Answer:
(a) The strip should be 5ft wide
(b) The strip around the outside field is 10ft wide.
Step-by-step explanation:
Given:
Length of the rectangular field, L= 200 ft
width of the rectangular field, w = 100 ft
Area of the rectangular field, A = 200ft x 100ft = 20000 ft^2
let the width of the strip = x
The strip around the outside field = 2x
If the field is increased by 15.5%
New area of the field = 1.155 x 20000 = 23,100 ft^2
The increase in area of the field = 3,100 ft
3,100 = New area of field - old area of the field
3100 = (200 + 2x)(100 + 2x) - 20000
3100 = 20000 + 400x 200x + 4x^2 - 20000
3100 = 600x + 4x^2
Divide through by 4
775 = 150x + x^2
x^2 + 150x - 775 = 0
Factorize
(x + 155)(x-5) = 0
x = 5 ft
The strip should be 5ft wide.
The strip around the outside field = 2 x 5 ft = 10 ft
Thus, the strip around the outside field is 10ft wide.
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
f⁻¹(-2)=3
f⁻¹(1)=0
Step-by-step explanation:
inverse function flips x any coordinate into y and x
Help me quick please
Answer:
if i counted correctly its 15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
Ok, so on this chart, each blue dot represents one person, so add up all the dots, and we get 15.
Write an explicit formula an, the nth term of the sequence 23,25,27
Answer:
2n+21
Step-by-step explanation:
rule = 2 so 2n
if n=1, 1x2=2 23-2=21
so +21
A jet flies from New York to Los Angeles , a distance of 2,450 miles, and then flies back. The speed from NY to LA was 140 mph faster than the speed from LA to NYIf the total time in the air was 12 hours, what was the jet's speed from NY to LA?
Answer:
Speed from NY to LA is 172 mph
Step-by-step explanation:
Let the jet’s speed from NY to LA be x mph.The speed form NY to LA would be (x-140) mph
Mathematically, we know that distance = speed * time
The total speed will x + x -140 = 2x-140
Now;
12(2x-140) = 2450
24x - 1680 = 2450
24x = 2450 + 1680
24x = 4130
x = 4130/24
x = 172.1 which is approximately 172 mph
What is the length of AC?
Answer:
A
Step-by-step explanation:
We can see that the two triangles are similar, and are in a 17:1 ration since 51/3 = 17
Now we can set up the equation
144-x = 17x
adding x to both sides we get
144 = 18x
dividing by 18 we get
x = 8
Now we plug x = 8 back in and get
144-8 = 136
the table shows ordered pairs of the function y=16+0.5x. Which ordered pair could be the missing values represented by (x,y)?
Answer:
(2,17)
Step-by-step explanation:
This is because x is the input and y is the output. All you have to do is create a value for x the substitute it in the equation. Next solve for y 0.5 times 2 is 1, plus 16 is 17. Then just put your values in an order pair.
Answer:
8,20
Step-by-step explanation:
An aeroplane covers a distance of 1500km in a certain time at a certain speed.After increasing the speed by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time. Find the previous speed of the aeroplane.
this is from quadratic equations CBSE grade 10
please answer ASAP
Answer: U = 600 m/s
Step-by-step explanation:
Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.
After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.
From the first statement
Speed = distance/ time
Distance = speed × time
1500 = Ut
Make t the subject of the formula
t = 1500/U ..... (1)
From the second statement
Distance = speed × time
1500 = (U + 100) × ( t - 0.5 )
Open the bracket
1500 = Ut - 0.5U + 100t - 50
Collect the like terms
1550 = Ut - 0.5U + 100t .... (2)
Substitutes equation 1 into 2
1550 = 1500U/U - 0.5U + 100(1500/U)
1550 = 1500 - 0.5U + 150000/U
1550 - 1500 = (150000 - 0.5U^2)/U
Cross multiply
50U = 150000 - 0.5U^2
0.5U^2 + 50U - 150000 = 0
Divide all by 0.5
U^2 + 100U - 300000 = 0
Using completing the square method
U^2 + 100U = 300000
U^2 + 100U + 50^2 = 300000 + 50^2
(U + 50)^2 = 302500
U + 50 = sqrt(302500)
U + 50 = +/-(550)
U = 50 + 550 or 50 - 550
U = 600 or - 500
Since U is of the same direction, it is
positive. Therefore, the previous speed of the aeroplane is 600 m/s
Answer:
500km/hr
Step-by-step explanation:
The formula for Speed (km/hr) = Distance / Time
Where S = Speed
D = Distance
T = Time
S = D/T
From the question, the aeroplane covered a distance of 1500 km
S = 1500/ T
ST = 1500
Time taken( T ) = 1500/S ......... Equation 1
We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time
This is expressed mathematically as:
The new speed =S + 100km/hr
The new Time taken = 1500/ S - 1/2....... Equation 2
Also since Time = Distance / Speed
The new Time taken also = 1500/ S + 100 ......... Equation 3
Step 1
We would simplify Equation 2:
Time = 1500/S - 1/2
Find the Lowest common multiple = 2
Time = (2 × 1500 - S )/ 2S
Time = 3000 - S / 2S ......... Equation 4
Step 2
Equate Equation 4 and 3 together since they are both equal to time taken
1500/ S + 100 = 3000 - S / 2S
We cross multiply
2S × 1500 = (S + 100) ( 3000 - S)
3000S = 3000S - S² + 300000 - 100S
3000S - 3000S + S² - 300000 + 100S = 0
S² + 100S - 300000 = 0
Step 3
We solve for S = Speed by using factorisation method.
S² + 100x - 300000 = 0
S² - 500S + 600S - 300000 = 0
(S² - 500S) + (600S - 300000) = 0
S(S - 500) + 600(S - 500) = 0
(S - 500) (S + 600) = 0
S - 500 = 0, S = 500
S + 600 = 0 , S = -600
Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr
what is the slope of the linear relationship shown in this table?
Answer:
-1/2
Step-by-step explanation:
Slope is change in x over change in y
so..
2-(-4)
over
-1-11
so...
-6/12 or -1/2
AC is included between
1
A
c
O A. ZA and ZC
O B. ZA and ZB
O C. AB and BC
O D. BC and AC
Since angle A and angle C forms side AC, AC is included between: A. ∠A and ∠C.
What is an Included Side?An included side is a side that is in between two angles in a triangle, where the rays of the angles overlap.
Thus, in triangle ABC, side AC lies in between angle A and angle C.
Therefore, since angle A and angle C forms side AC, AC is included between: A. ∠A and ∠C.
Learn more about included side on:
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Answer: A
Step-by-step explanation:
Use FOIL and the distributive property to derive (a-b)^3
Answer:
(a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]
Step-by-step explanation:
(a-b)^3 = (a-b)(a-b)(a-b)
According to the perfect cube formula (a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]
And there you have it! The perfect cube formula already solved your equation!
Plzzzzzz answer fast I need help
Answer:2,3,4
Step-by-step explanation:
what is the surface area of cylinder with base radius 4 and height 7? either enter an exact answer in term of pi or use for 3.14 for pi and enter your answer as a decimal
Answer:
Step-by-step explanation:
The surface area of the sides of the cylinder is A = 2πrh, where r is the radius and h is the height.
Here this comes out to A = 2π(4)(7) = 56 π units^2
If you also want the combined area of the two ends (top and bottom of the cylinder), here's the calculation:
A = 2πr² = 2π(4 units)² = 32π units²
Answer:
its 88 pi
Step-by-step explanation:
i did it on khan
A card is drawn at random from a standard pack of 52 playing cards. What is the probability of drawing a number greater than 5
Answer:36/52, simplified to 9/13 or 69.23%
Step-by-step explanation:
Need to pick 6, 7, 8, 9, 10, J, Q, K, A (9 cards per suit)
4 suits x 9 cards
36 cards
Answer:
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh sorry needed the points lol
Please answer !!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
B)
D)
Step-by-step explanation:
B) 1 and 13 are x intercepts so true
D) greatest profit is when price is 7; after that profit is getting smaller because function is decreasing
Which graph could represent the price of a fence selling at a unit rate of R dollars per foot?
Answer:
the middle one is the correct answer
Step-by-step explanation:
Answer:
the answer is (1,R)
Step-by-step explanation:
3. Shenker has 45 CDs.
He gives 10 CDs to his brother.
a) Write an equation you can solve to find how many CDs
Shenker has left.
b) Solve the equation.
Answer: The equation is 45-10=x the answer is 35
Step-by-step explanation: To make the equation you need to have and = sign so, we can do what he has (45) and subtract what he gives away (10) which would equal what he has left (x)
Answer:
45 (initial amount) - 10 (given to brother) = x (number of cd's left)
Equation:
45 - 10 = x
Answer:
35 CDs
Please help!
there were 6000 people at a football match
10% of them left 2 minutes before the end of the game to avoid traffic
50% of the rest left as soon as the match ended
a) how many people in total had left the football match when it ended?
b) what percentage of the original crowd was still there?
10%+50%=60%
60% of 6000=3600
a)3600 people had left the match when it ended
b)6000-3600=2400
40% of the crowd was still there
Aiden is putting a carpet on the floor of his bedroom. The carpet is 6 feet long and 7 feet wide. What is the total area of Aiden's carpet?
6 × 7 = 42 because area = length × width
The pyramid below has a rectangular base and E is directly above A. find the volume of the pyramid
if you answer i’ll give you brainlest
Step-by-step explanation:
According to the information given and the formula
base area= 9cm × 4cm = 36
ht= 10cm
(1/3) × 36cm × 10cm = 120
Therefore, the volume of pyramid with base dimensions of 9 cm by 4 cm and height 10 cm will be 120 cm³.
What is Pyramid?
A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle which is called a lateral face.
Given are the dimensions of the base of a rectangular pyramid as 9 cm by 4 cm. Length AE is equal to 10 cm.
The volume of a pyramid is given by -
V[P] = 1/3 x B[A] x height
where
B[A] is Base area.
Base area will be equal to Area of rectangle with dimensions 9 cm by 4 cm. Therefore, the base area will be - B[A] = 9 x 4 = 36 cm²
Now, the volume will be -
V[P] = 1/3 x 36 x 10
V[P] = 12 x 10
V[P] = 120 cm³
Therefore, the volume of pyramid with base dimensions of 9 cm by 4 cm and height 10 cm will be 120 cm³.
To solve more questions on Pyramid's, visit the link below-
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What is this problem
Answer:
[tex]m=A-\frac{2n}{Z}[/tex]
Step-by-step explanation:
Multiply by 2:
2n = Z(A - m)
Divide by Z:
[tex]\frac{2n}{Z} =A-m[/tex]
Subtract A:
[tex]-m=\frac{2n}{Z}-A[/tex]
Multiply by -1:
[tex]m=A-\frac{2n}{Z}[/tex]
Q1.work out the sum of the interior angles of a pentagon.
Q2.work out the size of one interior angle of a regular octagon.
Q3.work out the size of one exterior angle of a regular hexagon
Answer:
Question 1:
The sum of interior angles of a polygon can be found by the following formula:
(n-2) × 180
Where n is the no. of sides
A pentagon has 5 sides
So,
= (5-2) × 180
= (3) × 180
= 540 degrees
Question 2:
Since The sum of interior angles of a regular octagon is 1080 and the total interior angle are 8
So, Measure of interior angle = [tex]\frac{1080}{8}[/tex]
Measure of interior angle = 135 degrees
Question 3:
Since, one interior angle in a hexagon measures 120 degrees.
So,
The interior angle should be subtracted by 180 to get the exterior angle.
Exterior angle = 180-120
Exterior Angle = 60 degrees
I WILL GIVE YOU BRAINLIEST!!!!!
Answer:
Brainelist goes to me!
Step-by-step explanation:
-6/3 = -2
Answer:
B
Step-by-step explanation:
Given
[tex]\frac{3-x}{x-6}[/tex] ← substitute x = 9 into the expression
= [tex]\frac{3-9}{9-6}[/tex]
= [tex]\frac{-6}{3}[/tex]
= - 2 → B
Help PLEASE!
Two distinct number cubes are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?
Enter your answer, in simplest fraction form, in the box.
Answer:
The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3
P( E∪F) [tex]= \frac{24}{36}[/tex]
Step-by-step explanation:
Given Each number cube has sides numbered 1 through 6
Two distinct number cubes are rolled together
Total number of exhaustive cases n(S) = 36
Let 'E' be the event of getting sum is even
n(E) = {(1,3),(1,5), (2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4), (4,6),(5,1),(5,3),(5,5),(6,2),(6,4),(6,6)} = 17
[tex]P(E) = \frac{n(E)}{n(S)} = \frac{17}{36}[/tex]
Let 'F' be the event of getting sum that is a multiple of '3'
n(F) = {(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3),(6,6) = 12
[tex]P(F) = \frac{n(E)}{n(S)} = \frac{12}{36}[/tex]
n((E∩F) = {(2,4),(3,3),((4,2),(5,1),(6,6)} =5
[tex]P(En F) = \frac{n(En F)}{n(S)} = \frac{5}{36}[/tex]
The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3
P( E∪F) = P(E) + P(F) - P( E∩F)
[tex]\frac{17}{36} +\frac{12}{36} - \frac{5}{36} = \frac{24}{36}[/tex]
Convert the following time to 24-hour clock time. a) 5:00 pm b) 6:45 p.m c) 8:05 a.m d) 12:59 a.m III. Convert the following time to 12-hour clock time. a) 0400 hours b) 1500 hours c) 0010 hours d) 0240 hours
Answer:
5:00 pm -> 1700 hours
6:45 pm -> 1845 hours
8:05 am -> 0805 hours
12:59 am -> 0059 hours
0400 hours -> 4:00 am
1500 hours -> 3:00 pm
0010 hours -> 12:10 am
0240 hours -> 2:40 am
Step-by-step explanation:
12:xx am -> 00xx
all times from 1:00 am to 9:59 am stay nearly the same 0100 to 0959
all times 10:00 am to 12:59 pm stay nearly the same 1000 to 1259
all times 01:00pm to 12:00pm + 12 -> 1300 to 2400
Patty’s gymnastics class is 5/6 of an hour long. Patty practices five different skills and spends the same amount of time on each skill. How can you find how much time she spent on each skill? Explain how to use an area model to solve the problem.
Answer:
10 minutes
Step-by-step explanation:
5/6 of an hours is 50 min. Assume x is the time she spends on each skill.
5x=50
x=10
She spent 1/6 of an hour i.e. 10 minutes on each skill.
What is area model?In area model for multiplication a rectangle is used to represent multiplication between two quantities. Width and Length of the rectangle are assigned the numerical value of the two quantities being multiplied.
Solution
Let the number of skills be represented by the length of the rectangle in the figure.
Let the time spent(in hours), which is same for all skills, on each skill be represented by the width of the rectangle in the figure.
The area of the rectangle = length × width = 5 × t = 5t hours.
This area represents total time spent on five skills, which is 5/6 hours.
The smaller rectangles into which the whole rectangle is divided have area 1 × t = t hours. This represents time spent on one skill.
From the figure, such five smaller and equal rectangles constitutes the whole rectangle.
So, area of one smaller rectangle = Area of big rectangle / number of small rectangles = (5/6)/5 = 1/6 hours.
Since, this represents time spent on one skill. So, the required time is 1/6 hours.
She practice each skill for 1/6 of an hour.
Learn more about the area model here
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find,in terms of pie,the curved surface area of a cone with circular base diameter 10cm and height 12cm
Answer: 65π
Step-by-step explanation:
you can draw the cone to make it easier for you to understand.
to find the curved surface area of a cone, you multiply the base radius of the cone by pie. Then multiply your answer by the length of the side of the cone.
to do this you need the length of the side and the radius of the cone.
to find radius, divide the diameter by 2.
[tex]\frac{10}{2}[/tex] = 5
then use the right angle triangle in the cone to find the length of the side
use Pythagoras theorem which states that a² + b²= c²
a= 5, b= 12, c= x (length of side)
∴[tex]x^{2} 5^{2} + 12^2 =x^{2} \\25 + 144 = x^{2} \\169= x^{2} \\x=\sqrt{169} \\x= 13[/tex]
no that you have found the length
multiply the base radius by pie
which is:
5 ×π = 5π
then multiply this by the length of the side
5π × 13 = 65π
there you go!
hope it helps!
ran 42 miles per hour in 8 hours whats his miles per hour
Students in a political science course were asked to describe their politics as "Liberal", "Moderate", or "Conservative." Here are the results:
Politics
Liberal
Moderate
Conservative
Total
Female
40
34
14
88
Male
48
50
26
124
Total
88
84
40
212
Given that the student is male what is the probability that he considers himself to be a "Liberal"? Round your answer to three decimal places if necessary.
a.
0.226
c.
0.387
b.
0.415
d.
0.455
Please select the best answer from the choices provided
A
B
C
D
Answer:
Answer is a (A)
Step-by-step explanation:
Answer is a (A)
the lines shown below parallel. if the green line has a slope of -1, what is the slope of the red line
Answer:
-1
Step-by-step explanation:
Parallel lines have the same slope
If the green line has a slope of -1, the red line has a slope of -1
how can you use scientific notation to compare the mass of an electron to the mass of a proton
Answer:
explained below
Step-by-step explanation:
Because the electro has a smaller mass than the mass of the proton, scientific notation is usually used so that the numbers are on the same "scale" but if we see the scientific notation we may be able to identify which is greater and which is less, due to that the exponent is less the number is smaller and on the contrary if the number is greater, it is a larger number.
In the image I leave an example of the use of scientific notation in this area