The area of the window that lets in the most light will be the one that causes the window to transmit the most light overall.
To find the proportions of the window that will admit the lightest, we need to maximize the total area of the window while keeping the perimeter fixed. The total area of the window is the sum of the area of the rectangle and the area of the semicircle. The area of the rectangle is the product of its length and width, and the area of the semicircle is half the product of its radius and the area of a full circle with the same radius.
Since the perimeter is fixed, the length and width of the rectangle are also fixed. The radius of the semicircle can be found using the perimeter and the length and width of the rectangle.
Once we have the radius of the semicircle, we can find the area of the rectangle, the area of the semicircle, and the total area of the window. Since the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does, we will have to multiply the area of the semicircle by 0.5 to find the total amount of light transmitted by it.
Finally, we will have to compare the total amount of light transmitted by the window for different values of the length and width of the rectangle. The proportion of the window that admits the most light will be the one that results in the maximum total amount of light transmitted by the window.
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math. f(x)=8x-7;f(x)=9
Answer:
65
Step-by-step explanation:
We are given f(x) = 9
Substitute 9 for x in f(x) = 8x - 7
f(x) = 8 (9) - 7
f(x) = 72 - 7
f(x) = 65
fill in the table using this function rule. y=6x-36
Find volume of cylinder
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
The volume of the cylinder on the image is:
v = 36,424 in³
So the correct option is the second one.
What is the volume of the cylinder?We know that for a cylinder of diameter D and height H, the volume is given by the formula:
V = pi*(D/2)²*H
Where pi = 3.14
Here we know that:
D = 40 inches.
H = 29 inches.
Replacing that in the formula for the volume we will get:
V = 3.14*(40 in/2)²*29 in = 36,424 in³
So the correct option is the second one.
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A large cuboid-shape box has dimensions of 70cm by 40cm by 40cm. Work out the maximum number of smaller cube-shaped boxes with sides of length 10cm that will fit in the large box
Given ,
A large cuboid-shape box has dimensions of 70cm by 40cm by 40cmLength of the cube shaped boxes are 10cmTo Find : Maximum number of small cube shaped boxes that can fit in the cuboid
Volume of the Cuboid = [tex]2(lb+bh+lh)[/tex]
Volume of the cuboid = [tex]2(70X40+40X40+70X40)[/tex]
= [tex]14400cm^{3}[/tex]
Now to find the volume of a cube,
[tex]V = a^{3}[/tex]
[tex]V = 10X10X10[/tex]
[tex]V = 1000cm^{3}[/tex]
Number of boxes that can fit in a cuboid = [tex]\frac{14400}{1000}[/tex]
= [tex]14boxes[/tex]
Hence , the number of cube shaped boxes that can fit in a cuboid are 14
Each of the students in class writes a different 2 digit number on the whiteboard. The teacher claims that no matter what the students write there will be at least three numbers on the white board whose digits have the same sum what is the smallest number of students in the calls for the teacher to be correct?
Answer: The teacher's claim is that there will be at least three numbers on the whiteboard whose digits have the same sum, no matter what the students write. To see if this claim is true, we can consider different cases for the number of students in the class.
If there are only two students in the class, the teacher's claim is not true. The two students can write any two different two-digit numbers, and it's not guaranteed that the digits in those numbers will have the same sum.
If there are three students in the class, the teacher's claim is true. The three students can write any three different two-digit numbers, and at least one of those numbers is guaranteed to have digits that have the same sum as one of the other numbers.
If there are more than three students in the class, the teacher's claim is true. No matter what numbers the students write, there will always be at least three numbers whose digits have the same sum.
Therefore, the smallest number of students for the teacher's claim to be true is three students.
It's worth mentioning that the teacher's claim is not necessarily true for all cases, it's only true that any three numbers picked out of the two-digit numbers set, will have digits with the same sum.
Step-by-step explanation:
Exit ticket
The length of the sides of two triangles is as follows:
ZY = 14, YX = 9, XZ = 8 PR = 5, RQ = 7, and QP = 4
is AZXY~ AQPR? Use a flowchart to organize your facts and conclusions.
Therefore , the solution of the given question triangle comes out to be
triangle PQR to triangle ZXY is 3/2
Defining a triangleYou can link any three points in a plane to form triangles, which have three sides and three angles. They were among of the first geometric forms to be examined. Since triangles may be divided into any polygon, regardless of whether it has four, five, six, or n sides, they are very significant.
Here,
Consider PR and ZY as a point of comparison.
PR = 5
ZY = 14
Suppose the scaling factor is r and that
5 * r = 14
r = 14 / 5
r = 14/5
examining other sides
RQ to PR
right 5 * 12/3 = 20
To YX, QP
Correct answer is 4 * 9/3 = 12.
Thus,
triangle PQR to triangle ZXY
Therefore , Triangle PQR to Triangle ZXY equals 3/2, which is how the given question's solution is determined.
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A kite is shaped like an isosceles triangle. To the nearest tenth what is the length of the spine?
The length of the spine will be;
⇒ 48.2 cm
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
A kite is shaped like an isosceles triangle.
Now,
Since, A kite is shaped like an isosceles triangle.
Hence, Two sides of a triangle is equal to each other.
Let the length of the spine = x
So, We can formulate by the Pythagoras theorem,
⇒ Hypotenuse² = Base² + Perpendicular²
⇒ 62² = (78/2)² + x²
⇒ 3844 = 39² + x²
⇒ 3844 = 1521 + x²
⇒ 3844 - 1521 = x²
⇒ 2323 = x²
⇒ x = √2323
⇒ x = 48.2 cm
Thus, The length of the spine = 48.2 cm.
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(x + 7 ) + 3y help me please
Answer:
x+7+3y
Step-by-step explanation:
You just remove the parentheses in this case since you don't have to change any of the operations.
Answer:
Step-by-step explanation:
x+7+3y simplifed
15. Find the lengths of the sides of the kite KITE. (Answer in simplest radical form and show work)
The lengths of the sides of the kite LM is 13√2.
How does Pythagoras' rule work?According to the Pythagorean theorem, the hypotenuse of a right-angled triangle's other two sides add up to a square whose length equals the hypotenuse's.
The hypotenuse (longest side) of a right-angled triangle's square is equal to the sum of its other two sides, according to the Pythagoras theorem (base and perpendicular). Hypotenuse2 = Base2 + Perpendicular2 is how this is expressed. A2 + B2 = C2 is the formula for the hypotenuse.
According to question:-
LM = 13√2
Hypotenuse = Base 2 + Perpendicular 2.
So,
LM = √7² + 17²
LM = √49 + 289
LM = √338
LM = 13√2.
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What are the potential solutions to the equation below? 1ln(x+3)=0
A. x = -3 and x = -4
B. x = -2 and x = -4
C. x = 2 and x = -3
D. x = 2 and x = 4
The potential solutions to the equation are x = -2 and x = -4
What is logarithm ?A logarithm is the power to which a number must be raised in order to get some other number .
The given expression is ln(x + 3) = 0
It can be rewritten as
[tex]ln _e (x + 3) = 0[/tex]
[Since base of a natural logarithm is considered as e]
[tex]e^0 = (x + 3)[/tex]
Since in a logarithmic function if log b with base e = c
Then we further solve the expression to get the possible roots.
x + 3 = 1
x = 1-3
x = -2
Therefore, the potential solutions are x = -2 and x = -4
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•40 POINTS• don’t explain.
Answer:
ASA-------------------------
We can see two angles marked as same, one of them is a right angle.
The included vertical side is common to both triangles so is a congruent side.
Since we have congruence of two angles and the included side, it is Angle-Side-Angle or ASA.
HELP I HAVE 25 POINTS AND I WILL MARK U AS BRAINLIST A granola recipe calls for 3 cups of oats, 1 cup of almends. 1 cup of pecans, and 1 cup of dried fruit. What is the ratio of fruit to eats? Yolanda says that for every 2 cups of nuts, there are 2 cups of fruit. Explain why her answer is incorrect and give the correct ratio of nuts to fruit. Explain your answer.
Answer:
Yolanda's answer is incorrect because the recipe calls for 1 cup of almonds, 1 cup of pecans, and 1 cup of dried fruit, which totals 3 cups of nuts. The correct ratio of nuts to fruit in this recipe is 3:1. This means that for every 3 cups of nuts, there is 1 cup of fruit.
How do you find the angles of an isosceles triangle given three sides and no angles?
The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.
Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:
c² = a² + b² - 2abcosC
Therefore, you can rearrange the equation to solve for angle C:
C = arccos((a² + b² - c²) / (2ab))
For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.
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THIS HAS BEEN KILLING ME!!!!!
The function y=-1/3x is reflected across the x-axis. What's the equation of the new function?
- explain step by step, please.
Check the picture below.
let's bear in mind that the -(1/3)x has a negative slope, namely going down, so a reflection over the x-axis will yield the same points pretty much, but instead of the IV Quadrant, on the I Quadrant, above, whilst the slope remains the same, it simply turns positive.
Tyrese works each day and earns more money per hour the longer he works. Write a function to represent a starting pay of $20 with an increase each hour by 3%. Determine the range of the amount Tyrese makes each hour if he can only work a total of 8 hours.
The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is 20 ≤ x ≤ 24.80
What is a range?The range is the space between the highest and lowest numbers.
Given: Tyrese works every day and gets paid more per hour the more time he puts in. Create a function to represent a starting wage of $20 that rises by 3% each hour.
To find: Establish the range of Tyrese's hourly pay if he can only work a total of 8 hours.
The beginning wage is $20.
Suppose x hours are in a day.
A $20 salary is offered, with a 3% hourly raise.
e.g., increment = (3/100)*20*x = (3/5)x
A function's maximum possible earnings are
y = 20 + (3/5)x
He is only allowed to work a total of 8 hours, per our instructions.
Therefore, the most money she can make in 8 hours is
y = 20 + (3/5)*8
y = 20 + 4.8
y = 24*8
$20 is the first sum.
As a result, if Tyrese can only work a total of 8 hours every day, the range of his hourly wage is .
Therefore, the correct answer is option B) 20 ≤ x ≤ 24.80.
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Solve 84=3u^2, where u is a real number.Round your answer to the nearest hundredth.
3u^2-84 = 0 then u=5.29 is the nearest hundredth
What are real numbers?The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.
This category includes all natural integers, decimals, and fractions.
In the number system, real numbers are only the fusion of rational and irrational numbers.
These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.
Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Examples of actual numbers include 23, -12, 6.99, 5/2, and so forth.
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Please answer this by 11/01/22. Thank you.
Answer: a) AE || BC b)AB=BC c)AE⊥ED &ED⊥CD
Step-by-step explanation:
a) The line segments that have the arrow sign on them mean that they are parallel, so AE || BC ( || = parallel to).
b) When two line segments have a dashed line on it, it shows that they are the same length, so AB is equal to BC.
c) when two segments intersect with a 90° angle, they are perpendicular, so AE⊥ED &ED⊥CD(⊥ = perpendicular to).
What is complete angle Class 7?
The angle with the measure 360° is known as a complete angle. A complete angle is one full rotation measuring 360°.
When the final point coincides with the initial point, after one whole rotation, then the angle so created is known as the complete angle. A complete angle is also known as a full angle or a round angle.
The measure of a complete angle is equal to 2π radians = 360 degrees which is the central angle of a circle. Also, if we combine four right angles or two straight angles it makes a complete angle. A complete angle is identical to a zero angle but the difference is only the amount of rotation.
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In a classroom, 1 10 of the students are wearing blue shirts , and 2 5 are wearing white shirts. There are 20 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts
Answer:
10 students are wearing shirts other than blue or white.
Step-by-step explanation:
1 10 of the students in the classroom are wearing blue shirts, which is 1/1020 = <<1/1020=2>>2 students.
2 5 of the students in the classroom are wearing white shirts, which is 2/5*20 = 8 students.
Altogether, 2+8 = <<2+8=10>>10 students are wearing either blue or white shirts.
There are 20 students in the classroom, so 20-10 = <<20-10=10>>10 students are wearing shirts other than blue or white.
Theoretically, if a fruit is chosen 300 times, how many times would you expect to pick an apple or banana?
The answer is 90 times to expect picking an apple or banana.
If the fruit is chosen 300 times, then it would be a 1:3 ratio of apple or banana to the other fruits. This means that 100 times out of the 300 times, you would expect to pick an apple or banana.
Predicting the outcome using the experiment results because 300 times is a sizable number.
8+4 is either an apple or a banana in 40 times.
Therefore, the solution would be x in 300 times.
[tex]x = \frac{300}{40}[/tex] x12
x = 90
Therefore, the probability of picking an apple or banana is 90 times.
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Solve the following system of equations algebraically:
y = x² - 15x + 60
y=x-3
Since the square root of a negative number does not exist in the real numbers, there are no real solutions for x. Therefore, the system of equations has no solutions.
Define Algebric expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
What is variables and constants ?A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.
To solve this system of equations algebraically, we can substitute y = x-3 into the first equation
y = x² - 15x + 60
x-3 = x² - 15x + 60
x² - 16x + 63 = 0
We know that this quadratic equation has no real solutions because its discriminant (b^2 - 4ac) is negative, so the system of equations has no real solutions.
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A man bought an item for N5000.00 and sold it at a loss of 25%. How much did he sell it? A. N6250.00 B.N4750.00 C.N3750.00
D. N2250.00
Answer: B. 3750
Step-by-step explanation:
We start by converting the percentage 25% to the decimal 0.25.
Next, we multiply the original price by this decimal (5000*0.25=1250)
And Finally, Since it is a loss we subtract the 1250 from the original price.
5000 - 1250 = 3750
Elizabeth has a loyalty card good for a 10% discount at her local grocery store. What would her total in dollars and cents be, after the discount and before tax, if the total cost of all the items she wants to buy is $37. 60? Round to the nearest cent
The total amount for Elizabeth's purchase after 10 percent discount on her total bill is 33 dollars and 84 cents which is equivalent to 34 dollars.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Elizabeth bought the grocery for a total of 37 dollars and 60 cents.
She has a coupon of 10% discount.
Which means, she can get 10% discount on her total bill.
The amount of her total bill is $37.60.
So, calculate using percentage, the value of 10% of $37.60.
=(10 × 37.60/100)
= 376/100
= 3.76
So, Elizabeth would get a discount of $3.76 on her total bill -
= 37.60 - 3.76
= 33.84
Therefore, after the discount Elizabeth's total bill is $33.84 ≈ $34.
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Joules and calories are two different units of energy. The equation j=0. 239c relates the measures, where c stands for calories and j stands for joules. Complete the table
To complete the table, we can simply multiply the number of calories by 0.239 to find the equivalent amount of Joules.
The equation relates Joules to calories as j = 0.239c, where c stands for calories and j stands for joules. For example, 1 calorie is equal to 0.239 Joules, 2 calories is equal to 0.478 Joules, and so on.
Joules (j) Calories (c)
0.239c 1
0.478c 2
0.717c 3
0.956c 4
1.195c 5
1.434c 6
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. In the cafeteria
3 out of every 5
students prefer
pizza. If there are
200 students in the
cafeteria how many
students prefer
pizza?
Answer:
120
Step-by-step explanation:
3/5 of 200 = 120
Equilateral triangle T is inscribed in circle A , which has radius 10 . Circle B with radius 3 is internally tangent to circle A at one vertex of T . Circles C and D , both with radius 2, are internally tangent to circle A at the other two vertices of T. Circles B, C , and D are all externally tangent to circle E, which has radius m/n , where m and nare relatively prime positive integers. Find m+n
For the given figure, where m and nare relatively prime positive integers. The value of m+n is 32.
Explain Law of Cosines.The law of cosines, also known as the law of cosines, relates all three sides of a triangle to one angle of the triangle. Most useful for searching for missing information in triangles. For example, if you know all three sides of a triangle, you can use the law of cosines to find the measure of the angle. Similarly, if you know two sides and the angle between them, you can find the length of the third side by the law of cosines.
Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.
Since the radius of B is 3, AX = 4.
Assume AE = p.
Then EX and EY are radii of circle E and have length 4 + p.
AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.
Using the Law of Cosines on Δ CAE, we obtain
(6+p)² =p² + 64 - 2(8)(p) cos 60
The 2 and the cos 60 terms cancel out:
p² + 12p + 36 = p² + 64 - 8p
12p+ 36 = 64 - 8p
p = 28/20
= 7/5
The radius of circle E is 4 + (7/5)
= 27/5,
So, the answer is 27 + 5 = 32
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What is a 3 degree equation called?
A three-degree equation is referred to as a cubic equation. The polynomials are referred to as cubic polynomials if they have a degree of three.
what is cubic equation ?A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. The polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.
given
A three-degree equation is referred to as a cubic equation.
All cubic equations have roots that are either three real roots or one real root and two imaginary roots.
The polynomials are referred to as cubic polynomials if they have a degree of three.
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In order to summarize qualitative data, a useful tool is a____________.
A) histogram
B) stem-and-leaf diagram
C) scattergram
D) frequency distribution
A (A) histogram is a useful tool for condensing qualitative data.
What is a histogram?An effective tool for summarizing qualitative data is a histogram.
The distribution of numerical data is roughly depicted by a histogram.
Karl Pearson was the person who first coined the phrase.
The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.
The bins are often defined as a series of discrete intervals that don't overlap.
The bins (intervals) must be close together and frequently, though not always, have the same size.
Therefore, a (A) histogram is a useful tool for condensing qualitative data.
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A line starts at (negative 2, 0), goes to (5, question mark), and then goes down to (6, 0).
What would the height need to be for this curve to be a density curve?
One-fourth
One-half
StartFraction 1 Over 8 EndFraction
StartFraction 1 Over 16 EndFraction
answer is one fourth
What the height would need for this curve to be a density curve is; One-half
How to interpret Density Curves?The criteria for a curve to be a density curve is as follows;
1. The curve must always be non-negative. This tells us that the y-value of the curve must be greater than or equal to 0 at every given point.
2. The area under the curve must always be equal to 1.
Now, we are told that the curve starts at (-2, 0) and then goes to (5, question mark), and then goes down to (6, 0),.
This means that the area under the curve will be a trapezoid that has a height of question mark and then bases of length 3 (from -2 to 5) and length 1 (from 5 to 6).
The area of this trapezoid will be equal to the sum of the bases times the height divided by 2, or:
Area = ((3 + 1) × question mark)/2
Since the area under the curve must be equal to 1, we can set up the equation:
1 = ((3 + 1) × question mark) / 2
Solving for question mark, we will:
The question mark = 2/4
The question mark = 1/2
Therefore, we can conclude that the height of the curve is 1/2
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It is a problem about the systems of equations that do not arise.
It is desired to distribute 420 € among three people, so that the first has €40 more than the second, and the third has half of what they have between the first two.
a) It proposes a system of linear equations to calculate what corresponds to each one. b) It solves, using the Gauss method
The solution to the equations is
The value of first x = € 160
The value of second y = € 120
The value of third z = € 140
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first , second and third be represented as x , y , and z
The total amount to be distributed = € 420
So , x + y + z = € 420 be equation (1)
Now , first has €40 more than the second
So , x = y + 40 be equation (2)
And , third has half of what they have between the first two
So , z = ( 1/2 ) ( x + y ) be equation (3)
Substituting the value of x in the equation (3) , we get
z = ( 1/2 ) ( 2y + 40 )
z = y + 20 be equation (4)
Substituting the value of z and x in equation (1) , we get
( y + 40 ) + y + ( y + 20 ) = 420
On simplifying the equation , we get
3y + 60 = 420
Subtracting 60 on both sides of the equation , we get
3y = 360
Divide by 3 on both sides of the equation , we get
y = € 120
Therefore , the value of x = € 160
The value of z = € 140
Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420
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