Find the integers m and n such that (m+n√2)(1-√2)²=-2+2√2
m = n = 2 is the answer
Hope this helps
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what is the expanded notations for 232,913,805
Answer:
200,000,000 + 30,000,000 + 2,000,000 + 900,000 + 10,000 + 3,000 + 800 + 5
Step-by-step explanation:
An open-top box is to be made from a 12-inch by 24-inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What is the maximum possible volume, in cubic inches, of the box?
Answer:
The maximum possible volume = 332.685 cubic inches
Step-by-step explanation:
From the information given:
Let the height be = x
The length be = 24 - 2x
The width be = 12 - 2x
Then V = x (24 -2x) ( 12 - 2x)
V = x ( 288 -48x - 24x +4x²)
V = x(288 - 72x + 4x²)
V = 288x - 72x² + 4x³
[tex]\dfrac{dV}{dx}= (3x^2 - 36x+ 72)[/tex]
[tex]\implies x^2 - 12x + 24 = 0[/tex]
[tex]=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]=\dfrac{-(-12) \pm \sqrt{(-12)^2 - 4(1)(24)}}{2(1)}[/tex]
[tex]=\dfrac{12 \pm \sqrt{144 - 96}}{2}[/tex]
[tex]=\dfrac{12 \pm \sqrt{48}}{2}[/tex]
where;
[tex]x \ne \dfrac{12 + \sqrt{48}}{2}[/tex]
∴ [tex]x= \dfrac{12 - \sqrt{48}}{2}[/tex]
x = 2.536 ( since the length cannot be negative)
So, the length x = 24 - 2(2.535) = 18.93
The width = 12 - 2(2.535) = 6.93
heigth = 2.536
∴
V = 18.93 × 6.93 × 2.536
V = 332.685 cubic inches
A box is made from a plastic sheet by removing square from each corner, maximum volume of this box will be 332.55 cubic inches.
Volume of a cuboid: Volume of a cuboid or rectangular box is given by the expression,Volume = Length × Width × Height
Given in the question,
Plastic sheet with length = 12 inches Width of the sheet = 24 inches A square has been removed from each corner to fold the box.Let the measure of each side of a square removed = x inches
Therefore, length of the box = (12 - 2x) inches
Width of the box = (24 - 2x) inches
Height of the box = x inches
Volume of the box (V) = (12 - 2x) × (24 - 2x) × (x)
V = 4x³ - 72x² + 288x
To find the maximum volume of the box differentiate the expression with respect to 'x' and equate it to zero.
V' = 12x² - 144x + 288
For V' = 0,
12x² - 144x + 288 = 0
x² - 12x + 24 = 0
[tex]x=\frac{12\pm\sqrt{(12)^2-4(1)(24)} }{2(1)}[/tex]
[tex]x=(6\pm2\sqrt{3})[/tex]
[tex]x=9.46,2.54[/tex]
For x = 9.46,
Volume of the box = 4(9.46)³- 72(9.46)² + 288
= -2769.03 cubic inches
For x = 2.54,
Volume of the box = 4(2.54)³- 72(2.54)² + 288
= 332.55 cubic inches
Therefore, maximum volume of the box will be 332.55 cubic inches.
Learn more about the volume of a cuboid here,
https://brainly.com/question/25395659?referrer=searchResults
Simplify this expression
[tex]2 \sqrt{5(13 + \sqrt{2)} } [/tex]
Answer:
16.9789
You can round the answer
Answer:
D. [tex]26\sqrt{5} + 2\sqrt{10}[/tex]
Step-by-step explanation:
[tex]2\sqrt{5}(13+\sqrt{2})\\ \\26\sqrt{5}+2\sqrt{5}*\sqrt{2}\\\\\\26\sqrt{5}+2\sqrt{5}*2\\\\26\sqrt{5}+2\sqrt{10}[/tex]
Margaret packs colored cubes into shipping boxes. She has a function b(x)=x+2 that gives the edge length of the box, in centimeters, given the edge length x of the cube.
What is the volume, in cubic centimeters, of a shipping box for a colored puzzle cube with an edge length x of 8 centimeters, where V=x3?
a. 216
b. 512
c. 640
d. 1000
Answer:B. 512
Step-by-step explanation
8 x8= 64 x8= 512
Find the value x ?
(2x -10degree) (3x +20degree)
Answer:
If we do square on both sides we get two answers i.e. (x+12)^2=(3x+20)^2
(x^2)+24x+144=(9x^2)+120x+400
(8x^2)+96x+256=0
(x^2)+12x+32=0
(x+4)(x+8)=0
x= -4 or x= -8.
Else we have another method
x+12=3x+20
x+12–20=3x
x-8=3x,
Now square on both sides.
(x-8)^2=(3x)^2
x^2–16x+64=(9x^2)
(9x^2)-(x^2)+16x-64=0
(8x^2)+16x-64=0
(x^2)+2x-8=0
(x+4)(x-2)=0
x= -4 or x= 2.
But It Didn’t Satisfy for The Equation When
x=2 or x= -8,So The Value of x will be -4 which satisfies given question.
CH4 + O2 → CO2 + 2 H2O
write 6.085 in word form
Help me please!! I’ll mark as brilliant!!
Liam’s mass is 102.1 kg
Choose the best approximation of Liam’s mass
A. 1 x 10^1
B. 1 x 10^2
Earth has an estimated mass of 5,972,000,000,000,000,000,000,000 kg
Choose the best approximation of earth’s mass
A. 6 x 10^21
B. 6 x 10^24
Approximately how many times as large is earth’s mass as liam’s mass?
A. 6 x 10^20
B. 6 x 10^21
C. 6 x 10^22
The answers are :
1. Liam has approximated mass equal to 1 × 10² kg.
2. Earth has approximated mass equal to 6 × 10^24 kg
3. Earth's mass is larger than Liam's mass by 6 × [tex]10^{22}[/tex].
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
1)
Liam's mass is 102.1.
To represent the decimal number in approximation we need to multiply the first digit by power of 10 by moving the decimal place.
i.e., decimal number 102.1 can be written as :
= 1.02 × 10² kg
because decimal place moved towards left by 2 places.
or
= 1 × 10² kg
2)
Earth has an estimated mass of 5,972,000,000,000,000,000,000,000 kg.
This can be written as :
= 5.97 × 10^24
or
= 6 × 10^24 kg
3)
The earth's mass is larger than Liam's mass by :
= [tex]\frac{6 * 10^{24}}{1*10^{2} }[/tex]
= 6 × [tex]\frac{10^{24} }{10^{2} }[/tex]
= 6 × [tex]10^{22}[/tex]
Therefore , the answers are :
1. Liam has approximated mass equal to 1 × 10² kg.
2. Earth has approximated mass equal to 6 × 10^24 kg
3. Earth's mass is larger than Liam's mass by 6 × [tex]10^{22}[/tex].
Learn more about algebra here :
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Find the dimensions of a rectangle with area 729000 m2 whose perimeter is as small as possible. (Give your answers in increasing order, to the nearest meter.)
Step-by-step explanation:
Area of a rectangle = Length * Width
A = LW
729000 = LW .... 1
Perimeter of a rectangle P = 2L+2W
P = 2L+2W
From 1;
W = 729000/L
P = 2L + 2(729000/L)
P = 2L + 1458000/L
To minimize the perimeter, dP/dL = 0
dP/dL = 2 - 1458000/L²
2 - 1458000/L² = 0
2L² - 1458000 = 0
2L² = 1458000
L² = 729000
L = √729000
Length = 853.8m
W = A/L
Width = 729000/853.8
Width = 853.8
Hence the dimension to the nearest meter is 854m by 854m
On picture day, the students are placed in order from tallest to shortest. Place the following students in order from tallest to shortest.
Javien is 4 2/3 feet tall
Danny is 3 11/12 feet tall
Samiya is 4 1/6 feet tall
Taylor is 4 7/8 feet tall
Answer:
4 7/8, 4 2/3, 4 1/6, 3 11/12
Step-by-step explanation:
To make it easier, convert it into decimals
4 2/3=4.666...
3 11/12=3.9166...
4 1/6=4.166...
4 7/8=4.875
WHICH NUMBER MEANS THE SAME AS 2,000,000 + 70,000,000 + 6,000,000 +
300,000 + 40,000 + 2,000 + 100 +10 +7 ANSWER
78,342,117
Step-by-step explanation:
Just add! And yeah have a good day ^-^
Answer:im assuming we add them
Step-by-step explanation:
78342117
Please I really need help
For both questions please
Answer:
2 is A, 3 is C
Step-by-step explanation:
Reagan uses 2 3/4 cups of vinegar in her salad dressing recipe. How much vinegar would Reagan use to make 5 recipes?
Answer:
13 3/4
Step-by-step explanation:
2 3/4 is 11/4 when converted into an improper fraction.
5 is 5/1 when converted into a fraction.
11*5 is 55 (numerators)
4*1 is 4 (denominators)
55/4 is 13 with 3/4 remaining
13 3/4
if you do it ill mark you brainly plz do it
Answer:
A
Step-by-step explanation:
To find the change, we do final-beggining
since his first rating is -7 and his final rating is -2
-2-(-7)
triangle rst is congruent with VST is shown. given Line st is the perpendicular bisector of line RV prove triangle rst is congruent to triangle VST what is the missing reason in the proof
Answer:perpendicular bisector theorem
Step-by-step explanation:
Answer: A
Step-by-step explanation:
2. Determine whether each table of values represents a linear function. If so write the function. If not, explain why.
Answer:
lemme think i will anwser
Step-by-step explanation:
A linear function has a constant rate of change.
Table N represents a linear function
From the complete question (see attachment), we have the following highlights
Table M has the same x-values for y-values 2 and -3For each increment in the x-values of table N, there is a constant increment in the y-values.The above highlights mean that:
Table M does not represent a linear function because it does not have a constant rateTable N represents a linear function because it has a constant rateRead more about linear functions at:
https://brainly.com/question/20286983
Determine the slope of the line that contains the given points
(1-7) (5-7)
Answer:
the answer is 4
Step-by-step explanation:
Rise/run
y2-y1/x2-x1
7-7/1/5
4
Answer:
0/4
Step-by-step explanation:
7/5 - 7/1
Making the answer become 4
pls help i have pictures pls explain how you get your answer
Answer:
0.75
Step-by-step explanation:
To find the slope of the graph, you have to find the rise and the run by any two points on the graph. (I'm going to calculate using the two blue dots as shown in the picture)
[tex]\frac{rise}{run}[/tex] = [tex]\frac{(-2)-(-5)}{4-0}[/tex]
= [tex]\frac{-2+5}{4}[/tex]
= [tex]\frac{3}{4}[/tex]
= 0.75
A class roll has 30 students listed in alphabetical order. Exactly 5 of those students received A's in the course. What is the probability that at least two people who were adjacent on the alphabetical list both received A's?
Answer:tony stark
Step-by-step explanation:shake it out west
Write the ratio as a fraction in simplest form. A class has 8 boys and 14 girls. What is the ratio of boys to girls?
Answer:
4/7
Step-by-step explanation
8:14
8/14
4/7
So the answer is 4/7
Which statement is most likely to show a constant rate of change???
A. The outside temp compared with the time of day.
B. The cost of a new car compared with the number of tires it has.
C. The weight of a child compared with its age in months.
D.The distance traveled by a truck driving at a constant speed compared with time.
I believe you answer would be D) The distance traveled by a truck driving at a constant speed compared with time.
If LIAR is a parallelogram, what is the value of X?
R
A
377x+3)
(2x+3
O A. 42
O B. 20
O c. 71.5
O D. 35
O E. 82
O F. 38.
The answer is B) 20 .
37 + (7x + 3) = 180
7x = 180 - 37 - 3
7x = 140
x = 20
Therefore, x = 20.
Answer:
20
Step-by-step explanation:
The opera theater manager believes that 23#% of the opera tickets for tonight's show have been sold. If the manager is accurate, what is the probability that the proportion of tickets sold in a sample of 869869 tickets would differ from the population proportion by less than 3%3%
Answer:
0.9642
Step-by-step explanation:
Sample proportion p follows a Normal distribution with mean = p0 = 0.23 and Standard deviation = √P0(1 - P0) / n = √0.23(1-0.23) / 869 = 0.0143
Then Z = p - mean / Standard deviation = X - 0.23 / 0.01343
P(0.2<p<0.26) = P(p<0.26) - P(p<0.2)
= P(p-023/0.0143 < 0.26-0.23/0.0143) - P(p-0.23/0.0143 < 0.2-0.23/0.0143)
= P(Z < 2.1) - P(Z < -2.1)
= 0.9821 - 0.0179
= 0.9642
What is 20000000 in standard form
Answer:
twenty million
Step-by-step explanation:
there are 7 zeros so the "20" part would be one number then there would be a comma and the 3 zeros and then another comma then the other 3 zeros
Help with evaluate and graph PLEASE HURRY
Answer:
Box 1 = -1
Box 2 = 8
Box 3 = 14
Polly has 2 cups of cereal. How many 3/4 cup full servings can she make? Will she have any cereal left over?
Find the area of the triangle 8 cm 15 cm
Answer:
60 cm squared
Step-by-step explanation:
area of a triangle is [tex]\frac{bh}{2}[/tex]
base and height are interchangable; 8 cm and 15 cm
[tex]\frac{8(15)}{2}[/tex]
[tex]\frac{120}{2}[/tex]
60
Noah is growing three different types of trees. He is keeping track of the height of each tree over time.
This equation represents the height (in feet) of the Tree #1 over m months: h=3.5m
The information is in the table is for Tree #2:
time (months) height of tree (feet)
2 5
4 10
5 12.5
8 20
This graph shows how long, in months, it takes Tree #3 to grow h feet.
A graph. Height, in feet. Time, in months.
Which tree is growing the slowest?
Answer:
Tree 3
Step-by-step explanation:
The equation for the height of tree 1 is given as:
h = 3.5m
The equation for the height of tree 2 is gotten using the points from the table (2,5) and (4, 10)
Hence:
[tex]h-h_1=\frac{h_2-h_1}{m_2-m_1}(m-m_1)\\\\h-5=\frac{10-5}{4-2} (m-2)\\\\h-5=2.5m-5\\\\h=2.5m \\[/tex]
From the graph of tree 3, we get the points (2,4) and (4, 8)
Hence:
[tex]h-h_1=\frac{h_2-h_1}{m_2-m_1}(m-m_1)\\\\h-4=\frac{8-4}{4-2} (m-2)\\\\h-4=2m-4\\\\h=2m \\[/tex]
Therefore tree 3 grows the slowest
Solve the rational equation 2x+3/5=7/5
X=2
X=3.2
X=5
X=5.1
Answer:
x=0.4
Step-by-step explanation:
isolate the variable by dividing each side by factors that don't contain the variable