Answer:
(22/7)²
576/49
is your answer hope it's help u
Find the value of w A. 110 B. 141 C. 80 D. 100
================================================
Explanation:
The arc measures of 60 and x average to the angle 70, which is the the angle formed between the intersecting chords
70 = (60+x)/2
70*2 = 60+x
140 = x+60
x+60 = 140
x = 140-60
x = 80
The full 360 degree circle has the arc measures of 60, 79, x = 80, and w, where we don't know w yet. But we can add the four pieces of the circle to get 360
60+79+x+w = 360
60+79+80+w = 360
w+219 = 360
w = 360-219
w = 141
---------------
Or you could find angle z first
z+70 = 180
z = 180-70
z = 110
Then use the averaging technique done at the start of this problem
z = (79+w)/2
110 = (79+w)/2
2*110 = w+79
220 = w+79
w+79 = 220
w = 220-79
w = 141
An open-top box is to be made from a 42-inch by 48-inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What should be the length of the side x of the square cut out of each corner to get a box with the maximum volume
Answer:
x = 7.45 inch for the maximum volume.
The area of the square = x² = 7.45² = 55.5025 inch²
Step-by-step explanation:
From the given information:
An open-top box is to be made from a 42-inch by 48-inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side.
The objective is to determine the length of the side x of the square cut out of each corner to get a box with the maximum volume
The volume of the box = l×b×h
The volume of the box = [tex](42 - 2x) \times (48-2x) \times (x)[/tex]
The volume of the box = [tex](2016 - 84x - 96x +4x^2)x[/tex]
The volume of the box = [tex](2016 -180x+4x^2)x[/tex]
The volume of the box = [tex](2016x -180x^2+4x^3)[/tex]
The volume of the box = [tex]4x^3 - 180x^2 +2016x[/tex]
For the maximum volume V' = 0
V' = [tex]12x^2 - 360x + 2016[/tex]
Using the quadratic formula; we have:
[tex]= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
where;
a = 12 , b = -360 c = 2016
[tex]= \dfrac{-(-360) \pm \sqrt{(-360)^2 -4(12)(2016)}}{2(12)}[/tex]
[tex]= \dfrac{360 \pm \sqrt{129600 -96768}}{24}[/tex]
[tex]= \dfrac{360 \pm \sqrt{32832}}{24}[/tex]
[tex]= \dfrac{360 \pm 181.196}{24}[/tex]
[tex]= \dfrac{360 + 181.196}{24} \ \ \ OR \ \ \ \dfrac{360 - 181.196}{24}[/tex]
[tex]= \dfrac{541.196}{24} \ \ \ OR \ \ \ \dfrac{178.804}{24}[/tex]
[tex]= 22.55 \ \ \ OR \ \ \ 7.45[/tex]
For the maximum value , we check the points in the second derivative term
V'' = 24x - 360
V'' ( 22.55) = 24(22.55) - 360
V'' ( 22.55) = 541.2 - 360
V'' ( 22.55) = 181.2 (minimum)
V'' ( 7.45) = 24(7.45) - 360
V'' ( 7.45) = 178.8 - 360
V'' ( 7.45) = -181.2 < 0 (maximum)
Therefore, x = 7.45 inch for the maximum volume.
The area of the square = x² = 7.45² = 55.5025 inch²
The maximum volume of a box is the highest volume the box can take.
The side length that ensures maximum volume is 22.55 inches or 7.45 inches.
The dimension of the plastic is:
[tex]\mathbf{Length = 42}[/tex]
[tex]\mathbf{Width = 48}[/tex]
Assume the side length cut-out is x
So, the dimension of the box is:
[tex]\mathbf{Length = 42 - 2x}[/tex]
[tex]\mathbf{Width = 48 - 2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, the volume of the box is:
[tex]\mathbf{Volume = Length \times Width \times Height}[/tex]
This gives;
[tex]\mathbf{Volume = (42 - 2x) \times (48 - 2x) \times x}[/tex]
Expand
[tex]\mathbf{Volume = (42 - 2x) \times (48x - 2x^2)}[/tex]
Expand
[tex]\mathbf{Volume = 2016x - 96x^2 - 84x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V' = 2016 - 192x - 168x + 12x^2}[/tex]
[tex]\mathbf{V' = 2016 -360x + 12x^2}[/tex]
Rewrite as:
[tex]\mathbf{V' = 12x^2 -360x + 2016}[/tex]
Set to 0
[tex]\mathbf{12x^2 -360x + 2016 = 0}[/tex]
Divide through by 12
[tex]\mathbf{x^2 -30x + 168 = 0}[/tex]
Using a calculator, the values of x are:
[tex]\mathbf{x = 22.55\ or\ x = 7.45}[/tex] ------ approximated to 2 decimal places
Hence, the side length that ensures maximum volume is 22.55 inches or 7.45 inches.
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find the image of (1,2) after a reflection about y=-1 followed by a reflection over y=1
Answer:
(1, 6).
Step-by-step explanation:
The reflection of the x coordinate of (1, 2) creates a point with y -coordinate
-1 - 3 = -4 while the x-coordinate remains 1.
The point (1, -4) is now reflected about y = 1, so -4 translates to 1 + 5 = 6. and x stays at 1.
Answer is (1, 6).
On a 40‐point test, Steve received an 80%. How many points did he receive on the test?
Answer:
Steve got 32 points
Step-by-step explanation:
Take the total score and multiply by the percentage received
40 * 80%
Change to decimal form
40 * .80
32
Steve got 32 points
Two functions are shown in the table below:
Function
1
2 3 4 5 6
f(x) = -x2 + 4x + 12
g(x) = x + 2
Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).
O x = 2
Ox= 3
O x = 5
O x = 6
Answer:
The correct option is x = 5
Please find the attached graph of the function
Step-by-step explanation:
The given functions are;
1) f(x) = -x² + 4·x + 12
2) g(x) = x + 2
The table of values are therefore;
x, f(x), g(x)
-7, -65, -5
-6, -48, -4
-5, -33, -3
-4, -20, -2
-3, -9, -1
-2, 0, 0
-1, 7, 1
0, 12, 2
1, 15, 3
2, 16, 4
3, 15, 5
4, 12, 6
5, 7, 7
6, 0, 8
Therefore the solution to the equation f(x) = g(x), occurs at x = -2 and x = 5, where f(x) = g(x) = 0 and 7 respectively
To verify, we have;
Equating the two functions gives;
f(x) = g(x)
-x² + 4·x + 12 = x + 2
-x² + 4·x + 12 - (x + 2) = 0
-x² + 3·x + 10 = 0
(x + 2)(x - 5) = 0
x = 5 or -2
The correct option is x = 5.
Answer:
C. x=5
Step-by-step explanation:
Please see attachments. You'll see that at the x=5 y will equal 7.
Hope this helps!
Write the following solution in interval notation:
Z < 20
Answer:
(-infinity, 20)
Step-by-step explanation:
the lower bound is negative infinity because no lower bound was given. The higher bound is 20, and it has a parentathesis because it is less than.
There are 8 tennis balls in a bag. Five of
the balls are yellow and the other 3 are
green What's the probability of pulling out
a green ball without looking? Write your
answer as a decimal.
Answer:
3/8 or a a decimal 0.375
N general, how do you find the theoretical and experimental probabilities of a favorable outcome if there are n equally likely outcomes and p of them are favorable?
Answer:
Binomial Distribution
Step-by-step explanation:
Unlike the normal or Gaussian probability distribution, the binomial distribution gives a curve representing the coefficient of the outcomes of every item in a sample or population.
the formula is ;
mean ( υ ) = n x p
where p is the probability and n is the population.
The probability density function which generates the probability curve;
Binomial Distribution function= f( k, n, p ) = [tex]\frac{n!}{k!(n-k)}[/tex] [tex]P^{k}[/tex][tex](1- P)^{(n -k)}[/tex]
I need answers ASAP! Thanks!
Step-by-step explanation:
43. P, U
44. 7
53. Airplanes can be traveling on different planes, one plane above the other. Cars on the same intersection are on the same plane.
55
a. You can choose (4 * 3 * 2)/(3 * 2) = 4 groups of 3 points in which order does not matter.
One of those combinations does not have K, so 3 combinations of the 4 have K.
p = 3/4
b. p = 1 since any three points are always coplanar.
If you are on a ship at sea navigating to a point that is 300 miles north and 400 miles west, find the distance from tour ship to that point. Show your work.
Answer:
[tex]\huge \boxed{\mathrm{500 \ miles}}[/tex]
Step-by-step explanation:
A right triangle is formed.
300 miles and 400 miles are the legs of the triangle.
We can apply Pythagorean theorem.
[tex]c=\sqrt{300^2 +400^2 }[/tex]
[tex]c=\sqrt{90000 +160000}[/tex]
[tex]c=\sqrt{250000}[/tex]
[tex]c=500[/tex]
Which lists all the integer solutions of the equation |x| = 7? –7 and 7 7 only 0 and 7 –7 only
Answer:
aa
Step-by-step explanation:
help me please? :( (;´༎ຶД༎ຶ`)(;´༎ຶД༎ຶ`)(;´༎ຶД༎ຶ`)
Answer:
a) 22:53
b)213 min
Step-by-step explanation:
c) 10 17 + 4 = 14 17
she has 2 minutes to spare
Answer:
she has 2 minutes to spare
Step-by-step explanation:
Use the spider tool located on page 1 of this activity to draw a 12-pointed star for the new logo. (Hint:If the spider rotates 360 degrees -- or 720 degrees or 1080 degrees -- she will be facing in the same direction in which she started. When the spider is done drawing, you want her to be facing in the same direction in which she started. She'll be making 12 rotations, all the same size, so each rotation must be some multiple of 360/12 = 30 degrees.)
Please help urgently. Been stuck on this problem for around 45 minutes now. Thanks.
PLEASE HELPPPPP! IT SHOULD BE EASY IF YOU'RE SMART ENOUGH
Answer:
each of the 12 turns is 150°
Step-by-step explanation:
If we number the points of the star 1–12, in order for the star to be symmetrical, each point must connect to two points symmetrically located around the centerline.
That is, point 1 may connect to points {2, 12} or {3, 11} or {4, 10}, or {5, 9} or {6, 8} or {7, 7}. For each of these connections, the angle made at the point of the "star" is, respectively, 150°, 120°, 90°, 60°, 30° or 0°. For these angles, the figure obtained will be ...
150° - dodecagon, a 12-sided figure
120° - hexagon
90° - square
60° - equilateral triangle
30° - 12-pointed star
0° - straight line
The two 12-pointed figures are shown in the attachment.
__
We suspect the star you're interested in is the one with points that are 30°. In order to have that point angle, the spider must make a turn of 180° -30° = 150°.
The spider will make 12 turns of 150°, for a total of 1800°, for a total of 5 full turns of 360°.
Answer:
Move the spide by 100 units and then turn the spider by 150 degrees. Repeat until you complete the star.
Step-by-step explanation:
people above are correct! I'm just making the steps as clear as possible for those who need it :)
What is the domain and range of the graph below? You must use either interval notation or set notation
Answer:
See below.
Step-by-step explanation:
The domain of a function is simply the span of x-values the graph will encompass.
And the range of a function is simply the span of y-values the graph will encompass.
Since the function is a quadratic, the domain is all real numbers. From the graph, the graph will continue to expand left and right. Therefore, the domain is all real numbers.
In interval notation, this is:
[tex](-\infty,\infty)[/tex]
And in set notation, this is:
[tex]\{x|x\in\mathbb{R}\}[/tex]
For the range, notice that the graph is going downwards. In other words, the graph has a maximum value. From the graph, we can see that this maximum value is at y=-4. The graph never reaches any value above -4. Therefore, our range is all numbers equal to or less than -4.
In interval notation, this is:
[tex](-\infty,-4][/tex]
We use brackets because we include the -4 in the solution set.
Also, note that we write the infinity first because the smallest number should be on the left. [-4, -∞) would not be correct.
And in set notation, this is:
[tex]\{y|y\in\mathbb{R},y\leq 4}\}[/tex]
I need help... this is from a textbook Jamal and Moshe began a business with a capital of S7500. If Jamal furnished half as much capital as Moshe, how much did each furnish?
Answer:
Moshe made $1875 and Jamal made $5625
Step-by-step explanation:
divide it in half, then divde Moshe's half in half because he only made half as much,
hope this helps and remember to mark brainliest
Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.
What are linear equations?Linear equations are an equation involving constants and variables, where variables are raised to a power of not greater than 1.
How do we solve the given question?We are informed that Jamal and Moshe starts a business with a capital of $7500. Also, we are informed that Jamal furnishes half as much capital as Moshe does.
We will try to make a linear equation and solve for it to find the capital furnished by each of them.
Let the capital furnished by Moshe be $x.
Jamal furnishes half as much capital as Moshe does.
∴ Capital furnished by Jamal = 1/2 of Moshe's capital = 1/2 of $x.
∴ Jamal's capital + Moshe's capital = Total capital furnished
We know the total capital is $7500.
∴ Our linear equation is: 1/2 of $x + $x = $7500.
Now we solve this equation in the following ways:
or, (1/2)*x + x = 7500
or, x/2 + x = 7500
or, (x + 2x)/2 = 7500
or, 3x/2 = 7500
or, x = (7500*2)/3 = 15000/3 = 5000.
∴ x = 5000.
∴ Moshe's share = $x = $5000
Jamal's share = 1/2 of $x = 1/2 of $5000 = $2500.
∴ Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.
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Eight plus the quotient of a number and 3 is −2
Answer:
The number is -30.
Step-by-step explanation:
Given that,
Eight plus the quotient of a number and 3 is −2 . We need to find the number.
So, putting given condition into mathematical expression. Let the number is x. So,
[tex]8+\dfrac{x}{3}=-2[/tex]
Subtracting on both sides,
[tex]8+\dfrac{x}{3}-8=-2-8\\\\\dfrac{x}{3}=-10[/tex]
Now cross multiplying, we get
x = -30
So, the number is -30.
108/40 in its simplest form
Answer:
27/10
Step-by-step explanation:
A calculator can tell you the fraction value is 2.7. As the ratio of integers, this is ...
108/40 = 27/10
1-22. Find the perimeter and area of each figure below.
Answer:
a) Area=9 units²
Perimeter=18 units
b) Area=28ft²
Perimeter=24ft
c) Area=120cm²
Perimeter=46cm
Step-by-step explanation:
a) Area=9 units²
Perimeter=18 units
b) Area=28ft² (7x4)
Perimeter=24ft (7+5+7+5)
c) Area=120cm² (15x8)
Perimeter=46cm (15+8+15+8)
please help second question
Answer:
I have not J.H.S 3 , because the questions look like some J.H.S 3 ,so please I am very sorry that I can't help u in this questions . Thanks
find the perimeter of the square of the length 8cm
Answer:
[tex] \boxed{ \boxed{ \bold{32 \: cm}}}[/tex]Step-by-step explanation:
Length ( L ) = 8 cm
Perimeter of square = 4 L
( where L is the side of the square )
Plug the value of length
⇒[tex] \sf{4 \times 8}[/tex]
Multiply the numbers
⇒[tex] \sf{32 }[/tex] cm
Hope I helped!
Best regards!
Answer:
[tex]\huge \boxed{\mathrm{32 \ cm}}[/tex]
Step-by-step explanation:
The formula to calculate the perimeter of a square is given as:
[tex]\sf Perimeter = 4 \times side \ length[/tex]
The side length of the square is 8 centimeters.
[tex]P=4 \times 8[/tex]
Solve for the perimeter.
[tex]P=32[/tex]
The perimeter of the square is 32 centimeters.
h²=p²+b² make b the subject of formula
Answer:
done same as before put value and do process like simplify
determine how many solutions each equation has. If one solution, state the value of x. +6+8=2−+14
A boat travels x miles per hour upstream on the Mississippi River. On the return trip, the boat travels 2 miles per hour faster. How far does the boat travel upstream?
Answer:
Distance = 17.5 miles
Step-by-step explanation:
Note.
Given question is not complete
Given:
Speed upstream = x
Time taken in upstream = 3.5 hour
Speed in return trip = (x+2)
Time taken in return trip = 2.5 hour
Computation:
Distance = speed × time
Distance = x (3.5)
Distance = 2.5 (x+2)
Distance = 2.5x + 5
So,
2.5x + 5 = 3.5 x
1.5 x = 5
x = 5 miles/hour
Distance = x (3.5)
Distance = 5 (3.5)
Distance = 17.5 miles
Convert 12 km/hr into m/min
Answer:
200 meters per minute
Step-by-step explanation:
12/60 since hr into minutes
0.2 x 1000 since km and meters
What is the approximate area of the circle shown below?
18cm
A. 28.3 cm2
B. 1018 cm2
C. 254 cm2
D. 56.5 cm2
Answer
the answer is 254 cm 2
Step-by-step explanation:
The area of the circle will be 254 square cm. Then the correct option is C.
What is the area of a circle?Let r be the diameter of the circle. Then the area of the circle will be
A = (π / 4)d² square units
The radius of the circle is 18 cm.
Then the area of the circle will be
A = (π / 4) x (18)²
A = 254.46 ≈ 254 square cm
Then the correct option is C.
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nancy was saving to buy a brand new iphone. she had already saved $78.00. the cost of the phone that she wanted was $899 plus 8.50% plus tax. every day that she works at the car wash she makes. $42. approximately how many more days does she need to work at the car wash to have enough money for her iphone?
Answer:
21.37 days.
Step-by-step explanation:
Step 1
Find the total amount Nancy is paying for her iPhone
Cost of the phone = $899
Tax = 8.50%
Amount paid for tax = 8.5% × 899
= 8.5/100 × 899
= $76.415
Total amount Nancy is paying = Tax + Cost of the phone
= $76.415 + $899
= $975.415
Step 2
We are told in the question that Nancy had already saved $78
Hence, Totally amount left for Nancy to buy her iPhone = $975.415 - $78
= $897.415
Step 3
Nancy works at a car wash and earns $42 every day.
The number of days left for her to work in the car wash in order to buy her phone is calculated as:
$42 = 1 day
$897.415 = x days
Cross Multiply
= $42 × x = $897.415 × 1 day
x = $897.415/$42
x = 21.36702381 days.
Approximately, x = 21.37 days
Therefore, Nancy has to work for 21.37 days at the car wash to have enough money for her iphone
Which geometric figures are drawn on the diagram? Check all that apply. Line segment C A Ray A C ∠ABC Circle C Ray B E ∠BCE Line segment A E
The geometric figures are drawn on the diagram are option A,B,D, and F.
What is the circle theorem?One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.
we know that
case a) ∠ABC
The geometric figure is not drawn in the diagram case is b) ∠BCE
The geometric figure is drawn in the diagram case is c) line segment CA
The geometric figure is drawn in the diagram case is d) Ray CA
The geometric figure is drawn in the diagram case is e) Circle C
The geometric figure is drawn in the diagram case is f) Ray BE
The geometric figure is not drawn in the diagram case is g) LIne segment AE
Hence, The geometric figures are drawn on the diagram are option A,B,D, and F.
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The solutions to the equation 2x^2+x-1=2 are x=-3/2 or x= blank
Answer:
Step-by-step explanation:
hello :
2x²+x-1=2 means : 2x²+x-3=0
a=2 b= 1 c= -3
the solutios are : x1 and x2 when the product is : x1×x2 = c/a
let x1 = -3/2 you have : (-3/2)×x2 = -3/2 so x2 = (-3/2)/(-3/2) = 1
The solutions to the equation 2x²+x-1=2 are x=-3/2 or x= 1
evaluate the expression
Answer:
[tex]12-[20-2(6^2\div3\times2^2)]=88[/tex]
Step-by-step explanation:
So we have the expression:
[tex]12-[20-2(6^2\div3\times2^2)][/tex]
Recall the order of operations or PEMDAS:
P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.
E: Within the parentheses, if exponents are present, do them before all other operations.
M/D: Multiplication and division next, whichever comes first.
A/S: Addition and subtraction next, whichever comes first.
(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)
Thus, we should do the operations inside the parentheses first. Therefore:
[tex]12-[20-2(6^2\div3\times2^2)][/tex]
The parentheses is:
[tex](6^2\div3\times2^2)[/tex]
Square the 6 and the 4:
[tex](36\div3\times4)[/tex]
Do the operations from left to right. 36 divided by 3 is 12. 12 times 4 is 48:
[tex](36\div3\times4)\\=(12\times4)\\=48[/tex]
Therefore, the original equation is now:
[tex]12-[20-2(6^2\div3\times2^2)]\\=12- [20-2(48)][/tex]
Multiply with the brackets:
[tex]=12-[20-96][/tex]
Subtract with the brackets:
[tex]=12-[-76][/tex]
Two negatives make a positive. Add:
[tex]=12+76=88[/tex]
Therefore:
[tex]12-[20-2(6^2\div3\times2^2)]=88[/tex]
Solve: p+30 = 80
HELP !
Answer:
p=50
Step-by-step explanation:
Subtract 30 from both sides and you have your answer
Answer: 50
Step-by-step explanation:
p + 30 = 80
subtract 30 from both sides to isolate the value of "p". subtracting 30 from positive 30 cancels that out. 80 minus 30 is 50. you are left with p = 50, so the value of p is 50.