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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What number must be added to the expression below to complete the square? x²-7x
O A. 7/2
O B. -7/2
O C. -49/4
O D. 49/4
Answer:
D. 49/4
Step-by-step explanation:
Complete the square by squaring half the coefficent of the x term
(-7/2)² = 49/4
hey! can y’all help with this?
Answer:
11
Step-by-step explanation:
Answer:
A) [tex]\sqrt21[/tex]
Step-by-step explanation:
First you have to plug in the numbers into the Pythagreom Theroum:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]\sqrt{5} ^{2} +4^{2} =c^{2}[/tex]
(C represents you hypotnuse)
Then you square the numbers:
5 + 16 = [tex]c^{2}[/tex]
(If your confused why [tex]\sqrt5^{2}[/tex] just came out to be 5, the square and the square root cancel each other out)
Then you add the numbers:
21 = [tex]c^{2}[/tex]
Then you sqaure root both sides to cancel out the [tex]c^{2}[/tex]:
c = [tex]\sqrt21[/tex]
help! how do I do this??
Answer:
15 ft
Step-by-step explanation:
Using sinus law
sin(A) /a = sin(B) /b = sin(C) /c
Where smale letters indicate the sides
For this question :
(sin(90)*12)/sin(53)=15
Answer:
9.58
Step-by-step explanation:
Sin=opposite/hypotenuse
sin53=12/length of slide
Length of slide=12sin53
=9.58
Given the picture below, where would point A’ be located after a dilation of 2 centered at point D (red point)
After dilation, the co-ordinate of point A will be (-4,4) while B will be (2,4) and of C will be (-2,0).
After dilation, how do you locate points?The distance between the point of dilation and the point you are dilating must be multiplied by three if the point you are dilating is directly above the point of dilation and you are dilating by 3. You inserted your new point there.
How can a point be widened by two?The x-value of each point will be multiplied by 2 to enlarge the image by a factor of two. The x and y values of each point will be multiplied by 2 to enlarge the figure by a factor of 2.
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Two cards are chosen at random from a standard 52-card deck. What is the probability that the first card is a heart and the second card is a 10
The probability that the first card is a heart and the second card is a 10 is 1/51.
What is the probability?Probability with Replacement is used for questions where the outcomes are returned to the sample space again. This means that once the item is selected, it is replaced in the sample space, so the number of elements of the sample space remains unchanged.
The following combinations are possible:
When we choose first card, total no. of card is 52 and card of heart is 13
so the probability of the first card to be heart is
P(1)= 13/52
= 1/4
When we choose second card, total no. of card is 51 and card of 10 is 4
so the probability of the first card to be 10 is
p(2)= 4/51
So the final probability is
= P(1)* P(2)
= 1/4 * 4/51
= 1/51
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Triangle ABC has a perimeter of 22cm
AB = 8cm
BC = 5cm
By calculation, deduce whether triangle ABC is a right-angled triangle
PLSSS HELPPPP
***PLEASE HELP I'M TIMED***
Let f(x)=e^x and g(x)=x+6. What are the domain and range of (g0f)(x)? domain: x > 0 range: y > 0 domain: x > 6 range: y > 0 domain: all real numbers range: y > 6 domain: all real numbers range: all real numbers\
Answer:
Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively
Step-by-step explanation:
We have the functions, f(x) = eˣ and g(x) = x+6
So, their composition will be g(f(x)).
Then, g(f(x)) = g(eˣ) = eˣ+6
Thus, g(f(x)) = eˣ+6.
Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.
Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.
Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
Answer:
It is not D!!!! it is not all real numbers for both! I got it wrong!
Step-by-step explanation:
edge 2021
i had answered saying it was D but then I got it wrong, so I can't just delete my answer. But I can say it is absolutely not D.
Help me plz I’ll give brainliest and this also worth 25 points
Answer:
there r more students who way 60-69 kilograms and there r less students who way 90-100 kilograms
Step-by-step explanation:
Please Help! I need you to solve the inequality for the box. This is grade 7 math.
Answer:
Oki! Mizuki here to help!
The answer you fill in the box is 6!
Step-by-step explanation:
3.5s + 5.75 [tex]\leq[/tex] 26.75
3.5s + 5.75 - 5.75 [tex]\leq[/tex] 26.75 - 5.75
3.5s [tex]\leq[/tex] 21
s [tex]\leq[/tex] 6
Janine collects sports equipment. 1/2 of her collection are sports balls. Of the sports balls 1/4 of them are softballs. How much of the sport equipment are softballs?
Answer:
1/8
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
convert this to a decimal.
1/2 = 0.50
1/4 = 0.25
0.5 x 0.25 = 0.125
0.125 x 8 = 1
I need help asap please
Answer:
1)33.4096
2) 113.1
3) 268.08
4) 904.78
Step-by-step explanation:
Volume = 4/3π*r cubed
So, let's say π = 3.14
1) Radius =2
4/3*3.14 = 4.1762
4.1762*2*2*2
4.1762* 8
=33.51
2) Radius = 3
113.1
3) Radius = 4
268.08
4) Radius = 6
904.78
I hope this helps
Sorry if it's wrong, I am just 4th grade :(
Which strategies can be used to find the product of 1,587 x 1,000? Select two options
Answer:
Step-by-step explanation:
you can multiple and get 1,587,000]and then you divide to get 8 [tex]\sqrt{1587000[/tex]Find the value of y. Write your answer in decimal form. Round your answer to the nearest whole number.
Answer:
c
Step-by-step explanation:
heres a trick it says whole number so 10 is th eonly answer that is rounded
Help
Gcse Foundation.
Redraw the triangle just 1/2 the size
Answer:
Answer is in the image attached.
Step-by-step explanation:
Ricardo
1. A block of wood is 5 inches long, 2 inches wide, and 3 inches high. What 2 is the volume of this block of wood?
Please solve it's worth 12 points
Answer:
65
Step-by-step explanation:
260/4=65
65*4=260
Decide if the following statement is
valid or invalid.
If the base of a triangle is 3 and its
height is 4, then its area is 6. This
triangle has an area of 6, so its
base is 3 and its height is 4.
Step-by-step explanation:
the area of a triangle is base times height divided by 2.
A = (b × h) / 2
so, when b = 3 and h = 4, then
A = (3 × 4) / 2 = 12 / 2 = 6
correct.
now the other way around
we know the area (6).
=> 6 = (b × h) / 2
=> 12 = b × h
well, b=3, h=4 is one possible solution for this.
but so is e.g. b=2, h=6, or b=12, h=1, or ...
and that is just the natural numbers. then there are rational numbers and so on.
therefore there is an infinite set of possible (b, h) pairs that satisfy the equation 12 = b × h.
therefore the statement that we can conclude out of a given triangle area of 6 that b must be then 3 and h must be 4 is wrong.
simple - it is one equation with 2 variables and has therefore usually not just one solution.
The cafeteria sold 8 more turkey sandwiches than ham sandwiches. They sold 12 sandwiches in all. How many turkey sandwiches did the cafeteria sell?
Answer:The cafeteria sold 2 Ham sandwiches and 10 Turkey sandwiches
Step-by-step explanation:
Let the number of Ham sandwiches be rep as x
and turkey sandwiches be x+8
such that the equation to solve the question since total amount of sandwiches sold is 12 becomes '
x + x+8=12
2x+8=12
2x=12-8=44
x=4/2=2
Therefore number of ham sandwiches sold is 2
and number of turkey sandwiches sold is x+8=2+8=10
Can I add myself on Wikipedia?
One cannot add themselves directly to Wikipedia as this can cause harm to the platform and community in a later run. As one can start adding content and details on the page based on their personal opinions.
Therefore we can say that the answer is that we cannot edit or create our own Wikipedia page, because that would be a conflict of interest ,more on this later.
But the thing which one can do is to add themselves in the line ,to list themselves on Wikipedia’s repository of articles which are out there looking for creators who can help maintain the site.
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Classify each transformation by its properties.
The classification of the transformations based on the properties are presented as follows;
[tex]\begin{array}{|c|c|c|} & \mathbf{Preserves \ length} & \mathbf{Does \ not \ preserve \ lengths} \\\mathbf{Preserves \ angle \ measure} & Reflection\ Rotation &Translation \ followed \ by \ dilation \\&&Dilation \ with \ K > 1\\\mathbf{Does \ not \ preserve \ angle \ meas} & & \\\end{matrix}[/tex]
What are the different transformation effects?The transformations that preserves the lengths of the original figure or pre-image and also preserves the angle measure is a rigid transformation.
Rigid transformations includes; Reflections, rotations, and translations
Transformations that preserves the angle of measure but in which the lengths of the preimage is not preserved are non-rigid transformations
Non rigid transformations includes; Dilation with a scale factor
Transformations that does not preserve the angle measure includes; Shear transformation
A translation and a dilation transformation does not preserve the lengths of the original figure.
The classification of the transformations based on their properties are therefore presented as follows;
[tex]{}[/tex] Preserves lengths Does not preserve lengths
Preserves Reflection [tex]{}[/tex] Translation followed by dilation
angle measure Rotation [tex]{}[/tex] with k > 1
[tex]{}[/tex] Dilation with k > 1
Does not
Preserve angle
measure
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HELP!!!
Marta bakes 3 types of cake: chocolate, fruit, and sponge. The recipe for each cake includes flour and sugar and she uses 3.3kg of flour and 3.1kg of sugar in total.
Each chocolate cake uses 225 g of flour and 300g of sugar
Each fruit cake uses 320g of flour and 250g of sugar
Each sponge cake uses 400 g of flour and 325g of sugar
Marta sells chocolate cakes for $12, fruit cakes for $10, and sponge cakes for $8 and makes a total of $114
How many of each cake does she make?
(Answer in the back of the book: 4 chocolate, 5 fruit, 2 sponge cakes)
The three equations for this problem are:
The total amount of flour used: 3.3kg = (225g/cake) * (number of chocolate cakes) + (320g/cake) * (number of fruit cakes) + (400g/cake) * (number of sponge cakes)The total amount of sugar used: 3.1kg = (300g/cake) * (number of chocolate cakes) + (250g/cake) * (number of fruit cakes) + (325g/cake) * (number of sponge cakes)The total revenue from sales: $114 = ($12/cake) * (number of chocolate cakes) + ($10/cake) * (number of fruit cakes) + ($8/cake) * (number of sponge cakes)Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z
so the
first equation can be written as 3.31000 = (225x) + (320y) + (400z)second 3.11000 = (300x) + (250y) + (325z)and third one 114 = (12x) + (10y) + (8*z)let's use the third equation to get the value of x,y and z:
x = (114 - 10y - 8z) / 12y = (114 - 12x - 8z) / 10z = (114 - 12x - 10y) / 8If you get the values and substitute, then the answer would be:
4 chocolate cakes, 5 fruit cakes, 2 sponge cakes
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4x² - 20x = -21????????
Answer:
x=7/2
x=3/2
Step-by-step explanation:
Answer: ax^2+bx+c=0
(4x^2+20x+20=0)
Step-by-step explanation:
It may not make sense but...
Add -20 to both sides of the equation.
4x-20x=-20
Add -20 to both sides of the equation.
4x^2-20x+20=-20+20
Simplify the expression.
4x^2+20x+20=0
I hope this was what you were looking for. :) If not I'm still glad to help.
dividing decimals up to 2 decimal places
1.0.2÷6.11
Answer:
its 6.11
6.11 ÷ 1 = 6.11
Calculated to 2 decimal places.
6. 1 1
1 6. 1 1
− 6
0 1
− 1
0 1
− 1
0
N(t) = 8950 times (0.7)^2t
Answer: t = 0
Step-by-step explanation:
Expand 8950×0.7²: 4385.5t
8950(0.7) ²t
8950×0.49t = 4385.5t
N(t) = 4385.5t
N(t) - 4385.5t=0
Factor N(t) - 4385.5t: t (N - 4385.5)
t (N - 4385.5) =0
t=0
BROO PLS SOMEONE HELP IM SO CONFUSED
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
The 30th term of the arithmetic sequence is 265
What is an arithmetic sequence in math?
Arithmetic sequences are those in which each term is increased by the addition or subtraction of a constant k. In contrast to a geometric sequence, where each term rises by being multiplied by or divided by a constant k,A series of numbers is considered to be an arithmetic progression or sequence if there is a constant difference between the terms. Consider the mathematical progression with a common difference of 2 in the numbers 5, 7, 9, 11, 13, and so on.An is equal to a1 + d(n - 1), where d is the common difference across terms in the series, and a1 is the first term in the sequence.This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words, [tex]a_{n}[/tex]= [tex]a_{1}[/tex]+ d ( n - 1 )
Arithmetic Sequence: d = 9
This is the formula of an arithmetic sequence.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
Substitute in the values of [tex]a_{1}[/tex] = 4 and d = 9
[tex]a_{n}[/tex]= 4 + 9 ( n - 1 )
[tex]a_{n}[/tex]= 4 + 9n - 9
[tex]a_{n}[/tex] = 9n - 5
.30th term = [tex]a_{n}[/tex] = [tex]a_{1}[/tex]+ d ( n - 1 )
= [tex]a_{30}[/tex]= 4 + 9 ( 30 -1 )
[tex]a_{30}[/tex]= 4 + 9 x 29
[tex]a_{30}[/tex]= 265
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WILL MARK YOU BRAINLIEST PLEASE HELP ASAP
Answer:
29.5m because it is rectangular finger and one path is loss .loss Parth is triangle
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
D
Step-by-step explanation:
Answer:
D: because the factor, fraction, decimals wont be multiply hundreadths of it specially when you add 27 so D: is my answer
Step-by-step explanation:
Does this help?
How many possible real solutions are there?
The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
A linear equation (degree 1) has one real solution.
A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.
A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.
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Make up an equation of the form y = kx +b, the graph of which passes through the following points:
P (4, 1) and Q (3, –5)
Answer:
y=6x-23
Step-by-step explanation:
Step-by-step explanation:
m = (y2 - y1)/(x2-x1)
m = (-5 -1)/(3-4) = -6/-1 = 6
y = 6x + b
then
slope point form
y - y1 = m (x - x1)
y - 1 = 6 (x - 4)
y - 1 = 6x - 24
y = 6x - 23
How do you know if a linear system has one solution?
A linear system has one solution if the slopes of the equation of lines are different.
The 3 possible solutions of a linear system are:
- Unique or one solution
- Infinite solutions
- No solution
A linear equation is equal to the equation of a line, which has the form:
y = mx +b
where m = slope
If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.
Example:
2x + 5y = 34 .. .. (equation 1)
x + 5y = 32 .........(equation 2)
Change the equation 1 and equation 2 into slope-intercept form:
y = (-2/5) x + 34/5 ..... (equation 1a)
y = (-1/5) x + 32/5 ..... (equation 2a)
The slope of equation is (-2/5) while equation 2 is (-1/5), which is different from equation 1. Hence, the system of linear equation has one solution.
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