Step-by-step explanation:
length of the box is a = 25 -2x
width of the box is b =13 -2x
height of the box is x
and x < 6,5
so the volume of the box V=f(x) = x.(25-2x)(13-2x)= 4x^3 -76x^2 +325x
f'(x) = 12x^2 - 152x + 325
to maximize the volume of the box ( f(x) max ) then f'(x) = 0 --> x ≈ 2,72 and x ≈ 9,94
so x = 2,72 inches
Answer:
length of the box is a = 25 -2x
width of the box is b =13 -2x
height of the box is x
and x < 6,5
so the volume of the box V=f(x) = x.(25-2x)(13-2x)= 4x^3 -76x^2 +325x
f'(x) = 12x^2 - 152x + 325
to maximize the volume of the box ( f(x) max ) then f'(x) = 0 --> x ≈ 2,72 and x ≈ 9,94
so x = 2,72 inches
Step-by-step explanation:
What is the slope of the line that contains the points (9,-4) and (1, -5)
А 1/8
B. -1/8
C.-1
D. 1
Answer:
A. 1/8
Step-by-step explanation:
m = rise/run
m = (y2-y1)/(x2-x1)
m = (-5- - 4)/(1-9)
m = (-5+4)/(-8)
m = (-1)/(-8)
m = 1/8
Answer:
The answer is A.
Step-by-step explanation:
Given that the formula to find gradient, m, is :
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Then, you have to substitute the coordinates into the formula :
[tex]let \: (9, - 4) \: be \: (x1,y1) \\ let \: (1, - 5) \: be \: (x2,y2)[/tex]
[tex]m = \frac{ - 5 - ( - 4)}{1 - 9} [/tex]
[tex]m = \frac{ - 5 + 4}{ - 8} [/tex]
[tex]m = \frac{ - 1}{ - 8} [/tex]
[tex]m = \frac{1}{8} [/tex]
If the function m(x) has the point (5, 2) on its graph name a point that would be on the function m(5x). (10, 2) (5, 10) (25, 2) (1, 2)
Answer:
(1, 2)
Step-by-step explanation:
The function m(x) has the point (5, 2) on its graph is equivalent to say that m(x) evaluated at x = 5 gives 2 as result, that is, m(5) = 2.
f(kx) transforms point (x, y) into (x/k, y). Therefore: m(5x) transforms point (5, 2) into (5/5, 2) or (1, 2).
Here is a circle touching a square.
The area of the square is 36 cm2
Work out the area of the circle.
Give your answer in terms of pie .
Answer: 9πcm²
Step-by-step explanation: area of the square= 36cm²
Therefore, the area of one side= √area = √36 = 6cms
Since the circle is touching the sides of the square, the side of the square = the diameter of the circle
Therefore the radius of the circle= side/2 = 3cm
The formula for the ares of the circle is πr²
π*3*3 = 9πcm²
Given the figure below, find the values of x and z.
Answer:
X= 6°z= 112°Solution,
Finding the value of X,
[tex]11x + 2 = 68[/tex]
( being vertically opposite angles)
[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]
Value of X is 6
Now, finding the value of z
[tex]z + 68 = 180[/tex]
(sum of angle in linear pair)
[tex]z = 180 - 68 \\ z = 112[/tex]
Value of z is 112.
Hope this helps....
Good luck on your assignment...
Write the expression that is represented by the phrase. The product of a number plus 7 and 3.
plz help, I need it asap
Answer:
see below
Step-by-step explanation:
15+2x> 31
Subtract 15 from each side
2x > 16
Divide by 2
2x/2 > 16/2
x > 8
There is an open circle at 8
The line goes to the right
What is the distance to the earth’s horizon from point P? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. x = mi
Answer:
[Distance to the Horizon]^2 =Height of the skydiver x Diameter of the Earth
D^2 = 1.4 x 7918
D^2 = 11,085.2
D = Sqrt(11,085.2)
D = ~ 105.28628......miles - Distance to Horizon.
Step-by-step explanation:
Answer:
284.4 I took the test ;)
Simplify the expression –3(x + 3)² – 3 + 3x. What is the simplified expression in standard form?
Answer:
-3x^2-15x-30
Step-by-step explanation:
Follow order of operations
Answer:
-3x^2 -15x -30
Step-by-step explanation:
First you would square the parenthesis, and get x^2 +6x+9 inside the parenthesis, then you would multiply it by the -3 and get -3x^2 -18x-27-3+3x then you combine like terms to get the answer.
Find the factors of the polynomial 45 x2 - 20 y2
Answer:
The factors of the polynomial are 5, ( 3x - 2y), and (3x + 2y)
Step-by-step explanation:
The given polynomial is 45x² - 20y²
45x² - 20y² = 5 (9x² - 4y²)
45x² - 20y² = 5 [ (3x)² - (2y)² ]
Using difference of two squares, (3x)² - (2y)² = ( 3x - 2y)(3x + 2y)
45x² - 20y² = 5 ( 3x - 2y) (3x + 2y)
The factors of the polynomial are 5, ( 3x - 2y), and (3x + 2y)
Answer:
5(3x - 2)(3x + 2)
Step-by-step explanation:
Please indicate exponentiation with " ^ " : 45 x^2 - 20 y^2.
Identify the GCF and factor it out: 5(9x^2 - 4y^2)
Recognize that (9x^2 - 4y^2) is the difference of two squares, which factors into (3x - 2y)(3x + 2y)
Then 45 x^2 - 20 y^2 = 5(3x - 2)(3x + 2)
⚠ PLEASE HELP ⚠ Calculate the product. (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) will award BRAINLIEST.
Answer:
5/8
Step-by-step explanation:
The value of the expression is 8/15
What is expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)
The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)
We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n
Here, n = 15.
So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30
= 8/15
Hence, The value of the expression is 8/15
For more references on expressions, click;
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What is the ratio of 76,000 and 100,000
Answer:
19 : 25
Step-by-step explanation:
Trying to find the missing segment to the triangle in the attached image.
Answer:
25
Step-by-step explanation:
The Side Splitter Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally. Therefore:
6/15 = 10/?
6*? = 10*15
? = 10*15/6
? = 25
Which graph shows the system of equations 4 x + y = 3 and 2 x minus 3 y = 3? On a coordinate plane, a line goes through (0, negative 1) and (3, 1) and another line goes through (0, 3) and (1, negative 1). On a coordinate plane, a line goes through (0, 3) and (1, negative 1) and another line goes through (0, negative 3) and (3, negative 1). On a coordinate plane, a line goes through (0, 3) and (negative 1, negative 1) and another line goes through (0, negative 3) and (3, negative 1). On a coordinate plane, a line goes through (0, 3) and (negative 1, negative 1) and another line goes through (0, negative 1) and (3, 1).
Answer:
A is the correct answer
Step-by-step explanation:
Graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
The system of equations
4x + y = 3 and
2x - 3y = 3
In the first line, the slope is -4, and the y-intercept at (0,3)
In the second line, the slope is 2/3, and the y-intercept at (0,-1)
Thus, graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.
Learn more about the linear equation here:
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WILL GIVE BRAINIEST TO THE FIRST ANSWER
Answer:x − 3 y = − 36
Step-by-step explanation:
Answer: The initial form is called slope intercept form// and the equation in standard form is 3y=37
Step-by-step explanation:
standard form = ax+by=c so you basically just have to take that and put it into the formula
Hope this helps
The first jumbo jet was the Boeing 747, which is 70.5 meters long. The wingspan of the 747 is 60 meters. A model 747 has a wingspan of 80 centimeters. What should the length of the model be? tell your work.
Answer: The correct answer is 94 cm.
Step-by-step explanation:
wingspan length
60 meters 70.5 m
----------------- = ----------------
80 cm x
Cross multiply
(60 m)x = (70.5 m)(80 cm)
Solve for x by dividing both sides of equation by 60 m:
x = (70.5 m)(80 cm) / (60 m) = 94 cm
The length of the model is 94 cm.
Answer:
94 cm
Step-by-step explanation:
Write and solve an equation of ratios:
70.5 m 60 m
----------- = -----------
L 80 cm
Cross multiplying, we get:
(70.5 m)(80 cm) = (60 m)L
(70.5 m)(80 cm)
Then the model length, L, should be L = -------------------------
60 m
or
L = 94 cm
The table represents a linear function. What is the slope of the function?
Answer:
The slope of a linear function. The steepness of a hill is called a slope. The same goes for the steepness of a line. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run
Step-by-step explanation:
:)
You are taking 1500 US dollars on a trip. After checking the exchange rate, you figure out the exchange rate is 1 US dollar to 0.74 euros. Task: write an equation to convert US dollars to euros. Will mark most brainiest if you answer!
Answer:
y= 0.74x
0.74 (1500) = 1,110 euros
Step-by-step explanation:
Hi, to answer this question we have to write an equation with the information given:
Since: 1 US dollar = 0.74 Euros
To convert x US dollars to Euros we have to multiply it by 0.74:
y= 0.74x
Where:
y = value in EUROS
x = value in US dollars
For 1500:
y = 0.74 (1500) = 1,110 euros
Feel free to ask for more if needed or if you did not understand something.
rationalise the denominator and simplify 15÷
[tex] \sqrt{3} [/tex]
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
=> [tex]\frac{15}{\sqrt{3} }[/tex]
Multiplying and dividing by [tex]\sqrt{3}[/tex]
=> [tex]\frac{15}{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} }[/tex]
=> [tex]\frac{15\sqrt{3} }{(\sqrt{3})^2 }[/tex]
=> [tex]\frac{15\sqrt{3} }{3}[/tex]
=> [tex]5\sqrt{3}[/tex] (A Rationalized denominator!)
Answer:
5√3
Step-by-step explanation:
To rationalize the denominator, all you have to do is multiply both the numerator and the denominator by whatever is in the denominator, if it is only a single term in the denominator. This means you multiply [tex]\frac{15}{\sqrt{3} }[/tex] [tex]* \frac{\sqrt{3}}{\sqrt{3}}[/tex] . Since √3 divided by itself is 1, this doesn't change the value of the expression. Now multiplying this we get (15√3)/3. Now we can divide 15√3 by 3 to get 5√3, which is the final answer.
Katie has an antique glass cabinet in the shape of a triangular prism. The base is an equilateral triangle that has a side length of 2 feet and a height of 1.7 feet. The height of the entire cabinet is 4.5 feet. How many cubic feet of space are inside the cabinet? 7.65 ft3 15.3 ft3 27 ft3 30.4 ft3
Answer: 7.65 ft3
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Volume of a triangular prism = base area x height
Since:
Area of a triangle (base) = side length x height
Replacing with the values given:
A= (2 x 1.7 )/2 = 1.7 ft2
Back with the volume formula:
V = base area x height
Replacing with the values given:
V=1.7 x 4.5 =7.65 ft3
4x⁶-12x³+9 factorizar las expresiones
Answer:
(2x³ - 3)²
Step-by-step explanation:
4x⁶ - 12x³ + 9
2²x⁶ - 12x³ + 9
2²x²ˣ3 - 2 * 2x³ * 3 + 3²
2² * (x³)² - 2 * 2x³ * 3 + 3²
(2x³)² - 2 * 2x³ * 3 + 3²
(2x³ - 3)²
Hope this helped! :)
PLS HELPPPP MEEEE!!!
Answer:
No
Step-by-step explanation:
We have to check if 3/5 = 6/25. If we convert 3/5 into a fraction with denominator of 25 so that we can compare the two we get 15/25 and this is clearly not equal to 6/25. Therefore, the answer is no.
The numbers 1 through 10 are put in one bag, and the numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number? please answer as an unsimplified fraction.
Answer:
36/100
Step-by-step explanation:
this is because you find the overlapping ranges of each bag which is 5 - 10 on the first bag and 5 - 10 on the second bag. both bags have 10 total numbers, so 6/10 * 6/10 because there are six numbers on each bag and 10 overall choices, so we multiply these two because its an and statement which gives us 36/100.
The probability that we get the same number is 9/25.
What is probability?It is simply likeliness of happening an event. The probability of an event lies between 0 to 1.
How to find the probability?Numbers in first bag=10
Numbers in second bag=10
Common numbers=5,6,7,8,9,10
Total common numbers=6
So the probability that we get the same numbers will be
= 6/10* 6/10
=36/100
=18/50
=9/25
Hence the probability that we will get the same numbers is 9/25.
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Identify the surface area of the composite figure in terms of π.
Answer:
78π m²
Step-by-step explanation:
The lateral area of the cylinder is ...
LA = 2πrh
LA = 2π(3 m)(8 m) = 48π m²
The lateral area of one cone is ...
LA = πrh . . . . where h is the slant height
LA = π(3 m)(5 m) = 15π m²
Then the total surface area of the figure is the area of the two cones plus that of the cylinder:
S = 2(cone area) + cylinder area
S = 2(15π m²) +(48π m²)
S = 78π m²
How can this same solution be written using set builder notation? {x | x > }?
Corrected Question
The solution to an inequality is represented by the number line. How can this same solution be written using set-builder notation? {x | x > }
Answer:
[tex]\{x | x >3 \}[/tex]
Step-by-step explanation:
Given an inequality whose solution is represented by the number line attached below.
We observe the following from the number line
There is an open circle at 3, therefore the solution set does not include 3. (We make use of > or < in cases like that)
The arrow is pointed towards the right. All points to the right of 3 are greater than 3, therefore:
The solution in the number line can be written using set-builder notation as:
[tex]\{x | x >3 \}[/tex]
What is the new cost if a $2.75 toy is marked up by 29%?
Answer:
$3.55
Step-by-step explanation:
You need to add 29% of $2.75 to $2.75.
That means the price will be 129% of $2.75.
129% of $2.75 =
= 1.29 * $2.75
= $3.55
I will give you all ⭐⭐⭐⭐⭐ Try to zoom in or flip your phone to see better.
Answer:
The correct option is:
x+y = 2
Step-by-step explanation:
Street 1 is given.
If Street 2 is parallel to Street 1, then they will have the same slope.
Find slope of Street 1:
Take any 2 points on Street 1. Consider (-2,3) and (1,0)
Slope is given by:
m = (y₂ - y₁) / (x₂ - x₁)
m = 0-3 / 1-(-2)
m = -3/3
m = -1
For Street 2:
y = mx + c
y = -1x +c
As it passes through (-2,4), substitute the point in the above equation:
4 = -1(-2) + c
c = 2
So substitute m = -1 and c =2 into general form of equation:
y = mx + c
y = -x + 2
or
x+y = 2
Express as a product: 1+2cosα
Answer:
Step-by-step explanation:
1+2 cos α
[tex]=1+2(2 cos^{2} \frac{\alpha }{2} -1)\\=1+4 ~cos^2\frac{\alpha }{2} -2\\=4 ~cos^2\frac{\alpha }{2} -1\\=(2cos \frac{\alpha }{2} +1)(2 cos \frac{\alpha }{2} -1)[/tex]
50 points Please help Use the following random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question below. 3199 9288 1023 1130 0809 1770 6231 7538 8927 4761 7258 7111 0209 0916 1450 9848 4654 7579 6150 3093 9608 0061 4014 9501 0382 3052 2385 9074 1664 6551 6577 1811 3454 5870 1277 5056 1063 5697 9141 4120 9181 1343 0168 3693 0463 4842 1704 3774 4908 4161 6404 9675 2518 3988 4268 6083 0636 9634 5295 5656 1918 3133 6831 8393 6363 2452 1531 1638 1317 2279 9395 0702 2091 5269 0422 0275 3373 1424 1958 0356 5163 0743 6658 6257 2772 0570 4522 2665 0890 3560 5549 2238 2172 9715 9741 4975 6617 9034 4441 8220 Based on the results of the simulation, what is the experimental probability that a group will include only boys? Based on the results of the simulation, what is the experimental probability that a group will not contain four boys? Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls? Round your answer to the nearest number of groups.
Answer:
For the first question, there is a 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.
Step-by-step explanation:
100: 224 = 61:x → 61/100 = x/224
100x = 13664
x = 136.64 → 136 groups (You can't round up if you don't have enough people)
Hope this helped!
Answer: 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.
Step-by-step explanation:
:) The other answer is correct too! But just for clarification! :)
When graphed, which parabola opens downward?
Answer:
A
Step-by-step explanation:
Edge 2020
From the equation, find the axis of symmetry of the parabola.
y = 4x+ 32x+ 61
a. x= 3
x=-4
C.
b. X= 4
d. X=-3