The largest possible volume of the box is 6158.394 cm^3.
Define the dimensions of the box to be L, W, and H.
Square base, L = W
Area: A = L^2 * H
Surface Area (Base + Area of 4 sides):
1600 = L^2 + 4 (L*H) ⇒ H = (1600 - L^2) / (4L)
Area: A = 400L - (1/4)L^3
Maximum (Derivative) A' = 400 - (3/4)L^2
Solving for 0
0 = 400 - (3/4)L^2
L^2 ⇒ (40 * SQRT(3)) / 3 = 23.094 (Maximum)
Solving for dimensions, known L=23.094
L = 23.094 cm
W = 23.094 cm
H ⇒ (1600 - L^2) / (4L) = (20 * SQRT(3) / 3) = 11.547 cm
Volume ⇒ L*W*H = 6158.394 cm^3
To locate the most viable extent, add the greatest viable mistakes to every dimension, then multiply. To find the minimum viable volume, subtract the greatest feasible mistakes from each measurement, then multiply.
Volume is a scalar amount expressing the amount of 3-dimensional area enclosed by a closed surface. For example, the gap that a substance or 3-D shape occupies or consists of.
Learn more about volume here https://brainly.com/question/1972490
#SPJ4
What are the two binomial factors for x2 – 25? (x – 5)(x – 5) (x 5)(x 5) (x – 20)(x 5) (x – 5)(x 5)
Answer:
(x - 5)(x + 5)
Step-by-step explanation:
x² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 25
= x² - 5²
= (x - 5)(x + 5)
Answer:
Step-by-step explanation:
(x-5) +(x+5)
triangle abc is equal to
triangle pqr, angle p=8X+4,
angle a=5x+16 , and angle
q=10x+2. find angle r
a. 36
b.not enough info
c. 42
d 102
Answer:
d. 102°
Step-by-step explanation:
We can use the relations ...
corresponding angles in congruent triangles are congruentthe sum of angles in a triangle is 180°to write equations that let us find x and all of the angles in ∆PQR.
Corresponding anglesThe congruence relation ∆ABC ≅ ∆PQR tells us that ∠P = ∠A. Using the given expressions for these angles, we have ...
∠P = ∠A
8x +4 = 5x +16
3x = 12 . . . . . . . . . subtract (5x+4)
x = 4 . . . . . . . . . divide by 3
Then the measure of angle P is ...
∠P = 8x +4 = 8(4) +4 = 36 . . . . . degrees
Other anglesAngle Q in ∆PQR is given as ...
∠Q = 10x +2 = 10(4) +2 = 42 . . . . . degrees
Then the measure of angle R needed to make the total of angles in ∆PQR be 180° is ...
∠R = 180° -36° -42° = 102°
Angle R is 102°.
__
In summary:
x = 4∠P = ∠A = 36°∠Q = ∠B = 42°∠R = ∠C = 102°the milligrams of aspirin in a persons body is given by the equation a=500x(3/4)t, where t is the number of hours since the patient took the medicine.
A. how much aspirin will bein the patients body after two hours?
B. in the equation, about what does the 500 tell us the situation
C. in the equation, what does the 3/4 tells us about the situation.
The amount of aspirin that would be in the patient's body is; 281.25.
What is the amount of aspirin in the patient's body after 2 hours?A) The amount of aspirin in the patient's body after 2 hours can be evaluated as follows;
a = 500×(3/4)² = 4500/16 = 281.25.
B) The number 500 as used in the equation represents the amount of aspirin in the patient's body prior to taking the medicine, at time, t= 0.
C) The fraction 3/4 as used in the task content is the factor of change in aspirin content in the patient's body.
Read more on exponential functions;
https://brainly.com/question/14197900
#SPJ1
The following table shows a proportional relationship between jjj and mmm.
jjj mmm
444 333
121212 999
202020 151515
Write an equation to describe the relationship between jjj and mmm.
Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
Writing an Equation to Represent a Proportional Relationship
What is proportional relationship?
A proportional relationship between two quantities is when the two quantities vary directly with one and other. Meaning if one item is doubled, the other item is also doubled.
Going back to the given problem above, we have the table showing the proportional relationship between j and m.
j | 4 | 12 | 20 |
m | 3 | 9 | 15 |
Solution:
Step #1
The proportional relationship can be written as:
m/j = ¾ = 9⁄12 = 15⁄20 = ¾
Step #2
So, the equation representing this proportional relationship is:
m = ¾ × j/1 = 3j/4
Final Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
Look at this table.
Hours of Monthly
Pay
1220
1420
1620
1820
2020
2220
2420
Training
10
20
30
40
50
60
70
According to the table, how many hours of training would you need to have a
monthly pay of $1500?
Using a linear function, it is found that you would need roughly 24 hours of training to have a monthly pay of $1500.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Looking at the table, the pay increases $200 each 10 hours of work, hence the slope is:
m = 200/10 = 20
Then:
y = 20x + b
When x = 10, y = 1220, hence:
y = 20x + b
1220 = 20(10) + b
b = 1020.
Then the pay for x hours of training is:
y = 20x + 1020.
For a pay of $1500, we have that:
y = 20x + 1020.
1500 = 20x + 1020.
20x = 480
x = 24
You would need roughly 24 hours of training to have a monthly pay of $1500.
More can be learned about linear equations at https://brainly.com/question/24808124
#SPJ1
Which of the following situations involve opposite quantities combining to make 0?
·Krista has a new piggy bank. She adds 3 quarters on Tuesday, and then adds another 3 quarters on Thursday.
·Carlyns opens a new checking account with $30. His first purchase, made with his new debit card, totals $28.
·Bekzod makes 1.5 liters of lemonade and drinks it all during the afternoon.
·Daisy is writing a novel. She wrote 4 new pages to finish Chapter 1. When she reviews Chapter 1, she discards these 4 pages and an additional 4 pages.
Given: BC bisects ZABD
mZABD = 52°
Prove: mABC = 26°
A
D
B
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Statements Reasons
mZABD = 52
mZABC+ m ZABC = 52
Statements
mZABC=mZCBD
m/ABC+mZC=52
Reasons
BC bisects ZABD
mZABC+mZCBD =
m ZABD
A bisector is a line that divides a given line or angle into two equal parts or measures. So that the required statements and reasons are given below:
STATEMENT REASONS
1. BC bisects <ABD Given
2. m<ABC = [tex]26^{o}[/tex] Bisection property of an angle
3. 2(m<ABC) = [tex]52^{o}[/tex] Sum of angles of a bisected angle
4. m<ABC = m<CBD Congruent parts of a bisected angle
5. <mABC + m<ABC = [tex]52^{o}[/tex] Sum of an individual angle of a bisected angle
6. m<ABC + m<CBD = [tex]52^{o}[/tex] Sum of angles of a bisected angle
7. m<ABC + m<CBD = m<ABD Sum of the angles of a bisected angle
The above statements and reasons are majorly centered on a bisector, the angles formed due to the bisection of a given angle, and the bisected angle.
For more clarifications on the bisection of an angle, visit: https://brainly.com/question/5799105
#SPJ1
Answer:
1. BC bisects <ABD | Given
2.m<ABD=52 | Given
3.m<ABC = m<CBD | Definition of Bisector
4.m<ABC + m<CBD = m<ABD | Angle Addition Postulate
5.m<ABC + m<CBD =52 | Substitution Property
6.m<ABC + m<ABC =52 | Substitution Propery
7.2(m<ABC)=52 | Addition
8.m<ABC=26 | Division Property
Step-by-step explanation:
Edge 2022
In a group of 60 students, 18 students take Algebra I, 20 students take
Algebra II, and 10 students take both subjects. How many students don't take
either of these subjects?
A. 12
B. 32
C. 34
D. 36
Answer:
32...................
Let $m$ be a positive integer such that $m$ has exactly 5 positive divisors. How many distinct prime factors does $m$ have
If m has exactly 5 positive divisors then there can only be one prime factor.
According to statement
m has exactly 5 positive divisors AND
Let A^p,B^q,.... are the possible factors of integer m then
assume that p and q ≥ 1.
then the number of possible divisors cannot be 5 because there are no two integers p, q ≥ 1, such that (p +1)(q + 1) = 5
So, If m has exactly 5 positive divisors then there can only be one prime factor.
Learn more about FACTORIZATION here https://brainly.com/question/11434122
#SPJ4
Match each formula on the left with an equivalent formula on the right.
W = X-Y
W = X - //
W = 4 - Y
W = XY
Y
X =W₁ + ½
X = Z(W + Y)
X = WZ+Y
X = // +Y
The formulas and the equivalent formulas are
W = X - Y X = W +Y
W = X/Z - Y X = Z(W + Y)
W = (X - Y)/Z X = WZ+Y
W = XY X =W/Y
How to match the formulas?To do this, we simply make X the subject of the formula in expressions on the left.
So, we have:
W = X - Y
This gives
X = W + Y
W = X/Z - Y
This gives
X/Z = W + Y
X = Z(W + Y)
W = (X - Y)/Z
This gives
X - Y = WZ
X = WZ + Y
W = XY
This gives
X =W/Y
Read more about equivalent expressions at:
https://brainly.com/question/27733205
#SPJ1
Complete question
Match each formula on the left with an equivalent formula on the right.
W = X - Y X =W/Y
W = X/Z - Y X = Z(W + Y)
W = (X - Y)/Z X = WZ+Y
W = XY X = W +Y
Can someone pls help me?
Answer:
[tex] \frac{8}{24} [/tex]
Step-by-step explanation:
If Adam's family uses 8lb of apples to make pie. We know that 3 x 8 = 24, so it's probably approximately 3 out of 18.
3. Segment RU is an angle bisector. m/QRU = 70°.
What is mzQRS?
Q
70°
□A 70°
B 140°
C 35°
OD 20°
A
U
S
PLS HELP ME OUT
Answer:
b - 140
Step-by-step explanation:
an angle bisector divides an angle in half
so
half of the angle is 70
the other half is 70
so
70 + 70 = 140
b is your answer
Answer: B. 140°
Step-by-step explanation:
Hi!
An angle bisector just cuts the angle in half.
Therefore, if one half is 70°, the other half is also 70°!
To find the measure of the angle just add them!
70° + 70° = ?
= 140°
So, your answer is B. 140°
Hope this helps and have a great day!
(−7)^-2 and more letters cause needed
Answer:
1/49.
Step-by-step explanation:
(−7)^-2
= 1 /(- 7)^2
= 1/49.
a square room has a area of 49 square feet the height of the room is 4 feet. what is the area of one wall
Answer:
28 ft^2
Step-by-step explanation:
The room is in the shape of a square. That means the base of the room (width and length) will have the same dimensions.
Length x Width = 49 ft^2
Length = Width
Length^2 = 49 ft^2
Length = 7 feet
Width is also 7 feet
The height of the room is 4 feet, plenty for non-humans. One wall area would be (7 ft)*(4 ft) = 28 ft^2
CAN ANYONE HELP PLSS
Answer:
CD = 13
Step-by-step explanation:
since Δ ABD and Δ CBD are congruent , then corresponding sides are congruent, so
CD = DA = 13
Answer:
13
Step-by-step explanation:
We know that if two triangles are congruent, the corresponding element of those are also equal.
Given that,
ABD Δ ≡ CBD Δ
Therefore, the corresponding elements are also equal.
AD = CD
AD = 13 units
∴ CD = 13 units
Given that
x
= 8 cm and
y
= 23 cm, work out
∠
BCA rounded to 3 SF.
The value of the angle ∠BCA when approximated to 3 significant figures is; 20.4°
How to use Trigonometric Ratios?From the attached image of the triangle ABC showing the side lengths x and y, we can see clearly that it is a right angle triangle.
Now, since we want to find the value of the angle ∠BCA, then it means we have to use trigonometric ratio to get;
x/y = sin BCA
Plugging in the relevant values gives us;
8/23 = sin BCA
∠BCA = sin⁻¹(8/23)
∠BCA = 20.355
Approximating to 3 significant figures gives us;
∠BCA = 20.4°
Read more about Trigonometric Ratios at; https://brainly.com/question/13276558
#SPJ1
A room has a length of 8 m. A scale diagram is drawn of the room. In the diagram, the room has a length of 1 cm. What is the scale of the diagram? Give your answer as a ratio in the form 1 : k , where k is an integer.
The scale of the diagram as described in the task content is; 1: 8 where k= 8.
What is the scale of the diagram?It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.
Read more on scale of diagrams;
https://brainly.com/question/24255624
#SPJ1
A boy walks 58 feet up a ramp having a 22.5 degree inclination. how high is he standing from the ground?
Boy is 22.5 feet high from the ground
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
The given question can be solved by sin, as value of perpendicular is to be evaluated and height and angle is provided. Let height from the ground be x
sin(22.5°) = x / 58
x = 58sin22.5 = 58(.38258) = 22.5 feet high.
Thus the Boy is 22.5 feet high from the ground.
Learn more about trigonometry here :
https://brainly.com/question/26719838
#SPJ4
Which ratio is equivalent to 4:5 ?
Answer:
Step-by-step explanation:
Maybe..
8/10
12/15
16/20
20/25
24/30
28/35
32/40
36/45
40/50
Any one of these is equal to the ratio of 4 over 5.
Answer:
No, the person who answered first is wrong
I'll give you the correct answer
Step-by-step explanation:
He the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.
thank you, this is the correct answer
hope that hepls
help me i im not good in math
Number of shirts = dependent variable
Cost of the purchases = independent variable
Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water.
represents the volume of water Andrei uses (in liters) if he uses marbles.
What is the glass tank's volume?
______________liters
Answer: the amount of liters that would fill the glass tank's volume can not be found
Step-by-step explanation:
there is not enough information to find out how many liters could fill the glass tanks volume
The required volume of glass tank = Vb +Vw liters
Volume, is defined as the ratio of the mass of object to its density.
Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water.
Volume of pebbles = Vb
Volume of water = Vw
Volume of glass tank = Vg
Vg = Vb + Vw
Thus, the required volume of glass tank is = Vb + Vw liters
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ1
Please help ill give whoever answers the best the brainliest answer
Name the ordered pair that would be a reflection of (9, 2) over the y axis
Answer:
(- 9, 2 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(9, 2 ) → (- 9, 2 )
4
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
look at image............
Answer:
f(x)=2x-3
Step-by-step explanation:
cause fir example if you put x=2 the y became 1.
7. A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in miles, , and her running speed, in miles per hour, when she runs:
a. at a constant speed of 4 miles per hour for the entire 30 minutes.
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The distance travelled in 30 minutes is:
Distance = speed * time = 4 mph * 0.5 h = 2 miles
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Translate into an algebraic expression:
How much 50% of sugar syrup can you make if you have x grams of sugar?
(Need Urgent Help)
Answer:
Que is talking about a syrup which contains 50% of sugar .
Que asked : amount of sugar syrup from X grams of sugar.
Explanation :
if a sugar syrup contains 50% of sugar , that means that the half of the solution contains sugar and half is solvent .
means , 2 × amount of sugar = solution (syrup)
now , we are given x grams of sugar
then , solution can be made with x grams of sugar = 2 × (X grams) = 2X gram of solution or sugar syrup.
.
.
Mark BRAINLIEST!
Please help! I can't figure this out, i'll give a brainliest
The linear equation that best fits the data is: y = 10x + 15.
How to Write the Linear Equation of a Data?First, find the slope/unit rate (m) and the y-intercept/starting value, then substitute the values into y = mx + b.
Using two points on the graph, (1, 25) and (2, 35), find the slope (m):
Slope (m) = (35 - 25)/(2 - 1)
Slope (m) = 10/1
Slope (m) = 10
Substitute (x, y) = (1, 25) and m = 10 into y = mx + b to find b
25 = 10(1) + b
25 - 10 = b
b = 15
Substitute m = 10 and b = 15 into y = mx + b
y = 10x + 15
Learn more about the linear equation on:
https://brainly.com/question/15602982
#SPJ1
Solve each triangle – find any missing side and angle measures. Round answers to the nearest tenth.
Step-by-step explanation:
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.
----------------------
The car is 120 miles away when the motorcycle starts.
The bike gains on the car at 30 mph (70-40).
It takes 4 hours for the bike to close the gap (120/30).
In 4 hours, the bike and the car are 280 miles from the starting point.
---------
4*70 = 280
7*40 = 280
Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)
70T = 40T + 120
30T = 120
T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).
It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.
Learn more about Distance:
https://brainly.com/question/12356025
#SPJ4