Answer:
It is Option B
Hope it helps
PRACTISE NOW 11
Ex
15
Mr Lee drove from City P to City Q, which are 600 km apart. During his return journey,
his average speed was increased by 7 km/h and the time taken was 15 minutes less.
() If he drove at an average speed of x km/h on his journey from City P to City Q,
formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.
(ii
) Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to
2 decimal places.
(iii) Find the time taken for the return journey.
Answer:
i. x² + 7x - 16800 = 0 ii. x = 126.16 km/h or -133.16 km/h iii. 5.01 h
Step-by-step explanation:
i. If he drove at an average speed of x km/h on his journey from City P to City Q formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.
For the first journey from City P to City Q, with Mr Lee moving at an average speed of x km/h, he reaches there in time, t and covers the distance, d = 600 km
So, xt = 600 (1)
On his return journey from City Q to CIty P, his average speed increases by 7 km/h, so it is (x + 7)km/h and his time is 15 minutes less than his first journey. 15 min = 15/60 h = 0.25 h, we have that his time for the journey is (t - 0.25) h. Since the distance covered is the same d = 600 km,
We have (x + 7)(t - 0.25) = 600 (2)
Expanding the brackets, we have
xt - 0.25x + 7t - 0.25(7) = 600
xt - 0.25x + 7t - 1.75 = 600
From (1) t = 600/x and xt = 600
Substituting these into the equation, we have
600 - 0.25x + 7(600/x) - 1.75 = 600
simplifying
-0.25x + 4200/x - 1.75 = 600 - 600
-0.25x + 4200/x - 1.75 = 0
multiplying through by x, we have
-0.25x² + 4200 - 1.75x = 0
dividing through by -0.25, we have
-0.25x²/-0.25 + 4200/-0.25 - 1.75x/-0.25 = 0
x² - 16800 + 7x = 0
re-arranging, we have
x² + 7x - 16800 = 0
ii. Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to 2 decimal places.
Using the quadratic formula, we solve x² + 7x - 16800 = 0 for x
So, [tex]x = \frac{-7 +/-\sqrt{7^{2} - 4 X 1 X -16800} }{2 X 1}\\x = \frac{-7 +/-\sqrt{49 + 67200} }{2} \\x = \frac{-7 +/-\sqrt{67249} }{2} \\x = \frac{-7 +/- 259.32}{2} \\x = \frac{-7 + 259.32}{2} or x = \frac{-7 - 259.32}{2} \\x = 252.32/2 or x= -266.32/2\\x = 126.16 km/hor x = -133.16 km/h[/tex]
So, x = 126.16 km/h or -133.16 km/h
iii. Find the time taken for the return journey
The time taken for the return journey is t' = t + 0.25. Now. t = 600/x
Since x cannot be negative, we use x = 126.16 km/h.
So, t = 600/x = 600/126.16 = 4.76 h
t' = t + 0.25
t' = 4.76 + 0.25
t' = 5.01 h
A glass is
1
2
full. Then 65cm3 of orange juice is poured in.
The glass is now
6
7
full. What is the total volume of the glass?
Answer:
Answer is v=182
Step-by-step explanation:
v=volume of the glass
v/2+65=6v/7
Multiply by 14
7V+910=12V
910=5V
V=182
I hope it's helpful!
Ms. Abaza is a salesperson at a car dealership. She will receive
a bonus if she sells more cars this year than last year. Last
year, she sold 108 cars. This year, her goal is to sell 225% as
many cars. How many cars must she sell to reach her goal?
Plz help
Answer:
A
Step-by-step explanation:
Answer:243
Step-by-step explanation:
Please help! Will mark brainliest
Answer:
3!!!
Step-by-step explanation:
|2(-6)+5| - 8((1)/(2))
hope this helped ahahaa <3
I have 3 red markers, 3 blue markers, and 3 green markers. I take the caps off and put on the caps randomly. Find the expected number of markers that have the same color cap and marker.
Answer:
The expected number of markers that have the same color cap and marker is 3.
Step-by-step explanation:
Every marker has a [tex]\frac{1}{3}[/tex] chance to get the same color cap, because there are always 3 same caps, and 9 total caps. By linearity of expectation, the expected number of markers that have the same color cap and marker is equal to the sum of all marker's individual 'contribution' to the same color cap count. So the expected value is [tex]9 \cdot \frac{1}{3} = 3[/tex], precisely what we were after.
Answer:
3
Step-by-step explanation:
By running the following Python code, we can safely assume the answer to be 3:
---------------------
import random
def cap_throw():
cap_list = ['R', 'R', 'R', 'G', 'G', 'G', 'B', 'B', 'B']
random_cap_list = cap_list[:]
random.shuffle(random_cap_list)
counter = 0
for i in range(len((cap_list))):
if cap_list[i] == random_cap_list[i]:
counter += 1
return counter
results_list = []
for i in range(10 ** 6):
results_list.append(cap_throw())
print(sum(results_list) / len(results_list))
---------------------
Which gave 2.998795.
help plz i’ll give extra points
Because 10 lies between two consecutive perfect squares ___ and ___ square root of 10 is located between the square roots of these twi numbers. This means the square root of 10 is located between 3 and 4
Answer:
wut
Step-by-step explanation:
Amy and Katie have between $125 and $200 dollars to spend on jewelry for Christmas presents for their friends. If they buy 8 bracelets at $3.50 each and 6 necklaces at $12 each, how many pairs of earrings can they buy if they cost $6.00 each?
1/6(x+6)=11 Solve the equation.
1/6(x+6)=11
distribute
1/6x+1=11
-1 on both sides
1/6x=10
×6 on both sides
1x=60
x=60
Triangle abc is equilateral, solve for x and y
Answer:
x = 4
y = 3
Step-by-step explanation:
Remark
If a triangle is equilateral all three sides are equal. So each side has equal statements.
Solution
3x + 2 = 5x - 2y Subtract 3x from both sides
2 = 5x -3x - 2y Combine
2 = 2x - 2y divide by 2
x - y = 1 Equation 1
3x + 2 = 6y - 4 Equilateral triangles have equal sides. Subtract 6y
3x - 6y + 2= - 4 Subtract 2
3x - 6y = -4 - 2
3x - 6y = - 6 Divide by 3
x - 2y = - 2 Equation 2.
Now subtract equation 1 from equation 2
x - 2y = - 2
x - y = 1 Subtract
- y = - 3 Multiply by -2
y = 3
Put y = 3 into equation 1
x - y = 1
x - 3 = 1 Add 3 to both sides.
x = 4
Answer
x = 4
y = 3
the ratio of the measures of the sides of a triangle is 2:7:6. if the perimeter of the triangle is 345 yards, find the measure of the median side.
Answer:
the sides are 46, 161, 138 respectively to sides 2, 7, 6
Step-by-step explanation:
2+7+6=15
345/15=23 this is our factor
2x23=46
7x23=161
6x23=138
A total of $5000 is invested part of 6% and the remainder at 12% how much is invested at each rate if the annual interest is $480
Answer:
for 12% it would be $3,000
And, for 6% it would be $2,000
Step-by-step explanation:
The computation of the amount invested at each rate is shown below:
Let us assume the amount invested at 12% be x
So, the $5,000 - x be invested at 6%
The total interest earned is $480
So the equation would be
0.12x + 0.06($5,000 - x) = $480
0.12x + $300 - 0.06x = $480
0.06x = $80
x = $3,000
So for 12% it would be $3,000
And, for 6% it would be $2,000
A cheesecake recipe says:
Mix 12 ounces of cream cheese with 15 ounces of sugar.
1. What is the unit rate of cream cheese for sugar?
2. what is the unit rate of sugar for cream cheese?
(CORRECT ANSWER GETS A GOOD 5 STARS AND BRAINLESST)
Number 1 answer :
Cream cheese = 12 Sugar= 15 12 divided by 15 = 0.8
There are 0.8 ounces of cream cheese for every ounce of sugar.
Number 2 answer:
Sugar= 15 Cream cheese = 12 15 divided by 12 = 1.25
There are 1.25 ounces of sugar for every ounce of cream cheese.
Write down a
12
Write down a different ratio equivalent to 9: 12
No
-
Answer:
3 : 4
18 : 24
I hope it helps
2.5= -2B+6 Pls help me
Answer:
B=1.75
Step-by-step explanation:
The senior class at Clearville ISD is having a fundraiser to raise money for their prom. They are seling coupon books in the local community. The number currently sold by each of the students was used to create the box plot shown below. HHH 8 10 12 14 16 18 20 22 24 26 28 30 32 If one of the students calculated the mean of the data to be 14.5, would this be an appropriate mean? OA. Yes, the mean is appropriate. OB. There is not enough information to determine if the mean is appropriate. O C. No, the mean should be lower. OD. No, the mean should be higher. Reset Submit
Answer:
The answer is D
Step-by-step explanation:
If you add them all, and divide them it wouldn’t get 14.5
Answer:
No, the mean should be higher.
Step-by-step explanation:
Have a good day :)
What does 0.9a - 2.7b =
PLEASE HELP WITH I WILL GIVE FREE HUGS AND BRAINLIEST
Answer:
Step-by-step explanation:
a=1
b=-2
c=1.5
d=-20
A(n) is an expression that contains numbers, variable, and mathematical operations like addition, subtraction, multiplication and division and do not include equal signs.
Answer:
Variable Expression; Numeric Expression. A numeric expression consists of numbers and operations, but never include any variable. Some of the examples of numeric expressions are 10 + 5, 15 ÷ 2, etc. Variable Expression. A variable expression is an expression which contains variables along with numbers and operation to define an expression.
Step-by-step explanation:
Variable Expression; Numeric Expression.
What is an Expression?
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
Determining:Variable Expression; Numeric Expression. A numeric expression consists of numbers and operations, but never includes any variable. Some of the examples of numeric expressions are 10 + 5, 15 ÷ 2, etc. Variable Expression. A variable expression is an expression that contains variables along with numbers and operations to define an expression.
Learn more about Expressions:
https://brainly.com/question/1280754
#SPJ2
heyy pls help with these math questions hurry!
Answer:
m=2/5, y=3x7, (7,0), y=x-2, (0,-2)
Step-by-step explanation:
Which equation correctly describes photosynthesis?
water + sugar + oxygen
-
carbon dioxide + chlorophyll
O sunlight + water + carbon dioxide
oxygen + sugar
O sunlight + sugar – water + oxygen
carbon dioxide + oxygen
water + sugar + sunlight
Answer:
carbondioxide + oxygen
Answer:
carbon dioxide + oxygen → water + sugar + sunlight
Step-by-step explanation:
hope i helped
5 pts! (Yall I really need help) How much does a video game cost per in:
America
Great Britain
Japan
Answer:
there are millions of video games, ranging from all different prices, so it all depends on what game.
Step-by-step explanation:
The area, A, in square feet, of a rectangular storage bin in a warehouse is given by the function A(x) = x2 - 6x, where x is the width, in feet, of the storage bin.
Part A: Based upon this function, which statement would be true? Show your work or explain how you found the solution.
The x-intercepts of the function are 3 and -9, which are a lower bound and an upper bound for the possible values of the length of the storage bin.
The x-intercepts of the function are 3 and -9, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the length of the storage bin.
The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
Answer:
The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
Step-by-step explanation:
Given
[tex]A(x) = x^2 - 6x[/tex]
Required
Which is true about the x intercept
To do this, we make A(x) = 0.
Substitute 0 for A(x) in [tex]A(x) = x^2 - 6x[/tex]
[tex]0 = x^2 - 6x[/tex]
Rewrite as:
[tex]x^2 - 6x=0[/tex]
Factorize:
[tex]x(x - 6)=0[/tex]
Split:
[tex]x = 0\ or\ x - 6 = 0[/tex]
[tex]x = 0\ or\ x = 6[/tex]
Option D is correct
What is the value of 0.1322 rounded to the nearest hundredth place?
Answer:
Step-by-step explanation:
0.1322 ≅ 0.13
Answer:
0.13
Step-by-step explanation:
First we need to find the given place value, which is the hundreds place.
0.1322
Next, we look at the next number over, which is two.
0.1322
0-4 stays the same. 5-9 round up one. Doing so, we keep the number three the same.
0.1300
get rid of the extras.
(not a Bakogou reference)
0.13
~Hope this helps~
Only do what you know ! I know the answers thought but I wanna know what y'all know .
Answer:
A. Weeks
B. Fingernail growth
C. 1, 2, 3, 4 (weeks)
D. 0.7, 1.4, 2.1, 2.8 (mm)
Step-by-step explanation:
ez
jack is paid $54 for working 9 hours how many dollars would he earn for working 6 hours
Answer:
$36
Step-by-step explanation:
54/9=6
6*6=36
$36
Krutika and Natasha win some money and share it in the ratio 4:3. Krutika gets £7 more than Natasha. How much did they get altogether?
Answer:
49
Step-by-step explanation:
The computation of the total amount is shown below:
Let us assume the natasha be 4x
And, the krutika be 3x
Now as per the situation
4x = 3x + £7
x = £7
For natasha = 4(7) = 28
For krutika = 3(7) = 21
So, the total amount is
= 28 + 21
= 49
The mass of the particles that a river can transport is proportional to the fifth power of the speed of the river. A certain river normally flows at
a speed of 4 miles per hour. What must its speed be in order to transport particles that are 12 times as massive as usual? Round your
answer to the nearest hundredth.
Answer:
6.58 miles per hour
Step-by-step explanation:
Let the mass and speed be represented by m and s respectively. So that,
m [tex]\alpha[/tex] [tex]s^{5}[/tex]
m = k[tex]s^{5}[/tex]
where k is the constant of proportionality.
For a certain river, speed = 4 miles per hour.
m = k [tex](4)^{5}[/tex]
m = 1024k ............ 1
In order to transport particles that are 12 times as massive as usual;
12m = k[tex]s^{5}[/tex]
m = [tex]\frac{ks^{5} }{12}[/tex] ............. 2
Thus,
[tex]\frac{ks^{5} }{12}[/tex] = 1024 k
[tex]s^{5}[/tex] = 12 x 1024
= 12288
[tex]s^{5}[/tex] 12288
s = [tex]\sqrt[5]{12288}[/tex]
= 6.5750
s = 6.58 miles per hour
Therefore, its speed must be approximately 6.58 miles per hour.
Please help I will give brainliest
Answer:
c
Step-by-step explanation:
hope it helps if not sorry <3
If you solved the equation y=kx for k, what would k be equal to?
O k = xy
k = y/x
O k = x/y
O k = x+y
O k=y-X
Back
Nort
Answer:
k = [tex]\frac{y}{x}[/tex]
Step-by-step explanation:
y = kx
Divide by x on both sides to isolate k
k = [tex]\frac{y}{x}[/tex]