The map shows two biking trails that meet at a park, located at the coordinate (1, 9). Each unit on the map represents 0.5 mile.How many miles longer is Trail A than Trail B?
Answers
The length of the trails can be determined be using a formula related to
Pythagorean theorem, which makes use of the rise and run of a trail.
The number of miles longer Trail A is than Trail B is 4 milesReasons:
The location of the park = (1, 9)
The stating point of Trail A = (-7, -6)
Starting point of Trail B = (6, -3)
The length of a trail is adapted from the formula for the distance between points which is a form of Pythagorean theorem as follows;
[tex]Length \ of \ a \ trail, \ L = \mathbf{\sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}}[/tex]
Therefore;
[tex]Length \ of \ trail, \ A = \sqrt{\left (1-(-7) \right )^{2}+\left (9-(-6) \right )^{2}} = \mathbf{17}[/tex]
[tex]Length \ of \ trail, \ B = \sqrt{\left (1-6 \right )^{2}+\left (9-(-3) \right )^{2}} = \mathbf{13}[/tex]
The difference between the lengths of the trails = 17 mi - 13 mi = 4 miles
Therefore;
Trail A is 4 miles longer than Trail B
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Related Questions
using the letters from the word equation, how many 5-letter patterns can be formed in which q isfollowed immediately by u?
Answers
Using the arrangements formula, it is found that there are 720 words that can be formed.
The number of possible arrangements of n elements is the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem:
The non-qu letters of the word equation will be arranged in 5 positions.The "qu" can be positioned in 6 ways(letters 1-2 to letters 6-7), hence:[tex]T = 6 \times 5! = 6! = 720[/tex]
There are 720 words that can be formed.
To learn more about the arrangements formula, you can take a look at https://brainly.com/question/24648661
3 ½ pints = ___ cups
Answers
Answer:
8.40665 cups
Step-by-step explanation:
hope this is helpful!
Joseph invests money in an account paying a simple interest of 2.9% per year. If he invests $60 and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?
Answers
It costs Joseph 2.9% per year in interest.
This is a one step process, do 60 (money he invests) x .029 (interest) and you should get $1.74.
Add $1.74 + $60, and your answer is $61.74.
Thank you and I hope this helped you.
Fred is 5 inches shorter than the quotient of Rick’s height and 4. let r represent Rick’s height. Write an expression that represents Fred’s height
Answers
Answer:
[tex] \frac{r}{4} - 5[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
The expression till now
[tex]\\ \sf{:}\Rrightarrow \dfrac{r}{4}[/tex]
But we need the expression for five less than the quotient
[tex]\\ \sf{:}\Rrightarrow \dfrac{r}{4}-5[/tex]
What are the outliers for 7,1,9,9,12,25,9,7,7,
Answers
Each big square below represents one whole.
What percent is represented by the shaded area?
Answers
Answer:
the frist one
Step-by-step explanation:
hope it helps
Josue broke a cell sample into 12 batches, each weighing 6.9 x 10 ^-10
grams. How much did the original sample weigh? Use scientific notation to express your answer.
Answers
Using proportions, it is found that the original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
This question is solved by proportions, using a rule of three.The weight of 1 batch, in grams, is of [tex]6.9 \times 10^{-10}[/tex]. How much do the sample of 12 batches weigh?The rule of three is:
1 batch - [tex]6.9 \times 10^{-10}[/tex] grams.
12 batches - x grams
Applying cross multiplication:
[tex]x = 12 \times 6.9 \times 10^{-10} = 82.8 \times 10^{-10}[/tex]
Applying scientific notation:
[tex]8.28 \times 10^{-9}[/tex]
The original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
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Lizzy wants to solve the equation 6(2x + 1) = 4x – 5. Which step would be an appropriate first step for Lizzy to take to solve for x?
Answers
Answer:
distribute parenthesis
Step-by-step explanation:
6(2x + 1) = 4x - 5 ← distribute parenthesis on left side
12x + 6 = 4x - 5 ( subtract 4x from both sides )
8x + 6 = - 5 ( subtract 6 from both sides )
8x = - 11 ( divide both sides by 8 )
x = - [tex]\frac{11}{8}[/tex]
solve the equation below.
2/3 (9x - 12) - 6x
Answers
48
Step-by-step explanation:
idek I just need tge points so don't put what I put
Answer:
-8
Step-by-step explanation:
1. Simplify
2/3 (9x - 12) -6x —-> 2 (9x - 12) -6x/3
2. Distribute
2(9−12)/3 -6x
18x - 24/3 -6x
3. Find common denominator
18 −24/3 + 3(-6)x/3
4. Combine fractions with common denominator
18−24+3(−6)/3
5. Multiply the numbers
18−24+3(−6)/3 ——> 18−24−18/3
6. Combine like terms
18−24−18/3 ——> -24/3
7. Cancel terms that are in both the numerator and denominator
−24/3
−8
Hope it helps! Have a great day! :D
Find the volume of the figure below.
Answers
Answer:
0.6
Step-by-step explanation:
10ft of object and 6ft of ground side
What is 100 plus 300??????
Answers
Answer:
The answer is 400
Step-by-step explanation:
...........
Answer:
the answer is 400 darlin
Step-by-step explanation:
31. One serving of party drink is comprised of 3oz of syrup, 4oz of water, and 3oz of apple juice. If a large bowl of the drink contains 237oz of apple juice, how much of the total drink is in the bowl
Answers
Answer:
790 oz
Step-by-step explanation:
Ratio:
3oz syrup : 4oz water : 3oz apple juice: 1 serving: 10oz total mixture
We know there is 10oz total mixture because 3oz of syrup + 4oz of water + 3oz of apple juice = 10oz total mixture
We want to find
237oz apple juice: ?oz total mixture
To do this, we can multiply the ratio
3oz apple juice: 10oz total mixture by 237/3, because 237/3 * 3 = 237, getting us to 237oz apple juice on one side and maintaining the ratio so that we can find the total mixture amount, so we have
237oz apple juice: 10*237/3 oz total mixture = 10*79 = 790 oz
The blueprint for Moreno's living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new blueprint? (The width is 8)
Answers
List all congruent angles and write a proportion that relates the corresponding side
Answers
Proportion of corresponding side is FH/JH = HG/HK = FG/JK.
What are congruent triangles?Congruent triangles are triangles that are the same size and shape in every way. The sign for congruent is ≅ . Two triangles are considered to be congruent if the measurements of one triangle's three sides and three angles are the same as those of another triangle's sides and three angles.
Given triangles are similar ΔFGH ∼ ΔJKH
We can make the angles of this statement that correspond to each other congruent. We can then write a proportion that relates the corresponding sides to one another because the sides of similar triangles are proportional to one another.
so angles ∠GFH ≅ KJH; ∠GHF ≅ ∠KHJ; ∠HFG ≅ ∠HJK
and proportion of corresponding side is FH/JH = HG/HK = FG/JK.
Hence the proportion that relates the corresponding side are FH/JH = HG/HK = FG/JK.
Learn more about congruent triangles;
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Change one digit from the number 238882 so that it is divisible by 3 not not divisible by 2
Answers
Answer:
238882 -> 238881
Step-by-step explanation:
To make it not divisable by 2, you have to change the rightmost digit.
Simply divide the number by 3, round it, then multiply it by 3 again.
a point f(–3, 1) is translated along the vector ⟨5, –1⟩.what are the coordinates of the image f′ ?
Answers
Hope this helped :)
How do you add 11/11 + 23/45? And what is the answer? Explain how you got that answer
Answers
Answer:
90
Step-by-step explanation:
first you do 11 + 11 =22
23+45=68
now im postitive you add 68 and 22 and get you final answer which is ...
90
Answer:
1 23/45
Step-by-step explanation:
Start by multiplying numerators and denominators to get the LCD in all fraction denominators
=11×45/11×45+23×11/45×11
Then rewriting the equation with the equivalent fractions
=495/495+253/495
With like denominators we can operate on just the numerators
=495+253/495
=748/495
Simplifying the answer
=68/45
=68/45
=1 23/45
On a coordinate plane, 2 lines are parallel to each other.This system of equations has .
PLS HELP
Answers
Answer:
No solutions
Step-by-step explanation:
The lines never meet, there for have no intersection point leading to no solution for the system of equations.
Hope that helps
What is the measure of each angle of a regular heptagon? If necessary, round to the
nearest tenth.
Answers
Answer:
Umer F. 51.43∘ is the measure of each exterior angle in a regular heptagon.
To round a number to the nearest tenth , look at the next place value to the right (the hundredths). If it's 4 or less, just remove all the digits to the right. If it's 5 or greater, add 1 to the digit in the tenths place, and then remove all the digits to the right.
Answer this .i will make you brainliest
Answers
[tex]\huge{\underline{\underline{\boxed{\sf{\purple{ǫᴜᴇsᴛɪᴏɴ}}}}}}[/tex]
(8) An aeroplane takes off from Dubai located in the +4 time zone at 13:00. It arrives in Manila in Philippines, located in the +8 time zone at 20:00.(1) Find the time in Manila when the aeroplane departsfrom Dubai.(ii) Find the time duration of the flight.(iii) What is the time in Dubai when the aeroplane arrives in Manila?[tex]\huge{\underline{\underline{\boxed{\sf{\ref{Answer}}}}}}[/tex]
(i)17.00(ii)3 hours(iii) 16.00[tex]\large\huge\green{\sf{♥ Explanation♥}}[/tex]
Dubai located +4 zone, takes off at 13.00,∴Hence, at standard it is 13.00-4 =99.00 STD talk
off reached at Manila +8 Zone at 20.00
∴Hence at standard & 2000 -8
reached.⇒ 12.00 STD
Hence time of flight was = 3 hours.(i) Time at Manila, whicle Plane de parts
12-3+8 ⇒9+8 → 17.00
(ii) duration = 3 hours.
(iii) in dubai 13.00 + 3 = 16,00
_____________________
Ans
i)17.0.0 (ii) 3 hours (iii) 16.00
________________________
♕ hence we done:) xD
8-kg lead brick falls from a height of 1.6 m.
(a) Find its momentum as it reaches the ground.
Ikg-m/s
(b) What Impulse is needed to bring the brick to rest?
N-s
(c) The brick falls onto a carpet, 2.0 cm thick. Assuming the force stopping it is constant, find the average force the carpet exerts on the brick
N
(d) If the brick falls onto a 6,0 cm foam rubber pad, what constant force is needed to bring it to rest?
Answers
The magnitude of the impulse needed to bring the brick to rest is given by the initial momentum of the brick.
The correct responses are;
(a) 44.8 kg·m/s(b) 44.8 N·s(c) 6,278.4 N(d) 2,092.8 NReasons:
The velocity of the brick as it reaches the ground is given by the formula;
v² = 2·g·h
v = √(2·g·h)
Where;
h = The height of the brick, h = 1.6 m
g = The acceleration due to gravity ≈ 9.81 m/s²
Therefore;
v ≈ √(2 × 9.81 m/s² × 1.6 m) ≈ 5.6 m/s
(a) Momentum = Mass × Velocity
The momentum of the brick = 5.6 m/s × 8 kg = 44.8 kg·m/s
(b) Impulse = Force × Δt = Mass × Δv
Mass × Δv = 8 kg × (5.6 m/s - 0) = 44.8 kg·m/s = 44.8 N·s
Therefore, the impulse = 44.8 N·s
(c) The distance over which the carpet stops the brick = 2.0 cm = 0.02 m
Initial energy in the brick, E = m·g·h
Which gives;
E = 8 kg × 9.81 m/s² × 1.6 m = 125.568 J
Energy = Force × Distance
[tex]\displaystyle Force \ carpet \ exerts \ on \ brick, \ F = \frac{125.568 \, J}{0.02 \, m} = \mathbf{ 6,278.4 \, N}[/tex]
The average force the carpet exerts, F = 6,278.4 N
(d) If the brick falls on a foam which is 6.0 cm (thickness), we have;
Distance = 6.0 cm = 0.06 m
Therefore;
[tex]\displaystyle Force, \, F = \frac{125.568 \, J}{0.06 \, m} = \mathbf{2,092.8 \, N}[/tex]
The constant force needed to bring the brick to rest is, F ≈ 2,092.8 N
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Please show any steps you used to solve the equation!
Solve the equation [tex]sec(theta)=2 \\0\leq theta\ \textless \ 2\pi[/tex]
I'll mark brainliest if correct!
Answers
sec(θ) = 2
By definition of secant,
cos(θ) = 1/2
Solve for θ :
θ = arccos(1/2) + 2nπ or θ = -arccos(1/2) + 2nπ
(where n is any integer)
θ = π/3 + 2nπ or θ = -π/3 + 2nπ
We get two solutions in the interval 0 ≤ θ < 2π :
θ = π/3 or θ = 5π/3
Which of the following is in the range of the function based on the input-output table below?
Answers
Answer:
A.
Step-by-step explanation:
The answer is A because first:
1. we are looking for y so B and D are off the table
2. It goes from least to greatest so C is also gone
3. You are left with A
Answer:
A
Step-by-step explanation:
The range is the y value.
In this table the y value is pay per month.
HURRY PLS
What is the equation of this line?
y=2x-3
y= -1/2x-3
y= -2x-3
y=1/2x-3
Answers
(7g+2)(5g+4)=
help please !
Answers
Answer:
35g^2+38g+8
Step-by-step explanation:
(7g+2)(5g+4)
35g^2+10g+28g+8
35g^2+38g+8
Can someone please help me with this
Answers
Step-by-step explanation:
when 2 lines cross, the angles on one side of one of these lines are mirrored to the other side.
and crossing a second, parallel line creates exactly the same angles there too, because crossing the second line is like crossing the first line. otherwise the 2 lines are not parallel. the second line is just a shifted version of the first line (and vice versa). all the other attributes are the same.
and all angles around a single point on one side of a line are together 180°.
because of all that,
angle 2 = angle 3 = angle 6 = angle 7 = 76°
angle 1 = angle 4 = angle 5 = angle 8 = 180-76 = 104°
solve the equations 3/4x = 21
Answers
Therefore, the answer is 28.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Y=x2+3x+1
when х= 5, y=?
Answers
Answer:
y = 41
Step-by-step explanation:
Substitute x = 5 into the equation
y = 5² + 3(5) + 1 = 25 + 15 + 1 = 41
Points A, B and C lie on a circle, centre O.
Angle AOC = 142°.
Find the value of y.
Answers
The value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
Let suppose that quadrilateral [tex]OABC[/tex] is a parallelogram. Then, the following conditions must be fulfilled:
[tex]\overline {OA} \cong \overline {BC}[/tex] [tex]\overline{AB} \cong \overline{OC}[/tex] [tex]\angle AOC \cong \angle ABC[/tex]In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:
[tex]\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}[/tex] (4)
If we know that [tex]\angle AOC = 142^{\circ}[/tex], then the value of [tex]\angle ABC = y = 142^{\circ}[/tex].
Based on all these finding, we conclude that the value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
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Evaluate the expression if a = 4, b = 9, and c = 1.
3b÷c1−a
–27
–9
9
27
Answers
Answer:
I used the discriminant which is √-4ac
Then I filled the numbers in, and found that 9 gets plug in for b and this becomes 9 squared, and that becomes 81. 4 is multiplied to 4 and 1 and becomes 16. Then 81 and 16 are subtracted and we get 65. We then find the square root, and will find that the answer is C.
Step-by-step explanation:
Answer:
3b÷c1−a
=3×9÷1×1-4
=27÷1-4
=27-4
=23