Given :-
5 years ago, Ram's mother was five times his age
Ram's Mother is now thrice as old as him.
To find :-
Present age of Ram
Present age of Ram's mother
Solution :-
Let the present age of Ram be x years
Let the present age of Ram's mother be y years.
As per the first condition,
5 years ago, Ram's mother was five times his age
5 years ago,
Ram's age = x - 5
Mother's age = y - 5
Let's represent the first condition mathematically to get our first equation.
y - 5 = 5 ( x - 5)
y - 5 = 5x - 25
5x - 25 = y - 5
5x - y = - 5 + 25
5x - y = 20 -----> 1
As per the second condition,
If his mother is now thrice as old as him
Ram's age = 3x
Mother's age = y
Let's represent this too mathematically. Here we will get just the value of one of the variables, either x or y.
y = 3x
Substitute, y = 3x in equation 1,
5x - y = 20 ----> 1
Plug in the value of y,
5x - 3x = 20
2x = 20
x = [tex]\frac{20}2}[/tex]
x = 10
Present age of Ram = x = 10 years
Substitute, x = 10 in equation 1,
5x - y = 20 ---> 1
5 ( 10 ) - y = 20
50 - y = 20
- y = 20 - 50
- y = - 30
[canceling minus from both sides]
y = 30
Present age of Mother = y = 30 years
•°• Present age of Ram = 10 years.
For first case :-
5 years ago, Ram's mother was five times his age
Present age of Ram = 10 years
5 years ago,
Ram's age = 10 - 5 = 5 years
Present age of Mother = 30 years
5 years ago,
Mother's age = 30 - 5 = 25 years
Let's check if the ages satisfies the first condition,
Mother's age = 5 ( Ram's age )
25 = 5 ( 5 )
25 = 25
LHS = RHS.
For second case :-
His mother is now thrice as old as him
Mother's age = 30 years
Ram's age = 10 years
Let's check whether the second condition is satisfied or not.
Mother = 3 ( Ram's age)
30 = 3 ( 10)
30 = 30
LHS = RHS.
Hence the answer is verified.
What is percent 10 1/4 of 66?
Please helpppppp????
Answer:
hii
Step-by-step explanation:
which question do you want
The value of 2 · 5^2 is 100. True or False?
If n = 4, the value of the expression 28 - 12 + ÷ 2 is _____.
A) 15 B) 17 C) 17/2 D) 21
Please answer both!
Show algebraically that f and g are inverse functions:
g = sqrt(x+8)-4
f=x^2+8x+8
Answer:
See Below.
Step-by-step explanation:
By definition, if two functions, f and g, are inverses, then:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
We are given the two functions:
[tex]\displaystyle g(x) = \sqrt{x + 8} -4 \text{ and } f(x) = x^2 + 8x + 8[/tex]
Find f(g(x)) and g(f(x)):
[tex]\displaystyle \begin{aligned} f(g(x)) &= (\sqrt{x + 8} -4)^2 + 8(\sqrt{ x+ 8}-4) + 8 \\ \\ &= ((x+8) -8\sqrt{x + 8} +16) + 8\sqrt{x + 8} - 32 + 8 \\ \\ &= x + (-8\sqrt{x+8} + 8\sqrt{x + 8}) +(16 - 32 + 8 + 8) \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned}g(f(x)) &= \sqrt{(x^2 + 8x + 8) + 8} - 4 \\ \\ &= \sqrt{x^2 + 8x+16 } - 4 \\ \\ &=\sqrt{(x+ 4)^2} - 4 \\ \\ &= (x +4) - 4 \\ \\ &= x \stackrel{\checkmark}{=} x \end{aligned}[/tex]
Hence, f and g are indeed inverses of each other.
11/14 as a repeating decimal using bar notation
Step-by-step explanation:
______
0.7857142
note the first 7 is not included in the bar
PLEASE HELP it’s been an hour and I can’t figure this out it’s about rate of change algebra 2 I can give brainlist
Answer:
part b is B
Step-by-step explanation:
not sure about the first part i dont want you to get it wrong i kind of forgot about it
PICTURE ABOVE ^^ PLEASE HELP
Answer: 4 /15
Step-by-step explanation:
[tex]0.2\overline{6}\\\\=0.2+\dfrac{1}{10} *\dfrac{6}{9} \\\\=\dfrac{1}{5} +\dfrac{1}{15} \\\\\\\boxed{0.2\overline{6}=\dfrac{4}{15} }\\[/tex]
f(x)=x2
g(x)=x−3
Find the composition of the two functions and show your process:
g(f(x))
Answer:
g(f(x)) = x² - 3
Step-by-step explanation:
g(f(x))=g(x²)
= x² - 3
Step-by-step explanation:
[tex]f(x) = {x}^{2} \\ g(x) = x - 3 \\ g(f(x)) = g( {x}^{2} ) = {x}^{2} - 3 \\ thank \: you[/tex]
Whitewater Rentals has 39 canoes and 25 solo kayaks. The canoes rent for $45 for a six-hour trip. The solo kayaks rent for $49 for the same trip. One day 8 canoes and 4 kayaks were not rented. How much money was collected for rent-als that day?
jennifer works at whataburger and earned 168.75 last week. If she worked 22.5 hours, how much does she earn per hour?
Answer:
7.5
Step-by-step explanation:
168.75 divided by 22.5 = 7.5
$7.50 dollars an hour.
7.50 x 22.5 = 168.75
if i pour 1/4 gallon of tea in each of the 4 pitchers. how many gallon in each pitcher
4. The sum of Mr. and Mrs. Bergen's ages is 100. The difference between their ages is 10. How old are Mr. and Mrs. Bergen?
100-10=90
90÷2=45
Mr Bergen's age=45+10
=55 years old
Mrs Bergen's age=45 years old
The height of a candle, in centimeters, can be modeled by the linear equation h = 28 - 2t, where t represents the hours that the candle has been burning.
Interpret the slope of this equation in the context of this problem:
The slope is -2. In context to this problem, the candle will burn away 2cm of its length every hour.
The slope of the equation, -2, means that the height of the candle reduces at a rate of 2 cm per hour.
Given the linear equation of the height of a candle that has been burning as: [tex]h = 28 - 2t[/tex].
This implies that:
28 in the equation represents the initial height of the candle = 28 cm.
-2 in the equation is slope, which is the rate of change at which the candle burns, meaning the height of the candle reduces by 2 cm every hour.
Therefore, the slope of the equation can be interpreted in the context of the problem as:
for every hour that passes, the height of the candle reduces by 2 cm.
Learn more about linear equation here:
https://brainly.com/question/19408983
A recipe for pancakes calls for 2 eggs, 1 cup of flour, and 1/2 cup of milk.
a) How much flour do you need if you use 5 eggs?
b) How much milk do you need if you use 5 eggs?
Answer:
a: 2 1/2 cups of flour
b: 1 1/2 cups of milk
Answer:
I think 10 cup flour beacuse 1 cup flour is double than that of eggHelp please help help please please please
Answer:
C. [tex] \frac{5}{4} [/tex]
D. [tex] \frac{6}{7} [/tex]
Step-by-step explanation:
C. [tex]2 - \frac{12}{16} [/tex]
[tex] = 2 - \frac{3}{4} [/tex]
[tex] = \frac{8 - 3}{4} [/tex]
[tex] = \frac{5}{4} [/tex]
D. [tex] \frac{20}{22} \times \frac{33}{35} [/tex]
[tex] = \frac{10}{11} \times \frac{33}{35} [/tex]
[tex] = 10 \times \frac{3}{35} [/tex]
[tex] = 2 \times \frac{3}{7} [/tex]
[tex] = \frac{6}{7} [/tex]
what insect is this??
Answer:
it's either an ant, small beetle, black termite, or something
Step-by-step explanation:
Find an equation for the nth term of the arithmetic sequence.
-15, -6, 3, 12, ...
The Answer is:
an = -15 + 9(n - 1)
Determine whether the variable is qualitative or quantitative. Explain your reasoning.
Favorite types of food
The variable is_____
because types are____
Miss Marple’sgrandfather passed away and she attended the reading of the will. The estate was valued at $8,424,000. It was decided that 23of the estate would be given to his children. Of the remainder, 15would be used to create a scholarship for mathematics majors at a local university and the rest would be divided evenly among his fourgrandchildren, of which Miss Marplewas one. a.How much money was used for the scholarship?[3 pts]b.What fractionof the estate did Miss Marpleend up inheriting?
The amount of money used for scholarship and the fraction of the estate gotten by Miss Maple are :
Scholarship amount = $561,600Fraction gotten by Miss Maple = 1/30The entire fraction of the estate = 1/1
Fraction given to children = 2/3
Fraction left = Total - fraction given to children
Fraction left = 1/1 - 2/3 = 1/3
For scholarship :
1/5 of fraction left :
1/5 of 1/3 = 1/5 × 1/3 = 1 /15
Fraction Given to grand children :
1/5 - 1/15 = 2/15
Amount of money used for scholarship :
1/15 × 8424000 = $561,600
B.)
Since There are four grand children and it was equally shared among them:
Miss Maple is one of the grand children:
Fraction each grandchild gets is :
2/15 ÷ 4
2/15 ÷ 4/1
2/15 × 1/4 = 2/60 = 1/30
Hence, miss Maple will get 1/30
Learn more : https://brainly.com/question/18109354
-3x + 6y = 18
-3x = 6y+14
a) What is the slope of the 1st equation?
b) What is the slope of the 2nd equation?
c) Are they parallel, perpendicular, or neither?
Step-by-step explanation:
-3x + 6y = 18
-3x = 6y+14
a) the slope of the 1st equation = -(-3)/6 = ½
b) the slope of the 1st equation = -3/6 = -½
c) they are niether parallel nor perpendicular
#1
-3x+6y=18-x+2y=62y=x+6y=x/2+3slope=1/2
#2
-3x=6y+146y=-3x-14y=-1/2x-7/3slope=-1/2
#3
Neither
Geometry PLEASE HELP
I’m right? Yes or no?
Answer:
B
Step-by-step explanation:
-2 + 12 = 10
Five times the difference of a number and 9 is equal to twice the number plus 15. What is the number?
Answer:
The number is 20
Step-by-step explanation:
Let the number be x
5(x - 9) = 2x + 15
5x - 45 = 2x + 15
5x - 2x = 15 + 45
3x = 60
x = 60/3
x = 20
Answer:
The number is 20
Step-by-step explanation:
Five times the difference of a number and 9
5(x-9)
is equal to twice the number plus 15.
=2x+15
5(x-9)=2x+15
Distribute
5x-45 = 2x+15
Subtract 2x from each side
5x-45-2x = 2x+15-2x
3x-45 = 15
Add 45 to each side
3x-45+45 =15+45
3x = 60
Divide by 3
3x/3 = 60/3
x =20
Please Help! I will give you a lot of points if you do!
--This is Hindu-Arabic math so you have to use their number system
Answer:
47
Step-by-step explanation:
According to the number system 7 lines and 12 dots, a line is 5 and a dot is 1
you do 5*7+12 which is equal to 47
So the answer is 47,
Hope this helps!
First look at the chart and then convert each symbols to their respective numbers
[tex]\\ \tt\longmapsto 6+14+13+4+0+10[/tex]
Now add[tex]\\ \tt\longmapsto 20+17+10[/tex]
[tex]\\ \tt\longmapsto 37+10[/tex]
[tex]\\ \tt\longmapsto 47[/tex]
convert 69 m 26cm into cm solv
Answer:
View explanation
Step-by-step explanation:
1 meter = 100cm, so with this logic
100 x 69 = 6,900cm
We have a standby 28 cm, so:
6,900 + 28 = 6,928
If this is the incorrect unit of measurement, let me know in the comments section so I can revamp my answer.
x – Зу +8x47+ 15 – 4у
Answer:
X-7y+391
Step-by-step explanation:
First multiply
8x47=376
Now group those that are the same together
X-3y -4y+376 +15
X-7y+391
Answer:
x - 7y + 391
Step-by-step explanation:
[tex]x - 3y + 8 \times 47 + 15 - 4y[/tex]
[tex]x - 3y + 376 + 15 - 4y[/tex]
[tex] - 3y - 4y = (- 3 - 4)y = - 7y[/tex]
[tex]x - 7y + 376 + 15[/tex]
[tex] = x - 7y + 391[/tex]
A forest contains 20 elks, of which 5 are captured, tagged, and then released. A certain time later 4 of the 20 elks are captured. What is the probability that 2 of these 4 have been tagged?
Answer:
Step-by-step explanation:
P{2 of 4 tagged}=(52)(152)(204)
=0.2167
A rectangle has perimeter 92 cm and length 39 cm. What is its width?
Multiply (-14/21) x5/9 Enter your fraction as a fraction, in simplest form.
Please help
Answer:
simplifed -10/27
Step-by-step explanation:
find the constant term in the expansion of (x +1/x)'8
[tex]\left( x+\frac{1}{x}\right)^{8} =\sum _{k=0}^{8}\binom{8}{k} \cdotp x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k}\\\\\\ \begin{array}{l}\text{We\ wish\ to\ find\ } x^{0} :\\\\x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k} =x^{0}\\\\\Longrightarrow x^{8-k} \cdotp x^{-k} =x^{0}\\\\\Longrightarrow \cancel{x}^{8-2k} =\cancel{x}^{0}\\\\\Longrightarrow 2k=8\\\\\Longrightarrow k=4\end{array}\\\\\therefore \binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8!}{( 8-4) !\cdotp 4!}[/tex]
[tex]\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8\cdotp 7\cdotp 6\cdotp 5\cdotp \cancel{4!}}{\cancel{4!} \cdotp 4\cdotp 3\cdotp 2\cdotp 1}\\\\\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4}=70\\\\\therefore \boxed{\boxed{\text{The\ constant\ term\ is\ } 70}}[/tex]
Evaluate the function f(x)=x^2+6x+2 at the given values of the independent variable and simplify.
a. f(-8)
b. f(x+2)
c. f(-x)
Answer:
a) 18
b)x^2+10x+18
c)x^2 -6x+2
Step-by-step explanation:
This is a case of plugging in the value into f(x).
a) f(-8)= -8^2 + 6(-8) +2
f(-8)= 64 + (-48) +2
f(-8)=64 + (-46)
f(-8)=18
b) f(x+2)= (x+2)^2+6(x+2)+2
So here I'll take a break to explain what's going on, because x+2 is a binomial meaning two terms and it is being squared I have to multiply the whole thing by itself. Meaning: (x+2) x (x+2), this is also known as foiling!! and for the next part its distributing 6 into x and 2.
f(x+2)= x^2+4x+4+6x+12+2
I'll reorder it
f(x+2)= x^2+4x+6x+12+2+4
f(x+2)= x^2+10x+18
c) f(-x)= -x^2+6(-x) +2
f(-x)= x^2 -6x+2
