Answer:
Step-by-step explanation:
Let the length of one side of the square base be x
Let the height of the box by y
Volume of the box V = x²y
Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy
S = x² + 4xy
Given
S = 7500sq in.
Substitute into the formula for calculating the total surface area
7500 = x² + 4xy
Make y the subject of the formula;
7500 - x² = 4xy
y = (7500-x²)/4x
Since V = x²y
V = x² (7500-x²)/4x
V = x(7500-x²)/4
V = 1/4(7500x-x³)
For us to maximize the volume, then dV/dx = 0
dV/dx = 1/4(7500-3x²)
1/4(7500-3x²) = 0
(7500-3x²) = 0
7500 = 3x²
x² = 7500/3
x² = 2500
x = √2500
x = 50in
Since y = (7500-x²)/4x
y = 7500-2500/4(50)
y = 5000/200
y = 25in
Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.
The Volume of the box V = 50²*25
V = 2500*25
V= 62,500in³
Hence the maximum volume is 62,500in³
Viktor purchases a car for $10,608. He makes monthly payments for 48 months in order to pay off the car. He does not pay interest. How much are his payments each month?
There are a total of 120 bicycles and tricycles in a shop. There are 302 wheels in allmany bicycles and how many tricycles are in the shop?
Answer: There are 62 tricycles in the shop.
Step-by-step explanation:
Given: Number of wheels in a bicycle = 2
Number of wheels in a tricycle = 3
Let x = Number of bicycles , y = Number of tricycles.
As per given , we have
x+y =120 (i)
2x+3y=302 (ii)
Multiplying 2 on both sides of (i)
2x+2y=240 (iii)
Subtract (iii) from (ii) , we get
y= 62
Put value of y in (i) , we get
[tex]x+62=120\\\\\Rightarrow\ x=120-62\\\\\Rightarrow\ x= 58[/tex]
Hence, there are 58 bicycles and 62 tricycles in the shop.
x - 2y + 3z= 7
2x+y+z=4
-3x + 2y – 2z = -10
Solve System of Equations
Answer:
(2, -1, 1)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Dwayne and Alisha both correctly graphed a standard normal curve. Which of the following statements is true? Neither the means nor the standard deviations of Dwayne’s and Alisha’s graphs must be the same. The means of Dwayne’s and Alisha’s graphs must be the same but not the standard deviations. The standard deviations of Dwayne’s and Alisha’s graphs must be the same but not the means. Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.
Answer: Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.
Step-by-step explanation:
Answer:
The last one is correct: Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.
Step-by-step explanation:
Just took the test
PLEASE ANSWER FIFTY POINTS AND BRAINLIEST!
Sketch the graph y=− |x−1|+3 and answer the questions:
b)
What are the coordinates of its vertex?
c)
What are the coordinates of x- intercepts? (theres two)
Answer: The picture I showed is the sketch of the graph y=-|x-1|+3
b) The coordinates for the vertex is (1,3)
c) One of the coordinates for the x intercepts is (-2,0)
The other is (4,0)
Step-by-step explanation:
b)The vertex is the point I showed in the picture. It's where the graph moves in the opposite direction
c) The coordinates for the intercepts can be determined where the graph hits the x axis. At -2, the graph hits the x axis and at 4 the graph hits the x axis.
X intercepts always have a 0 for its y value of the coordinate. Therefore the coordinates are (-2,0) and (4,0)
Identify which of these terms do not belong with the other three: square,circle , hexagon or triangle and explain your reasoning
Answer:
Circle
Step-by-step explanation:
It dosen't have sides
Thomas got a haircut from the barber. If the
haircut costs $32 and he wants to leave a
18% tip, how much will he pay in total?
Five years ago, John’s age was half of the age he will be in 8 years. How old is he now? Show your steps.
Answer:
John is 18 years old at this point in time.
Step-by-step explanation:
This question is basic algebra. The equation you will need to write to solve it is (x-5) = (x+8)/2. When you solve this equation, the answer comes out to 18.
NEED HELP ASAP!! Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a congruence statement.
If no, justify your answer.
Answer:
did you got the answer
Step-by-step explanation:
because I need it too
please help me out
I've checked out and its AAA does not prove congruence. Triangles are not congruent. They are similar
but am not sure
The price of a pair of shoes increases from $52 to $64 . What is the percent of increase to the increase to the nearest percent ?
What is the annual interest for a principal of $3,500 at a simple annual interest
rate of 2.3%?
Answer:
Step-by-step explanation:
Given principal p =$3500
Time t =1 year
Rate of interest r =2.3%
So annual interest=p×r×t/100
=3500×2×2.3/100
=7000×2.3/100
=16100/100
=161.
So annual interest is $161
The length of a rectangle is 2 cm longer than its width. If the perimeter of the rectangle is 56 cm, find its length and width.
Answer:
Width = 13 Length = 15
Step-by-step explanation:
2+w=l
w+w+2+w+2+w=56
4w+4=56
4w=52
W=13
L=15
a teacher wants to arrange 16 chairs
Answer:
Okay, anything else along with that or was it just a statement?
Step-by-step explanation:
the graph of g(x)=5x is a transformation of the graph of f(x)=x what is the transformation
Answer:
Vertical Stretch of 5.
General Formulas and Concepts:
Alg II
Transformations
Parent Graph Transformations: y = ax + b
a = vertical shrink/stretchb = vertical movement up/downStep-by-step explanation:
Step 1: Define equation
Parent Graph: f(x) = x
Transformed Graph: g(x) = 5x
Step 2: Break
We see that we are increasing the slope. Therefore, it will have a steeper slope. That means we are manipulating the a variable and thus have a vertical stretch of a factor of 5.
PLEASE HELP! Determine the slope & the y-intercept of the following graphs.
Hey girl! It's me again to explain this to you :)
Number 21.) If we start from our y-intercept -2 and move up 2 on our y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.
Slope: 2/1 or just 2
Y-intercept: -2
You didn't ask for this but i'm gonna write it anyways. The equation for this line is y=2x-2
Number 22.) If we start from our y-intercept 2 and move down 2 on your y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.
Slope: -2/1 or just -2
Y-intercept: 2
Again you didn't ask for this but the equation for this line is y=-2x+2
Hope this helped you understand and again make this brainliest and reply if you need more help or have any more questions :)
Step-by-step explanation:
After 5 minutes, Pablo jumped 14.6 feet. After 10 minutes, he
jumped 14.1 feet. What are the two ordered pairs?
Answer:
Step-by-step explanation:
(5, 14.6)
(10, 14.1)
1. A restaurant supplier services the restaurants in a circular area in such way that the radius r is increasing at the rate of 2 miles per year at the moment when r = 5 miles. How fast is the area increasing?
Answer:
A= π*r²
dA/dt= π*r*dr/dt
dA/dt= π*5*2= 10π km/yr
Using implicit differentiation, it is found that the area is increasing at a rate of 62.8 miles squared per year.
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]A = 2r\pi \frac{dr}{dt}[/tex]
In this problem:
Radius increasing at a rate of 2 miles per year, hence [tex]\frac{dr}{dt} = 2[/tex].Moment of a radius of 5 miles, hence [tex]r = 5[/tex].Then:
[tex]A = 2r\pi \frac{dr}{dt}[/tex]
[tex]A = 2(5)\pi(2)[/tex]
[tex]A = 62.8[/tex]
The area is increasing at a rate of 62.8 miles squared per year.
A similar problem is given at https://brainly.com/question/9543179
Basketball shoes are on sale for 22% off. What is the regular price if the sale price is $42?
Answer:
x =53.85
Step-by-step explanation:
Let x be the original price
If the price is 22% of, you will pay 100% -22% = 78%
x * 78% = 42
Change to decimal form
.78x = 42
Divide each side by .78
.78x/.78 = 42/.78
Rounding to the nearest cent
x =53.85
What can you determine from the tape diagram
Please help me out. The topic is angles. Anything helps.
What is the slope
Please help
Answer:
2
Step-by-step explanation:
rise/run = 2/1
PQ is equal to RQ so b=?
Answer: 17
Step-by-step explanation:
What is the distance in units between 16 and -25?
Answer:
41
Step-by-step explanation:
Graph the line with the equation y = 2 x − 2
Answer:
The picture attached shows the graph. The y-intercept is -2 and it increases by 2. Hope this helps.
Step-by-step explanation:
rewrite the function f(x)=-3(x+3)^2-13
in the form f(x)=ax^2+bx+c
Answer:
-3x^2-18x-40
Step-by-step explanation:
(x+3)^2: x^2+6x+9
= -3(x^2+6x+9)-13
Expand:
-3(x^2+6x+9): -3x^2-18x-27
= -3x^2-18x-27-13
Final Answer: -3x^2-18x-40
Answer:
-3x^2-18x-40
Step-by-step explanation:
-3(x+3)^2-13
-3(x^2+6x+9)-13
-3x^2-18x-27-13
-3x^2-18x-40
To solve 5(2^x + 4) = 15 first divide each side by
Answer:
5
Step-by-step explanation:
if you divide by 5 on both sides then you would just be left with 2^x+4=3 and it would save you the trouble of having to simplify later on. hope this makes sense
Lara created a 15-pound platter of three different types of cookies for a banquet. The peanut butter cookies sell for $2 per pound, the sugar cookies sell for $3 and the chocolate chip cookies sell for $3.60 per pound. The entire platter is worth $40. The quantity of peanut butter cookies was 3 more than chocolate chips. How many pounds of each cookie was there. Answered with a chart.
Answer:
i need a bad bleep
Step-by-step explanation:
addison rae
The sum of two numbers is greater than 1. Which statement
Answer:
the sum of two whole numbers is always greater than either number because even if one of the numbers to be added is 0, the answer will, well, not be greater, but at least equal to it.
Step-by-step explanation:
plz mark as brainliest
PICTURE PLEASE TYSMMM
Answer:
(B).
Step-by-step explanation:
Statement B is not correct. PR and ST are not corresponding segments.
The temperature at Bar Harbor, Maine, was -3 0F. It then dropped during the night to be 4 times as cold.
1. 12
2. 7
3. -12
4. -7
please please please need help :(
Answer:
-12
Step-by-step explanation:
-3 x 4 = -12
because if you multiply a negative with a positive number, you get a negative number.
