9514 1404 393
Answer:
Jacob: 4his mother: 39Step-by-step explanation:
Let J and M represent the current ages of Jacob and his Mother.
currently:
M = 3 +9J
in 11 years:
M+11 = 5 +3(J+11)
Using the first equation to substitute for M in the second, we have ...
(3 +9J) +11 = 5 +3(J +11) . . . . . substitute for M
9J +14 = 3J +38 . . . . . . simplify
6J + 24 . . . . . . . . . . subtract 3J+14
J = 4 . . . . . . . . . . divide by 6
M = 3 +9(4) = 39
Jacob is 4 and his mother is 39.
In the American version of the Game Roulette, a wheel has 18 black slots, 18 red slots and 2 green slots. All slots are the same size. A person can wager on either red or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comes up, they win $10 otherwise they lose their wager. What is the expected value of playing the game once
Answer:
-$0.26
Step-by-step explanation:
Calculation to determine the expected value of playing the game once
Expected value= [18/(18+18+2) x $5)]- [20/(18+18+2) x $5]
Expected value= ($18/38 x $5) - (20/38 x $5)
Expected value= ($2.37-$2.63)
Expected value= -$0.26
Therefore the expected value of playing the game once is -$0.26
1.Find the first five terms of the recursive sequence.
Answer:
4.5, - 27, 162, - 972, 5832
Step-by-step explanation:
Using the recursive rule and a₁ = 4.5 , then
a₂ = - 6a₁ = - 6 × 4.5 = - 27
a₃ = - 6a₂ = - 6 × - 27 = 162
a₄ = - 6a₃ = - 6 × 162 = - 972
a₅ = - 6a₄ = - 6 × - 972 = 5832
The first 5 terms are 4.5, - 27, 162, - 972, 5832
the polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.
Answer:
Smaller factor/larger figure = 3/6 = ½
Step-by-step explanation:
Scale factor of similar figures is usually the ratio of one to the other.
In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.
Length of smaller figure = 3
Corresponding length of larger figure = 6
Scale factor = smaller figure/larger figure = 3/6
Simplify
Scale factor = ½
What is the value of f(x) = 2 • 2 x for f(–2)?
Answer:
-8
Step-by-step explanation:
you know, all you have to do in such a case is simply taking the given -2 and put it, where there is "x" in the function expression and then calculate this. if necessary with a calculator.
2×2×x with x=-2 is
2×2×-2 = -8
Answer:
- 8
Step-by-step explanation:
f ( x ) = 2 . 2 x
f ( - 2 )
= 2 . 2 ( - 2 )
= 2 x 2 x ( - 2 )
= - 8
Help!!!!!!!!!!!!!!!!
502.5 = -502.5
Now
x = -502.5
= -5025/10
= -1005/2 feet
Answered by Gauthmath must click thanks and mark brainliest
How do I solve this?
Answer:
y = 0.8x – 2
Step-by-step explanation:
Slope (m) =
ΔY/ ΔX = 4 /5 = 0.8
y=.8x+b
plug in point
b=-2
What is the correct answer
Answer:
cột số 2
Step-by-step explanation:
please help me with this question <3
9514 1404 393
Answer:
a) 30.7 million
b) 1.5% per year
c) 42.0 million
d) 2017
Step-by-step explanation:
a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.
__
b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.
The population is growing by 1.5% per year.
__
c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.
P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0
The population in Canada in 2021 is predicted to be 42.0 million.
__
d) For this we need to solve for t when P(t) = 40.
40 = 30.7·1.015^t
40/30.7 = 1.015^t
Taking logarithms gives ...
log(40/30.7) = t·log(1.015)
t = log(40/30.7)/log(1.015) ≈ 17.773
In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.
_____
Additional comment
The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.
Which function has a domain of all real numbers?
Answer:
c part ....
please mark brainlest
Translate sentence into equation
nine more than a product of a number and 4 is 8
Answer:
If x is the required number, equation will be 9+4x=8
DEFG is a cyclic quadrilateral. If ∠E = 27°, find ∠G.
For a cyclic quadilateral, the combination of opposite angles = 180°. So <G is opposite to <E so G must be 153°
Express as a trinomial (2x-10)(2x+6)
Answer:
4x² - 8x - 60
Step-by-step explanation:
Given :-
(2x - 10 )(2x + 6)Simplify ,
2x ( 2x + 6) -10(2x +6) 4x² + 12x - 20x -60 4x² -8x -60Trinomial expression :-
4x² - 8x - 60The polynomial function [tex](2x-10)(2x+6)[/tex] expressed as a trinomial is [tex]4x^2 - 8x - 60[/tex].
Given data:
The polynomial function is represented as A.
Now, the value of [tex]A=(2x-10)(2x+6)[/tex].
On simplifying the equation:
From distributive property to multiply the terms:
[tex]A=2x * 2x + 2x * 6 - 10 * 2x - 10 * 6[/tex]
[tex]A=4x^2 + 12x - 20x - 60[/tex]
On simplifying the equation:
[tex]A=4x^2 - 8x - 60[/tex]
Hence, the trinomial is [tex]4x^2 - 8x - 60[/tex].
To learn more about polynomial equations, refer:
https://brainly.com/question/13199883
#SPJ6
Find the measure of angle BAC.
Answer:
[tex]\angle 72=BC-86/2[/tex]
[tex]144+86=BC[/tex]
[tex]BC=230[/tex]
[tex]BC=230/2[/tex]
[tex]\angle BAC= 115[/tex]°
~OAmalOHopeO
Helppppp please
What is the slope of the line shown below?
Answer:
A.
[tex]{ \tt{slope = \frac{ - 4 - 2}{ - 1 - 2} }} \\ \\ = { \tt{ \frac{ - 6}{ - 3} }} \\ = 2[/tex]
The power 9 squared is equivalent to 81. What is the value of 9 Superscript negative 2?
Answer:
1/81
Step-by-step explanation:
9^2 = 81
We know that a^ -b = 1/a^b
9^-2
1/9^2
1/81
Answer:
1/81
Step-by-step explanation:
Edge
Which of the following equations correctly represents the law of sines?
Answer:
Option c is correct
Step-by-step explanation:
From the screenshot I attached.
sinA/a=SinC/c
a/c=SinA/SinC
Thus a=cSinA/SinC
(25 POINTS)Please help me, and show all of your work step by step.
Now say you invest $6,500 and the highest interest rate you can find is 2.5% compounded annually, but you would have to leave this investment in the account for a minimum of 5 years. If you decide to wait 5 years to buy the car, how much more money will you have to save to buy a car at the price of $8,000? Use the compound interest formula A = P(1 + i)^n.
A = accumulated amount
P = principle
i = interest rate
n = number of years
Answer:
$ 645.85
Step-by-step explanation:
First you would plug 6,500 into P. The plug 2.5% as 0.025 into i. And plug the years (5) into n.
A = 6500 (1 + 0.025)^5 = 7354.15
That is the amount that would be in the account at the end of the 5 years.
Then you take the cost of the car (8,000) and subtract the money left in the account (7,354.15).
8000 - 7354.15 = 645.85
Your final answer would be rounded to the nearest cent, or the hundredths place.
What is the range of 58, 59, 57, 59, 55
Answer:
4
Step-by-step explanation:
Hi there!
Range = largest number from data given - smallest number from data given
From the given data, 58, 59, 57, 59, 55,
59 is the largest number and 55 is the smallest number
So the range = 59 - 55 = 4
Bike speed of 21miles per hour. What is the speed per minute how many miles will the cyclist travel in 10 minutes
Answer:
First part: 0.35 miles per minute
Second part: 3.5 miles in 10 minutes
Step-by-step explanation:
Think about this as a fraction. Fractions can't be added nor subtracted unless they share the same denominator. So for this case, we have to turn hours into minutes. So 21 mph becomes 21 miles per 60 minutes. Then, we divide 60 from each side to find the speed per minute. 21/60 = 0.35, so the answer to the first part is 0.35 miles per minute.
Using what we got, we can answer the second part of the distance covered in 10 minutes. So, we just multiply 0.35 by 10 which is 3.5 miles covered in 10 minutes.
A mixture of jellybeans is to contain twice as many red as yellow, three times as many green as yellow, and twice as many pink as red. Red jelly beans cost $1.50 per pound, yellow cost $3.00 per pound, green cost $4.00 per pound, and pink only costs $1.00 per pound. How many pounds of each color jellybean should be in a 10 pound canister that costs $2.20 per pound?
Polygon D is a scaled copy of Polygon C using a scale factor of 6.
How many times as large is the area of Polygon D compared to the area Polygon C?
Answer:
The area of D is 36 times bigger than C
Step-by-step explanation:
The scale factor is 1:6
We know the ratio of the areas is the ratio of the scale factor squared
1^2 : 6^2
1:36
The area of D is 36 times bigger than C
Solve for X
5x^2 + 6 =17x
Answer: x= 2/5 or x= 3
how?
Step 1: Subtract 17x from both sides
5x² + 6 -17x = 0
*PUT THEM IN ORDER* --> 5x² -17x + 6= 0
Step 2: Factor left side of equation:
(5x-2) (x-3) = 0
Step 3: Set factors equal to 0.
5x−2=0 or x−3=0
which gives us an answer of x= 2/5 or x=3
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{5x^2 + 6 =17x}\\\\\large\textsf{SUBTRACT 17x to BOTH SIDES}\\\\\mathsf{5x^2 + 6 - 17x = 17x - 17x}\\\\\mathsf{5x^2 - 17x + 6 = 0}\\\\\large\textsf{SET the LEFT SIDE to equal 0}\\\\\mathsf{(5x -2)(x -3)=0}\\\\\large\textsf{SET the FACTORS to EQUAL to 0}\\\\\mathsf{5x - 2 = 0\ or\ x - 3 = 0}\\\\\large\textsf{SIMPLIFY ABOVE AND YOU HAVE YOUR RESULT}\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf x = \dfrac{2}{3}\ or\ x = 3}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 10 hours? What is the rate of speed of the jet?
980 miles
Step-by-step explanation:
5 hours =490miles
1 hour =490/5=98miles
10hours = 98×10=980miles
6.7.35
Question Help
As(t)
800-
A toy rocket is launched from the top of a building 360
feet tall at an initial velocity of 112 feet/second. The
height of the rocket t seconds after launch is given by
the equation s(t)= - 16t2 + 112t+ 360. When does the
rocket reach its greatest height? What is the greatest
height?
600-
400-
200-
0-
0 1
8 9 10
The rocket reaches its greatest height at
feet after
second(s)
Answer:
Step-by-step explanation:
This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!
The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.
If:
[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:
v(t) = -32t + 112 and solve for t:
-112 = -32t so
t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.
Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:
[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and
s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.
answer nowwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
7/6
Step-by-step explanation:
(7x/12)/(x/2)
=7/6
Write an equation of a polynomial with the given characteristics: a quadratic function has x -intercepts of -3 and 1, and a y-intercept of (0,9).
Answer:
f(x) = -3(x+3)(x-1)
Step-by-step explanation:
x = -3 & 1; f(x) = 9
f(x) = a(x-r1)(x-r2)
f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)
9 = a(3)(-1); 9 = a(-3)
a = -3
f(x) = -3(x+3)(x-1)
Answer:
f(x) = -3x^2 - 6x + 9.
Step-by-step explanation:
As the x intercepts are - 3 and 1 we can write it as:
f(x) = a(x - 1)(x + 3) where a is a constant to be found.
As the - intercept is at (0, 9), x =0 when f(x) = 9 so we can also write:
a( 0 - 1)(0 + 3) = 9
(-1)(3)a = 9
a = 9 / -3
= -3.
So the equation is f(x) = -3(x - 1)(x + 3)
In expanded form it is
-3(x^2 + 2x - 3)
= -3x^2 - 6x + 9.
If b = -1, which one is the value of b^3?
Answer:
b=-1Put the value of b in b^3[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]
Hence b^3=-1
Which expression is equivalent to √-80? 0 -4ſ5 O -4.5 O 4.5 O45
Answer:
None.
Step-by-step explanation:
There is no expression for the square root of negative numbers. In other words it is undefined.
Answer:
4√5
Step-by-step explanation:
please me in math
[tex] \frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1} [/tex]
Step-by-step explanation:
hope this helps you thank you
[tex]\boxed{ \sf{Answer}} [/tex]
[tex] \large{\sf\frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1}} [/tex]
Use the algebraic identities ⟶
[tex]{\sf(a - b)(a + b) = {a}^{2} - b ^{2}} [/tex][tex]{\sf(a + b) {}^{2} = {a}^{2} + 2ab - {b}^{2}} [/tex][tex]{\sf(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2}} [/tex]Squaring on both the sides
[tex] {\sf\frac{(a + 1 {)}^{2} + ( {a - 1)}^{2} }{(a - 1)(a + 1)}} [/tex]
[tex]=\frac{ {a}^{2} + 2a + 1 + {a}^{2} - 2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} +\bcancel 2a + 1 + {a}^{2} - \bcancel2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} + {a}^{2} + 1 + 1 }{ {a}^{2} - 1}[/tex]
[tex]\large\boxed{\sf{⟹\frac{ {2a}^{2} + 2}{ {a}^{2} - 1 }}} [/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
3y^4/3y^2-6=10 please help I will.mark it as the brainliest answer!
Answer:
y=4
Step-by-step explanation:
you multiply through by 3y^2
3y^4 - 18y^2 =30y^2
Collect like terms
3y^4=48y^2
divide through by y^2
3y^2=48
divide through by 3
y^2=16
take the square root of both sides
y=4
