Domain of the function is: 0 < x < 12.
Volume of the box = 4x(12-x)²cm^3
Volume of a cuboid:Volume is the measure of how much space a given substance takes up inside a closed, three-dimensional object. A cuboid's volume given by its length (l), breadth (b), and height (h) is as follows:
According to the given data:Side of square = 24cm
(a) Volume of the box
Let the squares used to create a box have a side of "x" cm.
so,
length will be = 2(12 - x)
Width will be = 2(12 - x)
Hight will be = x
Volume of the Square box (V) = l x b x h
= 2(12 - x) * 2(12 - x) * (x)
= 4x(12-x)²cm^3
(b) The domain of the function V(x)
We see that:
x is length, x >0
x cm of the side's length of 24 cm are removed from both ends.
so that 2x<24
Domain of the function is: 0 < x < 12.
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I understand that the question you are looking for is:
An open box of maximum volume is to be made from a square piece of material, 24 centimeters on a side, by cutting equal squares from the corners and folding up the sides.
If V is the volume in cubic centimeters and x is the height of the box in centimeters, find V in terms of x. Determine the domain of the above function
What is the solution to this equation?
x + 4(x + 5) = 40
A. X= 4
B. X= 7
C. x=9
D. x = 12
Answer:
A
Step-by-step explanation:
x + 4(x + 5) = 40 ← distribute parenthesis and simplify left side
x + 4x + 20 = 40
5x + 20 = 40 ( subtract 20 from both sides )
5x = 20 ( divide both sides by 5 )
x = 4
Some friends are going to be driving to a city 900 miles away from home. They are planning to stay the night in a city 420 miles away, then drive the rest of the distance the following day. If they plan to drive on average 60 miles per hour, how long will they be driving the second day?
The total time they will be driving the second day is 8 hours
The total distance they are planning to go = 900 miles
Distance travelled on first day = 420 miles
Distance yet to be travelled on second day = Total distance - distance covered = 900 miles- 420 miles= 480 miles
The speed of the car = 60 miles per hour
60 miles of distance covered in time = 1 hour
1 mile of distance covered in time = 1 hour /60 miles = 1 minute
This is solved using Unitary Method
1 hour = 60 minutes
480 miles can be covered in time = 1 minute × 480 miles
= 480 minute
=8 hours
Hence, The total time they will be driving the second day is 8 hours
Distance and displacement are two quantities that appear to mean the same thing but have very different meanings and definitions. Distance is defined as "how much ground an object has covered during its motion," whereas displacement is defined as "how far out of place an object is."
Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.
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What is 0.904 subtract 0.01?
Answer:
0.894 is your correct answer.
Answer:
0.894 because the 0.01 will affect the hundredths so the 0 will be affected in 0.904 and the 9 will change to an 8 because there's nothing left in 0 so you have to substitute.
Arika and Savroop have 19 ½ cups of flour. They want to make loaves of banana
bread for a bake sale. Arika had a recipe for banana bread that calls for 1 ⅞
cups of flour. Savroop has a recipe that calls for 1 ½ cups of flour. Select all the
statements that are true about the recipes.
O Arika's recipe will make 10 whole loaves of banana bread.
O Savroop's recipe will make 14 whole loaves of banana bread.
O There will be less flour leftover if Savroop's recipe is used.
( There will be less flour leftover if Arika's recipe is used.
D More loaves of bread can be made using Arika's recipe than using Savroop's recipe.
Statements A and C are correct.
Here, we are given that Arika and Savroop have 19 ½ cups of flour. Arika had a recipe for banana bread that calls for 1 ⅞ cups of flour. Savroop has a recipe that calls for 1 ½ cups of flour.
Let us evaluate each option one by one-
A. Arika's recipe will make 10 whole loaves of banana bread.
Arika's recipe requires 1 ⅞ cups of flour = (8 + 7)/8
= 15/8
Total flour they have = 19 ½ = (19 × 2 + 1)/2
= 39/2
Thus, Arika's recipe will make = 39/2 ÷ 15/8
= 39/2 × 8/15
= 13 × 4/ 5
= 52/5
= 10.4
Thus, the given statement is correct.
B. Savroop's recipe requires 1 ½ cups of flour = (2+ 1)/2
= 3/2
Thus, Savroop's recipe will make = 39/2 ÷ 3/2
= 39/2 × 2/3
= 13
Thus, the given statement is incorrect. Savroop's recipe will make only 13 whole loaves.
C. As we can see above, Arika's recipe will make 10.4 loaves and thus 0.4 cups of flour will be left over. Whereas, in case of Savroop, no flour will be left over. Thus, the given statement is true.
D. By the same reasoning given above, the given statement is false as there will be less flour leftover if Savroop's recipe is used.
E. The given statement is again false as Arika's recipe will make only 10 loaves whereas Savroop's recipe will make 13.
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Determine the translation.
The sum of two numbers is 172. The first is 8 less
than 5 times the second. Find the first number.
Answer:
X+Y=172 OE X=172-Y
X=5Y-8
5Y-8=172-Y
5Y+Y=172+8
6Y=180
Y=180/6
Y=30 ANS
X=172-30
X=142 ANS.
Step-by-step explanation:
A bank Teller's annual salary will increase by 12% next year to an annual salary of
$48,000. What is the teller's annual salary now?
Answer:
$42,857.14
Step-by-step explanation:
12% = 12/100 = 0.12
If the teller's current salary is D and it increases by 12% in one year, the salary next year would be
X(1+0.12) = 1.12X
We know that salary next year is 48000
Using this fact,
1.12X = 48000
Dividing by 1.12 on both sides,
X = 48000/1.12 = 42,857.14
Find the value of f(-2)
Answer:
y= -3 or just -3
Step-by-step explanation:
. f(x) = 2x-5; Find f(-8)
5y + 7x = -1
-2y = -5x - 23
Elimination
Step-by-step explanation:
+25y + 35x = -1. × 5
+35x - 14y = -161. × 7
-. +. +
39y = 156
y=4
putting value of y in 5y + 7x =-1
5×4+7x =-1
7x = -21
x= -3
the product of two consecutive integers is 420. which quadratic equation can be used to find x, the lesser number? x2 1
The quadratic equation, x(2) + 2 =420 can be used to find x.
you can use trial and error
x(2) + 2 =420
210(2)=420 but we need to add the two so lower the [tex]120[/tex]
209(2)=418+2 = 420
so, the x value must less than 21.
How do you write a quadratic equation in standard form?A quadratic equation with variable x is written in standard form as [tex]ax2 + bx + c = 0[/tex], where a, b, and c are constants such that the value of an is non-zero but the values of b and c can both be zeros.
Let's change [tex]ax2 + bx + c = 0[/tex] from its standard form to its vertex form, which is [tex]a (x - h)2 + k = 0[/tex], where (h, k) is the vertex of the quadratic function [tex]f(x) = a (x - h)2 + k[/tex]. Keep in mind that 'a' has the same value in both equations. Just set them equal so we can determine how the variables relate to one another.
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Find the difference in altitude between a mountain that has an altitude of 2593feet and a desert valley that is 394feet below sea level.
The difference in altitude between a mountain that has an altitude of 2593feet and a desert valley that is 394feet below sea level is
dA=2987feet
What is the difference in altitude?
Generally, the equation for the difference is mathematically given as
dA= mountain altitude - desert valley
Therefore
dA=2593-(-394)
dA=2593+394
dA=2987feet
In conclusion, The height of a mountain that is located at an elevation of 2593 feet compared to the elevation of a valley in the desert that is 394 feet below sea level is the difference in altitude.
dA=2987feet
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Bella and her friends have a half-day at school, so they plan to spend the afternoon
paddleboarding at Lake Evergreen. They want to spend the rest of the day on the water, but
it starts to rain after paddleboarding for only of an hour! Bella is disappointed when she
of a
realizes the sun doesn't go down for another 4
hours.
Use an equation to find the amount of time Bella planned to spend paddleboarding.
Jen planned to spend 19/4 hours paddleboarding
Bella and her friends spent 3/4 hour at the Lake paddleboarding
Proportions: A proportion is an equation that can be solved and is made up of two ratios that have been set equal to one another.
When I state that a proportion is the product of two ratios that are equal to one another, I mean that two fractions must also be equal to one another.
Also, the sun doesn't go down for another 4 hours
So, 4 + 3/4 = 4.75 hours = 475/100 = 19/4 hours
Hence, Jen planned to spend 19/4 hours paddleboarding
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Parallel to 4x — 6y = -36 passing through (2,3)
An equation which is parallel to 4x - 6y = -36 passing through points (2, 3) is y = 2x/3 + 5/9.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.
This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Simplifying the equation, we have:
4x - 6y = -36
6y = 4x + 36
Dividing both sides by 6, we have:
y = 2x/3 + 6
m₁ = m₂ = 2/3.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (2, 3), we have:
y - 3 = 2/3(x - 2)
y - 3 = 2/3(x - 2)
y - 3 = 2x/3 - 4/3
y = 2x/3 - 4/3 + 3
y = 2x/3 + 5/9
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PLEASE HELP
question down below
Answer:
Draw a line going down from the 300, with a break in the middle and finish it out at the 6 hr mark.
Step-by-step explanation:
Start at the 300 and draw that line down to the 180 mark lined up with the 2 hour dot. Then draw a horizontal line from there to the middle of the 2 and the 4. Then draw a line from where you ended the break with the same slope as the beginning.
Hope this helps!
plss help(image attached que 5)
Answer:
3300cm² is the answer of this question i guess so
50,500-35,675 and work for it
Answer: 14,825 is the answer
Step-by-step explanation:
Answer: 14,825
Step-by-step explanation:
its easy.
PLEASE HELP ASAP! WILL GIVE BRAINLIEST!
Describe the pattern.
1, 2, 3, 4, 10, 19, 36, 69, 134, 258, 497, ...
Answer: the front of the four numbers is always the total
Step-by-step explanation: like 258 + 134 + 69 + 36= 497
Find the product.
2 1/3 ⋅ 3 1/2
Write the answer as a mixed number.
Is it possible to calculate the cube root of a negative number?
Answer:
Yes, the cube root of a negative number can be calculated.
Step-by-step explanation:
what is it called when you make predictions about data that is not recorded, but falls between the data collected?
when you make predictions about data that is not recorded, but falls between the data collected it is called Predictive analytic.
What is Predictive analytics?Data mining, predictive modeling, and machine learning are only a few of the statistical methods included in predictive analytics, which examine current and past data to anticipate future or otherwise unknowable occurrences.
Predictive models are used in business to detect risks and opportunities by making use of trends observed in historical and transactional data. In order to estimate the risk or potential associated with a certain set of variables and guide decision-making for possible transactions, models contain interactions among many different elements.
When we make a prediction about data is called predictive analytic.
But when it's not recorded it's called extrapolation.
But if it falls between data collected it called Predictive analytic.
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what is the step-by-step answer to
-3(X + 2)=-18
Answer:
x = 4Step-by-step explanation:
Simplify both sides of the equation:−3 (x+2) = −18
(−3) (x) + (−3) (2) = −18 (Distribute)
−3x + −6 = −18
−3x −6 = −18
Add 6 to both sides:−3x −6 +6 = −18 + 6
−3x= −12
Divide both sides by -3:−3x/−3 = −12/−3
x = 4
10 QUESTIONS IM ON 3
Answer:
x = 9
m<H = 38 degrees
Step-by-step explanation:
Answer: 9
Step-by-step explanation: sub in 9 for x in 5x-7. we get 38. add 38 and 89 and then subtract that sum from 180, which is 53. now add 53 to 14x+1 and make it equal to 180. To solve for x, subtract 54 from both sides, which gives us 14x=126. Divide both sides by 14 and we get x =9. Now that we know that 9 works for x in both equations, the answer is 9.
Can someone please send the answers to these questions with explanation? (Attachment) (30 POINTS)
Answer:
Step-by-step explanation:
a) this graph is that of a parabola that opens up. As is the case for all parabolas, the domain is the set of all real numbers. The range begins with the smallest y-value, which is -4, extending upwards from there: [-4, infinity)
b) this graph's shape most closely resembles that of a polynomial; as we move from left to right, y increases, reaches a local maximum, decreases to a local minimum, and then continues to increase with x. As is the case for all polynomials, the domain is the set of all real numbers. As we move from x = 0 to the left, y decreases without bound; from x ≥ 12 onward, y increases without bound; thus, the range is (-infinity, +infinity).
c) The graph represents a quarter of an ellipse for which x begins at -40 and ends at [4, -16]. Thus, the domain is [-40, 4]. By inspection we see that the smallest y value is -16 and the largest is 4; thus, the range is [-40, 4].
" .
8x + 4 = -28
solve for x
Answer:
x=-4
Step-by-step explanation:
8x+4=-28
8x=-28-4
8x=-32
x=-4
Moo berry creamery uses 2 cups of ice cream in each milkshake. How many milkshakes can they make with 1 gallon of ice cream?
Moo berry can make 8 milkshakes with 1 gallon of ice cream.
How to calculate the number of milkshakes ?Moo uses 2 cups of ice cream in each milkshake
He is using 1 gallon of ice cream
Therefore the number of milk shakes he can produce can be calculated as follows
16 cups makes 1 gallon
= 16/2
= 8
Hence 8 milkshakes can be made with one gallon of ice cream
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Calculate the distance between the points P= (-7, 8) and J =(-3, 1) in the coordinate plane.
Give an exact answer (not a decimal approximation).
Distance:
The distance between the given points P(-7,8) and J(-3,1) is √65 = 8.06225775
Given that, The points are P=(-7,8) and J = (-3,1).
A coordinate plane is a surface formed by two dimensional lines .
The distance between the points is calculated using the distance formula that is, distance between A(x1,y1) and B(x2,y2) is,
√[(x2-x1)²+(y2-y1)²], by using this formula you can find the distance between any two points on the plane.
Therefore the distance between the given points P and J is ,
PJ = √[(-3+7)²+(1-8)²]
= √[(4)²+(-7)²]
= √[(16) + (49)]
= √[16+49]
= √[65]
= 8.06225775
PJ = 8.06225775
Therefore the distance between the given points P(-7,8) and J(-3,1) is 8.06225775
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Explain how you can use a graphing calculator to determine if a table of values represents a proportional function.
Table: x and y increments must be the same. X and y increments need not be the same.
The x and y exponents should be 1. Linear equation.
Graphs should be straight.
This is further explained below.
Explain how you can use a graphing calculator to determine if a table of values represents a proportional function:Generally, Based on the table, you need to ensure that the increments for the x values and the y values are the same.
It is not necessary for the increment to be the same for both the x and y values.
The following conclusion may be drawn from an equation: both the x and y exponents should be set to 1.
It seems like we need a line equation for this problem.
In conclusion, Inferred from a graph: the shape of the graph ought to be that of an unbroken line.
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What is the value of x² + 2x + 3 when x = 3/4
27/4
81/16
6
69/16
HELP ANSWER PLSSSSSSSSSSSS
The degrees of the whole segment is 90 because we know that a right angle is 90 degrees and can be shown with a square in the corner. One angle inside the 90 degrees is 50 degrees and the other two values are the same. Since 90 - 50 = 40, we know that the remaining is 40 degrees. Since x is the same, we divide 40 by 2, getting 20 degrees.
ANSWER: x = 20 degrees