Answer:
Step-by-step explanation: you are sped that is the answer black n
What is the slope of the line?
In the figure, if I and K are parallel lines, what is the value of x+y in degrees?
Based on the figure, if I and K are parallel lines, the value of x+y in degrees is 62°.
The correct answer choice is option A.
What is the value of x+y in degrees?From the diagram
x + 149° = 180° (Sum of angle on a straight line)
x = 180° - 149°
x = 31°
Also,
y = 31° (alternate angles are equal)
Therefore,
x + y = 31° + 31°
= 62°
Hence, the sum of angle x and angle y is 62°.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. 19.8
B. 15.9
Step-by-step explanation:
A.
To find the geometric mean between two numbers, you multiply them together and then take the square root of the product.
28 × 14 = 392
[tex]\sqrt{392}[/tex] = 19.799 ≈ 19.8
B.
7 x 36 = 252
[tex]\sqrt{252}[/tex] = 15.8745 ≈ 15.9
which of the following exponential regression equations best fits the data shown below?
The exponential regression equation that best fits the data is y = 2^x.
To determine which exponential regression equation best fits the given data points (2, 4), (3, 8), (4, 16), and (5, 32), let's analyze the options for regression equations:
Option 1: y = 2^x
Option 2: y = 3^x
Option 3: y = 4^x
Option 4: y = 5^x
To find the best fit, we need to compare the predicted y-values from each equation with the actual y-values of the given data points.
The equation that produces the least amount of error or the closest predicted y-values to the actual ones will be the best fit.
Let's calculate the predicted y-values for each option using the given x-values:
Option 1: [tex]y = 2^2, 2^3, 2^4, 2^5 = 4, 8, 16, 32[/tex]
Option 2:[tex]y = 3^2, 3^3, 3^4, 3^5 = 9, 27, 81, 243[/tex]
Option 3:[tex]y = 4^2, 4^3, 4^4, 4^5 = 16, 64, 256, 1024[/tex]
Option 4:[tex]y = 5^2, 5^3, 5^4, 5^5 = 25, 125, 625, 3125[/tex]
By comparing the predicted y-values with the actual y-values of the data points, we can determine which option provides the closest fit.
Based on the given data points, we can observe that the predicted y-values from Option [tex]1 (y = 2^x)[/tex] match the actual y-values most closely.
The predicted values for Option 1 are 4, 8, 16, and 32, which exactly match the given data points.
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The complete question may be like: Consider the following data points: (2, 4), (3, 8), (4, 16), (5, 32). We need to determine which exponential regression equation best fits this data. Please provide the options for the regression equations so that I can assist you in finding the best fit.
Naomi wants to earn an A (90%) in her math class. On her first three tests, she scored 87%, 98% and 86%. What score will she need to earn on her fourth test in order to have an average of 90%?
Answer:
Naomi will need to score at least 89% on her fourth test to have an average of 90% in her math class.
Step-by-step explanation:
To find out what score Naomi needs to earn on her fourth test in order to have an average of 90%, we can set up an equation.
Let's denote the score on the fourth test as "x". Naomi has taken three tests, and their scores are 87%, 98%, and 86%. To find the average, we sum up all the scores and divide by the number of tests:
(87 + 98 + 86 + x) / 4 = 90
Now we can solve for x:
(87 + 98 + 86 + x) = 4 * 90
271 + x = 360
x = 360 - 271
x = 89
Naomi will need to score at least 89% on her fourth test to have an average of 90% in her math class.
Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. The hotel served 540 gallons of orange juice last year. This year, the hotel served 5% less orange juice than it did the previous year. How much was served this year
The amount of juice served this year is given as follows:
513 gallons.
How to obtain the amount of juice?The amount of juice served this year is obtained applying the proportions in the context of the problem.
The amount last year was given as follows:
540 gallons.
The percentage of this year's amount relative to last year's amount is given as follows:
95%, due to the decay of 5%, 100 - 5 = 95%.
Hence the amount of juice served this year is given as follows:
0.95 x 540 = 513 gallons.
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solve x^2+1/2x+_=2+_
The complete equation is x² + 1/2x -2 = 2 + 2
The given equation can be rewritten as:
x² + (1/2)x + () = 2 + ()
Since the equation involves two missing values, let's consider them one by one.
Solve for the first missing value indicated by (_):
To find the missing value indicated by (_), we equate the quadratic equation to 2:
x² + (1/2)x + (_) = 2
Comparing this with the standard form of a quadratic equation,
ax² + bx + c = 0, we have:
a = 1, b = 1/2, c = (_ - 2)
Using the quadratic formula, x = (-b ± √(b²- 4ac)) / (2a), we can substitute the values:
x = (-(1/2) ± √((1/2)² - 4(1)(_-2))) / (2(1))
x = (-1/2 ± √(1/4 + 8(1)(_-2))) / 2
x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2
Therefore, the first missing value is represented by (_ - 2).
Solve for the second missing value indicated by (_):
To find the missing value indicated by (_), we equate the constant term to 2:
(_) = 2
This indicates that the second missing value is equal to 2.
Putting it all together, the solution to the equation x² + (1/2)x + _ = 2 + _ is:
x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2
with (_ - 2) representing the first missing value, and the second missing value is 2.
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(~Q → P) ⋀ ~P
Truth Table
| P | Q | ~Q | ~Q → P | ~P | (~Q → P) ⋀ ~P |
|---|---|----|--------|----|----------------|
| T | T | F | T | F | F |
| T | F | T | T | F | F |
| F | T | F | T | T | T |
| F | F | T | F | T | F |
To construct a truth table for the logical statement (~Q → P) ⋀ ~P, we need to consider all possible truth values for the variables Q and P. The symbol "~" represents negation or "not" in logic, so ~Q denotes "not Q" and ~P denotes "not P".
In the above table, we first list all possible truth values for P and Q and then determine the truth values for ~Q, ~Q → P, and ~P based on these values. Finally, we evaluate the logical statement (~Q → P) ⋀ ~P based on the truth values for (~Q → P) and ~P to determine the overall truth value of the statement for each combination of P and Q.
The output of the above truth table shows that the statement (~Q → P) ⋀ ~P is true only in one case when P is false and Q is true. In all other cases, the statement is false. Therefore, we can infer that the statement is not always true and hence it is not a tautology. The statement is only true in one specific case where P is false and Q is true.
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I need some help with this
O is the center of the regular octagon below. Find its perimeter. Round to the nearest tenth if necessary.
The correct answer is 86.08, as the octagon is given and the apothem given here is 13 units. The calculation after putting the value in formula is 86.08.
An octagon is a polygon with eight sides and eight angles. It is a two-dimensional geometric shape. Each angle in a regular octagon measures 135 degrees, and all sides of a regular octagon are of equal length.
The formula is given below,
P= side length ×n
Apothem of octagon =13 units,
side length is = tan (360° / (2 × 8)) = (n/2) ÷ 13
= tan (360° / (2 × 8)) = n/26
tan 22.5°= n/26
n/26 = 0.4142
n = 10.76
perimeter of octagon = 8 × 10.76 = 86.08
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Solve for z. z² = 36 Enter your answer in the box. z =
Answer:
Step-by-step explanation:
z=6
Using synthetic division, what is the quotient of this expression?
When dividing the polynomial[tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2), the quotient is [tex]5x^2 + 10x + 20.[/tex]
To find the quotient when dividing the polynomial [tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2), we can use synthetic division. Synthetic division is a method used to divide polynomials quickly and efficiently.
First, we set up the synthetic division table by writing the coefficients of the polynomial in descending order:
2 | 5 -3 4
|___________
Next, we bring down the first coefficient, which is 5:
2 | 5 -3 4
|___________
| 5
To calculate the next row, we multiply the divisor (2) by the value in the previous row (5) and write the result below the next coefficient:
2 | 5 -3 4
|___________
| 5
|___________
10
We add the values in the second and third rows:
2 | 5 -3 4
|___________
| 5
|___________
10 7
We repeat this process until we reach the last coefficient:
2 | 5 -3 4
|___________
| 5
|___________
10 7
20 34
The quotient is given by the numbers in the bottom row: [tex]5x^2 + 10x + 20.[/tex]
Therefore, when dividing the polynomial[tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2), the quotient is [tex]5x^2 + 10x + 20.[/tex]
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The complete question may be like:
Using synthetic division, what is the quotient when dividing the polynomial [tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2)? human generated answer without plagiarism. 200 words.
Select the three inequalities that include 3 in the solution set.
x > 1.4
x < 2.6
x > 4.2
x < 5.1
x < 8.2
The solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.
Given the inequalities that include 3 in the following inequalities
x > 1.4, x < 2.6, x > 4.2, x < 5.1 and x < 8.2.
To find the solution set which include 3, write the solution set which consists of integer.
The solution set of x > 1.4 is { 2, 3, 4, 5, 6, ........}
The solution set of x < 2.4 is { 2, 1. 0, -1, ...............}
The solution set of x > 4.2 is { 5, 6. 7, 8, ...............}
The solution set of x < 5.1 is { 5, 4, 3, 2, 1, ...............}
The solution set of x < 8.2 is { 8, 7, 6, 5, 4, 3, ...............}
Hence, the solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.
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100 Points! Geometry question. Photo attached. Determine whether each pair or figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning. Please show as much work as possible. Thank you!
The figures are similar because the ratio of segment BC to segment EF is equal to the of segment AB to segment DE.
The scale factor is equal to 3/2.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following:
Scale factor = BC/EF = AB/DE
Scale factor = 9/6 = 6/4
Scale factor = 3/2 = 3/2 (similar)
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A recipe calls for 3.5 cups of rice. If a cup of rice weighs 158 grams, and a bag of rice weighs 2 pounds, how many bags would be needed to make 80 recipes? (2.2 lbs. = 1 kg, 1kg = 1000 g) (Convert 80 recipes to bags)
The number of bags of rice that would be needed to make 80 recipes is 48.664 bags.
How many bags would be needed to make 80 recipes?1 recipe = 3.5 Cups of rice
If
1 cup of rice = 158 grams
1 bag of rice = 2 pounds
2.2 lbs. = 1 kg,
1kg = 1000 g
80 recipes = 3.5 cups 80
= 280 cups
1 cup of rice = 158 grams
280 cups = 158 × 280
= 44,240 grams
1kg = 1000 g
44,240 grams = 44.24 kg
2.2 lbs. = 1 kg; x lbs = 44.24
2.2/1 = x/44.24
x = 2.2 × 44.24
x = 97.328 pounds
1 bag of rice = 2 pounds ; x bags = 97.328 pounds
1/2 = x/97.328
97.328 = 2x
x = 48.664 bags
Hence, 48.664 bags of rice is needed for 80 recipes.
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How many degrees must Figure A be rotated counterclockwise around the origin in order to line up with Figure B?
A. 90
B. 180
C. 270
D. 360
The number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B is = 270°
Given data ,
Let the number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B be represented as A
Now , the triangle is represented by the figure A with coordinates as
A ( -2 , 3 )
And , the coordinates of the rotated triangle is A' ( 3 , 2 )
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
So , the triangle is rotated 270° counterclockwise rotation
Hence , the rotation is 270° counterclockwise
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Find the missing side length.
1) 10 / ?
2) 24 / 15
( look at photo )
What is the distance between $500 and $-61.63
Answer: $561.63
Step-by-step explanation: To find the distance you subtract 500 by -61.63
You get the equation 500--61.63
The two negative signs cancel out to become a positive sign
So the new equation is 500+61.63
So the distance is $561.63
Answer:
$561.63
Step-by-step explanation:
To find out the distance between 500 and -61.63 it will be $500-$-61.63. So 500 - (-61.63) becomes 500 + 61.63 because 2 negatives in a row make a positive. So when you do 500+61.63, you'll get 561.63.
Use the formula ω = (θ/t) to find the value of the missing variable. Give an exact answer unless otherwise indicated. ω = (π/8) radian per min, t = 11 min
Answer:
The missing variable θ is equal to (11π)/8.
Step-by-step explanation:
Given:
ω = π/8 radian per min
t = 11 min
Step 1: Identify the formula and the missing variable.
The formula is ω = (θ/t), and we are trying to find the value of θ.
Step 2: Rearrange the formula to solve for the missing variable.
To isolate θ, we can multiply both sides of the equation by t:
ω * t = θ
Step 3: Substitute the given values.
Substituting the given values into the rearranged formula, we have:
θ = (π/8) * 11
Step 4: Simplify the expression.
To multiply fractions, we multiply the numerators and multiply the denominators:
θ = (π * 11) / (8 * 1)
θ = (11π) / 8
Step 5: Finalize the answer.
The value of the missing variable θ is (11π)/8. This is the exact answer unless otherwise indicated.
Therefore, the step-by-step process shows that the missing variable θ is equal to (11π)/8.
carlos tiene 18 años y juan 42en cuantos años la edad de juan sera el doble de la de carlos es ese entonces
In 6 years Juan will have the double of Carlos age.
When Juan will have double of Carlos's age?The ages of each one are:
Carlos = 18 years old.
Juan = 42 years old.
In x years, they will have:
C = 18 + x
J = 42 + x
Carlos will have the double of Juan's age when:
J = 2*C
Replacing the equations we will get the linear equation:
42 + x = 2*(18 + x)
Solving for x we will get:
42 +x = 36 + 2x
Solving for x:
42 - 36 = 2x - x
6 = x
So Juan will have the double of Carlos age in 6 years.
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Pleaseseee help
Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Remember that each equation must include at least one variable
please help
The road trip will take approximately 5 hours.
Two one-step equations:
a) 2x + 5 = 13
In this equation, the variable 'x' represents an unknown number. By performing one step of subtraction, we can find the value of 'x' that makes the equation true.
The solution is x = 4.
b) 3y - 7 = 16
Similar to the first equation, 'y' represents an unknown number.
By adding 7 to both sides of the equation, we can isolate the variable and solve for 'y.'
The solution is y = 7.
Two equations with fractions:
a) (1/3)x + 2 = 5
Here, the variable 'x' is multiplied by a fraction.
To isolate 'x,' we can subtract 2 from both sides and then multiply both sides by the reciprocal of 1/3, which is 3/1.
The solution is x = 9.
b) (2/5)y - 3 = 1
In this equation, 'y' is multiplied by a fraction.
We can isolate 'y' by adding 3 to both sides and then multiplying both sides by the reciprocal of 2/5, which is 5/2.
The solution is y = 4.
One equation with the distributive property:
a) 2(x + 3) = 10
This equation demonstrates the distributive property.
By applying it, we multiply 2 by both x and 3, resulting in 2x + 6 = 10.
We can then solve for 'x' by subtracting 6 from both sides.
The solution is x = 2.
One equation with decimals:
a) 0.4x + 0.8 = 1.6
In this equation, 'x' is multiplied by a decimal.
To isolate 'x,' we subtract 0.8 from both sides and then divide both sides by 0.4.
The solution is x = 2.
Real-world problem:
Imagine you're planning a road trip.
The distance you'll be traveling is 250 miles, and your car's average speed is 50 miles per hour.
You want to determine how long the trip will take.
Let 't' represent the time in hours it will take to complete the trip.
The equation that represents this situation is:
50t = 250
By dividing both sides of the equation by 50, we find that t = 5.
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A custom cake baker charges a flat fee for each job, plus an hourly rate for the
number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h
where h is the hours it takes for the job.what does the coefficient of h, in the expression represent
The coefficient h in the expression means the time taken for the job to be completed in hours.
How to find the value of the coefficient in the expression?The custom cake baker charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h where h is the hours it takes for the job.
Therefore, the coefficient h in the expression can be interpreted as follows:
total amount of bills = 40 + 25h
where
40 dollars is the flat fee for each job
Then the coefficient h means the hourly rate for the time taken for the job to be completed.
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10. Given m AC = 85%,
find m
AEC
AEC =
and m2ABC = E
A
B
The measure of angle AEC is 225 degree.
Given ABCD square then all sides are equal and all angles are of 90°
AB=BC=CD=DA
and also CDE is an equilateral triangle
CD=DE=EC and all angles are of 60°
Now, In ΔADE, ∵AD=AE ⇒ ∠DAE=∠AED
∠ADE=∠ADC-∠EDC=90°-60°=30°
By angle sum property of triangle
∠ADE+∠DAE+∠AED=180°
30°+2∠AED=180°
2∠AED=150°
∠AED=75°
and, ∠EAB = ∠DAB-∠DAE = 90°-75° = 15°
Reflex angle ∠AEC= 360°-∠AED-∠DEC
=360° - 75° -60°
=225°
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The complete and correct question is attached below:
30 points !! :) Thank you in advance
The solutions of the quadratic equation are: x = 1
The x-intercept is x = 1
What is the Solution to the quadratic equations?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The y-intercept is the point at which the graph crosses the y-axis and in this case it is: y = 1
The x-intercepts are where the graph touches the x-axis and in this case, it is x = 1
The zeros of the quadratic equation are the x-intercepts and since the curve does not cross, then we can say that the zeros are x = 1 and x = 1 which signifies double root and as such the solution is x = 1
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Please help me with the 2 math questions and please include an explanation as well. Thank you!
I will delete answers that incomplete or has no explanation.
Answer:
13) 4.9 m
14) 0.9 m
Step-by-step explanation:
Question 13The given diagram shows the height of the same cactus plant a year apart:
Year 1 height = 1.6 mYear 2 height = 2 mWe are told that the cactus continues to grow at the same percentage rate. To calculate the growth rate per year (percentage increase), use the percentage increase formula:
[tex]\begin{aligned}\sf Percentage \; increase &= \dfrac{\sf Final\; value - Initial \;value}{\sf Initial \;value}\\\\&=\dfrac{ 2-1.6}{1.6}\\\\&=\dfrac{0.4}{1.6}\\\\&=0.25\end{aligned}[/tex]
Therefore, the growth rate of the height of the cactus is 25% per year.
As the cactus grows at a constant rate, we can use the exponential growth formula to calculate its height in Year 6.
[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Exponential Growth Formula}\\\\$y=a(1+r)^t$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value. \\ \phantom{ww}$\bullet$ $r$ is the growth factor (in decimal form).\\ \phantom{ww}$\bullet$ $t$ is the number of time periods.\\\end{minipage}}[/tex]
The initial value is the height in Year 1, so a = 1.6.
The growth factor is 25%, so r = 0.25.
As we wish to calculate its height in Year 6, the value of t is t = 5 (since there are 5 years between year 1 and year 6).
Substitute these values into the formula and solve for y (the height of the cactus):
[tex]\begin{aligned}y&=a(1+r)^t\\&=1.6(1+0.25)^5\\&=1.6(1.25)^5\\&=1.6(3.0517578125)\\&=4.8828125\\&=4.9\; \sf m\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, if the cactus continues to grow at the same rate, its height in Year 6 will be 4.9 meters (to the nearest tenth).
Check by multiplying the height each year by 1.25:
Year 1 = 1.6 mYear 2 = 1.6 × 1.25 = 2 mYear 3 = 2 × 1.25 = 2.5 mYear 4 = 2.5 × 1.25 = 3.125 mYear 5 = 3.125 × 1.25 = 3.09625 mYear 6 = 3.09625 × 1.25 = 4.8828125 m[tex]\hrulefill[/tex]
Question 14The given diagram shows the height of the same snowman an hour apart:
Initial height = 1.8 mHeight after an hour = 1.53 mWe are told that the snowman continues to melt at the same percentage rate. To calculate the decay rate per hour (percentage decrease), use the percentage decrease formula:
[tex]\begin{aligned}\sf Percentage \; decrease&= \dfrac{\sf Initial\; value - Final\;value}{\sf Initial \;value}\\\\&=\dfrac{1.8-1.53}{1.8}\\\\&=\dfrac{0.27}{1.8}\\\\&=0.15\end{aligned}[/tex]
Therefore, the decay rate of the snowman's height is 15% per hour.
As the snowman melts at a constant rate, we can use the exponential decay formula to calculate its height after another 3 hours.
[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Exponential Decay Formula}\\\\$y=a(1-r)^t$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value. \\ \phantom{ww}$\bullet$ $r$ is the decay factor (in decimal form).\\ \phantom{ww}$\bullet$ $t$ is the number of time periods.\\\end{minipage}}[/tex]
The initial value is the snowman's initial height, so a = 1.8.
The decay factor is 15%, so r = 0.15.
As we wish to calculate the snowman's height after another 3 hours, the value of t is t = 4 (i.e. the first hour plus a further 3 hours).
Substitute these values into the formula and solve for y (the height of the snowman):
[tex]\begin{aligned}y&=a(1-r)^t\\&=1.8(1-0.15)^4\\&=1.8(0.85)^4\\&=1.8(0.5220065)\\&=0.93961125\\&=0.9\; \sf m\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, if the snowman continues to melt at the same rate, its height after another 3 hours will be 0.9 meters (to the nearest tenth).
Check by multiplying the height each hour by 0.85:
Initial height = 1.8 mHeight after 1 hour = 1.8 × 0.85 = 1.53Height after 2 hours = 1.53 × 0.85 = 1.3005Height after 3 hours = 1.3005 × 0.85 = 1.105425Height after 4 hours = 1.105425 × 0.85 = 0.93961125Create TWO equivalent expressions for the following.
14(8−16x)+3x
Two equivalent expressions for the given expression 14(8 - 16x) + 3x are 112 - 221x and 112 - 221x.
Equivalent expression 1:
Expanding the expression 14(8 - 16x) and combining like terms, we get:
112 - 224x + 3x
Simplifying further, we have:
112 - 221x
Equivalent expression 2:
Distributing the coefficient 14 to both terms inside the parentheses, we have:
112 - 224x + 3x
Combining the terms with the same variable, we get:
112 - 221x
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The meaure of m∠KJL in the circle is:
m∠KJL = 25°
How to find the angle m∠KJL in the circle?Since ΔJKL is inscribed in circle P with diameter JK and mJL = 130°. Thus, m∠JLK is an inscribed angle.
Since an angle inscribed in a semicircle is a right angle.
Thus, m∠DFE = 90°
Since the measure of inscribed angle is half the measure of its intercepted arc. Thus:
m∠JKL = 1/2 * mJL
m∠JKL = 1/2 * 130
m∠JKL = 65°
Therefore:
m∠KJL = 180 - 90 - 65 = 25° (sum of angles in a triangle)
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Calculate the area of the composite figure
1. The area of composed figure is 52.26 cm².
2. The area of composed figure is 74 ft².
1. Area if Triangle
= 1/2 x b x h
= 1/2 x 6 x 8
= 24 cm²
Area of semicircle
= πr²/2
= 3.14 x 3 x 3
= 28.26 cm²
So, area of composed figure
= 28.26 + 24
= 52.26 cm²
2. Area of Trapezium
= 1/2 (7 + 13) x 5
= 1/2 x 20 x 5
= 50 ft²
Area of Triangle
= 1/2 x b x h
= 1/2 x 8 x 6
= 24 ft²
So, area of composed figure
= 24 + 50
= 74 ft²
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Lee and Olivia share some money. Lee has 7/11 of the money. If Lee gives Olivia £18 then they have the same amount of money How much money did they share? Lee Olivia
The total amount of money shared by Lee and Olivia is £132 and Lee and Olivia shared £84 and £48, respectively.
Lee has 7/11 of the total money, which means Lee has (7/11) × x amount of money.
When Lee gives Olivia £18, they have the same amount of money.
So Olivia's share becomes equal to Lee's share.
Therefore, we can set up the following equation:
(7/11) × x - £18 = (1/2)×x
To solve this equation, we can simplify it:
7x/11 - £18 = x/2
Multiplying both sides of the equation by 22 (the least common multiple of 11 and 2) to eliminate the denominators:
14x - 22 × £18 = 11x
14x - 396 = 11x
Subtracting 11x from both sides:
14x - 11x - 396 = 0
3x - 396 = 0
Adding 396 to both sides:
3x = 396
Dividing both sides by 3:
x = 396/3
x = 132
To find Lee and Olivia's individual shares, we can substitute this value back into the initial conditions:
Lee's share = (7/11)× £132 = £84
Olivia's share = £132 - £84 = £48
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Which of the following correctly order from least to greast 0.75,3/5,70%