Questions:
A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?
Answer:
32 units of fabrics
Step-by-step explanation:
Given
[tex]a = \sqrt{f + 4} - \sqrt{36 - f}[/tex]
Required
Find f when a = 4
Substitute 4 for a
[tex]4 = \sqrt{f + 4} - \sqrt{36 - f}[/tex]
Rewrite as:
[tex]\sqrt{36 - f} + 4 = \sqrt{f + 4}[/tex]
Square both sides
[tex](\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2[/tex]
[tex](\sqrt{36 - f} + 4)^2 = f + 4[/tex]
[tex]36 - f + 8\sqrt{36 - f} + 16 = f + 4[/tex]
Collect Like Terms
[tex]8\sqrt{36 - f}= f +f+ 4 - 36 -16[/tex]
[tex]8\sqrt{36 - f}= 2f -48[/tex]
Divide through by 2
[tex]4\sqrt{36 - f}= f -24[/tex]
Square both sides
[tex]16(36-f) = (f - 24)^2[/tex]
[tex]16(36-f) = f^2 - 48f + 576[/tex]
[tex]576-16f = f^2 - 48f + 576[/tex]
[tex]-16f = f^2 - 48f[/tex]
Collect like terms
[tex]f^2 - 48f + 16f = 0[/tex]
[tex]f^2 -32f = 0[/tex]
Factorize
[tex]f(f - 32) = 0[/tex]
[tex]f = 0[/tex] or [tex]f = 32[/tex]
f can not be 0 because some units must be ordered.
So, f = 32
Help me with this problem please!
Answer:
Step-by-step explanation:
i can barely see that maybe re upload a better picture and someone will help
GIVING BRAINLIEST FOR CORRECT ANSWER<3
Answer: 75 percent
Step-by-step explanation: I'm pretty sure
in isosceles trapezoid EFGH, FG parallel EH, FG=10, GH=12, and ∠E=60. Find the area of EFGH.
Answer:
22√3 units squared
Step-by-step explanation:
1) Draw the trapezoid
2) Notice you have to find the height to find the area of the trapezoid
3) Notice it is a 30 60 90 triangle when you draw the line to find the height
4) Solve for the 30 60 90 triangle and you get the height to be 2√3
5) Solve for the area of the trapezoid using this formula A= 1/2 h ( b1 + b2)
6) Fill in the numbers for the equation A= 1/2∙ 2√3 ( 10 + 12)
7) Keep aside the 1/2 for now
8) Simplify equation 2√3 + 22 or 2√3 + (10 + 12)
9) Simplify further 44√3
10) Now bring back the 1/2 and put it in the equation 1/2∙ 44√3
11) Simplify to get 22√3
12) 22√3 is the area of the trapezoid
13) 22√3 units squared is the final answer
I will put a my drawing of the trapezoid for reference and this is what I used to solve the question.
If you want to know how I solved the 30 60 90 triangle please let me know.
Sorry I was one week late I just saw it today.
:D
Help me please will mark brainliest
Answer:
197in^2
Step-by-step explanation:
5x5=25(top face)
5x5=25(left face)
9x5=45(bottom face)
6.4x5=26(right face)
Front and behind face: trapezoid area (trapezoid formula h x (a+b)/2)
(5+9)/2 x 5=7x5=35
35+35+25+25+45+25=197in^2
HELP ASAP ASAP EXTRA POINTS
Answer:
The slope is -2
Step-by-step explanation:
Pls help, for 10 points!
Answer:
I think 9 but dont quote me on it
Answer:
2
Step-by-step explanation:
in khan academy i put 9 because thats what the last person said here but it was wrong and the correct answer was 2 so its 2 for sure.
Find the value of or in the triangle shown below. 97 47
Complete the statement. 400 mm = ___ cm
Answer:
40 cm
Step-by-step explanation:
divide the length value by 10
400 / 10 = 40
Answer:
400 mm = 40 cm
Step-by-step explanation:
I need the answers to this: 3(2x-5)= 27
Answer: x=7
Step-by-step explanation: First, remove 3 from both sides by dividing. You will end up getting 9. Since 2x-5 = 9, add 5 from both sides by adding leaving you with 2x = 14. Divide 14 by 2 to get 7.
please help me with this question!
If there are 36 apples in 2 boxes, then
there are
apples in 5 boxes.
Answer:
90 apples in 5 bboxes
Step-by-step explanation:
I don’t understand this A gym has 11 rows of elliptical machines with 13 machines in each row. The gym also has 14 rows of treadmills with 12 treadmills in each row. What is the maximum number of people that can use the elliptical machines and the treadmills at the same time?
Answer:
311
Step-by-step explanation:
11x13=143
14x12=168
143+168=311
Sergio passes by a bike store on Monday and sees his dream bike in the window. It cost 120 . He passes by on Wednesday and is thrilled to see that is marked down by 1/4 . What is the new price of the bike
Answer:
90
Step-by-step explanation:
120 - (120/4)
120 - 30 = 90
30 POINTS PLEASE HELP ASAP !!!
Answer:
1: x = 29
2: Angle C is 93 degrees
Step-by-step explanation:
For 1 angle C has to equal 93 degrees since 52 + 35 = 87 and 180 - 87 = 93, and a triangles interior angles add up to 180 degrees.
From there create an equation: 3(x + 2) = 93 then solve
3x + 6 = 93
-6 from both sides
3x = 87
/3 from both sides
x = 29
For 2 just plug in x (29)
3(29 + 2)
87 + 6
93
help pls lollll
10th grade mathematics
Answer:
I think it's a because
12÷42= 3.5
and
56÷16=3.5
so
10×3.5=35
Step-by-step explanation:
A group of 5 friends is out to dinner. Each of the friends will order the dinner special, and they
have a coupon for $10 off the entire bill. Which equation can be used to find the total cost of
all the dinners after the coupon is applied?
10d - 5 = 0
100 + 5 = 0
5d + 10 = 0
5d - 10 = 0
I NEED HELP BUT I DONT HAVE THE FREE TRIAL THING
Answer:
5d-10 =0
Step-by-step explanation:
Answer: 5d - 10 = C
-tay
Álgebra 1.
Calculate the slope
Answer:
slope: -1/4x
Step-by-step explanation:
i hope this helps :)
how do you find the x for this and the angles, thanks in advance
HOPE THIS HELPS...
Hooke's law is a law of physics that states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram.[1][2] He published the solution of his anagram in 1678[3] as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660.
Hooke's equation holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, and a musician plucking a string of a guitar. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.
Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.
On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock.
The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.
In this general form, Hooke's law makes it possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness k directly proportional to its cross-section area and inversely proportional to its length.
Step-by-step explanation:
2x + 15° + x = 180° { Being co-interior angles }
3x = 180°- 15°
3x = 165°
x = 165° / 3
x = 55°
2x + 15° = 2 *55° + 15° = 125°
Hope it will help :)❤
Please help me Mr Thompson!!! MY HOMEWORK!
Answers:
C) Factored form.C) Standard form.D) -8B) y = x^2B) 2 solutions: x = plus/minus 5======================================================
Explanations:
Factored form is whenever we have two or more expressions being multiplied like you see here. A more simpler example may be breaking 36 into 12*3, or 36 = 12*3. We say that 12*3 is the factored form of 36. The two pieces 12 and 3 multiply to 36.Standard form for quadratics is ax^2 + bx + c. The exponents count down: 2,1,0. You can think of it as ax^2 + bx^1 + cx^0. In this case, a = 2, b = 1, c = -3.The y intercept always occurs when x = 0. Plugging this value in leads to y = -8. The y intercept is located at (0,-8). The last value at the end, the constant term, is always the y intercept. This is one handy feature of standard form quadratic equations.The parent function of any quadratic is always y = x^2. From this parent function, we can derive any scaled version in the form y = ax^2, and we can also apply shifting to get y = (x-h)^2 or y = x^2+k. All together, we can generate y = a(x-h)^2 + k to represent both scaling and shifting. That last equation is vertex form which can convert to standard form shown in choice C. There are two solutions and the solutions are x = -5 and x = 5. Note how x^2 = (5)^2 = 25 and x^2 = (-5)^2 = 25. The two negatives cancel out when we multiply. Be sure to have the negative inside the parenthesis. We don't say -(5)^2 = -25.Who is correct? Fred or Felicity?
Answer: Felicity
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I hope this helps, and enjoy the rest of your day!
Max read 1/3 of his at school. He reads 22 more pages when he arrives home, making 127 pages read so far. How many pages are in Max's novel?
Answer:
315
Step-by-step explanation:
127-22=105
105 times 3 is equal to 315.
Answer:
Step-by-step explanation:
315!!!!!
is this a right triangle 6,12,8
Answer:
No it is a obtuse triangle
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
please help a girl out:
Please help , will mark brainliest
Answer:
Should be 360
Step-by-step explanation:
The Science Club went on a two-day field trip. The first day the members paid $40 for transportation plus $19 per ticket to the planetarium. The second day they paid $90 for transportation plus $16 per ticket to the geology museum. Write an expression to represent the total cost for two days for the n members of the club.
Answer:
total cost = $130 + $35n
Step-by-step explanation:
Cost incurred on the first day.
Fixed cost = $40. this amount is fixed because it does not depend on the number of students that take the trip
variable cost = $19n. It is variable because it depends on the number of students that take the trip. the more the club members that take the trip, the higher the cost
Total cost on the first day = $40 + $19n
Cost incurred on the second day
Fixed cost = $90. this amount is fixed because it does not depend on the number of students that take the trip
variable cost = $16n. It is variable because it depends on the number of students that take the trip. the more the club members that take the trip, the higher the cost
Total cost on the second day = $90 + $16n
Total cost incurred would be the sum of the two costs incurred on the two days
total cost = $40 + $19n + $90 + $16n
= $130 + $35n
A dessert recipe calls for image cups of milk and makes 5 servings. How many cups of milk are needed for 8 servings?
Answer:
1.05
Step-by-step explanation:
Answer:
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Step-by-step explanation:
The question says “the system below has been solved by graphing. How many solutions does it have?”
Answer:
Infinitely many solutions
Step-by-step explanation:
3x+y=1
15x+5y=5
Step: Solve3x+y=1 for y:
3x + y +−3 x = 1 + −3x (Add -3x to both sides)
y=−3x+1
Step: Substitute−3x+1 for y in 15x+5y=5:
15x+5y=5
15x+5(−3x+1)=5
5=5(Simplify both sides of the equation)
5+−5=5+−5(Add -5 to both sides)
0=0
so there are infinite solutions
What is your favorite sport? Sample is chosen from people attending
games
Answer:volleyball
Step-by-step explanation:
Answer:
My fav sport is badminton...
Step-by-step explanation:
Hope it's help u
If wrong then sry sry
1 point An amusement park charges $45 to enter and $0.55 per ride ticket. Write an expression to represent the total amount spent by a guest.
A.45-0.55r
B.45+0.55r
C. 0.55 + 45
D.45/0.55r
An isosceles triangle has an angle that measures 102°. Which other angles could be in that isosceles triangle?
Answer:
(180-102)/2 = 39° each (remaining 2)