You have $270 in your bank account. You plan to save $80 from your paycheck each week. Which graph shows your bank account balance at the end of each week?
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If you want to know how to do it just let me know
Answer: The below graph shows the given situation.
Step-by-step explanation:
Let x represents the number of week, and y represents the total balance in the account after x weeks.
Since, initially the amount in the account = $ 270
According to the question,
Every week $80 is saved.
Thus, the total saving in x weeks = 80 × x = 80x
Since the total amount in x weeks = Initial amount + total saving.
⇒ y = 80x + 270
Which is the equation of line that shows the given situation.
x-intercept of the line is (-27/8,0)
y-intercept = (0,270)
If x=1 y = 350
If x=2 y= 430
If x=3 y =510
Thus, the points of the line are (1,350), (2,430), (3,510)
Hence we can draw the graph with help of above information.
Related Questions
Each month, the census bureau mails survey forms to 250,000 U.S. households asking questions about the people living in the household and about things such as motor vehicles and housing costs. Telephone calls are made to households that don't return the form. In one month, responses were obtained from 240,000 of the households contacted. The population of interest is A.the 240,000 households contacted. B.the 250,000 households contacted. C.only U.S. households with phones. D.all U.S. households.
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Because the 240,000 responses are from them. Furthermore, with the given information you do not know how many of those responses came due to the frist contact (by mail) or due to the phone call made to the houses that didn't return the form when received the mail.
if x=y and y=2 then 3x=
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try urself and tell me the result
What is the period of y = 5 cos x?
What is the period of y= cos 5x
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first case, B = 1
Second case, B = 2
so period of 5*cos x is 2pi/1 = 2pi
period of cos 5x is 2pi/5
hope this help
Does 1/3 divided by 4 equal 1/12
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minimize Q=x^2+2y^2, where x+y=3
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To minimize the function Q=x^2+2y^2, substitute x=3-y and expand the expression. Use the vertex formula to find the minimum value of Q. The minimum value is 13.5 when x=1.5 and y=1.5.
Explanation:To minimize the function Q=x^2+2y^2, where x+y=3, we can substitute x=3-y into the function to get Q=(3-y)^2+2y^2. Expanding this expression gives Q=9-6y+y^2+2y^2. Combining like terms, we have Q=3y^2-6y+9.
To find the minimum value of Q, we can use the vertex formula. The x-coordinate of the vertex of the parabola represented by Q=a(x-h)^2+k is x=-h. In our case, h=-(-3)/2=1.5. Substituting this value of x into the equation Q=3y^2-6y+9 gives Q=3(1.5)^2-6(1.5)+9=13.5-9+9=13.5.
Therefore, the minimum value of Q is 13.5 when x=1.5 and y=1.5.
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Given 9801 = 3x3x3x3x11x11 , find √9801 (square root i think) ...?
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Is the root of 9801
find the HCF of 140,210,315
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The answer is 35, let me know if you can't read anything or have any questions. Hope this helped :)
hope this helps you
How many times does the graph of the function below intersect or touch the x-axis? y=-3x^2+x+4 ...?
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So, putting y =0
0 = -3x^2 + x +4
so, if you factoriazte it
−3x^2++4x−3x+4=0
−3x(x+1)+4(x+1)=0
(x+1)+(−3x+4)=0
x=−1,4/3
So, two time at -1 and 4/3 it touches the x-axid
Answer:
The answer is 2 times.
What is the correct radical form of this expression? (32a^10b^5/2)^2/5
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The 2/5 outer most exponent means that we can break it down into 2*(1/5). The 2 is going to apply as an exponent for the whole parenthesis group. The 1/5 indicates we have a 5th root (similar to a square root or cube root,but instead of 2 or 3, it's 5)
In essence, I'm saying that [tex]\LARGE x^{m/n} = \sqrt[n]{x^m}[/tex]
Hey guys I have 2 short Q! Ill mark as brainliest whoevr helps me ^~^ ThankU x3 (IMAGE is Below for both Qs!)
What is the length of leg y of the right triangle?
A right triangle with hypotenuse 37 and legs 35 and y
A) 2
B) 8
C) 12
D) 35
#2: Which of the following shows the length of the third side, in inches, of the triangle below?
A right triangle is shown. One side of the triangle is labeled as 25 inches. The height of the triangle is labeled as 15 inches.
A) 20 inches
B) Square root of 850 inches
C) Square root of 10 inches
D) 40 inches
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35^2 + y^2 = 37^2
y^2 = 37^2 - 35^2
y^2 = 1369 - 1225
y^2 = 144...take sqrt of both sides, eliminating the ^2
y = sqrt 144
y = 12 <===
a^2 + b^2 = c^2
15^2 + b^2 = 25^2
b^2 = 25^2 - 15^2
b^2 = 625 - 225
b^2 = 400
b = sqrt 400
b = 20 <===
q plus 12 minus 2=????
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whats the inverse function of f(x)=3x-1
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Which of these transformations are isometries? The diagrams are not drawn to scale.
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First and second we flipped horizontaly while last one we flipped both verticaly and horizontaly but sides and angles remained the same.
Answer:
the answer is D. I, II, and III
Step-by-step explanation:
Solve the equation for the letter L: A=LW
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Answer:
[tex]L=A/W[/tex]
Step-by-step explanation:
we have
[tex]A=LW[/tex]
Solve for L means -------> isolate the variable L
so
Divide by [tex]W[/tex] both sides
[tex]A/W=LW/W[/tex]
Simplify
[tex]L=A/W[/tex]
PLEASE HELP!
The initial amount of people that are sick with the flu is 36 and growing at a rate of 8% every day.
How many people will be sick with the flu in 11 days?
Round to the nearest whole number.
Answers
Answer: 84
Step-by-step explanation:
36 Counts as day 0
Day 1 : 36 x 1.08 = 38.88
Day 2 : 38.88 x 1.08 = 41.9904
Day 3 : 41.9904 x 1.08 = 45.349632
Day 4 : 45.349632 x 1.08 = 48.97760256
Day 5 : 48.97760256 x 1.08 = 52.8958107648
Day 6 : 52.8958107648 x 1.08 = 57.127475625984
Day 7 : 57.127475625984 x 1.08 = 61.69767367606272
Day 8 : 61.69767367606272 x 1.08 = 66.6334875701477376
Day 9 : 66.6334875701477376 x 1.08 = 71.964166575759556608
Day 10 : 71.964166575759556608 x 1.08 = 77.72129990182032113664
Day 11: 77.72129990182032113664 x 1.08 = 83.9390038939659468275712
83.9390038939659468275712 rounded to the nearest whole number is 84.
Based on the number of people who were initially sick and the rate of increase, the number who will be sick in 11 days is 84 people.
To find the number who will be sick in 11 days use the future value formula:
= Initial people x ( 1 +rate) ^ number of days
Solving will give:
= 36 x ( 1 + 8%) ¹¹
= 83.9
= 84 people
In conclusion, 84 people will be sick.
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Which equation shows y=−1/2x+4 in standard form?
A. 2x+y=8
B. x+2y=8
C. x+2y=-8
D. 2x-y=8
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Answer: B. x+2y=8
Explanation:
The original equation is:
[tex]y=-\frac{1}{2}x+4[/tex]
The problem asks us to convert the equation in the standard form, so in the form
[tex]ax+by=c[/tex]
with a,b and c being integers.
In order to do that, first of all let's bring on the same side both x and y:
[tex]y+\frac{1}{2}x=4[/tex]
Now we want the coefficient in front of x to be an integer, so let's multiply each term by 2, and we get
[tex]2y+x=8[/tex]
and this corresponds to option B.
The equation that represents y = -1/2x + 4 in standard form is 2x + y = 8.
The equation that shows y = -1/2x + 4 in standard form is 2x + y = 8.
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Trylon Eager took out an $85,000, 20-year term policy at age 40. The premium per $1,000 was $5.00. He will be 60 years old this year. The premium per $1,000 will be $5.90. The percent increase to the nearest whole number is ____%. (Enter only the number.)
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What is the day 1,000,000 days from now?
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One million days from now would be roughly the year 3759 AD. The exact day and month would fall sometime in March or April due to the complexities of our modern calendar system.
Explanation:To answer your question of what is the day 1,000,000 days from now, we'll need to do some calculations. There are approximately 365.25 days in a year (this includes the extra day every four years for leap years).
1,000,000 divided by 365.25 equals approximately 2737.85 years. This means that 1,000,000 days from now it would be the year 3759 AD (assuming the current year is 2022).
As for the exact day, we'll consider that a year is made up of 365 days, and the .25 accounts for leap years. However, the calculation of the exact date and month is quite complex due to the irregularities in our Gregorian calendar. It would fall sometime in March or April of 3759 AD.
Note that this calculation does not consider minute changes in Earth's rotation over time or potential changes in our calendar system.
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30/20=w/14 solve for w
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30 x 14 = 20 x w
so
w = 420/20
w = 21
Find the zeros of g(x)=x2+5x−24g
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x^2+5x-24 = 0
(x+8)(x-3) = 0
x+8 = 0 or x-3 = 0
x = -8 or x = 3
The zeros or roots are x = -8 or x = 3
gx+24g=x^2−24g+5x+24g
gx+24g=x^2+5x
❀Now you are going to factor out variable g:
g(x+24)=x^2+5x
❀Finally divide both sides by x+24:
[tex] \frac{g(x+24)}{x+24 } = \frac{x^2+5x }{x+24 } [/tex]
❀Your answer is:
[tex]g= \frac{x^2+5x }{x+24 } [/tex]
❀Good Luck❀
You have been hired as an efficiency expert for Math Nerds Inc. The company wants to cut costs and increase profits by increasing the number of math problems their employees can solve in a day. Your job is to help the Math Nerds employees solve math problems more quickly. Show the Math Nerds employees how to rework each problem below using a polynomial identity. (x2+y2)2=(x2-y2)2+(2xy)2
Show the Math Nerds employees how much time you save on each problem by using the polynomial identity to simplify.
1) ( x+2 ) 2 (x+2) 2 = (x+y) 2 =x 2 +2xy+ y 2
2) ( x−3 ) 3 (x−3) 3 = (x−y) 3 =x 3 −3 x 2 y+3x y 2 − y 3
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(x+2)2
without writing (x+2)(x+2)=x2+2x+2x+4=x2+4x+4 instead say y=2 and use the identity to get
x2+2×2x+2^2=x2+4x+4
plz help asap!!!! the perimeter of a rectangle is 200 cm. what is the length of the rectangle if the width is y cm?
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the length is 80
For every problem-solving activity it's crucial that no less than five alternatives be considered.
True
False
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Problem-solving activity includes
1.Understanding the problem,that is nature of the problem, then Completely define in your own way.
2. Determining why this problem has accrued,
3. Identifying the ways to solve the problem,
4. Prioritizing the given alternatives that is ways and then arranging the alternatives for a solution,
5. Then applying the best solution or arrangement for the given problem.
There are two ways considered for problem-solving activity
(1). Trial and Error (2) Reduction in steps
It totally depends on the kind of problem , which you are solving. There may be Less than five alternatives ,equal to five alternatives or more than five alternatives to solve the problem.
Option B: False
How can an expression written in either radical form or rational exponent form be rewritten to fit the other form?
Answers
An expression when written in either radical form or rational exponent form be rewritten to fit the other form as well.
When we write in different forms the Denominator defines as the Index and the Numerator defines as Power on the variable.
For Example:-We can write [tex]4^{\frac{2}{3}[/tex] as [tex]\sqrt[3]{4^2}=\sqrt[3]{16}=\sqrt[3]{8*2}=2\sqrt[3]2}[/tex]
Again, vice versa,
For example:-We can write [tex]\sqrt[5]{x^4}[/tex] as [tex]x^{\frac{4}{5}[/tex]
Therefore , we can written in other forms as well to fit .
Learn more about Numerator and Denominator here : https://brainly.com/question/10667435
To convert from radical form to rational exponent form, use [tex]\( \sqrt[n]{a} = a^{1/n} \),[/tex] and vice versa for conversion.
An expression written in radical form can be rewritten in rational exponent form and vice versa using the following conversions:
1. From Radical Form to Rational Exponent Form:
- For a radical expression [tex]\( \sqrt[n]{a} \), where \( n \)[/tex] is the index and [tex]\( a \)[/tex] is the radicand:
- The equivalent expression in rational exponent form is [tex]\( a^{1/n} \)[/tex].
2. From Rational Exponent Form to Radical Form:
- For an expression [tex]\( a^{m/n} \)[/tex], where [tex]\( a \)[/tex] is the base, [tex]\( m \)[/tex] is the numerator, and [tex]\( n \)[/tex] is the denominator:
- The equivalent expression in radical form is [tex]\( \sqrt[n]{a^m} \).[/tex]
These conversions allow us to switch between radical form and rational exponent form easily. It's important to remember that the index of the radical corresponds to the denominator of the rational exponent, and the exponent of the base corresponds to the numerator of the rational exponent.
Lynn and dawn tossed a coin 60 times and got heads 33 times what is the experimental probability of tossing heads using Lynn and dawns results
Answers
Answer: Experimental probability of tossing head is [tex]\frac{11}{20}[/tex]
Step-by-step explanation:
Since we have given that
Number of times Lynn tossed a coin = 60 times
Number of times head comes = 33
Experimental probability of tossing heads using Lynn and drawn results is given by
[tex]\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\\\\=\frac{33}{60}\\\\=\frac{11}{20}[/tex]
Hence, Experimental probability of tossing head is [tex]\frac{11}{20}[/tex].
Answer:
experimental probability of tossing heads using Lynn and dawns results is [tex]\frac{11}{20}[/tex].
Step-by-step explanation:
Given :Lynn and dawn tossed a coin 60 times and got heads 33 times
To find : what is the experimental probability of tossing heads using Lynn and dawns results.
Solution : We have given that
Number of times Lynn tossed a coin = 60 times.
Number of times head comes = 33.
Probability of tossing heads using Lynn and drawn results is given by:
= N[tex]\frac{number of favouable outcome }{total possible outcome}[/tex]
= [tex]\frac{33}{60}[/tex].
On simplification
=[tex]\frac{11}{20}[/tex].
Therefore, experimental probability of tossing heads using Lynn and dawns results is [tex]\frac{11}{20}[/tex].
ALGEBRA 1 help please!! Urgent
Answers
9/10x + y = 5/3...multiply entire equation by common denominator 30
27x + 30y = 50 <==
What's the answer I don't know it
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A high school chorus has $1000 in its school account at the beginning of the year. They are putting on a fall concert to raise money for a trip later in the year. At the concert last year they sold tickets for $10 each. If they sell tickets at the same price the total amount in the chorus account can be represented by the linear function T = 10x + 1000. If they increase the ticket price to $15, how many tickets will they have to sell to have a total of $4000 in the account?
A) 100 tickets
B) 150 tickets
C) 200 tickets
D) 250 tickets
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Jake earns $7.50 per hour working at a local car wash. The function, ƒ(x) = 7.50x, relates the amount Jake earns to the number of hours he works. Write the inverse of this relation
Answers
where x is the number of hours that Jake works.
f ( x ) = y
y = 7.50 x
x = y / 7.50
Answer:
The inverse is:
y = x / 7.50
For this case we have the following function:
[tex] f(x) = 7.50x
[/tex]
An equivalent way to write this function is:
[tex] y = 7.50x
[/tex]
From here, we clear the value of x.
We have then:
[tex] x = \frac{y}{7.50}
[/tex]
Returning the variables we have that the inverse of the function is:
[tex] f (x) ^ - 1 =\frac{x}{7.50}
[/tex]
Answer:
the inverse of this relation is:
[tex] f (x) ^ - 1 =\frac{x}{7.50}
[/tex]
Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains
x(t) pounds of salt in 200 gallons of brine, and tank B contains
y(t) pounds of salt in 300 gallons of brine. The mixture in each tank is kept uniform by constant stirring. When t = 0, brine is pumped from tank A to tank B at 20 gallons/minute and from tank B to tank A at 20 gallons/minute. Find the amount of salt in each tank at time t if x(0) = 10 and y(0) = 40.
Answers
The pump is just mixing the water among the 2 tanks continuously. So eventually the concentration in each tank will be the same as concentration of both tanks put together.
Total gallons = 500, Total Salt = 50
Concentration = 50/500 = 1/10
If tank A has this concentration , then salt = 20
For tank B the salt amount is then 30.
This gives us 2 points, an initial amount and a finishing amount as t -> infinity.
To find functions for x(t) and y(t) , we need to look at the rate of change.
[tex]Rate = R_{in} - R_{out} [/tex]
For tank A, 20/300 or 1/15 of tank B salt is coming in. While 20/200 or 1/10 of its own salt is leaving.
For tank B its just the other way around.
This will give a system of 2 differential equations:
[tex]\frac{dx}{dt} = \frac{y}{15} - \frac{x}{10}[/tex]
[tex]\frac{dy}{dt} = \frac{x}{10} - \frac{y}{15}[/tex]
From this we can say:
[tex]\frac{dy}{dt} = -\frac{dx}{dt}[/tex]
[tex]y = -x+C[/tex]
Plug this in for y in the dx/dt equation:
[tex]\frac{dx}{dt} = \frac{-x+C}{15} -\frac{x}{10} = -\frac{x+C}{6} [/tex]
Solving this differential equation gives:
[tex] \int \frac{dx}{x+C} = \int -\frac{dt}{6} [/tex]
[tex]\ln (x+C) = -\frac{t}{6} +k[/tex]
[tex]x = k e^{-t/6} +C[/tex]
The dy/dt equation is solved exactly the same way, so you have:
[tex]y = k e^{-t/6} +C[/tex]
All thats left is to apply initial and final conditions to get constants.
The final solution is:
[tex]x(t) = -10e^{-t/6}+20[/tex]
[tex]y(t) = 10e^{-t/6}+30[/tex]