Answers
The measure of the numbered angles of the quadrilaterals in the question are presented as follows;
14. m∠1 = 54°, m∠2 = 36°, m∠3 = 54° m∠4 = 108°, m∠5 = 72°
15. m∠1 = 90°, m∠2 = 45°, m∠3 = 45°, m∠4 = 45°, m∠5 = 45°
16. m∠1 = 64°, m∠2 = 64°, m∠3 = 26°, m∠4 = 90°, m∠5 = 64°
What is a quadrilateral?A quadrilateral is a four sided polygon.
14. The figure is a rectangle
The two diagonals of a rectangle are the same length and the diagonals of a rectangle bisect each other, therefore;
The triangles formed by the diagonals of the rectangle are isosceles triangles.
The angle at the vertex of the isosceles triangle that has 36° as the base angle of the triangle is therefore; (180° - 2 × 36°) = 108°
The angle ∠4, is a vertical angle to the angle calculated above, therefore;
m∠4 = 108°
m∠5 = (360° - 2 × 108°) = 72°
m∠5 = 72°
The similar triangles formed by the diagonals indicates that we get;
m∠2 = 36°
m∠1 = (180° - m∠5)/2
Therefore; m∠1 = (180° - 72°)/2 = 54°
m∠1 = 54°
∠1 ≅ ∠3
Therefore; m∠3 = m∠1 = 54°
m∠3 = 54°
15. The quadrilateral is a square, therefore;
The diagonals bisect each other and are perpendicular.
m∠1 = 90° (Definition of perpendicular angles)
m∠5 = (180° - 90°)/2 = 45°
m∠5 = 45°
∠3 ≅ ∠5, therefore;
m∠3 = m∠5 = 45°
m∠3 = 45°
m∠3 + m∠2 = 90° (The vertex angles of a square are 90°)
m∠2 = 90° - m∠3
m∠2 = 90° - 45° = 45° (Substitution property)
m∠2 = 45°
16. The quadrilateral is a rhombus, therefore;
The diagonals of a rhombus perpendicular
Adjacent angles are supplementary
The opposite angles of a rhombus are congruent
The opposite sides of a rhombus are parallel
Diagonals of a rhombus bisect the interior angles
The above properties indicates that we get;
90° + m∠1 + 26° = 180°
m∠1 = 180° - 26° - 90° = 64°
m∠1 = 64°
m∠4 = 90°
The angle ∠3 and the 26° angle are alternate interior angles. Alternate interior angles between parallel lines are congruent, therefore;
m∠3 = 26°
m∠1 = m∠2 (definition of bisected angle), therefore;
m∠2 = m∠1 = 64°
m∠2 = 64°
∠2 and ∠5 are alternate interior angles, therefore;
∠2 ≅ ∠5
m∠5 = m∠2 = 64°
m∠5 = 64°
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Related Questions
A bag of m & m is dumped on the table and you count 82 blue pieces.approximately how many m&ms do you expect to be in the entire bag based on the entire class. Round to the nearest whole m&m
Answers
Answer: Based on the information provided, we can use the proportion of blue m&ms found in the sample (82 out of some larger total number of m&ms) to estimate the total number of m&ms in the entire bag.
If we let x be the total number of m&ms in the bag, we can set up the proportion:
82/x = blue m&ms / total m&ms
To solve for x, we can cross-multiply and divide by 82:
x = 82 * total m&ms / blue m&ms
x = 82 * 1
x ≈ 82
Therefore, based on the sample, we expect there to be approximately 82 m&ms in the entire bag, rounded to the nearest whole m&m.
It's worth noting that this is an estimation, and the actual number of m&ms in the bag may be different.
Step-by-step explanation:
One side of triangle is 6 more than 2 times the shortest side. The third side is 8 feet more than the shortest side. The perimeter is 54 . Find all three sides.
Answers
Answer:
Shortest = 10ft
Middle = 18 ft
Longest = 26ft
Step-by-step explanation:
(btw u can make a diagram to make it easier to visualise)
Let shortest side of triangle be x
So:
1st side = 2x+6
2nd side = x
3rd side = x+8
These sides all equal to 54 ft (perimeter)
2x+6 + x + x+8 = 54
4x + 14 = 54
4x = 40
x = 10
Now that we know the shortest side just sub it back into the equations!
TUESDAY 1. Allison had one string that was 10 meters long. She used 5.834 meters for her project. What is the length of the string in meters Allison had left?
Answers
Each cut piece measures 6.25 meters in length.
What is dividing?One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.
One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.
Given
The thread was divided into 4 equal pieces after being cut at 25 meters.
= 25/4 \s = 6.25.
The thread was divided into 4 equal pieces after being cut at 25 meters.
= 25/4 \s = 6.25.
Each cut piece measures 6.25 meters in length.
The complete question is,
A 25 meter distance. Cindy cut the string into four equal pieces. each component's quality.
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Write the following set as an interval using interval notation.
{x|−7
Answers
Answer: The set {x|−7 < x} can be written in interval notation as (-infinity, -7) < x.
This set represents all real numbers greater than -7. The interval notation uses the less-than symbol (<) to represent that all values of x greater than -7 are included in the set. The interval notation uses the infinity symbol to represent the fact that there are no limits on the lower end of the interval.
It's important to note that the interval notation includes the endpoint values when it is in the form of (a,b) or [a,b) but it does not include endpoint values when it is in the form of (a,b] or [a,b].
Step-by-step explanation:
Assume that K and M are two unlinked genes that affect hearing. The dominant K allele is necessary for hearing, and the dominant M allele causes deafness regardless of the other genes present. What fraction of the offspring of parents with the genotypes KkMm and Kkmm will most likely be deaf?
**Please draw the punnet sqaure and explain the answer in detail.
a) 1/4
b) 3/8
c) 1/2
d) 5/8
Answers
The dominant K allele is necessary for hearing, and the dominant M allele causes deafness regardless of the other genes present. What fraction of the offspring of parents with the genotypes KkMm and Kkmm will most likely be deafi is 1/2 so c option is correct
The percentage that the offspring will be deaf is 75%. Two punnet squares are needed each for km and Kkmm individuals. In punnet square 1, half of the genotypes are Km and km while half are Mm and kk in punnet square 2. The two punnet squares are then combined to form a final one where a quarter of the offspring is deaf.
What does genotype mean?
In a wide sense, the word"genotype" refers to the genetic makeup of an organism; it defines an organism's complete set of genes. In a more thin sense, the term can be used to guide the alleles, or variant forms of a gene, that are carried by an organism.
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Which is a better deal 5 tickets for $12.50 or 8 tickets for $20.60
Answers
Answer:
5 tickets for $12.50
Step-by-step explanation:
because in that deal the ticket only costs $2.05
and in the second deal which is 8 tickets for $20.60 the ticket costs 2.57
Translate these statements into English, where the domain for each variable consists of all real numbers.
a) ∀x∃y(x < y)
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))
c) ∀x∀y∃z(xy = z)
Answers
a) ∀x∃y(x < y): For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0)) : For any numbers x and y if x is greater tha or equal to 0 and y is greater than or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z) : For any numbers x and y there exist number z such that the product of x and y is equal to z.
We know that a mathematical statement is nothing but a sentence which is either true or false.
We need to translate these statements into English.
The meaning of some mathematical symbols:
∀ : for all
∃ : there exists exactly one
∧ : and
Here, x, y, z are real numbers.
Consider given mathematical statements.
a) ∀x∃y(x < y)
For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))
For any numbers x and y if x is greater tha or equal to 0 and y is greater tha or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z)
For any numbers x and y there exist number z such that the product of x and y is equal to z.
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umb
1 MP Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 1/8 pounds of soil
and a box with 1 3/4pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
Answers
No, she does not have enough soil as she needs 4 pounds of soil.
What is meant by soil?
A mixture of organic material, minerals, gases, liquids, and living things make up soil, often known as earth or dirt, and they work together to support life. Certain scientific definitions separate dirt from soil by limiting the former term to just displaced soil.The field of edaphology investigates how soils affect living beings.The study of how soils are formed, described (morphology), and categorized in their natural environments is known as pedology.In engineering, the term "soil" is used to refer to loose material that is present on the Moon and other celestial bodies, as well as other loose material that is found above the bedrock.she as = 2 1/8 + 1 3/4
= 17/8 + 7/4
= 17+ 7 × 2 / 8
= 17 + 14 / 8
= 31/8
= 3 7/8 pounds
≤ 4 pounds.
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Can you please explain step by step more brought and clearly that how 2x^3-x^2-2x+1 becomes (x-1)(2x^2+x-1)
i am not able to understand please answer Asap
I will make you Brainiest
Answers
Answer:
Step-by-step explanation:
it is simply factorized.
as we have 2x³-x²-2x+1
we will take common number and variable from it
So as we can see that in this polynomial we can take x-1 common
we will take x-1 common and write the rest polynomial
As we will multiply x-1 with 2x²+x-1
it will give the previous answer or nmber
lucy is five years older than linus. four years ago, eight times linus' age equaled three times lucy's age.
Answers
Answer: 3
Step-by-step explanation:
2/3 4/6
Express the answers to the following operations with the
proper number of significant figures.
(a) (1.600 × 10-¹)(2.1 × 10³)
(b) (1.33)³
(c) 1.93.x 2.651
(d) 4.4/2.200
I don’t understand what it is asking for, help please!
Answers
Expressed the answers to the given operations with the proper number of significant figures:
(a) (1.600 × 10-¹)(2.1 × 10³) = 336
(b) (1.33)³ = 2.352637
(c) 1.93.x 2.651 = 5.11643
(d) 4.4/2.200 = 2
What's meant by integers?In calculation, single integers called integers are used to represent values. To represent all fine values, the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in colorful combinations and reiterations.
A number is a symbol that can be used to represent any of the ten integers ranging from 0 to 9. an illustration of a two- number.
When a number has two integers, it's called a 2- number . 2- number figures have two integers and range from 10 to 99.
They're unfit to begin with zero since it'll also be regarded as a single- number .
Any number between 1 and 9 can be used as the number in the knockouts place. For case, the figures 45, 78, and 12 have two integers.
a) (1.600 × 10-¹)(2.1 × 10³)
= 1.6 × 2.1 × 10⁻¹⁺³
= 3.36 × 10²
= 336
b) (1.33)³
= 2.352637
c) 1.93 × 2.651
= 5.11643
d) 4.4/2.200
= 2.0
= 2
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The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
Group of answer choices
68
33
47
40
Answers
Number of shingles in the 6th row is 110.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given;
Each row has 7 fewer shingles than the row below it
First row has 75 shingles
Now,
a=75
D=7
n=6
a_{n}=a_{1}+(n-1)d
a6=75+(6-1)7
a6=75+35
a6=110
Therefore, the answer of arithmetic sequence will be 110.
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Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. (75 -7) On the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33
in a flight simulation test, a particular pilot among a group of pilots receives a very low score. however, when he takes the test after six months, he performs considerably better and his scores are closer to the average of the group. which of the following is most likely to account for the higher scores?
Answers
Regression toward the mean is most likely to account for the higher scores. So the option 2 is correct.
The answer to this query is based on a long-term investigation. An observational study that tracks the same people across time, sometimes from birth to death, is called a longitudinal study.
The right response is regression to the mean. When a sample point for a random variable is extreme, regression toward the mean is the phenomena that results, with subsequent measurements, in a point that is closer to the mean or average.
This is your response with justification. You can find me in the comments section if you have any questions or doubts about the question or the answer, though.
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The complete question is:
In a flight simulation test, a particular pilot among a group of pilots receives a very low score. However, when he takes the test after six months, he performs considerably better and his scores are closer to the average of the group. Which of the following is most likely to account for the higher scores?
1. instrument decay
2. regression toward the mean
3. carryover effects
4. fatigue effects
Abby was cycling to her school from home .on her way she meets her friend Betty who says that the roads were blocked and the shool was closed.Abby goes back home .
Abby"S distance from home is given with the function : s= 100t 2 +400 t
t is time in minutes .Find after how many minutes , after leaving from home , did Abby meet Betty ?
Answers
After 2 minutes of leaving home, Abby meet Betty.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Abby's distance from home is given with the function :
S{t} = 100t² + 400t, where {t} is time in minutes.
The given function is -
S{t} = 100t² + 400t
dS{t}/dt = 0
200t = 400
t = 2
Therefore, after 2 minutes of leaving home, Abby meet Betty.
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Please solve ASAP.
Will give brainliest!!
Thank you!
Answers
Answer:
Step-by-step explanation:
5
Which inequality is graphed below?
-6
-5
Ox≤-2
Ο x > - 2
Stry
x < -2
Ox>-2
Answers
The inequality that is graphed on the number line is:
x > -2
Which inequality is graphed below?Here we can see the graph of an inequality on a number line, on it, we can see a blue line that starts with a open circle (which means that we need to use the symbols < or >) at x = -2
Then the line extends to the right of that number, so the allowed values of x are larger than -2, then the inequality graphed is:
x > -2
Thus the correct option is the fourt one.
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help me slove this math please
Answers
By Linear Function f(x) = -4 + 2 and g(x) = x - 3 this we get the Value -2.
How to Find a Linear Function?The slope-intercept form or the point-slope form are used to find a linear function.
With the aid of an example, the procedure for determining a linear function is the same as determining a line's equation.
When "m" and "b" are real numbers, then a function has the form f(x) = mx + b.
Examples :
f(x) = -4 + 2,g(x) = x - 3: -2
Steps
Find f ° g given f(x) = -4 + 2, g(x) = x - 3
f ° g = f(g (x))
Constant function results in a constant
f (x ) = -4 + 2
-4 + 2 = -2
Answer = -2.
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4/7 x 3/8 then simplify
Answers
Answer:
0.2142857143
Step-by-step explanation:
4/7 × 3/8
=12/56
=0.2142857143.
F(x)=4x^3+7x^2+8x and g(x)=7x^2-7x, find (f-g)(x) and (f-g)(0)
Answers
Answer:
(f-g)x is the same as f(x)-g(x)
(f-g)x= 4x^3+7x^2+8x-(7x^2-7x)
= 4x^3+7x^2-7x^2+8x+7x
=4x^3+0+15
=4x^3+15
(f-g)0= 4(0)^3+15
=0+15
=15
Select <,>, or = from the drop-down box to compare the two fractions 4/5 and 2/6
Answers
Answer:
4/5 < 2/6
Step-by-step explanation:
Hope it helps! =D
3xcube+x-200 divide by x-4
Answers
When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.
What is division?Division is the process of splitting a number or an amount into equal parts.
Given is an expression, 3x³+x-200 which is divided by x-4,
Therefore,
(3x³+x-200) / (x-4)
Step 1)Divide the leading term of the dividend by the leading term of the divisor:
3x³/x = 3x²
Multiply it by the divisor: 3x²(x−4)=3x³−12x²
Subtract the dividend from the obtained result:
(3x³+x−200)−(3x³−12x2) = 12x²+x−200
Step 2)Divide the leading term of the obtained remainder by the leading term of the divisor: 12x²/x = 12x
Multiply it by the divisor: 12x(x−4) = 12x²−48x
Subtract the remainder from the obtained result:
(12x²+x−200)−(12x²−48x) = 49x−200
Step 3)Divide the leading term of the obtained remainder by the leading term of the divisor: 49x / x = 49
Multiply it by the divisor: 49(x−4) = 49x−196
Subtract the remainder from the obtained result:
(49x−200)−(49x−196) = −4
Hence, When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.
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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = 5 3√x , y = 0, x = 1
Answers
The volume of the cylinder is
V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
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The volume of the cylinder is V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
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Ivan's company makes solid spherical balls out of scrap metal for various industrial uses. A large order just came in to make lead balls with a radius of 3in. If Ivan uses, on average, 28,260in3 of lead each day making these balls, how many balls does he make, on average, each day?
If necessary, refer to the list of geometry formulas.
For your calculations, do not round any intermediate steps, and use the π button on the ALEKS calculator. Round your answer to the nearest hundredth.
balls
Answers
Answer: To find the number of balls Ivan makes each day, we need to divide the total volume of lead used each day by the volume of one ball.
The formula for the volume of a sphere is:
V = (4/3) * π * r^3
Where V is the volume, π is pi and r is the radius of the sphere.
We know the radius of the sphere is 3 inches so we can use this information to find the volume of one ball.
V = (4/3) * π * 3^3
V = (4/3) * π * 27
V = 36 * π
Now we know the volume of one ball is 36π cubic inches, we can divide the total volume of lead used per day by the volume of one ball to find the number of balls made per day.
28,260 in^3 / 36π in^3/ball = 785.833 balls/day
Rounding to the nearest hundredth, Ivan on average makes 785.83 balls/day.
Step-by-step explanation:
Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and the length of E D is x + 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent.
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
D
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
Answers
Applying the Midsegment Theorem, the length of BC is: 10.
What is the Midsegment Theorem?The Triangle Midsegment Theorem states that in a triangle, a line segment connecting the midpoints of two sides is parallel to the third side and is half as long.
From the information given we know that:
E is the midpoint of BC and D is the midpoint of AC.
Thus, applying the Midsegment Theorem, we have:
ED = 1/2(BA)
Substituting the values not expressive, we would get:
x + 2 = 1/2(4x - 6)
2(x + 2) = 4x - 6
2x + 4 = 4x - 6
2x - 4x = -4 - 6
-2x = -10
x = 5
BE = x = 5
Therefore, BC = 2(5) = 10.
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In the figure below, suppose that m∠PSQ=(5x−12)∘ and m∠QSR=(10x−3)∘. What is the value of x?
Please and thank you!!!
Answers
Considering the figure, the value of x is calculated using adjacent angles concept and it is solved to be
7How to solve for xThe angle at PSR is 90 degrees
Also, angle PSQ and angle QSR are adjacent angles hence
angle PSQ + angle QSR = angle PSR = 90
90 = (5x − 12)∘ + (10x − 3)
opening the parenthesis
90 = 5x − 12 + 10x − 3
collecting like terms
90 + 12 + 3 = 5x + 10x
105 = 15x
isolating x by dividing through by 15
15x / 15 = 105 / 15
x = 7
hence the value of x is 7
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Plot the image of point QQQ under the translation (x,y)\to(x+1,y+2)(x,y)→(x+1,y+2)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 1, comma, y, plus, 2, right parenthesis.
Answers
The coordinates of the image of the point Q is Q'(3, 6).
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
From the given graph, we have point Q(-4, 4).
Here the point is translated.
After translation, the original figure is shifted from a place to another place without affecting it's size.
The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).
So the given point is (-4, 4).
(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).
So the required point is (-3, 6).
Hence the image of point Q is (-3, 6).
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Your question is incomplete, Probably, the correct graph for the question is given below.
Please help me I don’t know
Answers
Note that in the above problem where a marine biologist uses the triangles shown in the diagram to measure the width of an oil spill in the bay from a safe distance on shore, note that the width of the oil spill is 20m. See the proof below.
What is the rationale for the above response?In ΔABC and ΔDEC, Note that since
DC = BC; and
EC = AC
It means that ∠DCE = ∠ACB (Diagonal Equality)
⇒ ΔABC ≅ ΔDEC
Therefore:
DE = AB
Since AB = 20m,
DE is also = 20m.
Thus, it is correct to state that the width of the oil spill is 20m.
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if interest is compounded monthly, then the actual amount you would owe in the situation of part (b)is given by $7000 ✕ 1.01612. What is the actual amount you would owe at the end of the year? (Round your answer to the nearest cent.
Answers
If you look at this rationally I believe it will be 7.0 with the odd number.
There are 100 teachers in a school. 60 teach science, 25 teach humanities, 15 teach both science and humanities. 6Find the number of teachers who teach: (a) science but not humanities. (b) Humanities but not science. (c) Humanities or science.
Answers
The number of teachers who teach:
(a) science but not humanities = 45
(b) Humanities but not science = 10
(c) Humanities or science = 70
Finding the number of teachers:To find the number of teachers that teach only Science we can subtract the number of teachers who teach both subjects from the number of teachers that teach science.
Similarly, to find the number of teachers that teach only Humanities we can subtract the number of teachers who teach both subjects from the number of teachers that teach Humanities.
To find the number of teachers who teach Humanities or science we use the elementary set formula,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)Here we have
Total number of teachers = 100
No of teachers who teach Humanities, n(H)= 25
No of teachers who teach Science, n(S) = 60
No of teachers who teach both Science and Humanities, n(H ∩ S) = 15
The number of teachers who teach science but not humanities
= No of teachers who teach Science - No of teachers who teach both
= 60 - 15 = 45
The number of teachers who teach Humanities but not science
= No of teachers who teach Humanities - No of teachers who teach both
= 25 - 15 = 10
The number of teachers who teach Humanities or Science
As we know n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
The number of teachers who teach Humanities or Science
= n(S) + n(H) - n(S ∩ H)
= 60 + 25 - 15
= 70
Therefore,
The number of teachers who teach:
(a) science but not humanities = 45
(b) Humanities but not science = 10
(c) Humanities or science = 70
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a norman window has the shape of a rectangle surmounted by a semicircle. if the perimeter of the window is 30 ft, express the area a of the window as a function of the width x of the window.
Answers
The area a of the window as a function of the width x of the window 12x -(4 + π)x2/8
Let y be the height of the window's rectangular part, and let P represent the window's perimeter.
P then equals x plus 2y plus the length of the semicircular part. The radius of the semicircular part is x/2.
So, P = x + 2y + (1/2)(circumference)
P = x + 2y + (1/2)(2)π(x/2)
P = x + 2y +πx/2 = 24
2y = 24 - x - πx/2
y = 12 - x/2 - πx/4 = 12 - (2 + π)x/4
A = xy + (1/2)π(x/2)2
= x(12 - (2 + π)x/4) + πx2/8
= 12x -(2 + π)x2/4 + πx2/8
= 12x - (4 + 2π)x2/8 + πx2/8
= 12x - 4x2/8 - πx2/8
= 12x -(4 + π)x2/8
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