===================================================
Explanation:
G = amount of money George starts with
T = amount of money Tia starts with
Initially the ratio of their money is 9:4 so G/T = 9/4. Solve for G to get G = (9/4)T.
--------
After George spends 24 dollars he's left with (G-24) dollars. Tia gains 11 dollars so she has (T+11) dollars. They have the same amount of money after these two events occur, so G-24 = T+11.
Plug in G = (9/4)T and solve for T
G-24 = T+11
(9/4)T-24 = T+11 ... replace G with (9/4)T
4*[ (9/4)T-24 ] = 4*[ T+11 ] ... multiply both sides by 4 to clear out fraction
9T - 96 = 4T + 44 ... distribute
9T - 4T = 44 + 96
5T = 140
T = 140/5
T = 28
Tia started off with 28 dollars. We could stop here because your teacher is only asking about Tia's initial amount.
----------
If you want to find how much George started with, then plug T = 28 into G = (9/4)T to get...
G = (9/4)T
G = (9/4)*28
G = 2.25*28
G = 63
George started off with 63 dollars
The ratio of 63:28 reduces to 9:4 after dividing both parts by the GCF 7. This confirms the first fact we're given.
Notice how 63 drops to 63-24 = 39 after George spends $24. At the same time, Tia's amount increases to 28+11 = 39, which is the same as George's updated amount. Both facts match the description, so we have confirmed the answer.
Answer:
$28
Step-by-step explanation:
Which letter has a line of symmetry?
Answer:
D. all of the above
Step-by-step explanation:
All the letters from the options have a line of symmetry.
Ronald bought a car for 2,500. The value of the car depreciates by 6 percent each year. What type of function is this ?
Answer:
Exponential
Step-by-step explanation:
The liner function represents that there is a constant change in the original value of the asset
While on the other hand the ex[onential function refers to that function in which there is an increase or decreased in the value of the asset that contains the current value of the asset
Hence, the given situation denotes the exponential function
Find the solution of y= 4x+ 2 for x = -5.
Answer:
[tex]y=-18[/tex]
Step-by-step explanation:
[tex]y=4x+2[/tex] for [tex]x=-5[/tex]
[tex]y=4(-5)+2\\y=-20+2\\y=-18[/tex]
Answer:
y = -18
Step-by-step explanation:
y = 4x+2
Let x = -5
y = 4(-5) +2
y = -20 +2
y = -18
Wally rides his bicycle at an average speed of 13 miles per hour. How many miles will he travel in 4 1/2 hours? Please answer this quickly!
Answer:
58.5
Step-by-step explanation:
Distance = rate * time
so if it's 4.5 hours:
Distance = 13 mph* 4.5 hours
= 58.5 miles
Please help ive been trying and i just cant get it right
Nine less than five times a number is three more than twice the number?
Answer:
x = 4
Step-by-step explanation:
5x-9 = 2x+3
3x = 12
x = 4
Answer:
4
Step-by-step explanation:
Tahmar knows the formula for simple interest is I = Prt, where I represents the simple interest on an amount of money, P, for t years at r rate. She transforms the equation to isolate P : P = P : P equals StartFraction I Over r t EndFraction.. Using this formula, what is the amount of money, P, that will generate $20 at a 5% interest rate over 5 years?
$
Answer:
80 dollars
Step-by-step explanation:
l=prt ⇒ p=l/rt
20=p(0.05)(5)
P=20/0.25=80 dollars
Answer:
The answer is $80
Step-by-step explanation:
I just got it right
Graph the equation y = -x2 + 5x + 24. How do the values of x = 8 and x = -3 on the graph relate to this situation? Find the width of the archway.
Answer:
The values of x = 8 and x = -3 are the x-intercepts of this equation. The width of the archway is 11 units.
Step-by-step explanation:
Let be [tex]y = -x^{2}+5\cdot x +24[/tex], which is now graphed with the help of a graphing tool, the outcome is included below as attachment. The values of x = 8 and x = -3 are the x-intercepts of this equation, that is, values of x such that y is equal to zero. Algebraically speaking, both are roots of the second-order polynomial.
The width of the archway ([tex]d[/tex]) is the distance between both intercepts, which is obtained by the following calculation:
[tex]d = |x_{1}-x_{2}|[/tex], where [tex]x_{1} \geq x_{2}[/tex].
If [tex]x_{1} = 8[/tex] and [tex]x_{2} = -3[/tex], then:
[tex]d = |8-(-3)|[/tex]
[tex]d = 8 +3[/tex]
[tex]d = 11[/tex]
The width of the archway is 11 units.
A circle has a radius of sqrt 37 units and is centered at (1.3, -3.5) write the equation fo the circle
Answer:
(x-1.3)^2 + (y+3.5)^2 = 37
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-1.3)^2 + (y--3.5)^2 = (sqrt(37))^2
(x-1.3)^2 + (y+3.5)^2 = 37
PLEASE HELP!!!
What is the interquartile range of this data set?
1,5, 27, 29, 34, 46, 48, 61, 64, 84, 96
Answer:
37
Step-by-step explanation:
Answer:
D. 37
Step-by-step explanation:
Your choice is correct!
If approximately 10% of people are left-handed, how many lefties would you expect in a high school graduating class of 424
Answer:
42
Step-by-step explanation:
P(left) = 0.10
Expected number of lefties among high school grads of 424
= 424 * 0.10
= 42 (to the nearest person)
Answer:
you do 20% of 424
1 0% of 424 =42.4
you could round it to 42
A certain server works four 6-hour shifts a week at a restaurant and has a base salary of $9.75/ℎ. An average server sells $1400 in a single shift. If the server makes an average of 14% tip of a bill, what is the annual gross income of the server?
Answer:
The annual gross income of the server is $52936
Step-by-step explanation:
The server works four 6-hour shift a week.
the server earns $9.75/h
An average seller sells $1400 in a single shift, and makes 14% tip of a bill.
For the 6-hour shift, the server earns
6 x $9.75 = $58.5 a shift
in a week, the total money made for the four shifts in a week will be
4 x $58.5 = $234
The server makes an average of 14% of a bill, and makes about $1400 in a single shift.
In a single shift he makes a tip of
14% of $1400 = 0.14 x $1400 = $196
in a week he makes 4 x $196 = $784
Total money the server makes in a week is
==> $234 + $784 = $1018
There are 52 weeks in a year.
The server's annual gross income will be
52 x $1018 = $52936
If 35%discount is given on a trouser which costs #3,000.00k,how much will a buyer pay for the trouser?
Answer:
1950
Step-by-step explanation:
3000×35/100
=1050
so 3000-1050
=1950
Two cars leave the park at the same time one travels north at a speed of 50 km an hour for two hours the second car travels west at a speed of 80 km an hour for two hours after the two hours how far apart are the two cars
Answer:
50 km/hr * 2hr = 100km
80 km/hr * 2hr = 160km
using pythagorean theorem: x = sqrt((a^2)+(b^2))
x = sqrt ((100^2) + (160^2)
x = 188.67 km
Step-by-step explanation:
What is the value of n in the equation 3n + 2(n + 2) = 9n + 12? −4 −2 2 4
Answer:
-2
Step-by-step explanation:
3n+2n+4=9n+12
5n+4=9n+12
5n-9n=-4+12
-4n=8
n=8/-4
n= -2
Answer:
-2
Step-by-step explanation:
I got this right in my assignment.
The probability that a plane departs on time at a certain airport is .87 The probability that a plane arrives on time given it departed on time is .93 Find the probability that a plane departed and arrived in time. Write answer to four decimals. 3 points
Answer:
0.9355
Step-by-step explanation:
What we will use here is conditional probability formula.
let A be the event that the plane departs on time
and B be the event that it arrives on time
P(A) = 0.87
P(B|A) = 0.93
P(B) = ?
P(A n B) = ?
Mathematically;
P(B|A) = P(B nA)/P(A)
0.93 = 0.87/P(A)
P(A) = 0.87/0.93
P(A) = 0.935483870967742
which is 0.9355 to four decimal places
Help ASAP! Will name brainliest!
Answer:
2 by 3
Step-by-step explanation:
please mark brainliest if it helped
Find the midpoint of the segment between the points (−5,13) and (6,4)
Answer:
(0.5, 8.5)
Step-by-step explanation:
use this formula ((x1+x2/2), (y1+y2/2)) if you use desmos graphing calculator and you type this formula in, all you have to do it put in the correct numbers and you get your midpoint.
Hope this helped :)
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
We have given that, the points (−5,13) and (6,4)
We have to determine the midpoints
What is the formula for the midpoint?((x1+x2/2), (y1+y2/2))
x1=-5,x2=6,y1=13 and y2=4
-5+6/2=1/2=0.5
and next is,
13+4/2=17/2=8.5
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
To learn more about the midpoint visit:
https://brainly.com/question/5566419
#sPJ2
how do i solve for this help please \sqrt(x+5) = \sqrt(x)+1
Answer:
x=4
Step-by-step explanation:
sqrt(x+5) = sqrt(x)+1
Square each side
(sqrt(x+5))^2 = (sqrt(x)+1)^2
x+5 = (sqrt(x)+1)^2
Foil
x+5 = (sqrt(x)) ^2 + sqrt(x) + sqrt(x) + 1
x+5 = x + 2 sqrt(x) + 1
Subtract x from each side
5 = 2 sqrt(x) + 1
Subtract 1 from each sdie
4 = 2 sqrt(x)
Square each side
4^2 = (2 sqrt(x))^2
16 = 4 x
Divide by 4
16/4 = 4x/4
4 =x
Check to see if it is extraneous
sqrt(4+5) = sqrt(4)+1
sqrt(9) = sqrt(4) +1
3 = 2+1
3=3
It is a valid solution
Answer:
[tex]\boxed{x=4}[/tex]
Step-by-step explanation:
[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]
Take the square on both sides.
[tex]x+5=( \sqrt{x}+1)^2[/tex]
Expand brackets.
[tex]x+5=( \sqrt{x}+1) ( \sqrt{x}+1)[/tex]
[tex]x+5= \sqrt{x} ( \sqrt{x}+1) +1 ( \sqrt{x}+1)[/tex]
[tex]x+5= x+ \sqrt{x}+ \sqrt{x}+1[/tex]
[tex]x+5= x+ 2 \sqrt{x}+1[/tex]
Subtract 2√x, x, and 5 on both sides.
[tex]x- 2 \sqrt{x} -x= 1-5[/tex]
[tex]-2 \sqrt{x} = -4[/tex]
Cancel negative signs.
[tex]2\sqrt{x} = 4[/tex]
Divide both sides by 2.
[tex]\sqrt{x} =2[/tex]
Square both sides.
[tex]x=2^2[/tex]
[tex]x=4[/tex]
Check if the solution in the equation works.
[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]
Let [tex]x=4[/tex]
[tex]\sqrt{4+5} = \sqrt{4}+1[/tex]
[tex]\sqrt{9} = 2+1[/tex]
[tex]3=3[/tex]
The value of x as 4 works in the equation.
let [tex]p=x^{2}+6[/tex]
Which equation is equivalent to [tex](x^{2}+6)^{2}-21=4x^{2}+24[/tex] in terms of [tex]p[/tex]?
Answer:
Hello There. ☆~---~--___●♡●__~--☆ Since p = x² - 7, you can substitute/plug in p for x² - 7
So:
(x² - 7)² - 4x² + 28 = 5
(p)² - 4x² + 28 = 5 You can factor out -4 from (-4x² + 28)
p² - 4(x² - 7) = 5 Plug in p
p² - 4p = 5 Subtract 5
p² - 4p - 5 = 0 And, your correct answer is C.
Hope It Helps!~
ItsNobody~ ☆
Find the product.
(3x2+6x-5)(-3x)
PLEASE HELP!!! ASAP!!!
Answer:
[tex]\boxed{-9x^3-18x^2 + 15x}[/tex]
Step-by-step explanation:
(3x²+6x-5)(-3x)
Apply distributive law.
-3x(3x²)-3x(6x)-3x(-5)
Simplify.
-9x³ - 18x² + 15x
Answer:
[tex] \boxed{\red{ - 9 {x}^{3} - 18 {x}^{2} + 15x}}[/tex]
Step-by-step explanation:
[tex] ( - 3x)(3 {x}^{2} + 6x - 5) \\ - 3x(3 {x}^{2} ) - 3x(6x) - 3x( - 5) \\ = - 9 {x}^{3} - 18 {x}^{2} + 15x[/tex]
Frieda worked 26 hours 13 minutes last week. She earns $18.75 per hour. What is Frieda's pay for this work period? Round your answer to the nearest hundredth.
Answer:
$491.56
Step-by-step explanation:
Total number of hours worked by Frieda = 26 hours 13 minutes
lets convert 13 minutes to hour
60 minutes = 1 hour\
1 minutes = 1/60 hours
13 minutes = 13/60 hours
Thus,
Total number of hours worked by Frieda = (26 + 13/60) hours
In 1 hours Freida earns = $18.75
in (26 + 13/60) hours Frieda earns = $18.75((26 + 13/60)) = 487.5 + 4.06
in (26 + 13/60) hours Frieda earns = $491.56 (Answer)
Can someone help me with this?
Answer:
9 = k :)
Step-by-step explanation:
1. distribute 3 to the -1/4 k and to the 3 and get -3/4 k + 9 = 1/4 k
2. add 3/4 k to both sides and get 9 = k
Two circles are drawn below. The diameter of the smaller circle is a radius of the larger circle. What is the ratio of the smaller circle's circumference to the larger circle's circumference? Give your answer in fully simplified form. It should look like "x:y", where x and y are replaced by integers. [asy] size(4cm); pair o=(0,0); pair x=(0.9,-0.4); draw(Circle(o,sqrt(0.97))); draw(Circle((o+x)/2,sqrt(0.97)/2)); dot(o); dot(x); dot(-x); draw(-x--x); [/asy] Hint(s): Read the question carefully. Does it ask about a ratio of areas? Of radii? Of diameters? Of circumferences? Which question did you answer? Which was asked?
Answer:
1 : 2
Step-by-step explanation:
The ratio is ...
small dia : large dia = 1 : 2 = small circumference : large circumference
__
Further explanation
The diameter of the small circle is the radius of the large circle. Since the large circle's diameter is twice the length of its radius, the ratio of circle diameters is ...
small : large = 1 : 2
We multiply the diameter by π to get the circumference. Multiplying both these numbers by π will give the ratio of the circumferences. In order to reduce the ratio to lowest terms we must divide by π again:
dia ratio = circumference ratio = lowest terms ratio
1 : 2 = π : 2π = 1 : 2
Answer: 1:2
Step-by-step explanation:
plz plz, answer it hurry.
Answer:
c
Step-by-step explanation:
Answer:
I think it's b.
Step-by-step explanation:
Let's just say that in the first square, all sides equal 4. In this square, if you cut out a piece the perimeter will stay the same. Let's check:
First square: 4+4+4+4=16
Second square: 3+4+4+2+1+2=16
So yes, it's b.
Help again 《Brainlist》
A six faced dice with numbers 1 thru 6 is thrown twice. No fee is charges to the throws. If the organizer of the game has to payout as many dollars as the result every time an even sum comes up and will receive from the player as many dollars as the result if the sum is odd, in the very long run, when 1 million throws are made,
approximately how much is the winning or loss to the organizer?
Answer:
win-263889 loss-236111
Step-by-step explanation:
1:the guys throws the dice twice no charge for this
2:for every face the first time there is a chance of getting the others or the same face e.g round 1-1 round 2-(either 123456)
3:I drew a probability tree to get the sum
like if I got 1and1 then sum is 2 I did it for the rest
4:I got P of (even)=17/36 and for (odd)=19/36
5:then the organizer has to pay if it's even and there 1 million throws Wich means the probability he will lose is the probability of getting an even sum for 500000 throws and for winning is the probability of getting odd sums in those 500,000 throws
6: 500k is because only after it's thrown twice were there charges
AB and BC form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of BC?
A. x + 3y = 16
B. 2x + y = 12
C. -7x − 5y = -48
D. 7x − 5y = 48
===============================================
First we need the equation of line AB. Compute the slope through (-3,-1) and (4,4)
m = (y2-y1)/(x2-x1)
m = (4-(-1))/(4-(-3))
m = (4+1)/(4+3)
m = 5/7
This is the slope through points A and B, ie the slope of line AB.
To get the slope of line BC, we flip the fraction and change the sign.
Doing so has us go from 5/7 to -7/5. Note how 5/7 and -7/5 multiply to -1.
The slope of line BC is -7/5. Let m = -7/5.
--------
Use (x,y) = (4,4) along with m =-7/5 to find the equation of line BC
y = mx+b
4 = (-7/5)(4) + b
4 = -28/5 + b
20 = -28 + 5b ... multiply every term by 5 to clear out the fraction
20+28 = 5b
48 = 5b
5b = 48
b = 48/5
With m = -7/5 and b = 48/5, we go from y = mx+b to y = (-7/5)x+48/5
The slope intercept form for line BC is y = (-7/5)x+48/5
--------
Let's get this into standard form Ax+By = C
y = (-7/5)x+48/5
5y = -7x + 48 .... multiply everything by 5
7x+5y = 48 .... is one way to represent the equation in standard form
-7x - 5y = -48 ... your teacher has decided (for some reason) to multiply both sides by -1
Answer:
-5y-7y=-48
Step-by-step explanation:
distance between BC (4,4) C(x,y)
BC is perpendicular on AB (perpendicular line has opposite reciprocal slope)
slope of AB=y2-y1/x2-x1=4-(-1)/4-(-3)=5/7
slope of BC=-7/5
now input the value of B (4.4) and C(x,y)
y=mx+b
4=-7/5(4)+b
b=4+28/5
b=48/5
y=-7/5x+48/5
5y=-7x+48
5y+7x=48 multipy by -1
-5y-7y=-48
A unicorn daycare center requires there to be 2 supervisors for every 18 baby unicorns. Write an equation that shows the relationship between n, the number of supervisors, and u, the number of baby unicorns.
Answer:
18x-2
Step-by-step explanation:
Answer:
u=9n
Step-by-step explanation:
Expand. Your answer should be a polynomial in standard form. 3x(x to the second power, -5x+6)
Answer:
3x³ - 15x² + 18x
Step-by-step explanation:
Given
3x(x² - 5x + 6) ← distribute the parenthesis by 3x
= 3x³ - 15x² + 18x ← in standard form
Describe methods you can use to show a proportional relationship between two variables ,x and y. Each method, explains how you can find the unit rate and the slope.
Answer: Find answer and explanation in the attached document.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Tables of value: The ratio of Y to X gives the unit rate slope.
Equation: Make a table of VALUES. The ratio of Y to X gives the unit rate and slope.
Graph: The SLOPE of the graph is also the unit rate.