The height, width and length of a small box are consecutive integers with the height being the smallest
of the three dimensions. If the length and width are increased by 2 cm each and the height is tripled,
then the volume of the box is increased by 552 cm3
. Use algebraic techniques to find the dimensions of
the original small box.
Answers
9514 1404 393
Answer:
4 cm, 5 cm, 6 cm
Step-by-step explanation:
If x represents the height of the original box, the other two dimensions are ...
width = x+1
length = x+2
and the volume is ...
V = HWL = x(x +1)(x +2) = x³ +3x² +2x
__
After the change in dimensions, the height is 3x, the width is x+3, and the length is x+4. The new volume is ...
V = HWL = 3x(x+3)(x+4) = 3x³ +21x² +36x
The difference in volumes is ...
(3x³ +21x² +36x) -(x³ +3x² +2x) = 552
In standard form, this equation is ...
2x³ +18x² +34x -552 = 0
Factoring out 2 gives ...
x³ +9x² +17x -276 = 0
Possible rational roots are 1, 2, 3, 4, 6, and other divisors of 276. The largest possibility worth considering is less than ∛276 ≈ 6.5. Trial and error, or a graphing calculator can show us that x=4 is the only real solution to this equation.
The dimensions of the original small box are 4 cm × 5 cm × 6 cm.
Related Questions
please help me with this
Answers
Answer:
28.24
Step-by-step explanation:
25 + 32/10 + 4/100
take lcm of the denominator
lcm = 100
25*100 + 32*10 +4*1/100
2500 + 320 +4/100
2824/100
28.24
Find the value of (1 point)
Answer D .28.24
Figure ABCDE has vertices A(-2, 3), B(2, 3), C(5,-2), D(0, -4), and E(-2,-2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles. Part A: How many triangles and rectangles did you make? (1 point) Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points) Part C: What is the area of Figure ABCDE? Show your work. (5 points)
Answers
9514 1404 393
Answer:
A: 1 rectangle and 2 triangles (or 1 trapezoid and 1 triangle)
B: AB = 4; AE = 5
C: area = 34.5 square units
Step-by-step explanation:
Part AThe figure can be decomposed into a right trapezoid and a triangle. The right trapezoid can be decomposed into a rectangle and a triangle.
easiest decomposition: 1 right trapezoid and 1 triangle
decomposition per instructions: 1 rectangle and 2 triangles.
__
Part BAB is a horizontal line, so its length is the difference of the x-coordinates of B and A: 2 -(-2) = 4.
AE is a vertical line, so its length is the difference of the y-coordinates of A and E: 3 -(-2) = 5.
AB = 4, AE = 5
__
Part CThe area of the trapezoid is given by ...
A = 1/2(b1 +b2)h
The figure shows the base lengths to be 4 and 7, and the height to be 5. The trapezoid's area is ...
A = 1/2(4+7)(5) = 27.5 . . . . square units
The area of triangle CDE is given by the formula ...
A = 1/2bh
The figure shows the base length to be 7 and the height to be 2 units. The triangle area is ...
A = 1/2(7)(2) = 7 . . . . square units
The total area of figure ABCDE is 27.5 +7 = 34.5 square units.
Answer:
Answer:
A: 1 rectangle and 2 triangles (or 1 trapezoid and 1 triangle)
B: AB = 4; AE = 5
C: area = 34.5 square units
Step-by-step explanation:
Part A
The figure can be decomposed into a right trapezoid and a triangle. The right trapezoid can be decomposed into a rectangle and a triangle.
easiest decomposition: 1 right trapezoid and 1 triangle
decomposition per instructions: 1 rectangle and 2 triangles.
__
Part B
AB is a horizontal line, so its length is the difference of the x-coordinates of B and A: 2 -(-2) = 4.
AE is a vertical line, so its length is the difference of the y-coordinates of A and E: 3 -(-2) = 5.
AB = 4, AE = 5
__
Part C
The area of the trapezoid is given by ...
A = 1/2(b1 +b2)h
The figure shows the base lengths to be 4 and 7, and the height to be 5. The trapezoid's area is ...
A = 1/2(4+7)(5) = 27.5 . . . . square units
The area of triangle CDE is given by the formula ...
A = 1/2bh
The figure shows the base length to be 7 and the height to be 2 units. The triangle area is ...
A = 1/2(7)(2) = 7 . . . . square units
The total area of figure ABCDE is 27.5 +7 = 34.5 square units.
Step-by-step explanation:
trust meh
Riley's cat has 8 kittens. Of those 8 kittens, 4 are brown, 1 is grey, and the rest are orange. Which of the following could be used to find the probability that the first kitten Riley picks up at random is NOT orange?
Answers
Answer:
5/8 or 62.5 percent
Step-by-step explanation:
There are 27 chocolates in a box, all identically shaped. They’re 10 are filled with nuts, eat with Carmel, and nine are solid chocolate. You randomly select one piece, eat it, and then select a second piece find the probability of selecting two solid chocolate in a row
Answers
There are 27 chocolates. 10 are nuts ( 37%). 9 are chocolates (33%). 8 are caremel (30%). So 37/2 = 16.5% is the answer.
Indicate the measure of each angle when ∠PTS=128
Answers
9514 1404 393
Answer:
∠PTR = 80°
∠PTQ = 45°
∠QTS = 83°
Step-by-step explanation:
The outer scale is useful for reading the values of angles that start with PT.
∡PTR = 80°
∡PTQ = 45°
The measure of angle QTS is found from ...
∡PTS = ∡PTQ +∡QTS . . . . . angle sum theorem
∡QTS = ∡PTS -∡PTQ . . . . . subtract ∡PTQ
∡QTS = 128° -45°
∡QTS = 83°
100 points if u get it right!!!
Answers
Answer:
To be honest I think its C but it may be A
Step-by-step explanation:
The ages of each of the basketball players on a team are given.
13, 13, 13, 14, 14, 17, 18, 18
What is the mean age of these players?
Answers
Answer:
15
Step-by-step explanation:
We add up the ages of all the basketball players.
13 + 13 + 13 + 14 + 14 + 17 + 18 + 18 = 120
Now we divide by the number of basketball players.
120 ÷ 8 = 15
The mean age of the basketball players are 15.
Answer:
Mean = 15
Step-by-step explanation:
Mean = sum of observation. ÷ total no. of observation
= 13 + 13 + 13 + 14 + 14 + 17 + 18 + 18 ÷ 8= 120 ÷ 8= 15csc theta * cos^2 theta +sin theta= csc theta
Answers
Step-by-step explanation:
[tex] \csc \theta \cos^{2}\theta + \sin \theta = \csc \theta(1 - \sin^{2}\theta) + \sin \theta[/tex]
[tex] = (\csc \theta - \sin \theta) + \sin \theta[/tex]
[tex] = \csc \theta[/tex]
Solve the compound inequality
Answers
Answer:
B
Step-by-step explanation:
Answer:
I'm so sorry I did not mean to answer! Ignore my response
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation
x^2 + 8x – 4 = 0, which number would have to be added to "complete the square"?
Answers
Step-by-step explanation:
everything can be found in the picture
11. f(x) = x + 3, g(x) = -x + 2. Find (f + g)(x)
Answers
Answer:
(f + g)(x) = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x + 3
g(x) = -x + 2
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in function values: (f + g)(x) = x + 3 - x + 2[Subtraction] Combine like terms (x): (f + g)(x) = 3 + 2Add: (f + g)(x) = 5Let the sequence be 1, 3, 5, 7, 9……… then this sequence is
Answers
the answer is 11 because 2 multiple are increasing
Answer:
An arithmetic sequence, The difference in any term with the previous term is same.
Step-by-step explanation:
See, ah this is a little bit easy question so let’s start solving it -:
Firstly, um see the difference between the given numbers-: 1, 3, 5, 7,9 _?
Between 1 and 3 the difference is 2
Between 5 and 3 the difference is 2
Between 7 and 5 the difference is 2
Between 9 and 7 the difference is 2
So, here we see the difference among all is same. So. it is an arithmetic sequence.
So, let's find the fourth term. We can either do it by arithmetic progression or by simply adding 2 to 7. I.ll first show you by doing A.P. then we will check the answer by adding 2 to 7.
So, as we know the basic formula of A.P. which is -: a1+(n-1)d
Here, a1=1, n=5, d=2
Let’s put the values in the formula-: 1+(5–1)2 = 1+(4)2 = 1+8 = 9
Now let’s check it. As the difference between each digit is same so definately the difference between 9 and the unknown number is 2.
Then, the unknown no. is 9+2 = 11
Hence, the answer is 11
A large university chemistry course has a required textbook available for $ 154 and a recommended supplement for $ 36. The university bookstore finds, over time, that 15% of students enrolled in the course purchase only the textbook, while 75% buy both the textbook and the supplement. No students buy only the supplement. a) What percent of students buy neither the textbook nor the supplement from the bookstore
Answers
Answer:
10% of students buy neither the textbook nor the supplement from the bookstore
Step-by-step explanation:
We have that:
15% buy only the textbook.
75% buy both the textbook and the supplement.
None buy only the supplement.
a) What percent of students buy neither the textbook nor the supplement from the bookstore
15% + 75% = 90% buy at least one of them. So
100% - 90% = 10% buy neither.
What is the distance between the two points? (-18, -6) & (-18,-1)
A. 4
B. 5
C.6
D. 7
Answers
Answer:
5
Step-by-step explanation:
D² = ( x2 - x1 )² + ( y2 - y1 )²
= [ (-18) - (-18) ]² + [ (-1) - (-6) ]²
= ( -1 + 6 )²
D² = ( 5 )²
hence, D = 5
Answer: B) 5
Step-by-step explanation:
Let's start by finding the distance from one x coordinate to the other. Remember subtracting by a negative is the same as adding a positive
-18-(-18)
-18+18
0
There is no distance away from the x value so the distance we need to count is from the y value
-1-(-6)
-1+6
5
The distance between the two points is 5.
The rate to rent a small moving van is $30 per day, plus $2 per mile. Jada rented a van to drive to her new home. It took
two days, and the total cost was $360. How many miles did she drive?
Answers
Help meeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
the answer is in the above image
What is the value of y in the equation 3y - 8 = 22?
7.3
8
10
14
Answers
WILL MARK BRAINLIEST!!
Which is the graph of g(x)
Answers
Answer:
the second one after first
Step-by-step explanation:
it strictly obeys the rules of boundary
A student is taking a multiple-choice exam in which each question has four choices.
Assume that the student has no knowledge of the correct answers to any of the questions.
She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box.
She randomly selects one ball for each question and replaces the ball in the box.
The marking on the ball will determine her answer to the question.
There are five multiple choice questions on the exam.
What is the probability that she will get
a. Five questions correct?
b. At least four questions correct?
c. No questions correct?
d. No more than two questions correct?
Answers
Answer:
d no more than two questions correct
plz it's do to day HELP PLZ
Answers
Answer:
9 units^3
Step-by-step explanation:
V = l*w*h
= 1 1/2 * 4 * 1 1/2
Change to improper fractions
= 3/2 * 4 * 3/2
= 36/4
= 9 units^3
Solve for M and N please help me
Answers
Answer:
M=4 N=6
Hope this helped!
An aeroplane descended 1.4 miles to an elevation of 0.6 miles as shown by the equation below.
Solve the equation to find the elevation of the plane before its descent.
x-1.4 = 0.6
A 0.8
B 1.0
C 2.0
D 1.2
Quick
Answers
Answer:
C 2.0
Step-by-step explanation:
x-1.4 =0.6
add 1.4 to both sides
x=2.0
You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest hundredth.
The probability of not spinning a red, flipping tails, then not spinning an even number is ?
Answers
Answer:
2 / 9
Step-by-step explanation:
From the spinner :
Number of reds = 1
Total number of colors = 3
P(not red) = Probability of not spinning red, = 1 - p(red) = 1 - 1/3 = 2/3
P(flipping tail) = a coin flip, P(tail) = 1/2
P(not even) = probability of not obtaining an even number) = 1 - p(obtaining an even number)
(1, 2, 3) ; not even = (1, 3)
P(not even) = 2 /3
Compound probability = 2/3 * 1/2 * 2/3 = 4 / 18 = 2 /9
A grocery store chain uses loyalty cards that offer discounts on sale attheir store. The probability that a randomly chosen shopper has a loyaltycard is 0.8. A group of shoppers have been selected at random to completea customer satisfaction survey. Let Xi be a random variable that equals 1 when a customer has a loyalty card and 0 otherwise.
Required:
a. Construct a joint probability table for the random variables X, and X.
b. Define the event that the first four customers sampled have loyalty cards in terms of the random variables X, X2, X3, and Xd. Then compute the probability of this event.
Answers
What is the quotient?
Answers
Answer:
A
Step-by-step explanation:
this is a fraction we two powers with the same base so we have tu subtract the exponents and maintain the same base
5^(-6-3) = 5^-9 = 1/5^9
Latoya Abdul and dale sent a total of 88 text messages over their cell phones during the weekend Latoya sent 8 more messages than Abdul.Dale sent 4 times as many messages as Latoya how many messages did they each send?
Answers
Answer:
Abdul - 8 messages
Latoya - 16 messages
Dale - 64 messages
Total - 88 messages
Step-by-step explanation:
A: (x)
L: (A + 8)
D: (L* 4)
A: 8 = 8
L: 8 + 8 = 16
D: 16 * 4 = 64
8 + 16 + 64 = 88
Hope this helps!
Find the equal measures of 1. 28 m = ________ km 2. 3899 ml = ______ l 3. 79 kg = _____ g Show the process of each
Answers
Answer:
1. 0.028 km
2. 3.899 L
3. 79,000 g
Jackson made 36 calls in 2.25 hours. How many calls per hour did he make?
Answers
Answer:
16 calls
Step-by-step explanation:
make an equation based off this ratio -- 36 calls: 2.25 hours and x calls: 1 hour
36/2.25 = x/1
cross multiply to get 36=2.25x
divided by 2.25 on both sides
x=16
Social scientists discovered that 1,013 General Social Survey (GSS) respondents in 2010 watched television for an average of 3.01 hours per day, with a standard deviation of 2.65 hours per day. Answer the following questions, assuming the distribution of the number of television hours is normal.
Required:
a. What is the Z score for a person who watches more than 8 hr/day?
b. What proportion of people watch television less than 5 hr/day? How many does this correspond to in the sample?
c. What number of television hours per day corresponds to a Z score of +1?
d. What is the percentage of people who watch between 1 and 6 hr television per day?
Answers
Answer:
Following are the responses to the given question:
Step-by-step explanation:
[tex]Sample \ size = n = 1013\\\\\mu = 3.01\\\\\sigma = 2.65[/tex]
For point a:
Using formula:
[tex]Z = \frac{(X - \mu)}{\sigma}\\\\X = 8\\\\Z = \frac{(8- 3.01)}{2.65} = 1.88\\\\[/tex]
For point b:
[tex]P(X<5)=?\\\\ x = 5\\\\ Z = \frac{(X - \mu)}{\sigma} = \frac{(5 -3.01)}{2.65} = 0.7509434\\\\P(Z< 0.7509434) = 0.7736566\\\\P(X<5) = P(Z< 0.7509434) = 0.7736566[/tex]
For point c:
[tex]X=? \\\\Z = 1\\\\\text{Formula for X score:}\\\\X = \mu + Z \times \alpha\\\\X = 3.01 + 1\times 2.65 = 3.01 + 2.65 = 5.66[/tex]
For point d:
[tex]P(1 \leq X \leq 6)=? \\\\P(1 \leq X \leq 6) = P(X \leq 6) - P(X\leq 1) = P(X< 6) - P(X<1)\\\\\text{Z score for x} = 6\\\\Z = \frac{(6 - 3.01)}{2.65} = 1.128301887 \\\\P(Z< 1.128301887) = 0.870403777 \\\\P(X<6) = P(Z< 1.128301887) = 0.870403777 \\\\\text{Z score for x} = 1 \\\\[/tex]
[tex]Z = \frac{(1 -3.01)}{2.65} = -0.758490566\\\\P(Z< -0.758490566) = 0.224078679\\\\P(X<1) = P(Z< -0.758490566) = 0.224078679 \\\\P(1 \leq X \leq 6) = P(X \leq 6) - P(X\leq 1) = P(X<6) - P(X<1) \\\\ = 0.870403777 - 0.224078679 = 0.646325097 \\\\\text{Required probability} = 0.646325097[/tex]
I need the area please
Answers
Answer:
120
Step-by-step explanation:
Figure shown is a parallelogram
Area of a parallelogram = base length times height
Given base length: 15in
Given height:8in
Area = 8 * 15 = 120in^2
Answer:
120 in.²
Step-by-step explanation:
8 in. × 15 in. = 120 in.²
