You want to construct an open-top box that is 6 inches deep, with a square base. It must have a volume of 864 cubic inches. You have one big piece of cardboard. You will start by cutting it down to a square, and then you will cut smaller squares out of each corner and fold up the sides.
Answers
The statements that are true are the volume of the box is v = lwh = 864 in³ and the volume can be expressed in an equation as v = 6x² = 864in³
Volume of a SquareThe volume of a square box is equal to the cube of the length of the side of the square box. The formula for the volume is V = l³, where "l" is the length of the side of the square box.
In the given problem, the volume of the box is 864 cubic inches.
However, we have to remember that the box isn't a square, but rather the base has a square shape.
The volume of the figure is
v = l * w * h
l = lengthw = widthh = heightIf we divide the volume by the height, we will have the area of the figure
Area = volume / height
Area = 864 / 6
Area = 144 square inches
Since the base has a square shape;
A = l²
144 = l²
l = √144
l = 12 in
The side length is 12 inches.
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Related Questions
Question 4 (1 point)
The image shows quadrilateral ABCD.
Find the area of ABCD. Explain or show your reasoning.
Answers
Answer:
25
Step-by-step explanation:
Using the Pythagorean Theorem, we can find the side length of each side.
a^2 + b^2 = c^2
=> 3^2 + 4^2 = x^2
=> 9 + 16 = x^2
=> x = 5
By applying the same formula for each side, we will get that each side is 5 units.
So, the area = 5*5 = 25
The quadrilateral is a square and the area of square is 25 square units.
What is a quadrilateral?
A quadrilateral is 2-dimensional geometric closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.
For the given situation,
The quadrilateral ABCD has points A(0,4), B(3,0), C(7,3), D(4,7).
The distance these points can be found by
[tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
AB = [tex]d=\sqrt{(3-0)^{2}+(0-4)^{2} }[/tex]
⇒ [tex]AB = \sqrt{3^{2}+4^{2} }[/tex]
⇒ [tex]AB=\sqrt{9+16}[/tex]
⇒ [tex]AB=\sqrt{25}[/tex]
⇒ [tex]AB=5[/tex]
BC = [tex]d=\sqrt{(7-3)^{2}+(3-0)^{2} }[/tex]
⇒ [tex]BC=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]BC=5[/tex]
CD = [tex]d=\sqrt{(4-7)^{2}+(7-3)^{2} }[/tex]
⇒ [tex]CD=\sqrt{(-3)^{2} +4^{2} }[/tex]
⇒ [tex]CD=5[/tex]
DA = [tex]d=\sqrt{(4-0)^{2}+(7-4)^{2} }[/tex]
⇒ [tex]DA=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]DA=5[/tex]
Since AB = BC = CD = DA, the quadrilateral is a square.
The formula of area of quadrilateral is
[tex]A=(side)^{2}[/tex]
⇒ [tex]A=5^{2}[/tex]
⇒ [tex]A=25[/tex]
Hence we can conclude that the quadrilateral is a square and the area of square is 25 square units.
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Find the missing length. The triangles in each pair are similar.
Answers
Answer:
........................................
What are the zeros of f(x) = x2 + 3x - 10?
A. X= -5 and x = 2
B. x= -5 and x = -2
C. X= 5 and x = -2
D. x = 5 and x = 2
Answers
Answer:
(x+5) (x-2)
SO -5 and 2 option A
Step-by-step explanation:
factor it. and set equal to zero.
How may candies did Thad get all together? Pls help quickly
Answers
Answer:
all together there is 141 candies in all
this is old work i forget how to do it
Answers
Answer:
1.101, 1.001, and 0.113
Step-by-step explanation:
the first on is the highest
plz leave a like and brainlest!! i need 10 to ask a quistion!!!
Answer:
Tenths place is a zero
↓
0.113 1.001 1.101
↑
One's place is a zero
please help!!No links
Answers
Jon is buying gas for his car. The cost of gas varies directly with the number of gallons of gas. If
he pays $8.75 for 5 gallons of gas, how much would it cost for 32 gallons?
Answers
Answer:
56 gallons of gas
Step-by-step explanation:
Jon paid $8.75 for 5 gallons.
So how much does 1 gallon cost?
=> 5 gallons = $8.75
=> 5/5 gallons = $8.75/5
=> 1 gallon = $1.75
So how much does 32 gallons cost?
=> 32 gallons = 32 * 1.75 = $56
Which of the following functions translates the graph of the parent
function f(t) = x² horizontally left 6 units?
Answers
Answer:
shawty us bad with the scratchers in
what is the circumference of circle P shown below
Answers
Answer:
8π units
Step-by-step explanation:
The circumference of a circle is calculated by using the following formula
2 × r × π (r: radius)
2 × 4 × π = 8π
The dollar store buys a hat for $0.80. Then they mark up the price by 20%.
How much will they sell the hat for?
Answers
Answer:
$0.96
Step-by-step explanation:
20% of 0.80 is 0.16
0.80 + 0.16 = 0.96
Answer:
$0.96
Step-by-step explanation:
Multiply 0.80 times 0.2
0.80 x 0.2=0.16
Then add up 0.16 and 0.80 to get your answer
0.80 + 0.16=0.96
Hope it helps
20) If the area of a rectangular playground is
p^2 -6p - 7 square feet, what is the perimeter of the
playground?
Answers
Answer:
Explanation:
Write an equation to solve the problem.
Area of rectangle = L(w)
Assuming that the width measures x meters, the length measures x + 5 meters.
500 = x(x + 5)
500 =
x
2
+ 5x
0 =
x
2
+ 5x - 500
As you may already know, a trinomial of the form
a
x
2
+ bx + c, a = 1, you must find 2 numbers that multiply to c and that add to b. Two numbers that multiply to -500 and add to +5 are +25 and -20
0 = (x + 25)(x - 20)
x = -25 and 20
Since a negative length is impossible, the width mesures 20 meters and the length measures 25 meters.
Practice exercises:
A rectangle has a perimeter of 90 meters. Find the maximum area.
The area of a right triangle is 120
m
2
. The base measures half the sum of the height and one. Find the perimeter.
Find the area and perimeter of a right triangle the has a height that is 2 more than the double of the width and that has a hypotenuse that measures
√
68
meters.
Good luck!
Step-by-step explanation:
Find the value of a. Round your answer to the nearest tenth.
Answers
Answer:
Polly do you know the formula for law of Cosines?
find it if you don't
Step-by-step explanation:
a = sqrt( b^2 +c^2 - 2bcCos(A) )
a = sqrt( 100 + 62.41 -34.197)
a = sqrt(128.213)
a = 11.323
a = 11.3 ( to the nearest tenth )
Select the statement that describes this expression: 10 + fraction 1 over 4x (5 + 3) − 3. (2 points)
10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3
fraction 1 over 4 of 10 times the sum of 5 and 3, minus 3
3 more than 3 plus 5 multiplied by fraction 1 over 4, then add 10
10 times fraction 1 over 4 plus 3 and 5, minus 3
Answers
Answer:
10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3
plz mark as brainliest
hope it helps
Answer:10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 2
Step-by-step explanation:
find the x-intercepts of y= x^2+4x+8 using the quadratic formula.
Answers
Answer: To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
2
+
2
√
3
,
0
)
,
(
2
−
2
√
3
,
0
)
y-intercept(s):
(
0
,
8
)
Step-by-step explanation: To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
2
+
2
√
3
,
0
)
,
(
2
−
2
√
3
,
0
)
y-intercept(s):
(
0
,
8
)
8.8C
What value of x makes this equation true?
12x - 15 = 6 - 3x
Answers
I hope this is helpful :)
PLEASE ANSWER NUMBER 4 NO BS PLEASE HELP ME I WILL GIVE BRAINLIEST ANSWER
Answers
Answer:
A'(1,-2)
L'(-3,-5)
T'(3,-1)
Reflection:
A'(-1,-2)
L'(3,-5)
T'(-3,-1)
Step-by-step explanation:
what is the discriminant of the polynomial below 2x^2+5x-8
A. 89
B. -39
C. 31
D. -59
Answers
Answer:
Hi! The answer to your question is A. 89
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
A pretzel maker was interested in knowing the number of pretzels in each bag is sold. The results of the research are shown in the box and whisker plot. What is the range in the number of pretzels? Please help
Answers
Answer:
23 pretzels
Step-by-step explanation:
The range value is obtained by taken the difference between the maximum and minimum values ;
The range = maximum - minimum
From the box and whisker plot attached ; the maximum value = 68
Minimum value = 45
Hence, the range in the number of pretzels :
68 - 45 = 23
Answer:
22
Step-by-step explanation:
Subtract the minimum (44) and the maximum (66) the answer to this question is 22
Find the slope of the line.
Will give brainiest if correct.
Answers
Answer:
1,2
Step-by-step explanation:
Answer:
The slope of the line is (2)
Step-by-step explanation:
Good luck ^_^
Which expression is equivalent to (3x2+3x−3)−(6x2−4x−2)?
A
−3x2+7x−1
B
−3x2−x−5
C
−3x2+7x−5
D
−3x2−x−1
Answers
Answer:
A. -3x^2+7x-1
Step-by-step explanation:
(3x^2+3x-3)-(6x^2-4x-2)
3x^2+3x-3-6x^2+4x+2
-3x^2+7x-1
Find the total length of rope that is brought on the trip.
A. 25 3 4 yards
B. 29 3 4 yards
C. 33 3 4 yards
D. 37 3 4 yards
Answers
i have the quiz before and the answer is D: 37 3/4 yards
:)
Hi! Please help on this question (you have to use the Pythagorean theorem method) and explain the steps *giving brainliest*
Answers
Answer:
The diagonal length is 50.
Step-by-step explanation:
Square the lengths of the legs: (30 yd)^2 + (40 yd)^2 and add these squares together. Taking the square root of this sum produces the length of the diagonal: d = √(900 + 1600) = √2500 = 50.
The diagonal length is 50.
I can choose and create diagrams to help me compare two situations.
SOMEONE PLEASE HELP MY TEACHER WANTS TO PUT ME IN SUMMER SCHOOL SO I NEED TO GET MY HW DONE ASAP SO PLEASE REPLY WITH AN ANSWER PLSS!!!
Answers
Answer:
blurred poate
Step-by-step explanation:
blurred po ate
The sum of -9 and 18/2
Answers
Answer:
0
Step-by-step explanation:
Sum means addition so:
-9 + 18/2
(18/2 = 9)
-9 + 9
0
Answer: 0
Step-by-step explanation: The answer I got was 0. I'm assuming that 18/2 is 18 divided by 2. 18 divided by 2 is 9 and if you add a positive and a negative its like subtracting. 9-9=0 so the answer is 0.
Meljer is selling a 9.25 oz bag of Doritos for $3.50. What is the cost per ounce of Doritos? Round your answer to the nearest penny (hundredths of a dollar).
Answers
Answer:
0.38
Step-by-step explanation:
We will use ratios:
[tex]\frac{9.25}{3.5} =\frac{1}{x} \\\\9.25x=3.5\\x=0.38[/tex]
prove this qsn plzz and fast
Answers
Step-by-step explanation:
Let use the first of the medians. Medians AX.
Median AX is the midpoint of BC so our median is
[tex] \frac{1}{2} (b + c) - a[/tex]
Let use the second median.
Median BY is the midpoint of AC so our median is
[tex] \frac{1}{2} (a + c) - b[/tex]
Let use the final median.
Median CZ is the midpoint of AB so our median is
[tex] \frac{1}{2} (a + b) - c[/tex]
Now add all them up
[tex] \frac{1}{2} (b + c ) - a + \frac{1}{2} (a + c) - b + \frac{1}{2} (a + b) - c[/tex]
[tex] \frac{1}{2} b + \frac{1}{2} c - a + \frac{1}{2} a + \frac{1}{2} c - b + \frac{1}{2}a + \frac{1}{2} b - c[/tex]
Add like terms.
[tex] \frac{1}{2} b + \frac{1}{2} b - b = 0[/tex]
[tex] \frac{1}{2} a + \frac{1}{2} a - a = 0[/tex]
[tex] \frac{1}{2} c + \frac{1}{2} c - c = 0[/tex]
[tex]0 + 0 + 0 = 0[/tex]
So
AX+BY+CZ=0
need help
problem/question in image below
Answers
Answer:
Option A would be the correct answer
I don't have an explanation to type but you can trust me :)
Please mark as brainliest for further answers :)Please helppp
The function ƒ(x) = 2x − 1 indicates:
a downward shift of 1 unit.
a shift of 1 unit to the left.
an upward shift of 1 unit.
None of these choices are correct.
Answers
Answer:
It is a downward shift of one unit
what's the answer to this problem?
[tex]5x + 35 = 45[/tex]
Answers
Answer:
5x+35=45
5x=45-35
5x=10
x=2
A quality control expert at a drink bottling factory took a random sample of 9 bottles from a
production run of over 1,000 bottles and measured the amount of liquid in each bottle in the
sample. The sample data were roughly symmetric with a mean of 505 mL and a standard
deviation of 6 mL.
Based on this sample, which of the following is a 95% confidence interval for the mean
amount of liquid per bottle (in mL) in this production run?
Answers
Answer: It's in the screenshot
Step-by-step explanation:
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 9 - 1 = 8 df, is t = 2.306.
The other parameters are given as follows:
[tex]\overline{x} = 505, s = 6, n = 9[/tex]
Hence:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 505 - 2.306\frac{6}{\sqrt{9}} = 500.39[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 505 + 2.306\frac{6}{\sqrt{9}} = 509.61[/tex]
The 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).
More can be learned about the t-distribution at https://brainly.com/question/16162795