The GCF: x
answer: x(x+2)
Which of the functions is represented by the graph
O f(x)=2x²+3
O f(x) = -x² + 3
O f(x) =1/2x² + 3
O f(x) = -1/2x +3
Number 1
Step-by-step explanation:
Number 1 it is a good answer
a rectangular container with a square base, an open top, and a volume of 4,000 cm3 is to be made. what is the minimum surface area for the container? enter only the minimum surface area, and do not include units in your answer.
A rectangular container with a square base, an open top, and a volume of 4,000 cm³. The minimum surface for the container is 1,200 cm².
The result is obtained by using the derivative.
Determine the minimum surface areaThese are the specified parameters:
Volume container is 4,000 cm³.
Let side of square base = a, and height of the container = h, so:
Volume = a × a × h
4,000 = a² h
h = [tex]\displaystyle \frac{4000}{a^2}[/tex] ... (1)
Surface area with a square base, an open top is area of a square + 4 times the vertical side.
Surface area (A) = a² + 4ah
Substitute the value of h = [tex]\displaystyle \frac{4000}{a^2}[/tex] into surface area.
A = a² + 4ah
A = a² + 4a ([tex]\displaystyle \frac{4000}{a^2}[/tex])
A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]
So that the surface area is minimal, when the derivative and equate to 0.
A = a² + 16000 a⁻¹
A' = 0
2 a²⁻¹ + (-1) 16000 a⁻¹⁻¹
2a - 16000 a⁻² = 0
2a - [tex]\displaystyle \frac{16000}{a^2}[/tex] = 0
2a = [tex]\displaystyle \frac{16000}{a^2}[/tex]
2a³ = 16000
a³ = [tex]\displaystyle \frac{16000}{2}[/tex]
a³ = 8000
a = ∛8000
a = 20
Surface area with a square base, an open top.
Substitute the value of a = 20
A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]
A = 20² + [tex]\displaystyle \frac{16000}{20}[/tex]
A = 400 + 800
A = 1200
The minimum surface for the container is 1,200 cm².
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What’s 2\3 - 5/9 ?
NEED HELP ASAP!
Answer:1/9 or decimal form it’s ≅ 0.111111
I need Help ASAP!!!! PLease help!!!
The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12).
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the given translation rule,
(x,y) → (x+8,y+7)
The next translation is (x,y) → (x-5,y+5)
The resultant translation will be,
(x,y) → (x+8,y+7) to (x+8-5,y+7+5)
⇒ (x+3,y+12)
Hence "The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12)".
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At 99°F, a certain insect chirps at a rate of 68 times per minute, and at 105°F, they chirp 80 times per minute. Write an equation in slope-intercept form that represents the situation.
Answer:y=mxb
Step-by-step explanation:
Answer:
The equation is: y = 5x - 268
Samantha is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission for every computer sale she makes. The equation P=6.25x+75 represents Samantha's total pay on a day on which she sells x computers. What is the slope of the equation and what is its interpretation in the context of the problem?
The slope is 6.25, it means that her day pay increases by $6.25 for each computer sold
What is the slope of the equation?
A general linear equation in the point-slope form is written as:
y = a*x + b
Where y and x are the two variables, a is the slope, and b is the y-intercept.
In this case, the linear equation is:
P(x) = 6.25*x + 75
We know that P(x) represents her pay, and x represents the amount of computers she sold.
Here we can see that the slope is 6.25, it means says how much her pay increases per computer sold.
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modeling real life an animal shelter director is planning to build a rectangular playpen. the playpen must have a perimeter of 150 feet and an area of at least 1000 square feet. describe the possible lengths of the playpen. the length must be at least feet and at most feet.
For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
As given in the question,
For the given rectangular playpen,
Perimeter of rectangular playpen is equal to 150 feet .
Area of the rectangular playpen is equal to at least 1,000 squared feet .
Area = length × width
Let x be the length of the rectangular playpen .
Then its width is equal to 1000 / x.
Substitute the value of length and width in perimeter we get,
Perimeter of rectangular playpen = 2 ( length + width )
⇒ 150 = 2 [ x + (1,000/x)]
⇒ 150 / 2 = ( x² + 1,000 ) / x
⇒ x² + 1000 = 75x
⇒ x² -75x + 1,000 =0
Simplify quadratic equation using discriminant we get,
x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)
⇒ x = ( 75 ± √5625 - 4000) /2
⇒ x = (75 ± 40.31) / 2
⇒ x = 57.66 or 17.35
Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
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Which statements are ALWAYS TRUE? (SELECT ALL THAT APPLY)
A rhombus is a parallelogram.
A square has congruent diagonals.
A square is a rectangle.
A parallelogram has four congruent sides.
Answer:
statement 1 is true
statement 2 is true
statement 3 is false
statement 4 is false
statement 5 is also false cause parallelogram has 2 pair of congruent sides
I WILL GIVE YOU 25 POINTS JUST PLEASE HELP ASAP! Wilma works at a bird sanctuary and stores birdseed in plastic containers. She has 3 small containers that hold 8 pounds of birdseed each and 8 large containers that hold 12 pounds of birdseed each. Each container was full until she used 6 pounds of birdseed. She wants to put some of the remaining birdseed into 23 bird feeders that can hold 2 pounds each. How much birdseed does she have left over?
Answer:
the amount of birdseed leftover is 32
Step-by-step explanation:
what is the coefficient of the term 4ab
There are 72 mg of choleterol in a 3. 6 ounce erving of lobter how much choleterol i in 11 ounce of lobter round to the nearet tenth place
Answer:
The amount of cholesterol in 11 ounces of lobster is 220 mg
Step-by-step explanation:
The amount of cholesterol in 11 ounces of lobster can be calculated as follows
The first step is to convert all units of measure from ounce to mg
1 gram = 0.0352 ounce
Divide both sides by 0.0352 to get the value of 1 ounce
[tex]\frac{1}{0.0352}[/tex] gram = [tex]\frac{0.0352}{0.0352}[/tex] ounce
28.35 gram = 1 ounce
Since 1 gram equals 1000 milligrams, then multiply the left side by 1000 and change the unit of measure to milligram
28.35 [tex]\times[/tex] 1000 mg = 1 ounce
28350 mg = 1 ounce
Convert 3.6 ounces to milligrams
3.6 ounces = 3.6 [tex]\times[/tex] 28350 mg
3.6 ounces = 102060 mg
Convert 11 ounces to milligrams
11 ounces = 11 [tex]\times[/tex] 28350 mg
11 ounces = 311850 mg
Since there are 72 mg of cholesterol in a 3.6 ounces serving of lobster, then the ratio equation to follow is
[tex]\frac{72}{102060}=\frac{x}{311850}[/tex]
Where x is the amount of cholesterol in 11 ounces of lobster
Multiply both sides by 311850 to isolate x
[tex]\frac{72}{102060}\times 311850=\frac{x}{311850}\times 311850[/tex]
[tex]\frac{22453200}{102060} =x[/tex]
Simplify the left side of the equation
220 = x
Since the value of x is 220, then the amount of cholesterol in 11 ounces of lobster is 220 mg
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2 1/2x + 1/4 + 3/4x = 1/8
[tex]\frac{5}{2}x+\frac{1}{4} +\frac{3}{4} x=\frac{1}{8} \\\\\frac{5}{2}(8)x+\frac{1}{4} (8)+\frac{3}{4}(8) x=\frac{1}{8}(8)\\20x+2+6x=1\\20x+6x=1-2\\26x=-1\\\frac{26x}{26} =\frac{-1}{26} \\x=-\frac{1}{26}[/tex]
Find one terminating decimal and one repeating decimal between -1/2and -1/3.
one example of terminating decimal and one repeating decimal between -1/2and -1/3
terminating decimal = -2/5
repeating decimal = -3/11
What is terminating decimal?A decimal with an end digit is referred to as a terminating decimal. It is a decimal with a limited number of digits.
examples of terminating decimal are
0.5 = 1/20.25 = 1/40.4 = 2/5 and many moreWhat is repeating decimal?When a number's digits are periodic and its indefinitely repeated portion is not zero, the representation of that number as a decimal is said to be repeating or recurring.
Examples of a repeating decimal are
1/3 = 0.333333333.....22/7 = 3.142.......Learn more about decimal here:
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Exercise equipment advertised at $2200 is sold on sale for $1950. What percentage discount is this?
Percentage discount is 11.36%
Given in question,
Marked price = MP = $2200
Selling price = SP = $1950
Discount = D
= MP - SP
= 2200 - 1950
= 250
Discount % = (D/MP)*100
= (250/2200)*100
= 250/22
= 11.36
Hence, discount percent is 11.36%.
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An employee opens a credit union account and deposits
$90 at the end of each month. After two years, the account
contains $2,177.48. What annual nominal rate compounded
monthly has the account earned?
Annual nominal rate compounded monthly has the account earned is 0.84% .
In the question ,
it is given that ,
An employee opened a credit union account ,
amount deposited each month (PMT) = $90
number of period (n) = 2 years = 24 months
Future value after 2 years (FV) = $2177.48
let the rate of interest compounded monthly has the account earned be "r"
we know that the future value formula is
Future Value = PMT× [tex](\frac{(1+\frac{r}{12})^{n} -1 }{\frac{r}{12} } )[/tex]
Substituting the value of n = 24 , PMT = 90 and FV = 2177.48 in the Future Value Formula ,
we get ,
2177.48 = 90 × [tex](\frac{(1+\frac{r}{12})^{24} -1 }{\frac{r}{12} } )[/tex]
[tex](\frac{(1+\frac{r}{12})^{24} -1 }{\frac{r}{12} } )[/tex] = 2177.48/90
( 1 + r/12 )²⁴ -1 = (r/12) × 24.194
Solving further , we get
r = 0.0084
that means rate is = 0.84%
Therefore , Annual nominal rate compounded monthly has the account earned is 0.84% .
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Write the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters
this is an arithmetic sequence whose n th term ( explicit formula) is
aₙ = a + (n - 1 )d
where d is the common difference and a the first term
The given sequence is 12,10,8,6
twelve comma ten comma eight comma six
d=10-12=-2
a=12
Apply in explicit formula
aₙ = 12+ (n - 1 )(-2)
aₙ = 12-2n +2
aₙ = 14- 2n
Hence aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
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A dressmaker sells a shirt for $75 she makes a 25% profit how much did it cost her to make the shirt?
Answer:
Explanation:
Selling price:$75
Profit made:25%
Cost price:100/100-25
100/75
1.3333
There are four consecutive odd integers such that five times the second number minus twice the fourth number is the third number subtracted by 252
If there are four consecutive odd integers such that five times the second number minus twice the fourth number is the third number subtracted by 252 then the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.
What are consecutive integers?
Whole numbers that follow each other without gaps are known as consecutive integers.
For example, the numbers 15, 16, and 17 are all consecutive integers.
If 'n' is an integer, then the following consecutive integers begin at n, n+1, n+2, n+3, and so on.
Let x be the 1st of the four consecutive integers.
the other three consecutive integers could be
(x + 1) , (x + 2), and (x + 3).
By using the given conditions, we get
From the question,
(x + 1) = (5 * (x + 2)) - (x + 3)
Expand, and subtract like terms:
x + 1 = 5x + 10 - x - 3.
Simplifying the above expression, we get
x + 1 = 4x + 7.
3x = -6.
x = -2.
Hence, the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.
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y = -4 and y = 7 determine if the equation is parallel, perpendicular, or neither.
Answer: Neither
Step-by-step explanation:
A regular polygon is shown. 12 sided regular polygon Determine the measure of one of its angles.
The measure of one of its angle is 150°
A Polygon is a two-dimensional closed figure made up of line segments (not curves). Polygon is a combination of two words, poly (which means many) and gon (which means shape) (means sides). To create a closed figure, at least three line segments must be connected end to end.
Given that
12 sided regular polygon
We can use the following formula to calculate the total number of degrees in any shape:
(n−2)⋅180
[Where n = number of sides]
(12−2)⋅180
(10)⋅180
=1800
So a 12-sided polygon has 1800 degrees. To calculate the measure of one angle, divide the total number of degrees (1800) by the number of sides, n.
(1800/12) = 150°
Therefore the measure of one of its angle is 150°
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Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the fu
decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?
O It is linear because the graph decreases over time.
O It is linear because there is both an independent and a dependent variable.
O It is nonlinear because linear functions are increasing functions.
O It is nonlinear because linear functions increase or decrease at the same rate.
It is nonlinear because linear functions, which correspond to option D on the provided graph, grow or shrink at the same rate.
What is linear function?On the coordinate plane, a straight line can be represented by a linear function. In the coordinate plane, for instance, the linear function denoted by the equation y = 3x - 2 is a straight line. The graph of a linear function is a straight line. The form of a linear function is depicted below. a + bx = y = f (x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
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There is a 10% off sale on laptops. If someone saves $35 on a laptop, what was its original cost
Answer: $350
Reason: 10% of $350 is $35.
what is the value of 36(3) - 8(-6)
Answer:
156
Step-by-step explanation:
36*3=108
8*-6=-48
108-(-48)=156
The solution of the expression 36(3) - 8(-6) will be 156.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 36(3) - 8(-6). the expression will be solved as below,
E = 36(3) - 8(-6)
E = 108 - ( -48 )
E = 108 + 48
E = 156
Hence, the solution will be 156.
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y = x² − 1
-7=-x²-y
What are the solutions?
Explanation: Please give brainly if it's right!
First move all the x and y values on one side, and the constants on the other:
-x² + y = − 1
-x² - y = -7
Multiply -1 to the 2nd equation to change signs and then solve:
-x² + y = − 1
+x² + y = +7
2y = 6
y = 3
Plug in y to either equation (I plug into the first one)
-x² + 3 = − 1
-x² = -4
x = 2
3. Look at the following points.
(4, 0), (3,-1), (6, 3), (2,-4)
Which are solutions to y = x - 4? Choose all correct answers.
(6,3)
(4,0)
(3,-1)
(2,-4)
The coordinates (4, 0) and (3, -1) represents the solution of the function f(x).
According to the question -
y = f(x) = x - 4
Case 1 : P(4, 0)
0 = 4 - 4 = 0
P (4, 0) represents a solution
Case 2: P (3, -1)
-1 = 3 - 4 = -1
P (3, -1) represents a solution
Determine whether the equation below has one solution no solutions or an infinite number of solutions afterwards determine to values of X to support your conclusion
X – 6 = 6 – X
∠1 and ∠2 are supplementary. m∠1=124°m∠2=(2x+4)° What is the value of x? Select from the drop-down menu to correctly answer the question. x = Choose... 13 26 40 36 41
Answer:
26
Step-by-step explanation:
Supplemental means that the two angles together equal 180
124 + 2x + 4 = 180 Combine like terms
128 + 2x = 180 Subtract 128 from both sides of the equation
2x = 52 Divide both sides by 2
x = 26
What is the geometric mean between 6 and 12?
Answer:the geometric mean is the product of all the numbers in a set, with the root of how many numbers there are.
here, there are two numbers, so a square root is used.
geometric mean of
3
and
12
:
√
3
⋅
12
3
⋅
12
=
36
√
36
=
6
the value of the geometric mean of
3
and
12
is
6
.
Step-by-step explanation:
a baker is deciding how many batches of muffins to make to sell in his bakery. he wants to make enough to sell to everyone and no fewer. through observation, the baker has established a probability distribution. what is the probability the baker will sell exactly one batch? (find p(x
Form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.
As given in the question,
Probability distribution established by baker :
x : 1 2 3 4
P(x) : 0.10 0.30 0.40 0.20
As it is give that number of batches made by baker to sell muffins .
For selling 1 batch x = 1.
For selling 2 batch x = 2.
For selling 3batch x = 3.
For selling 4 batch x = 4
Probability of selling exactly one batch by baker is given by when x =1
Probability of x = 1 is given by :
P( x = 1 ) = 0.10
Therefore, form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.
The complete question is :
A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.10 2 0.30 3 0.40 4 0.20 What is the probability the baker will sell exactly one batch.
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Solve for y
3+3(2y-3)=-3(3y-4)+y
Answer: y=9/7
Step-by-step explanation: