Answers
Answer:
1. Steve's age is 18 and Anne's age is 8.
2. Max's age is 17 and Bert's age is 11.
3. Sury's age is 19 and Billy's age is 9.
4. The man's age is 30 and his son's age is 10.
Step-by-step explanation:
1. Let us assume that:
S = Steve's age now
A = Anne's age now
Therefore, in four years, we have:
S + 4 = (A + 4)2 - 2
S + 4 = 2A + 8 - 2
S + 4 = 2A + 6 .................. (1)
Three years ago, we have:
S - 3 = (A - 3)3
S - 3 = 3A - 9 ................................ (2)
From equation (2), we have:
S = 3A - 9 + 3
S = 3A – 6 …………. (3)
Substitute S from equation (3) into equation (1) and solve for A, we have:
3A – 6 + 4 = 2A + 6
3A – 2A = 6 + 6 – 4
A = 8
Substitute A = 8 into equation (3), we have:
S = (3 * 8) – 6
S = 24 – 6
S = 18
Therefore, Steve's age is 18 while Anne's age is 8.
2. Let us assume that:
M = Max's age now
B = Bert's age now
Therefore, five years ago, we have:
M - 5 = (B - 5)2
M - 5 = 2B - 10 .......................... (4)
A year from now, we have:
(M + 1) + (B + 1) = 30
M + 1 + B + 1 = 30
M + B + 2 = 30 .......................... (5)
From equation (5), we have:
M = 30 – 2 – B
M = 28 – B …………………… (6)
Substitute M from equation (6) into equation (4) and solve for B, we have:
28 – B – 5 = 2B – 10
28 – 5 + 10 = 2B + B
33 = 3B
B = 33 / 3
B = 11
Substituting B = 11 into equation (6), we have:
M = 28 – 11
M = 17
Therefore, Max's age is 17 while Bert's age is 11.
3. Let us assume that:
S = Sury's age now
B = Billy's age now
Therefore, now, we have:
S = B + 10 ................................ (7)
Next year, we have:
S + 1 = (B + 1)2
S + 1 = 2B + 2 .......................... (8)
Substituting S from equation (7) into equation (8) and solve for B, we have:
B + 10 + 1 = 2B + 2
10 + 1 – 2 = 2B – B
B = 9
Substituting B = 9 into equation (7), we have:
S = 9 + 10
S = 19
Therefore, Sury's age is 19 while Billy's age is 9.
4. Let us assume that:
M = The man's age now
S = His son's age now
Therefore, now, we have:
M = 3S ................................... (9)
Five years ago, we have:
M - 5 = (S - 5)5
M - 5 = 5S - 25 ................ (10)
Substituting M from equation (9) into equation (10) and solve for S, we have:
3S - 5 = 5S – 25
3S – 5S = - 25 + 5
-2S = - 20
S = -20 / -2
S = 10
Substituting S = 10 into equation (9), we have:
M = 3 * 10
M = 30
Therefore, the man's age is 30 and his son's age is 10.
Related Questions
3. The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising. (a) What is the recursive rule for the sequence? (b) What is the iterative rule for the sequence?
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
(a) What is the recursive rule for the sequence?
Given the sequence
6, 18, 54, 162,...
Please note that each successive term is 3 times the previous term.
i.e. 18 = 6×3, 54 = 18×3, 162 = 54×3
Here, r = 3 is the common multiplier
In other words, every next term can be obtained by multiplying the previous term by a number 'r', using the recursive formula
[tex]a_n=a_{n-1}\times r[/tex]
Here, aₙ is r times the previous term aₙ₋1.
For example, in order to determine the 2nd term a₂, just put n=2 in the recursive formula
[tex]a_n=a_{n-1}\times r[/tex]
so substituting r = 3, and n = 1 in the recursive formula
[tex]a_2=a_{2-1}\times 3[/tex]
[tex]a_2=a_1\times \:3\:\:\:\:\:\:[/tex]
as
a₁ = 6
so
[tex]a_2=6\times \:3\:\:\:\:\:\:[/tex]
[tex]a_2=18[/tex]
(b) What is the iterative rule for the sequence?
Given the sequence
6, 18, 54, 162,...
A geometric sequence has a constant ratio 'r' and is defined as
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]\frac{18}{6}=3,\:\quad \frac{54}{18}=3,\:\quad \frac{162}{54}=3[/tex]
The ratio of all the adjacent terms is the same and equal to, so
r = 3
as
a₁ = 6
so substituting r = 3 and a₁ = 6 in the nth term of the sequence
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=6\cdot \:3^{n-1}[/tex]
Thus, the iterative rule for the sequence is
[tex]a_n=6\cdot \:3^{n-1}[/tex]a) The recursive rule for the sequence is [tex]a_n=3a_{n-1}[/tex]
b) The iterative rule for the sequence is [tex]a_n=2(3^n)[/tex]
The given sequence is:
6, 18, 54, 162, …
The common ratio, r = 18/6
r = 3
Let the last term be [tex]a_n[/tex]
Let the preceding term be [tex]a_{n-1}[/tex]
The recursive rule for the sequence is given as:
[tex]a_n=a_{n-1}r\\\\a_n=3a_{n-1}[/tex]
b) The iterative rule is gotten by using the formula:
[tex]a_n=ar^{n-1}[/tex]
Substitute a = 6 and r = 3 into the formula above
[tex]a_n=6(3)^{n-1}\\\\a_n=\frac{6}{3}(3^n )\\\\a_n=2(3^n)[/tex]
Learn more on sequence here: https://brainly.com/question/6561461
John had 2 ¼ cans of paint leftover after painting his mural. Ann had 3 ⅜ cans leftover. How much paint was leftover altogether?
Answers
Answer:
5 5/8 or Decimal: 5.625
Step-by-step explanation:
Hope this helps!!!
Brainliest?
Using point-slope form, write the equation of the line that passes through (–3, 2) and has a slope of 5. A. (y – 2) = 5(x + 3) B. (y – 2) = 5(x – 3) C. (y + 2) = 5(x – 3) D. (y + 2) = –5(x + 3)
Answers
Answer:
A. (y - 2) = 5(x + 3)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Point (-3, 2)
Slope m = 5
Step 2: Write Equation
Substitute in variables into general form.
y - 2 = 5(x + 3)
There is a 12% sale on glue sticks. The
original price was $3.00 What is the new
cost?
Answers
Answer:
$0.36
Step-by-step explanation:
12*3 36
____ =____
100 100
which of the following is a solution of 3x^2=7x-3
a.) -7(plus or minus) square root of 13 over 6
b.) 7(plus or minus) square root of 85 over 6
c.) -7(plus or minus) square root of 85 over 6
d.) 7(plus or minus) square root of 13 over 6
Answers
plz help! WILL GIVE BRAINLIEST
Answers
Answer:
3x+7=y
Step-by-step explanation:
HELPPP PLZZZ QUICKKK THIS IS DUE IN 2 MINUTESSSSSSS
Answers
Answer:$31.36
Step-by-step explanation:
It was a bumper crop for hominy this year, and The Hominy Man hoped to set a price for a case that can maximize profit. The annual fixed cost for the hominy harvesting and other equipment is $200 and the variable cost per case is $20. The price (p) is related to demand (v) according to the following equation: v = 800 - 16p. To maximize the profit, the optimal price of a case should be_____. The maximized profit is_____.
Answers
Answer:
optimal price = $35
Maximum profit = $3400
Step-by-step explanation:
We are given;
The annual fixed cost for the hominy harvesting and other equipment = $200
The variable cost per case = $20
Since demand is given as v, thus total variable cost = 20v
Thus;
Overall total cost = fixed cost + total variable cost = 200 + 20v
We are given relationship between p and v as;
v = 800 - 16p
Making p the subject gives;
p = (800 - v)/16
Now, total revenue is given by;
Total Revenue = vp
Thus;
Total revenue = v[(800 - v)/16] = 50v - v²/16
Now, profit will be;
Profit(P) = Total revenue - total cost
P = (50v - v²/16) - (200 + 20v)
P = 50v - (v²/16) - 200 - 20v
P = 30v - (v²/16) - 200
Maximum profit will be at dP/dv = 0
Thus;
dP/dv = 30 - (v/8)
At dP/dv = 0
30 - (v/8) = 0
v/8 = 30
v = 30 × 8
v = 240
Optimal price will be gotten by putting 240 for v in the price equation which is p = (800 - v)/16.
Thus;
p = (800 - 240)/16
p = 560/16
p = $35
So, optimal price = $35
Maximum profit will be at v = 240.so let's plug in 240 for v into the profit equation.
Thus;
P = 30(240) - (240²/16) - 200
P = 3400
Maximum profit = $3400
Given the third term is 12 and the rate of change is 3. What is the 5th term
Answers
Answer:
The 5th term:
a₅ = 18
Step-by-step explanation:
We know that Arithmetic sequences have a constant rate of change.
Given
a₃ = 12common difference = rate pf change = d = 3The nth term of the Arithmetic sequence with a₁ and 'd' is defined as
aₙ = a₁ + (n-1)d
Where
a₁ is the first term
d is the common difference
as
a₃ = 12
d = 3
so
Plug in n=3
a₃ = a₁ + (3-1)d
Now Plug in a₃ = 12 and d = 3
12 = a₁ + (3-1)3
12 = a₁ + 2(3)
12 = a₁ + 6
a₁ = 6
so
Formula to find the 5th term
a₅ = a₁ + 4d
Plug in a₁ = 6 and d = 3
a₅ = 6 + 4(3)
a₅ = 18
Therefore, the 5th term:
a₅ = 18
What is the Inverse function of F(x)=3x²?
Answers
Answer:
f⁻¹(x) = x+2 / 3
Step-by-step explanation:
i dont have one. i just did it.
equation 1: 5x + 3y=8
equation 2: 4x + 7y= 34
9x-10y=42 true
Answers
Answer:
true
Step-by-step explanation:
5x + 4x = 9x
3y + 7y = 10y
8 + 34 = 42
Answer:
False
Step-by-step explanation:
5x+3y=8
4x+7y=34
Then:
5x+4x+3y+7y=9x+10y
9x+10y=43 not 9x-10y
Helpp meeeeeee plzzz (13 points )
Answers
Answer:
that they both have right angles and have a leath of 5
Step-by-step explanation:
HELP!!! ASAP MARKING BRAINLIEST!!!
Answers
Answer:
it's the first one. I hope you get a good grade
whats 0.1 as a percent
Answers
Answer:
TO findt he percent move the decimal place to the right 2 times. THis applies for any decimal. Therefore the percent is 0.1--->10%
Step-by-step explanation:
Please help. Only if you know it.
Answers
Answer:
C (Lake Depth Answer)
Step-by-step explanation:
Here we want to find the math that ends up with 0.
The stock starts with 12$, but loses 16$.
That's -4$ total, not 0.
The ion starts with 19 protons, and 18 electrons. Protons are postive charges, electrons are negative.
This leaves us with 1 proton, not 0.
The lake depth increases by 6 inches, but evaporates 6.
This leaves us back where we started, with 0.
Ahmed spends 25$, but earns 30$.
This leaves us with $5, not 0.
Claire currently earns $25 per hour at her work. Her boss has decided to give her a 15% raise. What is Claire's new hourly wage?
Answers
Answer:
$28.75
Step-by-step explanation:
15% of 25 is $3.75 and that + the 25 that is already there is $28.75
Answer:
$28.75
15% of $25. is $3.75....add $25.00 + $3.75= $28.75
a coffee supplier finds that it cost $850 to roast and package 100 pounds of coffee in a day and $2850 to produce 500 pounds of coffee in a day. assume that the cost function is linear. express the cost as a function of the number of pounds of coffee they produce each day
Answers
Answer:
f(x) = 5x + 350
Step-by-step explanation:
Create 2 points using the information given, where x is the number of pounds of coffee and y is the cost.
The 2 points are (100, 850) and (500, 2850)
Then, use rise over run to find the slope:
(y2 - y1) / (x2 - x1)
(2850 - 850) / (500 - 100)
2000 / 400
= 5
Then, plug in the slope and a point into y = mx + b to find b:
y = mx + b
850 = 5(100) + b
850 = 500 + b
350 = b
Plug in the slope and y intercept into y = mx + b to get the equation:
y = 5x + 350
Put it into function form:
f(x) = 5x + 350 is the cost function
Order the following from least to greatest
( 94, 71 1/3, -8, -43 )
Answers
Answer:
-43, -8, 1/3, 71, 94
If you meant that 71 is a mixed fraction:
-43, -8, 71 1/3, 94
It is 5:15 pm now. What time will it be in 40 minutes?
5:45 am
A5:45 pm
c5:55 pm
6:00 pm
Answers
Answer:
C:5:55
Step-by-step explanation:
5:15 plus 40 minutes will be 5:55
Answer:
C. 5:55 itssssss easyyy
Step-by-step explanation:
5:15
+40
55
Slope and y intercept of y=2.7x+8
Answers
Answer:
slope: 2.7
y-intercept: (0,8)
Step-by-step explanation:
In the form y = mx + b, m is the slope and b is the y-intercept.
y-intercept : (0,8)
Find the perimeter of the large triangle
Answers
Answeeeeeeeeeeerrrrrrrrrrrrrrr:
36
1) Find the product of -5x2y4 and 3xy3
Answers
Answer:
Answer: -15x3y7
Step-by-step explanation:
Answer:
-15x3y7 is the answer
Step-by-step explanation:
All male teachers better dom me rn tell me to stop misbehaving or else
Answers
ma'am/sir please this is a Wendy's
A 3-yard roll of wrapping paper costs $8.64. What is the price per inch?
Answers
0.08$
Step-by-step explanation:
1yrd=36inch
3yard=108inch
108 inch costs 8.64$
8.64/108=0.08$ ( 1 inch cost)
How long will it take for $5,000 to double at the rate of 2.25% interest?
Answers
Answer:
31.15
Step-by-step explanation:
Ya tengo el resultado, debe ser "y=4x-4"
Pero le doy 15 puntos al que llegue a ese resultado y explique cómo llegó a él
El método de Descartes para determinar tangentes se basa en la idea de que para muchas gráficas, la recta tangente en un punto dado es una recta "única" que intersecta la gráfica solamente en ese punto. Aplicaremos ese método para determinar la ecuación de una recta tangente a la parábola y=x^2 en el punto (2,4).
Primero, sabemos que la ecuación de la recta tangente debe tener la forma de y=mx+b. Usando el hecho de que el punto (2,4) está en la recta, podemos resolver para b en términos de m y obtener la ecuación y=mx+ (4-2m). Ahora queremos que (2,4) sea la "única" solución del sistema
{ y=x^2
y=mx+4-2m
De este sistema obtenemos x^2-mx+(2m-4)=0. Usando la fórmula cuadrática obtenemos
m+- √(m^2-4(2m-4))
x= --------------------------------
2
Para obtener una solución única para x, las dos raíces deben ser iguales, en otras palabras, el discriminante m^2-4(2m-4) debe ser 0. Completa el trabajo para obtener m y escribe una ecuación de la recta tangente
Answers
Answer:
Ver desarrollo en los parrafos que siguen
Step-by-step explanation:
El problema describe todos los pasos para llegar al sistema the equaciones:
y = x^2
y = m x + 4 - 2 m
Luego igualamos las cantidades 'y" y llegamos a la siguiente ecuacion cuadratica en "x":
x^2 = m x + 4 - 2m
luego restamos "m x" y "4" de ambos lados, y sumamos "2 m" de ambos lados para terminar con una ecuacion cuadratica igualada a cero para poder aplicar la equacion cuadratica
x^2 - m x - 4 + 2 m = 0
similar a:
a x^2 + b x + c = 0
donde
a = 1; b = "-m"; y c = "2 m - 4"
Luego usando la ecuacion cuadratica:
nos da de resultado:
[tex]x=\frac{m+/-\sqrt{m^2-4(1)(2m-4)} }{2(1)}[/tex]
Y para que la solucion sea UNICA, es necesario que la cantidad dentro de la raiz sea "cero" de modo que de solamente la solucion
x = m/2
Ahora, requiriendo que el determinante the la ecuacion cuadratica sea cero es:
[tex]m^2-4(2m-4)=0\\m^2-8m+16=0\\(m-4)^2=0\\m-4=0\\m=4[/tex]
ya que reconocemos que el trinomio m^2-8m+16 es un binomio quadrado perfecto; (m-4)^2
Y pidiendo que that binomio quadrado sea cero, es lo mismo que requerir que el binomio (m-4) sea cero, lo que significa que m = 4.
De esta manera, obtuvimos la pendiente "m" de nuestra recta:
y = m x + b
y = 4 x + b
Y como conociamos el valor de "b" usando el hecho de que el punto (2, 4) esta en la recta:
4 = 4 (2) + b
4 = 8 + b
4 - 8 = b
b = -4
Por lo tanto, la ecuacion dela recta es:
y = 4 x - 4
please help!!!!!!
Matthew took a cab home from his office. The cab charged a flat fee of $4, plus $2 per mile. Matthew paid $34 for the trip Write an equation to show the number of miles Matthew drove
Answers
Answer:
(34-4)/2
Step-by-step explanation:
First you would subtract the flat fee of 4 dollars from the total ($34) which would give you 30 then you divide 30 by the rate or dollars per mile (2) which would leave you with 15 so he drove 15 miles and if you were to writ this as an equation (as shown above) it would look like this (34-4)/2 where you first subtract (hence the parentheses) then you would divide (hence the / ). I hope you found this helpful :D
match the equation with its graph . identify the slope and y-intercept y= -2/3x+1
Answers
Answer:
the slope is -2/3x and the y intercept is 1
Step-by-step explanation:
Plz helplplpp this is due NOWWW
Answers
Answer:
Option 2
Step-by-step explanation:
1/4 is equal to .25 or 25/100
Option 2
Explanation:
1/4 =0.25
0.25 x 5 = 1.25
1/4 x 5 = 1 1/4
21. Transportation A youth group with 26 members is going skiing. Each of the five
chaperones will drive a van or sedan. The vans can seat seven people, and the
sedans can seat five people. Assuming there are no empty seats, how many of each
type of vehicle could transport all 31 people to the ski area in one trip?
Answers
Answers:
2 sedans and 3 vans
=====================================================
Work Shown:
s = number of sedans
v = number of vans
1 sedan = 5 seats
s sedans = 5s seats
1 van = 7 seats
v vans = 7v seats
5s+7v = all seats
5s+7v = 31
Let's go through all the values of s to see which values of v work.
If s = 0, then the equation turns into 7v = 31, but the solution for v isn't an integer.If s = 1, then the equation turns into 5+7v = 31 and that solves to v = 26/7 = 3.71 which also isn't an integerIf s = 2, then the equation becomes 10+7v = 31 and that solves to v = 3. So we found the answer. This means we need 2 sedans and 3 vans.As a check:
2 sedans = 5*2 = 10 seats
3 vans = 7*3 = 21 seats
10+21 = 31 seats total
This confirms the answer.
The number of vans used is three and the number of sedans is two
Let :
v represent the number of vans
s represent the number of sedans
The following equations can be gotten
7v + 5s = 31 equation 1
v + s = 5 equation 2
The elimination method would be used to solve for v and s
Multiply equation 2 by 7
7v + 7s = 35 equation 3
Subtract equation 1 from 3
2s = 4
s = 4/2
s = 2
Substitute for s in equation 2
v + 2 = 5
v = 5 - 2
v = 3
To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults