Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets ofcardboard from which she cuts out 2-in squares from eachPLEASE CHECK PHOTO
Answers
Solution:
Given:
When the cardboard is folded to become a box (cuboid), it will have the following dimensions after the cut of squares from each corner;
[tex]\begin{gathered} l=(x+4)-2-2=x+4-4=x \\ w=x-2-2=x-4 \\ h=2 \\ \\ The\text{ volume }V=792in^3 \end{gathered}[/tex]The volume of a cuboid is given by;
[tex]\begin{gathered} V=lwh \\ 792=(x)(x-4)(2) \\ Dividing\text{ both sides by 2;} \\ \frac{792}{2}=x(x-4) \\ 396=x^2-4x \\ \\ Collecting\text{ all sides to one side to form a quadratic equation;} \\ 0=x^2-4x-396 \\ x^2-4x-396=0 \end{gathered}[/tex]Solve the quadratic equation by factorization;
[tex]\begin{gathered} x^2-4x-396=0 \\ x^2+18x-22x-396=0 \\ x(x+18)-22(x+18)=0 \\ (x-22)(x+18)=0 \\ x=22,x=-18 \\ \\ Since\text{ the dimension of a box can not be negative, then;} \\ x=22in \end{gathered}[/tex]Hence, the dimension of the original piece of cardboard is;
[tex]\begin{gathered} (x+4)\text{ by }x \\ \\ Substitute\text{ the value of x, the dimension of the cardboard is;} \\ (22+4)\text{ by }22 \\ 26in\text{ by }22in \end{gathered}[/tex]Therefore, the dimensions of the original piece of cardboard are 26 in by 22in
Related Questions
8. Use the point-slope formula to write an equationof a line in slope-intercept form using the points(1/2,5) and (5/2,9)
Answers
We have the next two points:
- (1/2,5)
- (5/2,9)
And we must use the point-slope formula to write an equation of a line in slope-intercept
First, we need to calculate the slope of the line using the point-slope formula
[tex]\begin{gathered} y_2-y_1=m(x_2-x_1) \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Where (x1, y1) and (x2, y2) are the two points
Now, replacing the points
[tex]m=\frac{9-5}{\frac{5}{2}-\frac{1}{2}}=\frac{4}{\frac{4}{2}}=\frac{4}{2}=2[/tex]Now, we must replace the slope and one of the two points in the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]Replacing m = 2 and (1/2, 5)
[tex]y-5=2(x-\frac{1}{2})[/tex]Finally, we must simplify to obtain the slope-intercept form
[tex]\begin{gathered} y-5=2x-1 \\ y=2x-1+5 \\ y=2x+4 \end{gathered}[/tex]ANSWER:
y = 2x + 4
K
A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.
Salary ($) Employees
5,001-10,000
10,001-15,000
17
15
15,001-20,000
20,001-25,000
25,001-30,000
OA. $7,376.62
B. $17,625
C. $15,862.50
D. $19,387.50
16
13
19
Answers
The mean salary of the employees is $17625.5.
The total number of employees in the company is 80.
The total salary for the first interval is [(5001+10000)/2]*17 = 127508.5.
The total salary for the second interval is [(10001+15000)/2]*15 = 187507.5.
The total salary for the third interval is [(15001+20000)/2]*16 = 280008.
The total salary for the fourth interval is [(20001+25000)/2]*13 = 292506.5.
The total salary for the fifth interval is [(25001+30000)/2]*19 = 522509.5.
In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers. The mean salary is the sum of all salaries divided by the total number of employees.
M = (127508.5 + 187507.5 + 280008 + 292506.5 + 522509.5)/80
M = 17625.5
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A school is organising a fun runThe fun run involves a 5
1
2
mile run around the field, then a 5
4
7
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
Answers
In mixed fraction the total distance of the fun run is 11 1/14
A school is organising a fun run. The fun run involves a 5 1/2
mile run around the field, then a 5 4/7 mile run back to the school.
The total distance is equal to summation of run around the field and run back to school.
total distance = 5 1/2 + 5 4/7
= 11/2 + 39/7
The L. C. M of 2 and 7 is 14
= [tex]\frac{11.7}{2.7} + \frac{39.2}{7.2}[/tex]
(77 + 78)/14
155/14
Upon dividing 155 by 14, the quotient is 11 and the the remainder is 1
In mixed fraction it is 11 1/14
So in mixed fraction the total distance of the fun run is 11 1/14
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Estimate [tex] \sqrt[3]{20} [/tex] between two integers.
Answers
Answer
∛20 is between 2 and 3.
Explanation
The question asks us to find the cube root of 20.
∛20
The key to doing this without the calculator is to take the cube of numbers and the one that has 20 in between them is the answer.
1³ = 1
2³ = 8
3³ = 27
We can see that 20 is between 8 and 27.
So,the cube root of 20 has to be betwen 2 and 3.
The other way to do this with the calculator is to actually find the cube root of 20
∛20 = 2.71
Which is between 2 and 3.
Hope this Helps!!!
w/2 + 4 is greater than 5
Answers
Answer:
I say w is equal to 4, because:
4 divided by 2 = 2
2 + 4 = 6
6 > 5
Step-by-step explanation:
Hope it helps! =D
7x — 9y = 12—7x – 7y = -28
Answers
In order to solve this system of equations, we can add both equations, this way we can find the value of y and then the value of x:
[tex]\begin{gathered} \begin{cases}7x-9y=12 \\ -7x-7y=-28\end{cases} \\ 7x-9y-7x-7y=12-28 \\ -16y=-16 \\ y=\frac{-16}{-16}=1 \\ \\ 7x-9=12 \\ 7x=21 \\ x=\frac{21}{7} \\ x=3 \end{gathered}[/tex]So the solution to this system is (3, 1).
Can somebody Answer this?
Answers
Garry needs 18.4 oz of glue and 9.2 oz of glitter to make 4 bottles.
What is direct proportion?In direct proportion between two or more than two quantities if one quantity is multiplied or divided by some constant k other quantities will also be multiplied or divided by the same constant k.
Given, Making 1 bottle of glitter glue Garyy requires 4.6 oz of glue and 2.3 oz of glitter.
∴ 4 bottles of glitter glue require (4.6×4) = 18.4 oz of glue and (2.3×4) = 9.2 oz of glitter.
As the no. of bottles is multiplied by 4 thus material requirements will also be multiplied by a factor of 4.
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Length is 3x − 4, area is 6x4 − 8x3 + 9x2 − 3x − 12
Answers
The width of the given rectangle is 2x²-3x+3.
Given that, area of rectangle = [tex]6x^4-8x^3+9x^2-3x-12[/tex] and the length of rectangle = 3x-4.
What is the area of a rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units. The formula to find the area of a rectangle = Length × Width.
Now, (3x-4) × width = [tex]6x^4-8x^3+9x^2-3x-12[/tex]
⇒ Width = [tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]
3x-4|[tex]6x^4-8x^3+9x^2-3x-12[/tex]|2x³-3x+3
[tex]6x^4[/tex] - 8x³
_________________
0+9x²-3x-12
(-) 9x²+12x
_________________
0+9x-12
(-) 9x(+)12
_________________
0
So, width = 2x²-3x+3
Therefore, the width of the given rectangle is 2x²-3x+3.
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find the distance from line y= -3x + 4 to line y = -3x - 1
Answers
In the accompanying diagram of BCD m
Answers
Given:
m∠C = 70°
m∠CDE = 130°
Question 1:
To find ∠CDB, let's use the exterior angle theorem.
The exterior angle theorem states that the sum of 2 opposite interior angles is equal to the exterior angle.
Thus,
m∠C + m∠B = 130
70 + m∠B = 130
Subtract 70 from both sides:
70 - 70 + m∠B = 130 -70
m∠B = 60°
Now, use the triangle angle sum theorem to find ∠CDB.
The triangle angle sum theorem states that the sum of interior angles in a triangle is 180°
∠CDB = 180 - 70 - 60 = 50°
∠CDB = 50°
Question 2:
∠CBA = ∠C + ∠CDB
∠CBA = 70 + 50 = 120°
∠CBA = 120°
ANSWER:
∠CDB = 50°
∠CBA = 120°
Which of these shows the result of using the first equation to substitute fory in the second equation, then combining like terms? y- 3x 3x+ 2y= 18 OA. 3y 18 B. 9x= 18 OC. 6x= 18 OD. 3x= 18 m
Answers
If the measure of ∠ C A B = 4 x + 14 and ∠ D A E = 6 x − 18 then find the measure of ∠ C A B
CAB and DAE are suplementary
Answers
Measure of CAB is 84.4, by using supplementary angle theory.
What is supplementary angle?
In geometry, two angles are referred to as supplementary angles if their sum is 180 degrees. For instance, if A + B = 180°, then A and B are considered supplementary angles. Complementary angles always result in a straight angle when combined (180 degrees).
Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.
We have given, CAB= 4x+14 and DAB = 6x-18
Both are supplementary angle
Therefore, CAB + DAB = 180
4x+14+6x-18=180
10x-4=180
10x=176
x=17.6
hence, CAB = 4(17.6)+14 = 84.4
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The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 m, find its area.
Answers
The area when the length of a rectangle is six times its width is 216m².
How to calculate the value?Let the width = w
Let the length = 6 × w = 6w
Therefore the perimeter will be:
= 2(Length + Width) = 84
2(w + 6w) = 84
2 × 7w = 84
14w = 84
Divide
w = 84 / 14
w = 6
Width = 6m
Length = 6w = 6 × 6 = 36m
The area will be:
= Length × Width
= 36m × 6m
= 216m²
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Given: f(x) =x^2 + 6x + 5Find the x and y value of the vertex (turning point)And what are the zeros of the parabola?
Answers
Solution: X-value of vertex=-3
Y-value of vertex=-4
Zeros of the parabola: X=-5 and x=-1
Analysis
We can find the x-coordinate of the vertex, calculating -b/2a. First, we identify the a and b values of y=ax^2+bx+c of your quadratic equation.
b=6
a=1
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{6}{2(1)}=-3 \\ \\ After\text{ we find x-coordinate, we can find y-coordinate of the vertex replacing x-value.} \\ f(x)=x^2+6x+5\text{ = }^^(-3\text{ }^2)+6(-3)+5 \\ f(x)\text{ = 9}-18+5 \\ f(x)=-4 \end{gathered}[/tex]Now, let's find the zeros of the parabola. We factorize the quadratic equation:
[tex]\begin{gathered} f(x)=x^2+6x+5 \\ f(x)=(x+5)(x+1) \\ Let^{\prime}s\text{ equal to zero} \\ (x+5)(x+1)=0 \\ (x+5)=\text{ 0 }(x+1)=0 \\ x=-5\text{ }x=-1 \end{gathered}[/tex]4626ххXхA school received 46 iPads. The school library took 26 of the iPads and the rest were split equally among 4 teachers to use in theirclassrooms. Using the strip diagram and the letter x to represent the unknown quantity, which equation could be used to find thenumber of iPads each teacher received?A)4x = 46 - 26B)4x +46 +264x - 26 - 46D)4x = 26 + 46
Answers
Given data:
The box is given.
The given expression can be written as,
[tex]\begin{gathered} 26+x+x+x+x=46 \\ 4x+26=46 \end{gathered}[/tex]Thus, the option (c) is correct.
A coordinator will select 5 songs from a list of 8 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
Answers
The number of lineups possible is the combination of selecting 5 songs from 8 songs.
8C5 = 56.
What is combination?A combination is a mathematical way that evaluates the number of possible arrangements within a collection of items, leaving behind of the order of selection. A combination can select items in any order. Combinations can be confused with permutations Water is a combination of hydrogen and oxygen. The car interior is available in various color combinations. The formula for combinations is nC_r = n/(r!*(n - r)!), where n is the number of items and r is the number of items selected at once. Let's look at an example of how combinations are calculated. There are 10,000 possible combinations of the numbers 0-9 in a 4-digit codeTo learn more about combination from the given link:
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
A car that travels from Las Vegas to Los Angeles averages about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles. Write a function to represent the distance d remaining on the trip t hours after departure.
Answers
The distance remaining is given by the equation d = 270 - 60t
How to solve an equation?Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let d represent the distance from Las Vegas to Los Angeles and t represent the remaining time after departure.
A car travels from Las Vegas to Los Angeles at about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles.
Hence distance remaining is:
d = 270 - 60t
The distance remaining is d = 270 - 60t
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please help
Which graph represents the solution set of the system of inequalities?
{y≥12x+1y>−x−2
Responses
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.,
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.,
Answers
The graph that represents the system of inequalities is the graph attached below.
How to Determine the Graph of a System of Inequalities?The graph that would represent the system of inequalities must be two lines that intersect each other and have the exact slope and y-intercept of each of the lines on the graph.
Determine the slope and y-intercept of each of the inequalities, and also determine their boundary lines based on which inequality sign they have.
The line that represents the inequality, y ≥ ½x + 1, will be a solid line that has a slope of ½, and a y-intercept of 1.
The second line that represents the inequality, y ≥ -x - 2, will be a dashed line that has a slope of 1, and a y-intercept of -2.
Therefore, the graph that represents the features stated above for both lines is shown in the diagram below.
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find X and Y X - 3 y + 3 15 12
Answers
To solve this problem we have to remember that diagonals of a parallelogram bisect each other. This means that they intersect in the midle point of each other. From this we can conclude that
[tex]\begin{gathered} x-3=15 \\ \text{and} \\ y+3=12 \end{gathered}[/tex]Once we have our equations we can solve them. Let's find x
[tex]\begin{gathered} x-3=15 \\ x=15+3 \\ x=18 \end{gathered}[/tex]Now, let's find y
[tex]\begin{gathered} y+3=12 \\ y=12-3 \\ y=9 \end{gathered}[/tex]Then x=18 and y=9,
I tried doing it but the whole thing is confusing
Answers
Given the equation:
y = 828000 - 2700x
Where y is the value of the building and x is the number of months of use.
Let's find when the value of the building will be $666,000.
To find when the value will be $666,000, substitute 666000 for y in the equation and solve for x.
y = 828000 - 2700x
666000 = 828000 - 2700x
Subtract 828000 from both sides:
666000 - 828000 = 828000 - 828000 - 2700x
-162000 = -2700x
Divide both sided by -2700:
[tex]\begin{gathered} \frac{-162000}{-2700}=\frac{-2700x}{-2700} \\ \\ 60=x \\ \\ x=60 \end{gathered}[/tex]The value of the building will be $666,000 after 60 months.
Now, let's convert from months to years.
Where:
12 months = 1 year
[tex]60\text{ months = }\frac{60}{12}=5\text{ years}[/tex]Therefore, the value of the building will be $666,000 after 5 years.
ANSWER:
5 years.
The formula S=
2S-a, n
Oan=- n
n(a₁ + an)
2
2S+ a₁n
an-- n
an-2S+a, n+n
a, 2S-a, n+n
gives the partial sum of an arithmetic sequence. What is the formula solved for a,,?
Answers
Answer:
2S-a1n/n
Step-by-step explanation:
S = n(a1 + an)/2
2S = n(a1 + an)
2S = na1 + nan
nan = 2S - na1
an = (2S - n a1)/n
3. Given: B is the midpoint of AC, AD = CD
Prove:
DAB = LDCB
Statements
1)
2) AB=CB
3) DB DB
4)
5) ZDAB=2DCB
A
1)
2)
3)
5)
Reasons
D
B
C
Answers
Using the congruency of the triangle we can prove all the conditions.
What do you mean by congruencey of the triangle?The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. Two triangles are said to be congruent if pairings of corresponding sides and corresponding angles are equal. They are the exact same size and form.
D is the midpoint of AC
so AB = BC
and also AD = CD
so the triangle ADB is congruent to triangle CDB
Therefore,
angle ADB = angle CDB
angle ABD = angle CBD
angle BAD = angle BCD
Using congruency of the triangle.
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Please show and explain this please
Answers
The graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
What is a graph of a function?Defining a function's graph: The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f(x). As a result, the graph of an equation is a particular instance of the graph of a function. We merely select a value for x, then determine the value of y that corresponds. Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3. Making points for the graph is simple.So, the function with which the given graph matches:
The graph of the option (E) f(x) = (x + 10)(x - 3)²(x + 1) is:(Refer to the graph attached below)We can easily see that coordinates of the given graph and the graph of equation (E) match.Therefore, the graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
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I don’t understand this paper and our sub has no idea, nor the other students so if someone could help me, that would be great.
Answers
By Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
Given two triangles are ABC and A'B'C'.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
1) Triangle ABC is reduced to triangle A'B'C'
∠ABC=∠A'B'C'=90°
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
2) Triangle ABC is enlarged to triangle A'B'C'
∠ABC=∠A'B'C'
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
Therefore, by Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
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5. Evaluate the following V16
Answers
A tank has two inlet pipes and one outlet pipe. The inlet pipes can fill the tank in 4 hoursand 10 hours. The outlet pipe can drain the tank in 2 hours. One day the outlet pipe was leftopen as the empty tank was being filled. Will the tank ever be full? If so, how long will ittake to fill the tank? If not, explain why not.
Answers
The two inlet pipes can fill the tank in 4 hours and 10 hours.
The work done by the inlet pipes per hour is calculated to be:
[tex]\Rightarrow\frac{1}{4}+\frac{1}{10}=\frac{7}{20}\text{ units per hour}[/tex]The outlet pipe drains the tank in 2 hours. The work done will be:
[tex]\Rightarrow\frac{1}{2}\text{ units per hour}[/tex]Therefore, if both inlet pipes and the outlet pipes are opened at the same time, the work done by the pipes combined will be:
[tex]\Rightarrow\frac{7}{20}-\frac{1}{2}=-\frac{3}{20}\text{ units per hour}[/tex]Since the work done to fill the tank is negative, it means that the tank will never get full as it empties faster than it fills up.
Winston is making a model of a statute using a scale where 2 inches equals 6 feet. If the actual height of
the statue is 20 feet, how tall is the model, in inches?
Answers
Answer:
6 2/3 inches
Step-by-step explanation:
2 inches / 6 feet * 20 feet = 6 2/3 inches
What is the slope and y-intercept?
y=-5x+6
Options:
Blank # 1
Blank # 2
Answers
The y intercept (c) is 6
any whole number is a proper subset or rational number
Answers
Answer:
The natural numbers, whole numbers, and integers are all subsets of rational numbers
Step-by-step explanation:
hope it helps
have a good day