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 540 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?
10 inches
9 inches
6 inches
3 inches
Answers
Answer:
C
Step-by-step explanation:
The volume of a box (rectangular prism) is given by:
[tex]\displaystyle V = \ell wh[/tex]
We are given that the desired volume is 540 cubic inches. The width is three inches longer than the length and the height is four inches longer than the length. Substitute:
[tex]\displaystyle (540) = \ell(\ell + 3)(\ell + 4)[/tex]
Solve for the length. Expand:
[tex]\displaystyle \begin{aligned} 540 &= \ell (\ell^2 + 7\ell +12) \\ 540&= \ell ^3 + 7\ell^2 +12\ell \\ \ell^3 + 7\ell ^2 +12\ell -540 &= 0\end{aligned}[/tex]
We cannot solve by grouping, so we can consider using the Rational Root Theorem. Our possible roots are:
±1, ±2, ±3, ±4, ±5, ±6, ±9, ±10, ±12, ±15, ±18, ±20, ±27, ±30, ±36, ±45, ±54, ±60, ±90, ±108, ±135, ±180, ±270, and/or ±540.
(If you are allowed a graphing calculator, this is not necessary.)
Testing values, we see that:
[tex]\displaystyle (6)^3 +7(6)^2 + 12(6) -540 \stackrel{\checkmark}{=} 0[/tex]
Hence, one factor is (x - 6).
By synthetic division (shown below), we can see that:
[tex]\displaystyle \ell^3 + 7\ell^2 +12\ell -540 =(\ell -6)(\ell ^2 + 13\ell +90)[/tex]
The second factor has no real solutions. Hence, our only solution is that l = 6.
In conclusion, our answer is C.
Answer:
6 inches
Step-by-step explanation:
I just took the test
Related Questions
solve for y
-10x + 2y =4
Answers
Answer:
y = 5x + 2
Step-by-step explanation:
Add 10x to both sides
2y = 10x + 4
Divide both sides by 2
y = 5x + 2
can someone help me with this one again bc I didn't show the decimal Decimal: 0.44
Answers
Step-by-step explanation:
The answer is 10 times
=> 4 hundredths x 10 = 4 tenths
=> 0.04 x 10 = 0.4, which is correct
Hope that helps
The height of a triangle is 5 cm more than its base. The area of the triangle is 52 square centimeters. What is the base of the triangle?
Answers
Answer:
the base is 8 cm
Step-by-step explanation:
basically, we need to set up a system of equations.
if we know the area of a triangle is 1/2bh, and that h = b + 5, (because we want them to equal one another in the equation), we can then make two different equations and substitute the h for b.
1/2bh = 52 and h = b+5
subsitute in the (b+5) for the h in the first equation to get
(1/2)(b)(b+5) = 52
multiply both sides by two to get rid of the 1/2
b)(b+5) = 104
now multiply the bs together!
b^2 + 5b = 104
If you know how to factor, we can make this
b^2 +5b -104 and then
(b+13)(b-8) = 0
solve for b to get b = -13, 8, and -13 isn't a real distance, so the only option for b is 8 square centimeters.
Plugging this back into the original equations to get the height (and checking that it is actually right,) we get a height of 13.
When you plug in the 13 and 8 into the area equation, you get
(8)(13)(1/2) = 52
52 = 52
so it works!
lmk if anything is confusing- i know I kind of breezed by the factoring part, but if you have a calculator you can keep dividing 104 by random numbers until you get the right difference if you get kind of lost. The formula
[-b+-sqrt(b^2-4ac)]/2a is another way you could always get the right answer, (from the form Ax^2 + Bx + C), but it's pretty time consuming and I'm not sure whether you've actually learned that yet..
hope that helps! :)
Select the best answer for the question.
13. What's the sum of 25 and 24?
A. %10
B.1%20
c.
D. 8/20
Answers
Answer:
Sum means addition so you add them together. I don't know why there are a bunch of percentage signs but the answer is 49.
Solve the following equation.
X - (-6) = 15
Answers
Answer: x=9
Step-by-step explanation:
x-(-6)=15
first the subtraction sign and the negative sign becomes a plus sign
x+6=15
-6 -6
Next you subtract 6 from both sides of the equation. And that leaves you with
x=9
please help with math
Answers
2.) -1.5, 3/4 (which, in decimal, is 0.75) , 3, sqrt 10 (which, in decimal, is about 3.1622…)
3.) -3/2 (which, in decimal, is -1.5), -3/7 (which, in decimal, is about -0.4285…) , 0.75, 2
Combine Like Terms
1. What is the simplest expression equivalent to 2 - 11 + 18 - 20.x ?
-7-21x
7-19x
7+21x
-7+19x
Answers
Answer:
-9x+20
Step-by-step explanation:
Is 4 or 3 bigger in a integer
Answers
Answer:
4 is bigger than 3
Step-by-step explanation:
4 is bigger than 3
But
-3 is bigger than - 4
Write an equation in slope-intercept form for the line with slope -3/2 and y -intercept -3
Answers
Answer:
It is
[tex]{ \underline{ \sf{y = - \frac{3}{2}x - 3 }}}[/tex]
Step-by-step explanation:
General equation:
[tex]{ \sf{y = mx + c}}[/tex]
m is the slope
c is the y-intercept
[tex]y = - \frac{ 3}{2} x - 3[/tex]
What is the quotient of 7.584 x 10^9 and 7.9 x 10^ 2 expressed in scientific notation?
Answers
Answer:
9.6 × 10 6
Step-by-step explanation:
(7.584 × ) ÷ (7.9 × 10²)
This gives;
× = 0.96 ×
Simplifying further gives;
9.6 × = 9.6 ×
Using rational numbers how do you solve -37 + (-64)
Answers
Answer:
-101
Step-by-step explanation:
An addition sign in front of the negative number means to subtract that number.
Another way to write -37 + (-64) is:
-37 - 64
-37 - 64 = -101
A worker earns the same amount for each
hour. If he earned $48.00 in 3 hours, how
much would he earn in 8? In 40?
Answers
Answer: 8 hours= $128 40 hours= $640
Step-by-step explanation:
$48.00 divided by 3 = $16.00 an hour. so 16x8=128 and 16x40=640
If a function is defined by the equation y = 1/2x -3/2 , which equation defines the inverse of this function?
Answers
Answer:
B
Step-by-step explanation:
Rearrange the equation making x the subject
y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ( multiply through by 2 to clear the fractions )
2y = x - 3 ( add 3 to both sides )
2y + 3 = x
Change y back into terms of x with x being the inverse function, that is
y = 2x + 3 → B
Find the missing angle.
Answers
Answer:
Angel V = 74
I hope it's helps you
The area of this shape is 24 square units. Which of these statements is true about the area ?
Answers
Because the area of an object is number of square units or square grids inside the shape.
Answer:
D.
Step-by-step explanation:
Write this as an algebraic expression:
You have $100 and make $25 a day
Answers
Answer:
25d + 100
Step-by-step explanation:
I will call "d" the days passed
25d + 100
Simplify show all steps thirty POINTS!
Answers
Hope it helped
Since you have to divide 6a AND 9 by 3 :)
express the following ratio as fraction and reduce them to their simplest form 200 meters : 1.4 kilometre
Answers
Step-by-step explanation:
200m:1.4km
200m:1400m
1:7
(-8, -2) and (1, 9) find the slope
Answers
Answer:
11/9
Step-by-step explanation:
To find the slope
m = ( y2-y1)/(x2-x1)
= ( 9 - -2)/(1 - -8)
= ( 9+2)/ (1+8)
= 11/9
what passes through the points (-1/2 4) and (1/2 6). show your work
Answers
Step-by-step explanation:
The equation of line which passes through these points is determined by:
p(x1,y1)=(-1/2,4) p(x2,y2)=(1/2,6)
[tex] \frac{y - y1}{y2 - y1} = \frac{x - x1}{x2 - x1} \\ \frac{y - 4}{6 - 4} = \frac{x + \frac{ 1}{2} }{ \frac{1}{2} + \frac{1}{2} } \\ \frac{y - 4}{2} = \frac{2x + 1}{2} \\ 2(2x + 1) = 2(y - 4) \\ 4x + 2 = 2y - 8 \\ 4x - 2y + 2 + 8 = 0 \\ 4x - 2y + 10 = 0[/tex]
Note:if you need to ask any question please let me know.
a line passes through the points 3, 0 and 4, 1. what is the y-intercept of the line
Answers
9514 1404 393
Answer:
(0, -3)
Step-by-step explanation:
The slope is the same for any segment of the line. The slope from (0, y) to (3, 0) is the same as from (4, 1) to (3, 0).
Δy/Δx = (y -0)/(0 -3) = (1 -0)/(4 -3)
y = -3(1/1) = -3 . . . . . multiply by -3
The y-intercept is (0, -3).
maths
class 8th
give answers
Answers
8/9 + -8/9 = 0
[2^-1 + 3^-2 + 4^-3]^0 = 1
The HCF of 8 , 12 and 24 is ______
Answers
Answer:
the Highest common factor (HCF)of 8,12,24 is 4
278 kg to pounds, rounded off to the nearest pound.
Answers
Answer:
About 613 pounds
Step-by-step explanation:
1 : 2.20462262
278 : 612.885089
612.885089 --> 612.89 --> 612.9 --> 613
What's (9+9i)(-1-5i) using foil method
Answers
Answer:
36-54i
Step-by-step explanation:
(9+9i)(-1-5i)
v
-9-9×5i-9i-9i×5i
v
-9-45i-9i-45i^2
v
-9-45i-9i-45×(-1)
v
(-9)-45i-9i+(45)
v
36(-45i)(-9i)
v
36-54i
HELP PLS IM BEGGING YOU PLS HELP, its due todayyy pls. Angle CBD is the only one i got right and the rest is wrong. I dont know how to answer it anymore.
Answers
Answer:
try It would be number 81
Step-by-step explanation:
Abc= 110
ceo=70
dbe=110 or 120
and abe= 60 70 or 81
Answer:
ABC=112 degrees
DBE=112 degrees
ABE=68 degrees
Step-by-step explanation:
CBD=ABE
ABE=68 degrees
First let's take these as X,
ABC=DBE=X(Vertically opposite angles)
ABC+DBE+CBD+ABE=360(angles around a point)
x + x +68 +68 =360
2x +136 =360
2x =360-136
2x = 224
x =112 degrees
therefore;
ABC=112 degrees
DBE=112 degrees
it takes a lady 26 minutes to travel 3 km by walking the first part at 6 km per hour and running the second part at 10 km per hour what distance does she walk
Answers
Answer:
78 meter 360meters 600 meters
-3(4x+3)+4(6x+1)43
please solve the problem fully
Answers
Answer and Step-by-step explanation:
First, distribute the numbers outside of the parenthesis to the numbers on the inside.
-12x - 9 + 24x + 4 = 43
Combine like terms.
12x - 5 = 43
Add 5 to both sides.
12x = 48
Divide by 12 on both sides of the equation.
x = 3 <- This is the answer.
#teamtrees #PAW (Plant And Water)
Leave any questions you have, put it in the comments below :)
please solve this question i need help
Answers
Answer:
4c/2a 60 degrees 3bf 2ad
Answer:
f=120
b=40
d=140
e=120
c=30
a=30
cho hàm số y= x^{3} +3x^{2} -1 .viết phương trình tiếp tuyến tại điểm có hoành độ bằng -1
Answers
hope you do not mind expressing this on in English ♂️