Answer:
Option B.
Step-by-step explanation:
The measure of cage is 90 feet by 40 feet.
Length of rope [tex]=40\sqrt{2}[/tex] foot
It is clear that, length of rope is greater than one side of cage and raw a line which divides the cage in two parts as shown in below figure.
We need to find the shaded area.
By Pythagoras theorem:
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex](40\sqrt{2})^2=(40)^2+perpendicular^2[/tex]
[tex]3200=1600+perpendicular^2[/tex]
[tex]3200-1600=perpendicular^2[/tex]
[tex]1600=perpendicular^2[/tex]
[tex]40=perpendicular[/tex]
So, it is a square.
From the figure it is clear that the shaded area contains 1/8th part of circle are half part of square.
Area of circle is
[tex]A_1=\pi r^2[/tex]
[tex]A_1=\pi (40\sqrt{2})^2[/tex]
[tex]A_1=3200\pi[/tex]
Area of square is
[tex]A_2=a^2[/tex]
[tex]A_2=(40)^2[/tex]
[tex]A_2=1600[/tex]
Area of shaded portion is
[tex]A=\dfrac{A_1}{8}+\dfrac{A_2}{2}[/tex]
[tex]A=\dfrac{3200\pi}{8}+\dfrac{1600}{2}[/tex]
[tex]A=400\pi+800[/tex]
[tex]A=400(\pi+2)[/tex]
The required area is [tex]400(\pi+2)[/tex] sq. ft.
Therefore, the correct option is B.
7x-y= 22
4x + 2y = 10
can someone help plz?
Answer:
x = 3
y = -1
Step-by-step explanation:
Based on the fact that our have two variables and two equations, I'm going to assume you are trying to find the values of x and y.
For these two equations, let's first find the value of x using the equation elimination method.
We're going to eliminate the y variable by multiplying the first equation by 2 and then adding that new equation to the second equation.
7x - y = 22 ==> 14x - 2y = 44
4x + 2y + (14x - 2y) = 10 + (44)
18x + 0y = 54
x = 3
Now we plug the value of x back into one of the equations to find the value of y.
7x - y = 22
7(3) - y = 22
-y = 22 - 21
y = -1
So our values are as follows:
x = 3
y = -1
Cheers.
Someone pls help thank you sm ..
Answer:
15 lawns
Step-by-step explanation:
The Xbox costs $400 and his parents gave him $100. He needs to earn $300 more. $20 each lawn so $100 for 5 lawns. 5 lawns times three.
Xbox cost =400
Daniel's money =100
Xbox cost - Daniel money=300
yard cost =20
therefore 400 -100 /20
Daniel's need 15 yards to get the xbox
5 diferrent representations of the value 3
Answer:
3
= 15/5
= [tex]\sqrt[3]{27}[/tex]
= 1.5*2
= 3/1
= 3*1
= 3¹
= 1/3⁻¹
= 3⁴ / 3³
= 3⁵ * 3⁻⁴
A stone is thrown downward straightly its speed at speed of 20 second what and it reaches the ground at 40 metre second what will be the height of building
Answer:
[tex]\Huge \boxed{\mathrm{61.22 \ m}}[/tex]
Step-by-step explanation:
A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)
The initial velocity ⇒ 20 m/s
The final velocity ⇒ 40 m/s
We can apply a formula to solve for the height of the building.
[tex](V_f)2 - (V_i)^2 =2gh[/tex]
[tex]V_f = \sf final \ velocity \ (m/s)[/tex]
[tex]V_i = \sf initial \ velocity \ (m /s)[/tex]
[tex]g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )[/tex]
[tex]h = \sf height \ (m)[/tex]
Plugging in the values.
Acceleration due to gravity is 9.8 m/s².
[tex](40)^2 - (20)^2 =2(9.8)h[/tex]
Solve for [tex]h[/tex].
[tex]1600 - 400 =19.6h[/tex]
[tex]1200 =19.6h[/tex]
[tex]\displaystyle h=\frac{1200}{19.6}[/tex]
[tex]h= 61.22449[/tex]
The height of the building is 61.22 meters.
Consider line A which is defined by the equation:
y=5/6x-5/2
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answer:
y = -6/5x +12/5distance from P to A: (66√61)/61 ≈ 8.4504midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
__
b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
__
c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
Why the answer question now correct
Answer:
461.58 in²
Step-by-step explanation:
The surface area (A) is calculated as
A = area of base + area of curved surface
= πr² + πrl ( r is the radius of base and l is slant height )
= 3.14 × 7² + 3.14 × 7 × 14
= 3.14 × 49 + 3.14 × 98
= 3.14(49 + 98)
= 3.14 ×147
= 461.58 in²
a broker gets rs 20000 as commission from sale of a piece of land which costs rs 8000000. Find the rate of commission.
Answer:
0.25%
Step-by-step explanation:
Rate of commission
= (commission*100)/cost of land
=( 20000*100)/8000000
= 2000000/8000000
=2/8
= 0.25%
To get from home to work, Felix can either take a bike path through the rectangular park or ride his bike along two sides of the park. How much farther would Felix travel by riding along two sides of the park than he would by taking the path through the park?
Answer:
c=5.9/6(G)
Step-by-step explanation:
first find the 2 distances.
a^2+b^2=c^2 c=2.4+.7
7^2+2.4^2=c^2 c=3.1
.49+5.85=c^2
c^2=6.34
c=√6.34
c=2.51.
next subtract the two distances to find the difference.
c=2.51-3.1
c=.59
so the distance would be .59 which can be rounded up to .60/G
explanation on how I knew the answer.
Im reviewing for the math 8th grade staar.
A line passes (-8,-2) and has a slope of 5/4. Write an equation in Ax + By=C
Answer:
5x-4y = -32
Step-by-step explanation:
First write the equation in point slope form
y-y1 = m(x-x1)
y - -2 = 5/4 ( x- -8)
y+2 = 5/4 (x+8)
Multiply each side by 4 to clear the fraction
4( y+2 )= 4*5/4 (x+8)
4y +8 = 5(x+8)
4y+8 = 5x+40
Subtract 4y from each side
8 = 5x-4y +40
Subtract 40 from each side
-32 = 5x-4y
5x-4y = -32
Answer:
The answer is
5x - 4y = -32Step-by-step explanation:
To write an equation of a line given a point and slope use the formula
y - y1 = m( x - x1)
where
m is the slope
( x1 , y1) is the point
From the question
slope = 5/4
point (-8 , -2)
So the equation of the line is
[tex]y + 2 = \frac{5}{4} (x + 8)[/tex]Multiply through by 4
4y + 8 = 5( x + 8)
4y + 8 = 5x + 40
5x - 4y = 8 - 40
We have the final answer as
5x - 4y = -32Hope this helps you
The circle shown below is a unit circle, where ∠a=π/3 and the radius of the circle is 1.
Answer:
Step-by-step explanation:
find the exterior angle of a triangle whose interior opposite angles are 43 degree and 27 degree
Answer:
[tex]\huge\boxed{Exterior\ angle = 70\°}[/tex]
Step-by-step explanation:
The measure of exterior angle is equal to the sum of opposite interior angles.
So,
Exterior angle = 43+27
Exterior angle = 70°
Arnold made the following grades on his quizzes and assignments: 80, 92, 88, 90, 75, 38, 92, 95 2. Arnold wants to present his scores as advantageously as possible. Should he use the mean or the median of this data set? What other strategies could he employ to yield a more favorable measure of center?
Answer:
Step-by-step explanation:
If he were to find the mean then he would need to add all the numbers up and divide by the number of numbers. The answer of this would 69.1
If you find the median you would need to put the numbers in order,
2, 38, 75, 80, 88, 90, 92, 92, 95, then find the middle which would be 88.
So the better option would be finding the median. I think that this would be the best way to get the the most favorable measure of center.
I hope this helps.
First Question The following table shows the length and width of a rectangle: Length Width Rectangle A 4x + 5 3x − 2 Which expression is the result of the perimeter of rectangle A and demonstrates the closure property? A.14x + 6; the answer is a polynomial B.14x + 6; the answer may or may not be a polynomial C.2x + 6; the answer is a polynomial D.2x + 6; the answer may or may not be a polynomial
Answer: A.14x + 6; the answer is a polynomial
Step-by-step explanation:
Since all of the variables have integer exponents that are positive this is a polynomial.
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6
Step-by-step explanation:
We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.
n/5 ≥ 11
Multiply by 5 on both sides.
n ≥ 55
Now, let's do the second one.
-3y ≤ -18
Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)
y ≥ 6
Without using a calculator, convert the fraction to a decimal
Answer:
what's the fraction though?
If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answer:
7800 brownies will be produced in an 8 hour shift
Step-by-step explanation:
Given : The production rate is 975 brownies per hour at a bakery
To Find : how many brownies will be produced in an 8 hour shift?
Solution:
No. of brownies produced in 1 hour = 975
We are supposed to find No. of brownies produced in 8 hour
No. of brownies produced in 8 hour = 975 x 8=7800
Hence 7800 brownies will be produced in an 8 hour shift
Hope this helps ФωФ
If the lengths of the legs of a right triangle are 3 and √10, what is the length of the hypotenuse?
Answer:
[tex]\sqrt{19}[/tex]
Step-by-step explanation:
We can use the pythagoren theorm (A^2 + B^2 = C^2) for right triangles, C being the hypotenuse.
3^2 + 10 = C^2
19 = C^2
C = [tex]\sqrt{19}[/tex]
The required length of the hypotenuse of triangle is √19.
Legs of right angle triangle is √10 and 3. Hypotenuse to be determine.
Legs in right triangle refers to the perpendicular and base.
Hypotenuse = [tex]\sqrt{perpendicular^2+base^2}[/tex]
= [tex]\sqrt{3^2+\sqrt{10}^2 }[/tex]
= [tex]\sqrt{19}[/tex]
Thus, the required length of the hypotenuse of triangle is √19.
Learn more about legs in triangle here:
https://brainly.com/question/344286
#SPJ5
A family has four children. What is the probability that two children are girls and two are boys? Assume the the probability of having a boy (or a girl) is 50%.
Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.
The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.
The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.
What the correct answer
Answer:
653.12 ft²
Step-by-step explanation:
2πrh + 2πr²
2(3.14)(8)(5) + 2(3.14)(8)²
251.2 + ²401.92 = 653.12
Step-by-step explanation:
Here,
radius of a cylinder (r)= 8 ft.
height (h)= 5 ft.
now,
area of a cylinder (a)= 2.pi.r(r+h)
now, putting the values we get,
a = 2×3.14×8(8+5)
after simplification we get,
Area of cylinder is 653.12 sq.ft.
Hope it helps....
Paul travels from Rye to Eston at an average speed of 90 km/h He travels for T hours.
Mary makes the same journey at an average speed of 70 km/h She travels for 1 hour longer than Paul.
Work out the value of T .
Answer:
3.5 hours
Step-by-step explanation:
Paul:
Speed = 90 km/hTime= T hoursDistance = 90T kmMary:
Speed = 70 km/hTime = T + 1 hoursDistance = 70(T+1) kmSince the distance is same, we have:
90T = 70(T+1)90T= 70T + 7090T - 70T = 7020T= 70T= 70/20T= 3.5 hoursAnswer: Paul's travel took 3.5 hours
All points of the step function f(x) are graphed
What is the domain of f(x)?
O {x4
O {x] -3 < x 54}
O {x|1 < x 54}
O {x|2
Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?
To get the area simply multiply the length by the width.
(3x^2+5x+10)(x^2-3x-1) = 3x^4 - 4x^3 - 8x^2 - 35x - 10
Answer:
the answer is A
Step-by-step explanation:
got it right on edge
Which of the functions below is not exponential or logarithmic?
Answer:
f(x) = 5x² + 3
Step-by-step explanation:
Exponential Function: [tex]a(b)^x+c[/tex]
Logarithmic Function: [tex]alog_bx+c[/tex]
5x² + 3 is a quadratic function. Therefore, it is not an exponential or logarithmic function and is incorrect.
log₅x is a logarithmic function. Therefore, it is correct.
5log₃x + 3 is a logarithmic function. Therefore, it is correct.
5ˣ + 3 is an exponential function. Therefore it is correct.
A ship sails 95 km on a bearing of 140 degrees,than further on 102km on a bearing of 260degrees,and than returns directly to its starting point.Find the length and bearing of the return journey
Answer:
1. 98.7 km
2. 303.5 degree
Step-by-step explanation:
Using the alternate angle, the angle at B will be 50 + 10 = 60 degree.
To calculate the length AC of the returning journey, use cosine formula to calculate it.
To find the bearing of the returning journey, use sine rule to calculate it.
Please find the attached file for the solution
WILL GIVE BRAINLIEST!!!!!! Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. Part B: The length of rod PR is adjusted to 17 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work.
A) Here, We'll use "Pythagoras Theorem" which tells:
a² + b² = c²
So, PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
In short, Your Answer would be 16.64 Feet
B) Again, Use the Pythagoras Theorem,
c² - a² = b²
18² - 14² = b²
b² = 324 - 196
b = √128
b = 11.31
In short, Your Answer would be 11.31 Feet
Part A: Using the Pythagorean Theorem. a^2 + b^2 = c^2
PQ^2 + QR^2 = PR^2 (The rods make a right triangle, where PR would be the hypotenuse, and QR and PQ would be legs a and b.)
14^2 + 9^2 = PR^2
196 + 81 = PR^2
Square root of 277 = PR
16.64 = PR
So, the hypotenuse would be equal to 16.64 ft.
Part B: Using the Pythagorean Theorem. a^2 + b^2 = c^2
PR^2 - PQ^2 = QR^2 (Trying to find the height of QR this time, not the hypotenuse, since we know what it is already. Subtracting the value of leg a from the hypotenuse will give us the value of leg b, QR.)
18^2 - 14^2 = QR^2
324 - 196 = QR^2
Square root of 128 = QR
So, the new height of QR would be 11.31 ft.
Astrid is in charge of building a new fleet of ships. Each ship requires 40 4040 tons of wood, and accommodates 300 300300 sailors. She receives a delivery of 4 44 tons of wood each day. The deliveries can continue for 100 100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 21002100 sailors.
Answer:
10 ships
Step-by-step explanation:
did it on Khan and
There can be many ways to solve this problem. Here, we will do this by thinking about units.
Let's say that Astrid can build
x
ships
xshipsx, start text, s, h, i, p, s, end text if she receives deliveries of wood for the maximum possible number of days, which is
100
days
100days100, start text, d, a, y, s, end text. How can we relate these two quantities with an equation?
100
days
⋅
y
ships
day
=
x
ships
100days⋅y
day
ships
=xships
So in order to find the number of ships
x
xx, we need to figure out the value of
y
yy, which is the rate of ships per day.
Hint #22 / 4
Notice what other information we are given:
40
tons
ship
40
ship
tons
40, start fraction, start text, t, o, n, s, end text, divided by, start text, s, h, i, p, end text, end fraction
300
sailors
ship
300
ship
sailors
300, start fraction, start text, s, a, i, l, o, r, s, end text, divided by, start text, s, h, i, p, end text, end fraction
4
tons
day
4
day
tons
4, start fraction, start text, t, o, n, s, end text, divided by, start text, d, a, y, end text, end fraction
2100
sailors
2100sailors2100, start text, s, a, i, l, o, r, s, end text
Which of these quantities can help us calculate a rate whose units are
ships
day
day
ships
start fraction, start text, s, h, i, p, s, end text, divided by, start text, d, a, y, end text, end fraction?
Hint #33 / 4
We can combine the following quantities:
4
tons
day
40
tons
ship
=
4
40
tons
day
⋅
ships
ton
=
0.1
ships
day
=
40
ship
tons
4
day
tons
=
40
4
day
tons
⋅
ton
ships
=0.1
day
ships
Now we can plug that in the original equation:
100
days
⋅
0.1
ships
day
=
x
ships
10
ships
=
x
ships
100days⋅0.1
day
ships
10ships
=xships
=xships
Hint #44 / 4
In conclusion, assuming Astrid receives the maximum possible amount of wood, she can build
10
1010 ships.
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help ill give brainly ;))
Answer:
See explanation
Step-by-step explanation:
a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes
b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes
c) 6:50 - 4:30 = 2 hours and 20 minutes
d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes
Answer:
a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes
b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes
c) 6:50 - 4:30 = 2 hours and 20 minutes
d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes
Step-by-step explanation:
Find the value of |5| - 4(32 - 2).
Answer:
115
Step-by-step explanation:
5 - 4(30)
5 - 120
115
Answer:
-115
Step-by-step explanation:
Since anything in between those two lines (absolute value) always comes out positive and the five inside there is already positive, we don't need to worry about it.
First let's look at what's inside the parenthesis.
5 - 4(32 - 2)
= 5 - 4(30)
Next, we'd multiply. (I'm going by PEMDAS)
5 - 120
Now that we've done that we just need to subtract. Generally, 120-5=115, so, we just need to make it negative.
Hope this helps!! <3 :)
Jack bought a car for $50,000. He spent $5000 on repairs. He sold the car at a profit of $5000. At what price did he sell the car.
Answer:$60,000
Step-by-step explanation:
If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because
60,000 - 55,000 = 5,000
using the property of squares find the value of the following 24 square - 23 square
Answer:
47
Step-by-step explanation:
Using the follwing property
[tex]x^{2} -y^2=(x+y)(x-y)[/tex]
in which x=24 and y=23
so
[tex]24^2-23^2=(24-23)(24+23)\\=1(47)\\=47[/tex]
Answer:
47
Step-by-step explanation:
Lets say 24 is x and 23 is y.
the equation would be x^2 - y^2
this is = to (x-y)(x+y)
substitute the numbers in
(24-23)(24+23)
which simplifies to
(1)(47)
which equals 47