Suppose two bicyclists start at the same location.
The first bicyclist rides due north and the other rides
due west. Find the speed that each bicyclist rode in
miles per hour if they are 8V2 miles apart after riding
for 2 hours at the same speed
Answers
Answer:
4 mi/h
Step-by-step explanation:
The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.
Their speed is (8 mi)/(2 h) = 4 mi/h.
_____
Additional comment
Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...
c² = a² +b² . . . square of hypotenuse is sum of squares of legs
c² = 1² +1² . . . . both legs are 1 in our example triangle
c² = 2
c = √2
That is, the hypotenuse is √2 times the leg length.
Related Questions
how do you evaluate numbers in math?
Answers
To evaluate an expression in maths, plug in he value of the variable, then simplify the expression following the order of operation.
Assuming we are given the expression, 3x + (2x - 1), and we are required to evaluate the expression, the following shown below is how to evaluate the expression if we are told that x = 1.
First step is to plug in the value of the variable, x, into the expression:3(1) + (2(1) - 1)
3 + 2 - 1
Using the order of operation, simply4
Therefore, to evaluate an expression in maths, plug in he value of the variable, then simplify the expression following the order of operation.
Learn more about evaluation on:
https://brainly.com/question/3590570
7. A cargo train covers 375 km in 15 hours. Find: b) time taken to travel 770 km.
Answers
Answer:
30 hours 48 minutes
Step-by-step explanation:
Using the relationship
average speed = [tex]\frac{distance}{time}[/tex] = [tex]\frac{375}{15}[/tex] = 25 Km / hour
Then
time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{770}{25}[/tex] = 30.8 hours = 30 hours 48 minutes
Answer:
30.8 or 30 hours and 48 mins
Step-by-step explanation:
375 km > 15 Hours
Divide 375 and 15, equals to 25.
So, to proof that 375 is equals to 15 hours, divide 375 and 25 then you will get the answer 15. :)
Now, divide 770 and 25 to get the time taken to travel 770km.
And the answer is 30.8 hrs or... 30hrs and 48mins
Welcome ;)
30 POINTS!!! A catfish weights about 0.2 pound and its weight increases by about 15% each week. Write an exponential equation that represents the weight of the catfish after t weeks.
Answers
Answer:
0.30 15 times 2 easy 30 and this percent so 0.30
Step-by-step explanation:
Someone help me please
Answers
Answer:
Step-by-step explanation:
any minus temperature is < 7oC
0 is < 7oC
1 ... 6 is < 7oC
Which expression are equivalent to -1+12x^2+x
Answers
Answer:
(3x+1)(4x-1)
Step-by-step explanation:
you can reorder the terms to make it less confusing to 12x^2+x-1
write x as a different 12x^2+4x-3x-1
factor out 4x 4x(3x+1)-3x-1
factor out the negative sign 4x(3x+1)-(3x+1)
factor out 3x+1
(3x+1)(4x-1)
if it takes 10 people working at the same rate 5 hours to pick 300 apples, how many hours would it take 1 person to pick 300 apples
Answers
Answer:
50 hours
Step-by-step explanation:
10 times 5 is 50 so the answer is 50 hours
Sponges are sold for 20 dollars. How many sponges per dollar.
Answers
Answer:
$1 or $1.25
Step-by-step explanation:
Not sure. Maybe
2x+5=10-3x please help
Answers
Step by step
2x + 5 = 10 - 3x
Let’s start with 2x + 5 = 7 and you bring the x with you which is 7x
Now you do 7x = 10 - 3x , equal sign is plus am guessing and then 10 - 3x is 7x so
7x + 7x = 14x
Tom, Kristen, and bill bought 3 granola bars to share amongst themselves. They divided each granola bar into 4 equal portions. Kristen ate 1 portion from each granola bar. Which equation represents how many granola bars Kristen ate.
Answers
Answer:
3/4 of a bar.
Step-by-step explanation:
Each piece of the granola bar is 1/4 of the bar. She ate 3 portions, so she ate 3/4.
how to find the domain and range of a piecewise function without a graph
Answers
Answer:
Step-by-step explanation:
The x component of a function is domain and the y component is range of a function . For example - R1={(3,4),(5,6),(7,9)} The domain of R1 ={3,5,7} The range of R1={4,6,9}
Find the value of x
6.1 - angles of polygons
Answers
Answer:
x = 46°
Step-by-step explanation:
The sum of interior angles = (n-2) × 180°
= (5-2) × 180°
= 540°
2x+3x+3x-4+3x+x-8 = 540°
12x = 552°
x = 46°
Nikita began with the figure shown.
A.
с
B
She completed the following actions to construct the angle bisector of ABC, but made a mistake in one of the steps. Select the step in which
her mistake was made.
Step 1: She placed the compass on point B and drew an arc which intersects ray BA at point D and ray BC at point E.
Step 2: Next, she placed the compass on point D and drew an arc on the interior of 2ABC.
Step 3: Then, she placed the compass on point and drew an arc on the interior of ZABC, which intersects the previous arc.
Step 4: She labeled the intersection of the two arcs as point F and drew the ray BF, which represents the angle bisector
of ZABC.
Answers
Answer:
no
Step-by-step explanation:
Answer:
Step three
Step-by-step explanation:
She placed the point on C when it was supposed to be on E
24) If the simple interest on $4,000 for 3 years
is $960, then what is the interest rate?
Answers
Answer:
8% annual
Step-by-step explanation:
first find the rate of 1 year. 960/3 = 320.
then find what % of 4,000, 320 is.
8%
What is the Equation of the line? slope: undefined; (7,-9)
Answers
Answer:
x = 7
Step-by-step explanation:
Answer:
x=7
Step-by-step explanation:
undefined slope means that there's a vertical line through the x-axis.
And since the point is at (7,-9) you only need to focus on the value of x, which in this case, is 7.
This trapezium is drawn on a centimetre grid.
Find the area of the trapezium.
Answers
Answer:
A = 21 cm²
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between bases and b₁, b₂ are the parallel bases
Here h = 3, b₁ = 9, b₂ = 5 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (9 + 5) = 1.5 × 14 = 21 cm²
Can someone help me with this please?
Answers
hey guys can you help me with this question? 20 points :)
Answers
Answer:
About 7 units
Step-by-step explanation:
About 7 units would be correct. 1 + 6 is 7
however 6 isn’t an option so the next closet thing is 7
HOPE THIS HELPED :3
Answer pretty sure that’s 7
Step-by-step explanation:
5x-15y=-20, 5x-4y=-9 systems of equations (elimination)
Answers
Answer:
(- 1, 1 )
Step-by-step explanation:
5x - 15y = - 20 → (1)
5x - 4y = - 9 → (2)
Multiplying (2) by - 1 and adding to (1) will eliminate the x- term
- 5x + 4y = 9 → (3)
Add (1) and (3) term by term to eliminate x
0 - 11y = - 11
- 11y = - 11 ( divide both sides by - 11 )
y = 1
Substitute y = 1 into either of the 2 equations and solve for x
Substituting into (1)
5x - 15(1) = - 20
5x - 15 = - 20 ( add 15 to both sides )
5x = - 5 ( divide both sides by 5 )
x = - 1
solution is (- 1, 1 )
PLEASE I NEED HELP RN
use the elimination method to solve. -7x+y=-19 -2x+3y=-19
Answers
Answer:
(x, y) = (2, -5)
Step-by-step explanation:
The coefficient of y in the second equation is an integer multiple of the coefficient in the first equation, so it is convenient to eliminate y. Subtracting 3 times the first equation from the second, we have ...
(-2x +3y) -3(-7x +y) = (-19) -3(-19)
-2x +3y +21x -3y = -19 +57 . . . . . . . eliminate parentheses
19x = 38 . . . . . . . . . simplify
x = 2 . . . . . . . divide by 19
-7(2) +y = -19 . . . . . substitute for x in the first equation
y = -5 . . . . . . add 14
The solution is (x, y) = (2, -5).
Paula has $3,281 in a savings account that earns 8% interest, compounded annually.
To the nearest cent, how much interest will she earn in 1 year?
(compound interest Formula)
Answers
Answer:
$262.48Step-by-step explanation:
Given:
Saving amount P = $3281Interest rate r = 8% or 0.08Compound number n = 1Time t = 1 yearFind the total amount in 1 year:
[tex]I = P(1 + r/n)^{nt}-P[/tex][tex]I = 3281*(1 + 0.08/1)^{1*1} -3281 = 3281*1.08 - 3281= 3281*0.08=262.48[/tex]
when the perimeter of a regular polygon is divided by 5 the lenght of a side is 25 cm what is the perimeter
Answers
Answer:
125 cmStep-by-step explanation:
when the perimeter of a regular polygon is divided by 5 the lenght of a side is 25 cm what is the perimeter?
A Regular polygon is a polygon with all sides of equal length
so
25 * 5 = 125 cm
help. please..
with steps.
Answers
Answer:
Option 2
Step-by-step explanation:
The account balance multiplier for the compound interest option is ...
(1 +r)^t = 1.05^8 ≈ 1.477455
The account balance multiplier for the simple interest option is ...
(1 +rt) = 1 +0.06·8 = 1.48
Jadwa should choose option 2 for this investment. It will earn about £5.09 more in interest over the 8-year period.
_____
£2000 · (1.48 -1.477455) ≈ £5.09
__
In the above formulas, r is the interest rate, and t is the number of years.
An Ipad that costs $500 is on sale for 15% off. Then has a 6% tax. What's the final price?
Answers
Answer:
subject tooo
Step-by-step explanation:
sorry
Answer:
$450.50
Step-by-step explanation:
Please help me on this question!
Answers
-8 to 8
Step-by-step explanation:
f(x) is the same as y when discussing functions. Therefore we look for the places where the line is above or touching the x axis
please help 31 pts and brainlist if you give me a step by step explanation on how to do this
Answers
Answer: Hence, by ASA ( Angle side Angle) Rule of congruency two triangles;
Angle ADE = CDF Hence proved.
Step-by-step explanation:Diagram of two triangles are given such that side ED = FD and <AED = < CFD = 90
To Find: TO prove <ADE = <CDF
Solution; In figure ; we can see that <EDA and <FDC are vertically opposite angles and hence are equal.
=> <EDA = <FDC |Vertically opposite angles
<DEA = <CFD = 90 |Given
Also, ED = FD |Given
Hence, by ASA (Angle Side Angle)
Rule of congruency two triangles; <ADE = <CDF
Hence Proved.
Factorize the following: 9x²+6x+1-25y²
Answers
Answer:
(3x - 5y + 1)(3x + 5y + 1).
Step-by-step explanation:
9x²+6x+1-25y²
= 9x^2 - 25y^2 + 6x + 1
= (3x - 5y)(3x + 5y) + 6x + 1
3x + 3x = 6x and 1 * 1 = 1 so we have:
= (3x - 5y + 1)(3x + 5y + 1)
9x2+6x+1−25y2
.......................... (3x)2+(2x3xx1)+(1)2−25y2
.................................applying Rule (a+b)2=a2+b2+2ab
.(3x+1)2−(5y)2
........................... . (3x+1+5y)(3x+1−5y)
.................................. .... applying Rule a2−b2=(a+b)(a−b)
How I can apply the distribute property to this question?
Answers
Answer:
6(4c+6d+3)
Step-by-step explanation:
First, find the greatest common factor, which is 6, in this case.
24/6=4
36/6=6
18/6=3
6(4c+6d+3)
-hope it helps
If AB∥ED and m∠ABC = m∠DEF. Prove CB|| EF.
Answers
Explanation:
( ) . . . . stuff that is given
∠ABE ≅∠DEG . . . . corresponding angles at a transversal
∠ABC +∠CBE = ∠ABE . . . . angle addition postulate
∠CBE = ∠ABE -∠ABC . . . . subtraction property of equality
∠DEF +∠FEG = ∠DEG . . . . angle addition postulate
∠FEG = ∠DEG -∠DEF . . . . subtraction property of equality
∠FEG = ∠ABE -∠ABC . . . . substitution property of equality
∠CBE = ∠FEG . . . . substitution property of equality
CB║EF . . . . converse of corresponding angles theorem
Need help!!!!!!!!!!!!!!!!!!!!!!!!
Answers
[tex]\mathfrak{( \frac { 6 x } { y } ) ( \frac { y } { 3 x - 3 } ) } [/tex]
[tex]\mathfrak{ \frac{6xy}{y\left(3x-3\right)} } [/tex]
[tex]\mathfrak{ \frac{6x}{3x-3} } [/tex][tex]\mathfrak{ \frac{6x}{3\left(x-1\right)} } [/tex]
[tex]=\boxed{\mathfrak{\frac{2x}{x-1} } }[/tex]
☆ Option 3 is correct.
[tex]\mathbb{MIREU} [/tex]
PLZZ HELP ASAP
Order these numbers from least to greatest
Answers
Answer:
1.4722, 2.901, 2.9, 2.91
Step-by-step explanation: