Answer:
5.9
Step-by-step explanation:
The mean means arithmetic average (some people just say average here).
The average of 4 numbers is the sum of those 4 numbers divided by the number of numbers which is 4 in this case.
So we have this formula:
[tex]\frac{3.8+4.2+5.3+x}{4}=4.8[/tex]
Multiply both sides by 4:
[tex]3.8+4.2+5.3+x=4(4.8)[/tex]
Simplify:
[tex]13.3+x=19.2[/tex]
Subtract 13.3 on both sides:
[tex]x=19.2-13.3[/tex]
Simplify:
[tex]x=5.9[/tex]
I’m trying to round the divisor to the nearest whole number
198,200 divided by 4.033
The divisor is 4.033 because it divides 198,200. Rounded to the nearest whole number, it is 4 because 0 is less than 5, so the next highest (whole) place is unchanged.
For this case we have a division where:
198,200 is the dividend4,033 is the divisorIf we want to round the divisor to the nearest whole number we have:
4.033 is equivalent to 4, because:
3 is less than 5, then we have 4.03
3 is less than 5, so we have 4.0 equivalent to 4.
Answer:
The divisor remains as 4, rounded to the nearest whole number.
Given the lengths of the sides, state if the triangle is acute, obtuse, or right. 24, 37, and 40 This is a(n) blank triangle.
Answer:
This is an acute triangle
Step-by-step explanation:
Pythagoras theorem is used to determine if a triangle is right, acute or obtuse
If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.
If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.
If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.
so,
[tex](40)^2 = (37)^2 + (24)^2\\1600 = 1369+576\\1600<1945[/tex]
As 1600<1945, the given triangle is an acute triangle ..
Evaluate 3(x-1)+1 when x=5
3(5-1)+1
(15-3)+1
12+1
13
[tex]\huge{\boxed{13}}[/tex]
Substitute. [tex]3(5-1)+1[/tex]
Subtract. [tex]3*4+1[/tex]
Multiply. [tex]12+1[/tex]
Add. [tex]\boxed{13}[/tex]
35.6 = the square root of 15.3^2 + the square root of x^2. Find x.
Answer:
x = 50.9
Step-by-step explanation:
35.6 = √(15.3²) + √(x²)
35.6 = 15.3 + x
x = 35.6 + 15.3
x = 50.9
Multiply (6 + 2i)(6 – 2i)
O 32
O 40
O 36 + 12i
O 36 - 12i
Answer:
40
Step-by-step explanation:
6*6/6*-2i/2i*6/2i*-2i
Answer:
40
Step-by-step explanation:
What are the coordinates of the vertices of the image of rectangle WXYZ after the transformation Ro, 90•(x,y)? W’(-4,-1)
Answer:
W (-1, 4) ---> W' (-4, -1)
X (-1, 2) ---> X' (-2, -1)
Y (2, 2) ---> Y' (-2, 2)
Z (2, 4) ---> Z' (-4, 2)
Step-by-step explanation:
We have with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.
We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).
So,
W (-1, 4) ---> W' (-4, -1)
X (-1, 2) ---> X' (-2, -1)
Y (2, 2) ---> Y' (-2, 2)
Z (2, 4) ---> Z' (-4, 2)
describe the graph of the equation y=0. is the equation a function
Answer:
The function is defined along the x-axis. Yes the equations y = 0 is a function
Step-by-step explanation:
It means that y is 0 in all values of x
The graph y = 0 would be a horizontal line that overlaps the x-axis. This would be a function because the y-value (zero) never has the same x-value. This means that it would pass the vertical line test since the graph would only pass through it once.
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the absolute value of I -32 I?
The absolute value of I-32I = 32
What is an absolute value of a number?"It is the distance of a number from zero, without considering direction.""It is always positive."For given question,
We need to find the absolute value of -32
We know that, for any number 'a',
the absolute value of a is |a| = a (positive value)
|-32| = 32
Therefore, the absolute value of I-32I = 32
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Melissa’s family is driving out of state to her grandmother’s house. They know that it takes 20 gallons of gas to get there, and the cost of three gallons of gasoline is $10.50. How much should the family budget to make the one-way trip?
Answer:
$70
Step-by-step explanation:
10.50/ 3 = 3.5
3.5 times 20 =70
A certain field has 3 mice. in five months, you now have 18 mice. if the population grows exponentially, how many mice will be in the field after 1 year?
The number of mice in the field after 1 year is 221 mice.
Given data:
If the population of mice in the field grows exponentially, we can use the exponential growth formula to determine the future population.
The exponential growth formula is given by:
P(t) = P₀ * e^(kt)
Where:
P(t) is the population at time t,
P₀ is the initial population,
e is Euler's number (approximately 2.71828), and
k is the growth rate.
So, the initial population (P₀) is 3 mice, and after five months, the population (P(t)) is 18 mice.
18 = 3 * e^(5k)
Dividing both sides by 3, we get:
6 = e^(5k)
To solve for k, we can take the natural logarithm (ln) of both sides:
ln(6) = 5k
k = ln(6) / 5 ≈ 0.35835
So, the growth rate is k = 0.3583
Now that we have the growth rate, determine the population after 1 year (12 months).
Substituting the values into the formula:
P(12) = 3 * e^(0.35835 * 12)
Calculating this expression, we find:
P(12) ≈ 3 * e^(4.3) ≈ 3 * 73.699 ≈ 221.09
Hence, it is expected that there will be approximately 221 mice in the field after 1 year if the population grows exponentially.
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Final Answer:
After 1 year, the field is expected to have approximately 221 mice.
Explanation:
To solve this exponential growth problem, we'll use the exponential growth formula:
[tex]\[ P(t) = P_0 \times e^{rt} \][/tex]
where:
- [tex]\( P(t) \)[/tex] is the population at time t,
- [tex]\( P_0 \)[/tex] is the initial population size,
- r is the growth rate,
- e is Euler's number (approximately 2.71828),
- t is the time in consistent units.
We need to find the growth rate r using the information that we have (the initial population [tex]\( P_0 \)[/tex] is 3, and after 5 months,[tex]\( P(5) \)[/tex] is 18). Then, we'll calculate the population after 1 year (12 months).
Let's apply the given values to the formula at t = 5 months:
[tex]\[ 18 = 3 \times e^{5r} \][/tex]
Now we need to solve for r. We start by dividing both sides of the equation by 3:
[tex]\[ 6 = e^{5r} \][/tex]
Next, we take the natural logarithm (ln) of both sides to solve for r. The natural logarithm of [tex]\( e^{5r} \)[/tex] is equal to 5r:
[tex]\[ \ln(6) = 5r \][/tex]
Now we divide by 5:
[tex]\[ \frac{\ln(6)}{5} = r \][/tex]
We can use a calculator to find r. The natural logarithm of 6 is approximately 1.79176, so:
[tex]\[ r = \frac{1.79176}{5} \\\\\[ r \approx 0.358352 \][/tex]
Now that we have the monthly growth rate r, we can use it to find the population after 12 months. Plugging r, [tex]\( P_0 \)[/tex], and t = 12 months into the exponential growth formula, we get:
[tex]\[ P(12) = 3 \times e^{0.358352 \times 12} \][/tex]
Using a calculator, we compute the value of [tex]\( e^{0.358352 \times 12} \)[/tex], which is approximately [tex]\( e^{4.300224} \)[/tex].
[tex]\[ P(12) = 3 \times e^{4.300224} \][/tex]
Using a calculator to find [tex]\( e^{4.300224} \)[/tex], we get a value of approximately 73.699.
[tex]\[ P(12) = 3 \times 73.699 \\\\\[ P(12) \approx 221.097 \][/tex]
Since we can't have a fraction of a mouse, we would round to the nearest whole number.
Thus, after 1 year, the field is expected to have approximately 221 mice.
Which of the following expressions results in 0 when evaluated at x = 4?
O A. (x - 10)(x - 4)
OB. (x + 4)(x - 10)
O C.
(x + 6)(x - 2)
OD. 4x(x-6)
Answer:
A. (x - 10)(x - 4)
Step-by-step explanation:
The product is 0 if one of the factors is 0.
(4 - 10)(4 - 4)
= (4 - 10)*0
= 0
Answer:
A. (x - 10)(x - 4)
Step-by-step explanation:
Let x=4
O A. (4 - 10)(4 - 4) = -6 * 0 = 0
OB. (4 + 4)(4 - 10) = 8* -6 = -48
O C. (4 + 6)(4 - 2) = 10 * 2 = 20
OD. 4*4(4-6)=16*-2 = -32
Using the piling method, which of the following can be constructed from polygons alone and discs alone
Check all that a
Options:
A-Cube
B-Cone (not including a vertex)
C-Pyramid(including a vertex)
D-Prism
E-Cone(including a vertex)
F-Cylinder
Answers: A: cube D: prism B: cone (not including the vertex) F : Cylinder
CORRECT ANSWER!!!!!!
Using the piling method, polygons alone can be used to construct a cube, pyramid, and prism. Discs alone can be used to construct a cylinder.
Explanation:The piling method involves stacking two-dimensional shapes to create three-dimensional solids. Using this method, the following can be constructed:
A-Cube: A cube can be constructed using polygons alone. It is made up of six equal square faces.C-Pyramid (including a vertex): A pyramid can be constructed using polygons alone. It has a polygonal base and triangular sides that converge to a common vertex.D-Prism: A prism can be constructed using polygons alone. It has two congruent polygonal bases and rectangular or parallelogram-shaped lateral faces.F-Cylinder: A cylinder can be constructed using discs alone. It has two congruent circular bases and a curved lateral surface.What is the slope of the line?
-2
-1/2
1/2
2
Answer:
[tex]\large\boxed{m=-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (2, 3) and (4, 2). Substitute:
[tex]m=\dfrac{2-3}{4-2}=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]
Other method.
Look at the picture.
[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]
[tex]\Delta y=-1\\\\\Delta x=2[/tex]
Substitute:
[tex]m=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]
What conic section is produced when both nappes of a right circular cone are
intersected by a plane that does not pass through the vertex of the cone?
A. Hyperbola
B. Parabola
C. Circle
D.Eclipse
Please help now !!!
Answer:
Option a) Hyperbola
Step-by-step explanation:
Conic sections are generated by intersection of plane with a cone.Various types of conic sections are obtained when a plane intersect with cone in different manners.Different possible conic sections are parabola, ellipse, hyperbola, circle.If a plane intersect cone in such a way that plane passes through both the nappes of the cone and does not pass through the vertex of the cone.If this plane is parallel to y-axis then, the resultant conic section is hyperbola.Thus, option a) is the correct answer.which of the following is the correct graph of the linear equation below?
y+2=1/5(x-1) giving brainlest answer
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y+2=\frac{1}{5}(x-1)[/tex]
This is the equation of the line into point slope form
The point is (1,-2) and the slope is m=1/5
we know that
To correctly identify the graph find out the x and y intercepts of the graph
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
For x=0
[tex]y+2=\frac{1}{5}(0-1)[/tex]
[tex]y=-\frac{1}{5}-2[/tex]
[tex]y=-\frac{11}{5}=-2.2[/tex]
The y-intercept is the point (0,-2.2)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0+2=\frac{1}{5}(x-1)[/tex]
[tex]10=x-1[/tex]
[tex]x=11[/tex]
The x-intercept is the point (11,0)
To graph the line plot the intercepts and join the points
see the attached figure
For his phone service, Justin pays a monthly fee of $24, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $113.28.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
M= 1488
This is how many number of minutes Justin has used his phone in a month.
I solved this by first subtracting 24 from 113.28, which is 89.28.
Next I knew multiplication would have to be involved.
I had to figure out 0.06 times what equals 89.28.
Well that would be 1488.
Please Vote my answer brainliest. thanks!
Based on the given monthly fee and per-minute charge for Justin's phone, if the minimum monthly charge is $113.28, this indicates that he has used his phone for at least 1488 minutes in that month.
Explanation:To solve this question, we can start by setting up an inequality because we want to find the possible numbers of minutes Justin can use his phone. Given that Justin pays a monthly fee of $24 and $0.06 per minute of use, the total charge (T) in a month is given by the equation:
T = 24 + 0.06m
It is stated that the least he has been charged in a month is $113.28. To find the possible number of minutes, we need to solve this inequality for m:
113.28 <= 24 + 0.06m
If we subtract $24 from each side, it becomes:
89.28 <= 0.06m
Then by dividing each side by 0.06, we get:
m >= 1488
So, Justin has used his phone for at least 1488 minutes in a month.
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what is the multiplicitive inverse of 3?
Answer:
1/3
Step-by-step explanation:
Multiplicative inverse means we want to end up with 1
3 * what = 1
Divide each side by 3
3* what /3 = 1/3
what = 1/3
The multiplicative inverse of 3 is 1/3
Answer:
1/3
Step-by-step explanation:
The mult. inverse of 3 is 1/3.
What are the solutions of 3x^2 - x+ 7 =0
[tex]3x^2 - x+ 7 =0\\\Delta=(-1)^2-4\cdot3\cdot7=1-84=-83\\x\in\emptyset[/tex]
no real solutions
What is the solution to the equation 6x + 2 = 9x - 1
Answer:
X=1
Step-by-step explanation:
1. You subtract 6x with 9x so it should equal 2=3x-1
2.You add 1 to the 2 so it should be 3=3x
3.You divide 3 on both sides so it should be 3/3=3x/3
4.After you divide you finally get the answer 1=x or x=1
6x + 2 = 9x - 1
6x - 9x = - 1 - 2
-3x = -3
x = -3/-3
x = 1
Prove:
Let x = 1
6x + 2 = 9x - 1
6(1) + 2 = 9(1) - 1
6 + 2 = 9 - 1
8 = 8
It checks to be true.
The answer is x = 1.
i dont understand this can someone please help me.
Answer:
Difference = 2.25°
Step-by-step explanation:
Here we are given that at depth the Temperature T is inversely proportional to the depth x.
[tex]T[/tex] ∝ [tex]\frac{1}{x}[/tex]
[tex]T= 4500 \times \frac{1}{x}[/tex]
Where 4500 is constant
Now we have to find the difference in the temperature at 1200 mts and 3750 mts
1. x=1200
[tex]T= 4500 \times \frac{1}{x}[/tex]
[tex]T= 4500 \times \frac{1}{1200}[/tex]
[tex]T= 3.75[/tex]
2. x=3750
[tex]T= 4500 \times \frac{1}{x}[/tex]
[tex]T= 4500 \times \frac{1}{3750}[/tex]
[tex]T=1.2[/tex]
Hence Difference is
T = 3.75 -1.20
= 2.25
Therefore The difference of the temperature at 1200 mts and 3750 mts is T=2.25°
About 50% of 5500 commuters carpool to work. Find the number of commuters who carpool
How many commuters carpool?
Answer:
2750
Step-by-step explanation:
5500 ÷ 2 (multiplying by 50% is the same as dividing by 2)= 2750
50% of 5500 commuters is calculated as 2750. Hence, 2750 commuters carpool to work.
Explanation:To find the number of commuters who carpool, we'll use a very basic principle in mathematics: percentage calculation. The problem states that 50% of the 5500 commuters carpool to work. To find the number of commuters carpooling, we multiply the total number of commuters by the percentage of those who carpool. In mathematical terms, it looks like this:(50/100) * 5500 = 2750. Therefore, 2750 commuters carpool to work.
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A square has a perimeter of 296 millimeters. What is the length of each side?
Answer:
74mm
Step-by-step explanation:
296 divided by 4 sides is 74 mm each side
What is the slope of a line that is parallel to the line whose equation is y= 4/5x−3 ?
Answer:
A line parallel to this line will have slope 4/5.
Step-by-step explanation:
2 parallel lines will have the same slope.
y = mx + c is the general form of the slope-intercept formula of a line, the slope is given by m.
y = 4/5 x - 3
-we see by comparing the 2 equations that the slope of this line (m) is 4/5.
Final answer:
The slope of a line parallel to the one given by the equation y = 4/5x - 3 is 4/5. This maintains the definition that parallel lines have identical slopes.
Explanation:
The slope of a line that is parallel to the line represented by the equation y = 4/5x - 3 is 4/5. This is because parallel lines have the same slope. In the context of algebra and straight lines, the slope of a line is a measure of its steepness, commonly identified as 'm' in the slope-intercept form y = mx + b, where 'b' is the y-intercept. Each of the provided figures and examples illustrate that the slope of a straight line remains constant regardless of other changes.
Looking specifically at the equation y = 4/5x - 3, this is in slope-intercept form where the coefficient of 'x' is the slope, which is 4/5. Therefore, any parallel line would have the same slope of 4/5.
Irunt
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each
notebook costs $3. Which of the following graphs represents the possible
combinations of pens and notebooks that she may purchase?
To find the possible combinations of pens and notebooks Amanda can purchase, we need to consider her budget and the cost of each pen and notebook. The correct graph representing these combinations is Graph B.
Explanation:To find the possible combinations of pens and notebooks that Amanda can purchase, we need to consider her budget and the cost of each pen and notebook.
Each pen costs $2 and each notebook costs $3.
Let's assume Amanda buys x number of pens and y number of notebooks.
So, the total cost of pens would be 2x and the total cost of notebooks would be 3y.
Given that Amanda has $30 to spend, we can set up the equation: 2x + 3y = 30.
To graph this equation, we can plot different points that satisfy this equation.
The graph that represents the possible combinations of pens and notebooks Amanda can purchase would be a line passing through points where the x-coordinate represents the number of pens and the y-coordinate represents the number of notebooks.
Answer: The correct graph is Graph B.
Amanda allocates $30 for pens and notebooks. Each pen costs $2, and each notebook is $3. The inequality 2P + 3N ≤ 30 is solved algebraically (P ≤ 15, N ≤ 10) and graphically, considering whole numbers for precision.
Amanda is limited to spending $30 on pens and notebooks. With each pen costing $2 and each notebook priced at $3, the total cost equation is C = 2P + 3N. The corresponding inequality is 2P + 3N ≤ 30.
Algebraically, solving for P and N involves finding values when N = 0 and when P = 0.
When N = 0:
2P ≤ 30
P ≤ 15
When P = 0:
3N ≤ 30
N ≤ 10
So, the solution is P ≤ 15 and N ≤ 10.
For a graphical representation:
Draw a coordinate plane.
Plot the points (15, 0) and (0, 10).
Shade the region below and to the left of the line formed by connecting these points.
The question probable may be:
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook costs $3. write inequality showing the relationship and solve them also solve them graphically.
If C(t) = 180 + 10t represents ISP A and C(t) =
25t represents ISP B, how long would the service
contracts need to be for the total costs to be the same?
Answer:
12
Step-by-step explanation:
You want the costs to be the same so set them equal.
180+10t=25t
Subtract 10t on both sides:
180. =15t
Divide both sides by 15:
180/15. =t
12. =t
So t=12 would give us the costs being the same.
Answer:
After 12 months, the service contracts will cost the same.Step-by-step explanation:
The given functions are
[tex]C(t)=180+10t\\C(t)=25t[/tex]
To answer the question, we just need to solve this system. We are gonna replace the second function into the first one,
[tex]C(t)=C(t)\\180+10t=25t\\15t=180\\t=\frac{180}{15}=12[/tex]
Therefore, after 12 months, the service contracts will cost the same.
Let f(x)=x^2+3 and g(x)= x+2/x . Find(fog)(2).
[tex]\bf \begin{cases} f(x)=&x^2+3\\\\ g(x)=&\cfrac{x+2}{x}\\\\ (f\circ g)(x)=&f(~~g(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(2)=\cfrac{(2)+2}{(2)}\implies g(2)=\cfrac{4}{2}\implies g(2)=\boxed{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{x=2}{f(~~g(2)~~)}=\left( \boxed{2} \right)^2+3\implies f(~~g(2)~~)=4+3\implies \stackrel{(f\circ g)(2)}{f(~~g(2)~~)}=7[/tex]
What is the solution to this equation?
X- 12 = 9
Answer:
X = 21
Step-by-step explanation:
X- 12 = 9
Add 12 to each side
X- 12+12 = 9+12
X = 21
The two sides of the triangle are 6 cm and 12 cm and the included angle is 60°. What's the measure of the third side.
A. 6.7
B. 8.5
C. 10.4
D. 12 5
Answer:
C. 10,4
Step-by-step explanation:
Using the Law of Cosines [Solving for Angle Measures → cos<A = -a² + b² + c²\2bc, cos<B = a² - b² + c²\2ac, cos<C = a² + b² - c²\2ab; Solving for Sides → a² = b² + c² - 2bc cos<A, b² = c² + a² - 2ac cos<B, c² = b² + a² - 2ab cos<C], set up your triangle with your angles and sides OPPOSITE from each other.
Suggestion: make Side b 12 and Side a 6, leaving you with Side c to find. According to the problem and how you set up your triangle, <C can be 60°. This is how you should set it up:
c² = 36 + 144 - 144 cos 60°; 108 = c²
The reason being is because 6² is 36, 12² is 144, 2ab → 2[12][6] is 144, and cos 60° is ½. Putting this altogether will give you 108 = c². Obviously, the final step is to take the square root of 108, which rounded to the nearest tenth, is 10,4.
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
**Whenever you are solving for an angle using the Law of Cosines, towards your final answer, use the cos⁻¹ function to cancel the cos to isolate your angle measure.
Final answer:
Using the law of cosines with the given sides 6 cm and 12 cm and included angle of 60 degrees, the length of the third side is approximately 10.4 cm, corresponding with answer choice C.
Explanation:
To calculate the length of the third side of a triangle when two sides and the included angle are known, we can use the law of cosines. The law of cosines states that c² = a² + b² - 2abcos(C), where a and b are the lengths of the sides, C is the included angle, and c is the length of the third side opposite to angle C.
In this question, we have been given two sides of lengths 6 cm and 12 cm with an included angle of 60 degrees. Plugging these values into the law of cosines formula, we get c² = 6² + 12² - [tex]2\(\cdot\)6\(\cdot\)12\(\cos(60^\circ)\)[/tex].
Since [tex]\(\cos(60^\circ)\)[/tex] equals 0.5, the calculation simplifies to c² = 36 + 144 - 72 = 108. Taking the square root of both sides, we find that c ≈ 10.4 cm, which aligns with answer choice C.
a cuboid with a volume of 924 cm3 has dimensions 4cm (x+1)cm and (x+11)cm. show clearly that x^2 +12x-220=0. show the equation by factorisation. State both values of x. and finally find the dimensions of the cubiod.
Answer:
4cm, 11cm, 21cm
Step-by-step explanation:
4(x + 1)(x + 11)
4(x ^ 2 + 12x + 44)
x ^ 2 + 12x + 11 = 231
x ^ 2 + 12x + 11 - 231 = 0
x ^ 2 + 12x - 220 = 0
(x - 10)(x + 22) = 0
x = 10 and x = - 22
4cm , 11cm , 21cm
Both values of x are 10 and -22
The dimension of the cuboid is 4cm by 11cm by 21cm
The formula for calculating the volume of a cuboid is expressed as:
Volume of a cuboid = Length * Width * Height
Given the following parameters
Length = 4 cm
Width = (x+1) cm
Height = (x+11) cm
Volume = 924cm³
Substitute into the formula as shown:
924 = 4(x+1)(x+11)
Factorize
924 = 4(x²+11x + x + 11)
924/4 = x²+12x+11
231 = x²+12x+11
Swap
x²+12x+11 = 231
x²+12x = 231 - 11
x²+12x = 220
x²+12x - 220 = 0 (Proved)
On factorizing
x²+12x - 220 = 0
x²+22x-10x - 220 = 0
x(x+22)-10(x+22) = 0
(x-10)(x+22) = 0
x = 10 and -22
Hence both values of x are 10 and -22
Get the dimensions
Length = 4cm
Width = x+ 1 = 10 + 1 = 11cm
Height = x+11 = 10 + 11 = 21cm
Hence the dimension of the cuboid is 4cm by 11cm by 21cm
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A club has 5 members. From these members, the position of president and Vice Presidents have to be filled. In how many different ways can these 2 positions be filled?
1,2
1,3
1,4
1,5
2,1
2,3
2,4
2,5
3,1
3,2
3,4
3,5
4,1
4,2
4,3
4,5
5,1
5,2
5,3
5,4
20 looks like the number.
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