Answer: 60 km/hr and 65 km/hr
Step-by-step explanation:
o-----------------------------------←500→-------------------------------------o
Bus 1: rate = r + 5 Bus 2: rate = r
time = 4 time = 4
distance = d distance = 500 - d
Use distance = rate x time
Bus 1: d = 4(r + 5) Bus 2: 500 - d = 4(r)
d = 4r + 20 -d = 4r - 500
d = 500 - 4r
Solve the System of Equations using the Substitution method:
4r + 20 = 500 - 4r
8r + 20 = 500
8r = 480
r = 60
Bus 1: rate = r + 5 Bus 2: rate = r
= 60 + 5 = 60
= 65
Distance between both buses = 500km
Time taken by them to meet each other = 4hr
Let speed of bus A be v km/hr.
ATQ, speed of bus B is 5km/ hr more than that of bus A.
∴ Speed of bus B will be (v + 5) km/hr.
★ Diagram :
[tex]\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,2)\thicklines\put(1,1){\circle*{0.2}}\put(5,1){\circle*{0.2}}\put(1,1){\vector(1,0){1}}\put(5,1){\vector(-1,0){1.5}}\put(0.2,0.9){A}\put(5.5,0.9){B}\put(1.4,1.2){v}\put(3.85,1.2){v+5}\put(2.35,0.4){\sf{500\;km}}\put(2.2,0.5){\vector(-1,0){1.3}}\put(3.55,0.5){\vector(1,0){1.5}}\end{picture}}[/tex]
★ As we know that,
Speed = Distance/Time ... (I)Assuming both buses as point masses,
Relative speed of object A wrt object B when the object B moves in the opposite direction of A is given by
[tex]\boxed{\bf{v_{AB}=v_A+v_B}}[/tex]Relative speed of bus A wrt B :
[tex]:\implies\:\sf{v_{AB}=v_A+v_B}[/tex]
[tex]:\implies\sf\:v_{AB}=v+(v+5)[/tex]
[tex]:\implies\bf\:v_{AB}=2v+5[/tex]
By substituting values in (I), we get
[tex]\leadsto\sf\:v_{AB}=\dfrac{d}{t}[/tex]
[tex]\leadsto\sf\:2v+5=\dfrac{500}{4}[/tex]
[tex]\leadsto\sf\:2v+5=125[/tex]
[tex]\leadsto\sf\:2v=120[/tex]
[tex]\leadsto\sf\:v=60\:kmph[/tex]
Speed of bus A = 60 kmphSpeed of bus B = (v + 5)
Speed of bus B = 65 kmphHope It Helps!Simplify to create an equivalent expression.
3(2 + 6d) – 5 =
Answer:
Step-by-step explanation:
6 + 18d - 5
1 + 18d is equivalent to the given expression
A family has 8 kids and 3 have brown eyes. What percent of their kids have brown eyes?
Answer: 37.5%
Step-by-step explanation: 1/8 is 12.5% and if you multiply 12.5 by 3 you get 37.5
Answer:
37.5%
Step-by-step explanation:
divide 3 by 8: 0.375
then multiply your answer by 100 to get a percentage: 37.5%
WILL MARK YOU BRAINLIEST!!!
10. x = 180-81= 99 = 180-(99+19)= 62°
11. x = 180-115= 65 = 180-(65+41)= 74°
12. x = 180-(36+42) = 102 = 180-102 = 78°
13. a = 180-(112+33) = 35°
14. b = 180-(71+35) = 74°
15. c = 180-(43+71) = 66°
What is 8/2(2+2) oof not enough characters
simplify the expression 8a-2b+4 for the value a=3 and b = -5
Answer:
38
Step-by-step explanation:
Simply plug in 3 where a is, and -5 where b is as such.
[tex]8(3) - 2(-5) +4[/tex]
[tex]24 + 10 + 4[/tex]
= [tex]38[/tex]
Answer:
38
Step-by-step explanation:
Don't worry this is pretty easy! Simply plug in your given values into the expression. So if a=3 and b=-5, we would put this in the equation.
8(3)-2(-5)+4
24+10+4<--- -2(-5) would be 10 since negatives cancel out. Remember to first to parentheses, then multiply/divide next.
38
if f(x) = 3x2 + 10, what is f( - 7)?
The value of function f(-7) is 157.
What is a function?Functions have the property that each input is related to exactly one output. The function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
For the given situation,
The function is f(x) = 3 x^2 + 10
Then f( - 7) becomes,
⇒ [tex]f(-7)=3(-7 )^{2} +10[/tex]
⇒ [tex]f(-7)=147+10[/tex]
⇒ [tex]f(-7)=157[/tex]
Hence we can conclude that the value of function f(-7) is 157.
Learn more about functions here
https://brainly.com/question/5830268
#SPJ2
The Initial count of a certain type of bacteria in a culture is 350. If the bacteria grows at the rate of 20% per hour, which
function models the number of bacteria after thours?
Answer:
I think it is 350(1.2)^t because you take the starting amount (350) and then multiple it by the growth rate (which is 20%, but when added to 100 and the put into a decimal is 1.2) raised by the number of hours (t).
I hope this helps.
Step-by-step explanation:
5 +5 + 9 + 0 + 2 + 8 + 9 - 5 °°
answer and ill give you brainlyest ∝ ω
Answer: 33
Step-by-step explanation: Hope this helps! :)
Answer:
-462 if the °° are 0's
Step-by-step explanation:
493 + 327 help me please
Answer:
820 p.s you shouldn't waste your points just google calculator and use it :)
Step-by-step explanation:
493
+327
7+3=1(0) carry the one on the 9
1+9+2=1(2) carry the 1 on the 8
1+4+3=(8)
820
√³512 =
what is the answer?
Answer:
8
Step-by-step explanation:
Write in exponential form, then simplify the root.
Answer:
67.882 about 67.9 or 68
Step-by-step explanation:
three square root 512
solve for r
-13=r/9+8
r=
Answer:
r = 1 [tex]\frac{53}{64}[/tex]
Step-by-step explanation:
2. Find the product of (x+1)(x^2-3x+7)
Answer:
x
2
+
3
x
−
7
=
0
Add
7
to both sides of the equation.
x
2
+
3
x
=
7
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
Add
7
to both sides of the equation.
x
2
+
3
x
=
7(
3
2
)
2
Add the term to each side of the equation.
x
2
+
3
x
+
(
3
2
)
2
=
7
+
(
3
2
)
2
Simplify the equation.
Tap for more steps...
x
2
+
3
x
+
9
4
=
37
4
Factor the perfect trinomial square into
(
x
+
3
2
)
2
.
(
x
+
3
2
)
2
=
37
4
Solve the equation for
x
.
Tap for more steps...
x
=
±
√
37
2
−
3
2
The result can be shown in multiple forms.
Exact Form:
x
=
±
√
37
2
−
3
2
Decimal Form:
x
=
1.5413812
,
−
4.54138126
Step-by-step explanation:
Answer:x^3-2x^2+4x+7
Step-by-step explanation:
if f(x) = 2(x-3) + 4, what is f(-2)?
Answer:
-6
Step-by-step explanation:
First, replace x with -2. your equation then looks like:2(-2-3)+4. Then, you multiply 2 by everything in the parenthesis. After you multiply -2 and -3, you are left with -4, -6 +4. You then add everything together, and you get -6.
I need a 2 step equation that equals 22
In a class of 35 students there are five more boys than girls how many boys are in the class?
Answer:
20 boys in class
Step-by-step explanation:
easy
x+(x+5)=35
30=2x
x=15
Answer:
let X be number of boys & y be number of girls in the class
x +y = 35 .....eq 1
x = y +5
y = x -5.......... eq 2
substitute eq 2 in eq 1
x + x -5 =35
2x = 40
x = 20
A bakery sold 168 mocha cupcakes in a day, which was 84% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
200 cupcakes
Step-by-step explanation:
We have, 84% × x = 168
or,
84/100 × x = 168
Multiplying both sides by 100 and dividing both sides by 84,
we have x = 168 × 100/84
x = 200
If you are using a calculator, simply enter 168×100÷84, which will give you the answer.
Answer:
200
Step-by-step explanation:
168 is 84/100 of the total cupcakes. You just need to divide by 84 and the multiply by 100. So:
168÷84=2
2×100=200
Been here for hours which one is it
Answer:
3 I do belive
Step-by-step explanation:
Answer:
-1/4 slope and 50 y intercept
Step-by-step explanation:
from,
m= (y-y1)/(x-x1)
just decide what values of x and y will be your y,x and y1 ,x1
y=50, y1=25,x=0,x1=100
m is the slope.
y intercept is the value of y
Simplify 8x – 3x – 2x – x
Answer:
2x
Step-by-step explanation:
13x < 6(3x – 4) – 6
show work please
Answer:
x > 6
Step-by-step explanation:
Step 1: Write equation
13x < 6(3x - 4) - 6
Step 2: Solve for x
Distribute 6: 13x < 18x - 24 - 6Combine like terms: 13x < 18x - 30Subtract 13x on both sides: 0 < 5x - 30Add 30 to both sides: 30 < 5xDivide both sides by 5: 6 < xRewrite: x > 6Kiran is spending $12 on games and rides at another carnival, where a game costs $0.25 and a ride costs $1.
Write an equation to represent the relationship between the dollar amount Kiran is spending and the number of games, x, and the number of rides, y, he could do.
Answer:
.25x+1y=12
Step-by-step explanation:
there is no step by step
You have decided to cash in all of the coins you have been saving for the summer. In total you have $7.20. You only have dimes and quarters, and you know that you have twice as many dimes as you do quarters. How many quarters do you have in total? How many dimes? (HINT: think about what you know of dimes and quarters!)
Answer:
The number of quarters in total = 16 quarters
The number dimes = 32 dimes
Step-by-step explanation:
The given information are;
The total amount of money in held = $7.20
The denomination of the money held = Dimes and quarters
The number dimes = 2 × The number of quarters
Given that a dime = 10 cents = $0.1
A dollar = 25 cents = $0.25
Let the number of quarters in the sum of money = X
Therefore, we have;
X × $0.25 + 2 × X × $0.1 = $7.20
X × $0.25 + X × $0.2 = $7.20
X × $0.45 = $7.20
X = $7.20/$0.45 = 16
Therefore, the number of quarters = 16
The number of quarters in total = 16 quarters
The number dimes = 2 × The number of quarters = 2 × 16 = 32 dimes
The number dimes = 32 dimes.
I’ll mark u BRILLIANT HURRY PLEASE Mr. Lange’s car has a gas tank that holds 12 gallons. He can drive 396 highway miles before he runs out of gas. Which shows the unit rate per gallon?
A. 23 miles per gallon
B. 28 miles per gallon
C. 30 miles per gallon
D. 33 miles per gallon
5
Answer:
D
Step-by-step explanation:
396 divided by 12
Answer:
D. 33 miles per gallon
Step-by-step explanation:
396/12 = 33
Am I correct here? All answers will be greatly appreciated!
Answer:
yes i believe you are correct
Step-by-step explanation:
hurry pls and ty :')
Answer:
5
Step-by-step explanation:
if -17 +5 are in value they should equal 12
5. The rectangular pool has an area of 520 square feet. The length of 3
more than its width. Which of the following equations represent length 2, in feet of the room?
a) z(z+11) =520
b) z(z - 11) = 520
c) z(11 - 2) = 520
d) - 112 - 520 = 0
e) 2 + 112 - 520 = 0
11z +520 =
Answer:
z*(z - 3) = 520
Step-by-step explanation:
Use the following representations:
Width: W
Length: L = W + 3, or W = L - 3
Area = L*W = L*(L - 3) = 520
Equation b) is the correct one: z*(z - 3) = 520
PLEASE HELP WILL GIVE BRAINLIEST AND 25 POINTS!!!
A model rocket is launched upward at a speed of 96 feet per second from a platform 7 feet above the ground. The path of the rocket can be modeled by the projectile equation, h(t)=-16t^2+v₀t+h₀
1. What is the maximum height the rocket will reach?
2. What is the average rate of change from the initial height to the maximum height?
Answer:
151 ft
48 ft/s
Step-by-step explanation:
h(t)=-16t^2+v₀t+h₀
v₀ = 96 and
h₀ = 7
h(t)=-16t^2+96t+7
The maximum height is at the vertex
The x values of the vertex is at
x = -b/2a = -96/ (2*-16) = -96/-32 =3
Substitute this into the function to find the maximum height
h(3) = -16 ( 3)^2 +96*3+7
-16*9 +288+7
151
The maximum height is 151 ft
Average rate of change from 0 to 3
h(3) - h(0)
---------------
3-0
151 -7
------------
3
144/3
48ft/s
HELPPP!!!
(6 points)
8. If you bought a $55 table and
paid an additional $4 in tax,
what percentage was the tax?
Answer:
7.27%
Step-by-step explanation:
If Mike runs 3/5 of a mile in 1/15 of an hour, how many miles would he walk in a full hour?
Answer:
9 miles
Step-by-step explanation:
The answer is 9 miles because if you divide 0.6 mile by 4 minutes, you will have an answer of 9 miles an hour, as 0.6x15=9. In a full hour, Mike would walk 9 miles.
Math question pls help
Answer:
(-4) - (+2) = -6
(+6) + (+9) = -3
(-36) divide (+3) = -12
(-12) x (-8) = 20
(-4) + (-7) = -11
(+7) - (4) = 11
(-5) - (+12) = 17
(+6) + (+9) = 15
(-10) + (+12) = -22
(+6) + (+6) = 12
(+10) divide (-10) = 1
(+4) + (-5) = -20
(-10) + (-10) = -20
(-4) x (+7) = 28
(+11) + (-2) = 9
(-2) - (-3) = 1
(-7) - (+1) = -8
(+1) + (+4) = 5
geez this took me a while lol
i hope that help!
Determine the function which corresponds to the given graph. (3 points)
A natural logarithmic function crossing the y axis at zero and going through the point 2,1.
The asymptote is x = -1.
what grade level is this