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
Indicate which is the largest decimal in each of the following pairs.
0.0006 and 0.006
Answers
Answer:
0.006 is the larger decimal
Answer:
0.006 is the right answer
Step-by-step explanation:
Since (0.006) has the least amount of zeros after the decimal, it would be larger than the other decimal that has more zeros after the decimal.
Irene has a checking account. On Monday she writes a $160 check for groceries. Then she deposits $125
into her account. Finally, she writes another check for $40. What was the total change in the amount of
money in Irene's account on Monday?
A. $85
B. - $85
C. $75
D. -$75
E. $325
F. - $325
Answers
Answer:
D. - $75Step-by-step explanation:
We mark checks as negative and a deposit as positive:
- 160 + 125- 40Add up to get the total change of:
-160 + 125 - 40 = - 75Correct choice is D
Answer:
Answer :-
Here, Irene is having a checking account. First she write a check of $160. Then means it has an decrease money. (-160) Now, She deposit $125. This means Now, the balance is -160 + 125 = $-35. She again write a check of $40. (-40). Total change =>
-40 - 35
-75
Option D is correct mate!
how to find the sum of 12 and 36 using the gcf and distributive property
Answers
What is 3/10 as a decimal?
Answers
Answer:
[tex]0.3[/tex]
Step-by-step explanation:
[tex]3 \div 10 = 0.3[/tex]
Answer: 0.3
Step-by-step explanation:
Can anyone help with this please
Answers
Answer:
None
Step-by-step explanation:
Simply, the absence of s^-1 shows the answer as none
What is the probability of all 3 coins landing on heads
Answers
There are 8 possibilities when flipping three coins and the possibility of getting all heads is 1 out of 8.
1. h h h
2. h h t
3. h t h
4. h t t
5. t t t
6. t t h
7. t h t
8. t h h
Therefore the probability is:1/8
The graph of the reciprocal parent function, f(x) = ), is shifted 9 units
down and 11 units to the right to create the graph of g(x). What function is
g(x)?
Answers
Answer:
g(x) = [tex]\frac{1}{x+11}-9[/tex] is my choice
Step-by-step explanation:
I. If move right is +x and move down is -y
then f(x) = [tex]\frac{1}{x}[/tex]
+x = 11, -y = -9
so g(x) = [tex]\frac{1}{x+11}-9[/tex]
Hope that help :D
Write an equivalent expression in standard form for
(5x + 4)(7x+ -12x + 27).
Answers
Answer: -25x² + 115x + 108
Concept:
When encountering questions that ask for simplifying polynomial expressions, using the method FOIL would be easier:
First, which means multiplying the first terms together;Outer, which means that we multiply the outermost terms when the binomials are placed side by side;Inner, which means multiply the innermost terms together;Last, which means multiplying the last term in each binomial together;Solve:
Given
(5x + 4) (7x + (-12x) + 27)
Combine like terms in the parentheses
=(5x + 4) (7x - 12x + 27)
=(5x + 4) (-5x + 27)
Expand parentheses and apply the FOIL method
=-25x² + 135x - 20x + 108
Combine like terms
= [tex]\boxed {-25x^2+115x+108}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\boxed {\boxed {\sf -25x^2+115x+108}}[/tex]
Step-by-step explanation:
We are asked to find an equivalent expression for (5x + 4)(7x+ -12x + 27). Note that we are multiplying 2 polynomials.
[tex](5x + 4)(7x+ -12x + 27)[/tex]
Notice that the second polynomial has like terms. There are 2 terms with an x (7x and -12x) and we can combine them.
[tex](5x + 4)[(7x+ -12x) + 27][/tex]
[tex](5x + 4)[(-5x) + 27][/tex]
[tex](5x+4)(-5x+27)[/tex]
Now we are multiplying 2 binomials. Therefore, we use the FOIL method. We multiply the First terms, the Outside terms, the Inside terms, and the Last terms.
First: 5x * -5x = -25x²Outside: 5x * 27 = 135x Inside: 4* -5x = -20x Last: 4 * 27=108[tex]-25x^2+135x-20x+108[/tex]
Notice there are 2 terms with an x ( 135x and -20x). They are like terms and can be combined.
[tex]-25x^2+(135x-20x)+108[/tex]
[tex]-25x^2+115x+108[/tex]
The equivalent expression in standard form is -25x²+115x+108
Can someone plz solve the math problem i attached as a screenshot. Thx
Answers
Answer:
[tex]radius \: of \: first \: circle \: = \frac{3}{2} = 1.5cm \\ radius \: of \: \: second = \frac{4}{2} = 2cm \\ radius \: of \: third = \frac{6}{2} = 3cm \\ then \: ab \: length \\ = radius \: of \: first + diameter \: of \: second \: +r adius \: of \: third \\ = 1.5 + 4 + 3 \\ = 1.5 + 7 \\ = 8.5 cm\\ thank \: you[/tex]
I need help on this problem expand 2-x(x+6)
(This is distributive property)
Answers
Answer:
2-x^2-6x
Step-by-step explanation:
2-x(x+6)
2-x^2-6c
URGENT. I NEED TO DO IT
Answers
Answer:
[tex]25x +10 \\ 25x \\ are \: the \: exprassion \\ thank \: you[/tex]
Answer:
2nd option and last option
Step-by-step explanation:
the first option is an equation: it has a solution.
the second option is an expression, and follows the criteria of an expression (can be made of co-effecients, symbols, operations, numbers, ect.), so it is one of our answers.
the third option is an equation since it has the equal sign, and thus, has a solution.
the fourth option is simply a number- a value. it does not fit as an equation (no solution) or an expression (can be made of co-effecients, symbols, operations, numbers, ect.)
lastly, our fith option is an expression. it is a coefficient (a multiplication problem between a known value and a variable). this is also one of our last answers.
<7 and <8 are complimentary angles. <5 = <8 and m<6 = 29. Find the measure of angle 7 and angle 5
Answers
Step-by-step explanation:
since < 5 = < 8, so,
< 7 = < 6 = 29°
and < 5 = 90° - 29° = 61°
Two less than the product of 3 and a number is equal to 6
Answers
Answer:
8/3
Step-by-step explanation:
Let x represent the number.
Create an equation to represent the situation, and solve for x:
3x - 2 = 6
3x = 8
x = 8/3
So, the number is 8/3.
a cylindrical barrel contains 42 gallons of oil the diameter is 18 inches. determine the radius of a barrel in centimetres
Answers
18 = 2*radius
Radius =18/2 =9 inches
PLS HELP! WILL GIVE BRAINLIEST
Answers
Answer:
csc x sec x
Step-by-step explanation:
csc = 1/sin
1/sin^2 / cos/sin = 1 / sin^2 * sin/cos = 1 / sin cos = csc sec
solve
pls need help
pls answer now
Answers
k/3 + 4 - 5k = -2k / · 3
k + 12 - 15k = -6k
k - 15k + 6k = -12
-8k = -12 / : (-8)
k = 12/8
k = 3/2 ← the end answer
Answer: A)
What is the sum? 4(^5sqrt x^2y)+3(^5sqrt x^2y)
Answers
Answer:
[tex]4( \sqrt[5]{ {x}^{2} y} ) + 3( \sqrt[5]{ {x}^{2}y } ) \\ [/tex]
factorise out the 5th root of x²y :
[tex] = \sqrt[5]{ {x}^{2}y } (4 + 3) \\ = 7( \sqrt[5]{ {x}^{2} y} )[/tex]
the set of all natural numbers less than 15 write set build notation
Answers
Answer:
{x : x Σ N, x<15}
Step-by-step explanation:
Set of all natural number less than 14 = {x : x Σ N, x<15}
Solve 1/3 (3x + 6) + 2x = 26
Answers
Answer: x = 8
Step-by-step explanation:
Given
(1/3) (3x + 6) + 2x = 26
Expand parentheses and apply the distributive property
(1/3) · 3x + (1/3) · 6 + 2x = 26
x + 2 + 2x = 26
Combine like terms
(x + 2x) + 2 = 26
3x + 2 = 26
Subtract 2 on both sides
3x + 2 - 2 = 26 - 2
3x = 24
Divide 3 on both sides
3x / 3 = 24 / 3
[tex]\boxed{x=8}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The school band has d drummers and 5 violinists. There are 2 more violinists than drummers. Which of the following equations represents the situation?
Answers
Answer:
A d = 5+2
Step-by-step explanation:
There are two more drummers than violinists
There are 5 violinists
5 + 2 = d
or in other words, d = 7
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
A ray extends forever. True or false
Answers
false
false
false........
false
Answer:
it extends forever in one direction. so false i guess
Step-by-step explanation:
Add the Following Fractions:
\large \frac{3}{8}+\frac{2}{8}=?
a. 5/16
:b. 5/8
c. 6/8
d. 1/8
Answers
Answer:
B. [tex]\frac{5}{8}[/tex]
Explanation:
Because the denominators (bottom numbers) of both fractions are the same, we simply just add the numerators (top numbers) and keep 8 as the denominator.
James had a peach that was 98 \text{ mm}98 mm98, start text, space, m, m, end text in diameter. One day he watered it with a magical solution, and it grew to 188{,}869 \text{ mm}188,869 mm188, comma, 869, start text, space, m, m, end text in diameter.
Approximately how many times as large did the diameter of the peach become after James watered it?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
2 \cdot10^32⋅10
3
2, dot, 10, cubed
(Choice B)
B
9 \cdot10^39⋅10
3
9, dot, 10, cubed
(Choice C)
C
2 \cdot10^42⋅10
4
2, dot, 10, start superscript, 4, end superscript
(Choice D)
D
9 \cdot10^49⋅10
4
9, dot, 10, start superscript, 4, end superscript
Answers
9514 1404 393
Answer:
A. 2×10³
Step-by-step explanation:
The ratio of diameters is ...
(189,869 mm)/(98 mm) ≈ 1927.3 ≈ 2000 = 2×10³
The diameter of the peach became about 2×10³ times as large.
(2x + 5) + (x + 4) =
Answers
Answer:
3x + 9
Step-by-step explanation:
(2x + 5) + (x + 4)
Distribute the + to all numbers/variables
2x + 5 + x + 4
Combine like terms:
2x + 5 + x + 4
3x + 5 + 4
3x + 9
Hope this helped.
which statement below correctly describes the diagram
Answers
9514 1404 393
Answer:
(a) the diagram is incorrect
Step-by-step explanation:
There is no overlap between the sets of rational and irrational numbers. The diagram is incorrect.
3/10 = 15/50 what is the multiplier
Answers
3/10=15/50
3/10 x 5/5 = 15/50
Answer:
the answer is 150
Step-by-step explanation:
you will do cross multiplication where 3 will multiply 50 and 15 will multiply 10. u will get 150=150
Nine times the difference of a number and 4 is the same as the product of 2 and the same
number plus 10. What is the number?
Answers
Answer:
x = 8
Step-by-step explanation:
9(x - 4) = 2(x + 10)
9x - 36 = 2x + 20
7x = 56
x = 8
Please mark as brainliest :)
Please help
Solve the inequality.
3 < 6x – 3 5 9
[?] = x= []
Answers
Answer:
(1 )= ..x = (2)
Step-by-step explanation:
(1) = x = (2)
Answer: 1 ≤ x ≤ 2
Step-by-step explanation:
Given inequality
3 ≤ 6x - 3 ≤ 9
Add 3 on all sides
3 + 3 ≤ 6x - 3 + 3 ≤ 9 + 3
6 ≤ 6x ≤ 12
Divide 6 on all sides
6 / 6 ≤ 6x / 6 ≤ 12 / 6
[tex]\boxed{1}[/tex] ≤ x ≤ [tex]\boxed{2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
what is the arithmetic sequence of a1=228 n=28 sn=2982
Answers
Answer:
use the formula sn= n(a1+an)/2
Step-by-step explanation:
2982=28(228+an)/2
5964=28(228+an)
5964/28=228+an
213=228+an
an=-15(last term)
to find difference use formula
an = a+(n-1)d
-15=228+(28-1)d
-243=27d
d=-243/27
d=-9
arithmetic sequence can be found be keep on subtracting 9 from 228
hence the arithmetic sequence is
228, 219, 210, 201, 192, 183, 174........-15
QOX
7. A total of 2000 people attended a benefit
concert was held to raise money for a
children foundation. Student ticket cost $2
and an adult ticket cost $3. If the organizer
raises a total of $5050, how many students
attended the concert?
Let x = number of students
Let 2000 - x = number of adults
Need explanation
Answers
Answer: Student ticket cost $2 and an adult ticket cost $3.
257 kids total attended
Step-by-step explanation:
