Answer:
(i) David: Daniel: Dennis= 2: 3: 7
(ii) David, Daniel and Dennis will get £1000, £1500 and £3500 respectively.
Step-by-step explanation:
(i) Let the amount of money obtained by David, Daniel and Dennis be x, y and z pounds respectively.
x +y +z= 6000 -----(1)
y= 1.5x -----(2)
z= 3.5x -----(3)
Let's write the amount of money each gets in terms of x.
David --- x
Daniel --- 1.5x
Dennis --- 3.5x
In ratio, David: Daniel: Dennis
= 1: 1.5: 3.5
= 2: 3: 7
This is obtained by multiplying 2 throughout the ratio as ratio is its simplest form is in whole numbers and does not have decimals.
_______
(ii) Now that we know how the money is shared in terms of ratio, we can easily determine how much each of them receives.
Total amount of money= £6000
Total number of units
= 2u +3u +7u
= 12u
Thus, 12 units represents £6000.
12u ----- £6000
1u ----- £6000 ÷12= £500
Amount of money David will receive
= 2u
= 2(£500)
= £1000
Amount of money Daniel will receive
= 3u
= 3(£500)
= £1500
Amount of money Dennis will receive
= 7u
= 7(£500)
= £3500
Extra notes:
• Units are represented by the letter 'u' in the working. They can also be called parts and their value is in relation to the total amount. Thus if David gets 2 units of the total money, and the total amount is 12 units, he receives 2/12 or ⅙ of the total sum of money.
A soccer game is 90 minutes long. 36 minutes have passed. What percentage of the game has passed?
Answer:
The answer is 40%
Step-by-step explanation:
Answer:
40% increase
Step-by-step explanation:
90 - 36 = 54
90 - 54 = 36
36 / 90 = 0.4
0.4 x 100 = 40%
Help please ! I need the answer ASAP
Answer:
[tex](f + g)(1) = - 3[/tex]
Step-by-step explanation:
[tex](f + g)(x ) = (2x - 3) + (4x - 6) \\ = 6x - 9 \\ \\ (f + g)(1) = 6(1) - 9 \\ = 6 - 9 \\ = - 3[/tex]
I hope I helped you^_^
Consider this function.
h(x) = (x - 2)^2+3
Which of the following domain restrictions would enable h(x) to have an inverse function?
a. x < 1
b. x ＞5
c. x < 3
d. x > 4
(Ps: all four answer and larger equal then or smaller equal then
Answer:
No inverse function: (a), (b), (c)
Inverse function exists: (d)
Step-by-step explanation:
The graph of h(x) = (x - 2)^2 + 3 is a parabola that opens upward and has vertex at (2, 3). If the entire graph is drawn, and the horizontal line test then applied, h(x) would not have an inverse, because the horizontal line would intersect the parabolic graph twice.
Note that if we restricted the domain to x ≥ 2, the resulting graph would pass the horizontal line test. This would also be true for x ≥ 3, x ≥ 4, and so on. Not so for (a) x < 1. False for x > -5. True for x < 3. True for x > 4.
No inverse function: (a), (b), (c)
Inverse function exists: (d)
(81)¾ - (27)⅓
\3 × 2³
Answer:
I won't tell you the answer but if you read the solution, you would understand it.
Step-by-step explanation:
81^3/4 is basically 3 times the fourth root of 81. What number multiplies 4 times to make 81? Then multiply that by 3.
Now we have the cube root of 27. If you have a fractional exponent with no numerator, that just means square root, cube root, fourth root.
Eg. the exponent 1/4 would just mean fourth root
Eg. The exponent 1/2 would just mean square root
The cube root of 27 is 3.
The denominator is 3 times 2 to the third power.
PEMDAS
Order of Operations tells us we do exponents first so 2 to the third power is 8 and multiply by that 3.
You have all the information you need. Now just use your arithmetic skills! Let me know if you need more help.
Amold uses
fence?
of a tin of paint to cover 1 z m of fence. What is the smallest number of tins he needs to cover 12 m of fence
78 decreased by half a number is 45 Find the number
Answer:
number is 66
Step-by-step explanation:
let the number be n , then
78 - [tex]\frac{1}{2}[/tex] n = 45 ( subtract 78 from both sides )
- [tex]\frac{1}{2}[/tex] n = - 33 ( multiply both sides by - 2 to clear the fraction )
n = 66
The required number is 66
Which of the following must be true?
Answer:
answer is B because in the property of parallelogram it says ad is parallel to bc
simplify root 12 over root 3
Answer:
4
√
3
Step-by-step explanation:
pls mark brainliest if possible
What is the value of the first term in the following arithmetic sequence?
-9, -2, 5, 12, ...
a. -9
b. 7
c. 9
d. -7
Answer:
-7
Step-by-step explanation:
Heyyyyyyyyyyyyyyyyyyyyyy
Answer:
7/12
Step-by-step explanation:
you have to find a common denominator, which would be 12. it would be 4/12 + 3/12. add them up, and you get 7/12
does any one know the Inequality Notation for this [9,∞)
Answer:
x>=9
Step-by-step explanation:
so, we can plot this on a number line
the point at 9 is a solid dot, since brackets (not parenthasis) indicates that we including the number. the shaded part of the line extends all the way to positive infinity. the shaded part means that it is a solution, while the un-shaded parts aren't solutions to [9,infinity) it is x>=9 and not x>9 because 9 is included.
x>=9 is the answer
simplify the expression below and rewrite it in rational exponent form
Colleen buys a robot priced at $33.If the sales tax is10%,how much tax will Colleen pay?
Answer:
$3.3 tax
Final price is 36.3
Step-by-step explanation:
Firstly, if the tax is expressed in percent, divide the tax rate by 100. You can do this by simply moving the decimal point two spaces to the left. In this example, we do 10/100 = 0.1
tax= 33 * 0.1
tax=3.3
Finally, add tax to the before tax price to get the final price including tax.
The final price including tax = 33 + 3.3 = 36.3
Three sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister’s age.
Answer:
youngest 17
middle 19
oldest 21
Step-by-step explanation:
Three sisters have ages that are consecutive odd integers
youngest = x
middle = x + 2
oldest = x + 4
--------------------
The sum of the age of the youngest
x
and three times the age of the oldest
+ 3(x + 4)
is five less than five times the middle sister’s age
= 5(x + 2) - 5
-----------------------
x + 3(x + 4) = 5(x + 2) - 5
Distribute
x + 3x + 12 = 5x + 10 - 5
Combine like terms
4x + 12 = 5x - 5
Subtract 4x from both sides
12 = x - 5
Add 5 to both sides
17 = x
youngest x = 17
middle x + 2 = 19
oldest x + 4 = 21
How to Solve 2x = 9?
=》2x = 9
=》x = 9/2
=》x = 4.5
■ Take all the numbers to the right side leaving the variable alone on the the other side of the equation & then simplify it.
_____
RainbowSalt2222 ☔
pls help me I give brainly
Answer:
B is the answer
Step-by-step explanation:
this is showing 2 being divided by 9 which must give a value less than one, in this case it is .2 repeating
Please help!!! I have to submit this by today.
[tex]i \div 8 = 12[/tex]
Answer:
i = 96
Step-by-step explanation:
i ÷ 8 = 12i = 12 × 8i = 96Your friend tried putting away the sugar for you and cannot get the 14 cups of sugar to fit in the containers! They determined you would need 9 containers to store the 14 cups of sugar.
They show you their calculations:
Answer the following questions.
What mistake did your friend make in calculating the number of containers needed?
*Hint* Look closely at the work shown to find the mistake
How many containers are needed to store the leftover sugar?
Answer:
21 containers
Step-by-step explanation:
When dividing fractions, you can multiply by the inverse of the fraction. For example, in this case, [tex]14 divided by \frac{2}{3} = \frac{14}{1}x\frac{3}{2}[/tex]. Whoever drew the calculations made the mistake of forgetting to flip the second fraction.
The actual solution of the problem is 42/2, or 21/1. 21 containers are needed to store the sugar.
graphically represent
The cuadratic relation
boberson is after then my mom
HELP1!!1!!1!
Solve your word problem using a model. Use complete sentences to describe your model, and interpret the quotient in the context of your word problem. If you wish, you may upload a copy of your model.
The model [tex]x = \frac{6}{3}[/tex], can be used to solve the world problem representing a scenario where John wants to share 6 apples amongst his three friends. x = 2, is the quotient which is interpreted as the number of apples each of John's friend will get.
Word problem describes real world situations which can be translated into expressions as a model.
For example, if John has 6 apples and John has three friends, how many apples would each of the friend get (x) if he is to share the 6 apples amongst the three of them?
To solve this, we can model the situation as follows:
Let x represent the number of apples each friend would get (quotient).
Thus:[tex]x = \frac{6}{3}\\\\\mathbf{x = 2}[/tex]
The quotient (x) in this model can be interpreted as the number of apples each of John's friend will get.Thus, the model [tex]x = \frac{6}{3}[/tex], can be used to solve the world problem representing a scenario where John wants to share 6 apples amongst his three friends. x = 2, is the quotient which is interpreted as the number of apples each of John's friend will get.
Learn more here:
https://brainly.com/question/13818690
A right triangle is one that contains a ______ degree angle
Answer:
90 degrees
Step-by-step explanation:
......
Answer: 90 degree angle.
Step-by-step explanation: A right triangle must have a right angle.
I WILL GIVE BRAINIEST, PLEASE HELP
Answer:
A = (1, 10)
B = (4,10)
C = (4, 14)
D = (1, 16)
Step-by-step explanation:
Okay, so first, we move, or translate the quadrilateral PQRS down -8 spaces on the graph, turning old points:
P (1, -2) = (1, -10) Q (4, -2) = (4, - 10) S (1, -8) = (1, -16) and R (4, -6) = (4, -14)
Now, we need to rotate this new box into -x, y. So our new points are:
(1, -10) = (-1, 10) (4, -10) = (-4, 10) (1, -16) = (-1, 16) and (4,-14) = (-4, 14)
Now we're reflecting off the y-axis, making our x change. So for our final points:
A(1, 10) B (4,10) D(1, 16) and C(4, 14)
Hope this helps! Please check my math and comment wether this worked or not! :)
Answer:
hi
Step-by-step explanation:
Kent drank
2
3
liter of water Monday before going jogging. He drank
3
4
liter of water after his jog. How much water did Kent drink altogether? Write your answer as a mixed number.
Answer: 1 5/12
Because 2/3 + 3/4 = 17/12, if you simplify that it would be 1 5/12
will mark brainly :)
y=1/2(x-3)^2
y=1/2(x+3)^2
y=2(x-3)^2
y=2(x+3)^2
Answer:
y = 1/2 (x-3) ^2
Step-by-step explanation:
I hope this helps!
The width of a rectangular parking lot at the meadowlands is 3/8 mile. If the area is 5/8 square mile, what is the length of the parking lot
let width is x and length is y
x * y = area
=> 3/8 * y = 5/8
=> y = 5/8 ÷ 3/8
=> y = 5/8 * 8/3 = 5/3
the length of the rectangular parking lot is 5/8 mile.
If x = -2, what does y equal if y = x3 + 7?
Answer:
y=1
Step-by-step explanation:
you plug-2 in for x and then the problem looks like this y=-2(3)+7.
then you follow order of operations and multiply-2 and 3, and you get -6 so the problem now looks like y=-6+7.
you then add -6 and 7 and you get 1. now the problem looks like y=1 and you are finished.
Choose the graph that represents the following system of inequalities: y ≥ −3x + 1 y ≤ 1 over 2x + 3 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.
Pls hurry- ill give 100 points.
C. Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1, and 1, negative 2, and is shaded below the line.
Answer:
Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1, and 1, negative 2, and is shaded below the line.
Step-by-step explanation:
1 trig review please please help
Answer:
[tex] \sqrt{73} mi[/tex]
what is the answer, i tried everything but i can’t seem to get the right answer
Answer:A
Step-by-step explanation: It never talks about 50 so i don't know why that is there so I think it is A because 21 dollars is more than 5+2.75, (not 100% sure but at least 85% sure)
Answer:
A
Step-by-step explanation:
The reason that this is A is because 5$ is the initial fee and you dont pay any more than that, since 21$ is the max you can afford it is going to be less than or equal to 21. and if it is 2.75$ per stop then it is the number of stops times 2.75. A is your answer.
edit: and the 50 kilometers doesnt have any value in the situation so basically it was just there to confuse you or throw you off.
In how many different ways can change be given for a 50 cent coin using only 20 cent, 10 cent, and 5 cent coins? Justify your answer.
Answer: 9
Step-by-step explanation:
20+20+10
20+10+10+10
20+10+5+5+5+5
10+10+10+10+10
10+10+10+10+5+5
10+10+10+5+5+5+5
10+10+5+5+5+5+5+5
10+5+5+5+5+5+5+5+5
5+5+5+5+5+5+5+5+5+5
Answer: 13 ways
Step-by-step explanation:
use the properties of addition to help
one way to solve this problem is
20+20+10
another way is
20+10+10+5+5
