all the side lengths given, we can create a pythagorean like equation with all three values:

= -45² + 27² + 85²

= -2,025 + 729 + 7,225

= 5929

= √5929

= 77

Best of Luck!

Find the area and perimeter of the given plain figure​

Answers

This shape is the rhombus, then ;

Rhombus area = side length × height

A= b × h

A= Rhombus area

h = height ; b = side length ( length of any side)

h= 3 inch ; b= 4.5 inch ; A=?

A= b × h

A= 4.5 × 3 = 13.5 inch²

____o__o_____

The perimeter of a rhombus = 4 × side of length

P = 4× a

P = The perimeter of a rhombus ; a = side of length

p= ? ; a = 4.5 inch

P = 4× a

P = 4× 4.5 = 18 inch

I hope I helped you^_^

I don’t really understand this…
Steps:
Calculate MU/P
Compare MUx with MUy
Choose highest MU
Continue until you spend all of your money


Answers

Answer:

In the real world, a consumer may purchase more then one commodity. Let us assume that a consumer purchases two goods X and Y. How does a consumer spend his fixed money income in purchasing two goods so as to maximize his total utility? The law of equi­-marginal utility tells us the way how a consumer maximizes his total utilit

m=8+n
PLZ HELP ASAP, WILL MARK BRAINLIEST!!!

Answers

[tex]\\ \qquad\quad\sf\longmapsto m=8+n[/tex]

Take n to left

[tex]\\ \qquad\quad\sf\longmapsto m-n=8[/tex]

Hence

if m=1

[tex]\\ \qquad\quad\sf\longmapsto n=m-8=1-8=-7[/tex]

if n=1

[tex]\\ \qquad\quad\sf\longmapsto m=8+1[/tex]

[tex]\\ \qquad\quad\sf\longmapsto m=9[/tex]

Plzzz help 10 points and will mark brainiest
hint: answer is a fraction

Answers

Answer:

1/3

Step-by-step explanation:

The left side of FA is 6 units.

The left side of FB is 2 units.

From 6 to 2, you divide by 3.

Same for the top,

FA is 9 units, while FB is 3 units.

I hope this helps!

pls ❤ and mark brainliest pls!

Match all the part of the circle to their correct name.

1. YW
2. Q
3. WX
4. W
5. ST
6. VQ
7. TW

a. Center
b. Secant Line
c. Chord
d. Radius
e. Point of Tangency
f. Diameter
g. Tangent Line

Answers

Answer:

halo

1. YW - chord

2. Q - center

3. WX - tangent line

4. W - point of tangency

5. ST - secant line

6. VQ - radius

7. TW - diameter

please mark brainliest???

The correct matches are,

1. YW - chord

2. Q - center

3. WX - tangent line

4. W - point of tangency

5. ST - secant line

6. VQ - radius

7. TW - diameter

What is diameter?

In geometry, a diameter of a circle exists as any straight line segment that passes via the center of the circle and whose endpoints lie on the circle. It can also be described as the longest chord of the circle. Both descriptions exist also valid for the diameter of a sphere.

The correct matches are,

1. YW - chord

2. Q - center

3. WX - tangent line

4. W - point of tangency

5. ST - secant line

6. VQ - radius

7. TW - diameter

To learn more about diameter refer to:

https://brainly.com/question/23220731

#SPJ2

a call centre aims to deal with calls in less than 5 minutes


calls come in randomly

Answers

Answer:

1/8

Step-by-step explanation:

Let "A" = the next call of a customer's complaint

Let "B" = the next call completed under 5 minutes

P(A) = 1/4

P(B) = 1/2

So ----> P(AB) = P(A) times P(B) P(AB)

                       = 1/4 times 1/2 = 1/8

Hey guys ♡
hw r u all doin
pls solve this question for me ⤵️

(m-1)/2 - (m-2)/3 = ( m - 4 )/7 ​

Answers

Answer:

m = - 31

Step-by-step explanation:

Given

[tex]\frac{m-1}{2}[/tex] - [tex]\frac{m-2}{3}[/tex] = [tex]\frac{m-4}{7}[/tex]

Multiply through by 42 , the LCM of 2, 3 and 7 , to clear the fractions

21(m - 1) - 14(m - 2) = 6(m - 4) ← distribute parenthesis

21m - 21 - 14m + 28 = 6m - 24

7m + 7 = 6m - 24 ( subtract 6m from both sides )

m + 7 = - 24 ( subtract 7 from both sides )

m = - 31

2 1/2 + 3 1/4 = ? pls

Answers

Answer:

5  [tex]\frac{3}{4}[/tex]    

Step-by-step explanation:

2 [tex]\frac{1}{2}[/tex] + 3 [tex]\frac{1}{4}[/tex]

= (2 + 3) + [tex]\frac{1}{2} + \frac{1}{4}[/tex]    Here we add the two whole numbers first

= 5 +  [tex]\frac{1}{2} + \frac{1}{4}[/tex]

= 5 + [tex]\frac{2}{4} +\frac{1}{4}[/tex]      Here you bring the two fractions to a common denominator     and to to this you find the highest common factor of the denominators.

= 5 + [tex]\frac{3}{4}[/tex]       Here we added 1/4 and 2/4

= 5  [tex]\frac{3}{4}[/tex]    This is the answer simply add 5 and 3/4

HOPE THIS HELPED

Answer:

Step-by-step explanation:

Your answer is 5 3/4

The cone in the figure below has a volume of 72π cubic centimeters and a height of 6
centimeters. What is the radius of the base of the cone, in centimeters?

Answers

Answer:

6 cm

Step-by-step explanation:

The volume of a cone = (1/3) πr²h

72π = (1/3) π r² 6

72 = (1/3) r² 6

Divide both sides by 6

12 = (1/3) r²

Multiply both sides by 3

36 = r²

So r (radius) = 6 cm

Analyze the diagram below and complete the instructions that follow.
10
6
B.
'C С
8
Find sin ZA
A 3
5
B. 4
C 1

Answers

Answer:4

Step-by-step explanation:just had this

Los científicos dicen que el universo fue por el big bang pero yo tengo una teoría


Mi teoría es

Que el universo no se creó siempre a estado siempre estuvo y siempre estará, que el universo no tienen edad que el universo es infinito y siempre lo será esa es mi teoría un poco corta

Answers

Answer  yo mbitaen digo lo mismo el universo siempre a eado hays sn niotrsoss oarlo

bet

Step-by-step explanation:

Write the equation of the circle in standard form with the center located at
(-2, 5) and radius of 3.

Answers

Answer:

(x+2)^2 + (y-5)^2 = 9

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x- -2)^2 + (y-5)^2 = 3^2

(x+2)^2 + (y-5)^2 = 9

Given that line a is parallel to line b and that line c isparallel to line d, if m<13 = (12x – 22)° and m<14 = (9x – 29)°, find m<2

Answers

Answer:

∠ 2 = 70°

Step-by-step explanation:

∠ 13 and ∠ 14 are adjacent angles and sum to 180° , then

12x - 22 + 9x - 29 = 180

21x - 51 = 180 ( add 51 to both sides )

21x = 231 ( divide both sides by 21 )

x = 11

Then

∠ 14 = 9x - 29 = 9(11) - 29 = 99 - 29 = 70°

∠ 7 = ∠ 14 = 70° ( Alternate angles )

∠ 2 = ∠ 7 = 70° ( Alternate angles )

i will mark brainliest!!!
Other answers: C. y=25x
D. y=25x+8.34

Answers

Answer:

Omg why are you soo beautiful? I love it

Answer:

y = 8.34x + 25

Step-by-step explanation:

(10, 108.4) (20, 191.8)

m = slope

m = (y2 - y1)/(x2 - x1)

m = 191.8 - 108.4/20 - 10

m = 83.4/10

m = 8.34

She collects rainwater in a large barrel that weighs 25 pounds (y-intercept) so therefore, our answer should be y = 8.34x + 25

Do these pairs of values (x and y) represent two quantities that are proportional?

X: 4, 6, 10, 14
Y: 2, 3, 5, 7

Answers

Answer:

No

Step-by-step explanation:

In a proportional relationship, it will be a straight line (it is here) that goes through the origin (it does not).  It would not go through (0.0), but would go through (2, 0)

A.0.16, 0.10, 0.07, -2.65, -1.43

B. -2.65, -1.3, 0.16, 0.10, 0.07

C.0.16, 0.10, 0.07, -1.43, -2.65

D.-2.65, -1.43, 0.07, 0.10, 0.16

Answers

Answer:

Step-by-step explanation:

The greatest value is 0.16. The least value is - 2.65

The least value (mathematically) is - 2.65

So C is the right answer.

The graph showing here is the graph of which of the following rational functions?

Answers

Answer: A

Step-by-step explanation:

The graph has a vertical asymptote at x = -2. In this situation, vertical asymptotes happen when the denominator equals zero, which leaves the function undefined. Therefore, find the answer choice whose denominator equals zero when x = -2.

A would be correct because when x = -2,

[tex]F(-2)=\frac{1}{-2+2}=\frac{1}{0}[/tex], which is undefined.

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