At the beginning of the year, Ian had $30 in savings and saved an additional $15 each week thereafter. Brayden started the year with $70 and saved $5 every week. Let II represent the amount of money Ian has saved tt weeks after the beginning of the year and let BB represent the amount of money Brayden has saved tt weeks after the beginning of the year. Graph each function and determine the amount of money Ian and Brayden have saved in the week that they have the same amount of money saved.
Answers
A linear equation can be written as:
[tex]y = a*x + b[/tex]
Where a is the slope and b is the y-intercept.
Defining x as the number of weeks since the start of the year, we can write the linear equations I and B as:
[tex]B(x) =\$70 + \$5*x[/tex]
(initial amount plus the amount that he saves each week times the number of weeks)
Similarly, for Ian we have:
[tex]I(x) = \$30 + \$15*x[/tex]
The graph of these lines can be seen below, where the blue one is I(x) and the green one is B(x).
Now we want to determine how much they had when they had the same amount.
This means that we need to solve:
B(x) = I(x)
Replacing the equations we get:
[tex]\$70 + \$5*x = \$30 + \$15*x[/tex]
Now we can solve this for x:
[tex]\$70 - \$30 = \$15*x - \$5*x[/tex]
[tex]\$40 = \$10*x[/tex]
[tex]\$40/\$10 = x[/tex]
[tex]4 = x[/tex]
So they have the same amount of money in week 4, and each one of them has:
[tex]B(4) = I(4) = \$70 + \$5*4 = \$70 + \$20 = \$90[/tex]
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Related Questions
A textbook store sold a combined total of 331 physics and sociology textbooks in a week. The number of sociology textbooks sold was 45 less than the number
of physics textbooks sold. How many textbooks of each type were sold?
Answers
Answer: Number of sociology books sold = 143 books
Number of physics books sold = 143 + 45 = 188 books
Step-by-step explanation:
Let us take the number of sociology books sold = x
Number of physics books sold = x+45
So now we can form an equation
x+x+45 = 331
2x+45 = 331
2x = 331-45
2x = 286
x = 286 ÷ 2
x = 143
To solve this system of equations using substitution, what could be substituted in place of x in the second equation?
2y + x = 11
31 - y = -4
a. 2y – 11
b. 11 – 2y
c. 3x + 4
d. y - 4/3
Answers
Answer:
b 11-2y
Step-by-step explanation:
A juice dispenser holds 11.5 liters of orange juice and
dispenses juice at a rate of 0.1 liters per second. If a student
dispenses juice into a pitcher for 36 seconds, how many
liters of orange juice will be left in the dispenser afterward?
Answers
Answer:
7.9 L
Step-by-step explanation:
Juice dispensed in 1 second=0.1 L
Juice dispensed in 36 seconds=3.6 L
Juice left=11.5-3.6=7.9 L
URGENT HELP I REALY NEED AN EXPERT HERE
Answers
Hi
P and Q only intersect for 2 as 2 is common for P and Q . So P U Q = 2
For the diagram :
One big circle name U with 1 on the
Far corner left and 9 on the far right corner.
Then on the left, a circle within circle U with the number Of P
Same with Q on the right.
But P and Q must intersect on number 2 as 2 is in both circles.
ps : nothing oblidge you to set the number on mathematical order. Of it'esasier to do the circles, do it whatever you like as long as you respect what is said.
Suppose a function f has an inverse. If f(2)=6 and f(3)=7, find: f^-1 (f(3))
Answers
9514 1404 393
Answer:
3
Step-by-step explanation:
The definition of an inverse function is ...
f^-1(f(x)) = x
Then ...
f^-1(f(3)) = 3
Which is the graph of f(x) = -(x + 3)(x + 1)?
8
4
22
2
2
2
-8
6
х
2
6 4
6
8
-6
4
X
2
-2
-2
19
2
Answers
Answer:
It's the second option
Step-by-step explanation:
Graph for -(x+3)(x+1)
The graph of f(x) = -(x + 3)(x + 1) is the option B.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given function is,
f(x) = -(x + 3)(x + 1)
Simplifying,
f(x) = - (x² + 3x + x + 3)
f(x) = -x² - 4x - 3
This is a quadratic function, the graph of which is a parabola.
Leading coefficient is negative, so the parabola opens downward.
Options are either A or B.
x coordinate of the vertex of a parabola of equation ax² + bx + c is -b/2a.
Here x coordinate = -(-4) / (2 × -1) = -2
The vertex of first graph is (2, 1) and that of second graph is (-2, 1).
The correct option is second graph.
Hence the second graph is the graph of the given function.
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Solve for X. Geometry
Answers
Answer:
11
Step-by-step explanation:
6+(2x+28)=x+23=-11 -> Answer can't be negative -> 11
Tommy stands on a diving bored that is 4 feet above the pool’s surface. He dives and touches the bottom of the pool, which is 12 feet below the pool’s surface. What is the total length of Tommy’s dive?
Answers
Answer:t below the pool’s surface. What is the total length of Tommy’s dive?
7 feet
Step-by-step explanation:
Solve for x.
x = [?]
5x – 16
X + 10
Answers
Answer:
If it is expression than answer 6x-6
If it is an equation 5x-16=x+10 than answer is 13/2
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
[tex]\\ \sf \longmapsto 5x-16=x+10[/tex]
[tex]\\ \sf \longmapsto 5x-x=10+16[/tex]
[tex]\\ \sf \longmapsto 4x=26[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{26}{4}[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{13}{2}[/tex]
HELP PLEASE
i would really appreciate if someone answered this correctly!
Answers
Answer:
n-32
Step-by-step explanation:
edmentum
Hong buys candy that costs $5 per pound. He will buy at least 7 lbs of candy. What are the possible amounts he will spend on candy? Use c for the amount (in dollars) Hong will spend on candy. Write your answer as an inequality solved for c.
Answers
Step-by-step explanation:
if he buys 7 pounds, it will cost 7×5 = $35
he might buy more than that (and it will then also cost more than that) , but not less than that.
so,
c >= $35
please help me with this
Answers
Answer:
a) 10
b) 2.5
Step-by-step explanation:
2^n = 1024
2^n = 2^10
n = 10
4^(2n-3) = 16
4^(2n-3) = 4^2
2n-3 = 2
2n = 5
n = 2.5
Solution:-1:-
[tex]\\ \sf\longmapsto 2^n=1024[/tex]
Equal the bases[tex]\\ \sf\longmapsto 2^n=2^10[/tex]
[tex]\\ \sf\longmapsto n=10[/tex]
Solution:-2:-
[tex]\\ \sf\longmapsto 4^{2n-3}=16[/tex]
[tex]\\ \sf\longmapsto 4^{2n-3}=4^2[/tex]
[tex]\\ \sf\longmapsto 2n-3=2[/tex]
[tex]\\ \sf\longmapsto 2n=2+3[/tex]
[tex]\\ \sf\longmapsto 2n=5[/tex]
[tex]\\ \sf\longmapsto n=\dfrac{5}{2}[/tex]
[tex]\\ \sf\longmapsto n=2.5[/tex]
When 12% discount is given a calculator is sold for Rs 1760 find the marked price of the calculator.
Answers
Answer:
- Hello Risap!
[tex] \large{ \red{\tt{❃ } \: \blue{ PROVIDED}}}[/tex] : Discount % = 12% & Selling price [ SP ] = Rs 1760[tex] \large{ \tt{ \red{❀ \: \blue{TO \: FIND}}}}[/tex] : Marked price of the calculator [ MP ][tex] \large{ \tt{ \green❊ \pink { \: S \: O \: L \: U \: T \: I \: O \: N} \green { \: ❊}}}[/tex]
[tex] \large {\tt{✢ \: SP = MP - dis\% \: of \: MP}}[/tex]
[tex] \large{ \tt{⟶ \: 1760 = MP - 12\% \: of \: mp}}[/tex]
[tex] \large{ \tt{⟶ \: 1760 = MP - \frac{12}{100} \: mp }}[/tex]
[tex] \large{ \tt{⟶ \: 1760 = \frac{100 \: MP - 12 \: mp}{100} }}[/tex]
[tex] \large{ \tt{⟶ \: 88 \: MP = 176000}}[/tex]
[tex] \large{ \tt{⟶ \: MP= \frac{176000}{88} }}[/tex]
[tex] \large{ \tt{⟶ \: MP = Rs \: 2000}}[/tex]
[tex] \large{ \boxed{ \boxed{ \tt{⤳ \: OUR \: FINAL \: ANSWER : \boxed{ \red{ \tt{MP = Rs \: 2000}}}}}}}[/tex]
Hope this helps! Let me know if you have any other questions regarding my answer and also , notify me if you need any other help! :)5. There are 5,280 feet in a mile. What part of a mile, in decimal form, will you drive until you reach the exit? I NEED THIS QUICK PLZ HELP I’LL GIVE YOU 30
Answers
Answer:
5.280
Step-by-step explanation:
i did this question and got it
Does the point (2, 6) lie on the circle shown? Explain.
O Yes, the distance from (3, 0) to (0, ) is 3 units.
O Yes, the distance from (0, 0) to (2, V6) is 3 units.
O No, the distance from (3, 0) to (2, 6) is not 3 units.
O No, the distance from (0, 0) to (2, 6) is not 3 units.
Answers
Answer:
A.
Step-by-step explanation:
the square root of 6 is roughly 1.57
so that means the ordered pair would read (2,1.57).
if you were to plot that point it would be on the circle.
Also the distance from the origin (0,0) to (3,0) is 3 units
We will see that the correct option is:
"No, the distance from (0, 0) to (2, 6) is not 3 units."
Does (2, 6) lie on the circle shown?
We know that the circle has a radius of 3 units, then we need to see if the distance between (0, 0) and (2, 6) is 3 units.
Here we have:
[tex]D = \sqrt{(6 - 0)^2 + (2 - 0)^2} = \sqrt{36 + 4} = \sqrt{40} \neq 3[/tex]
So the distance between (0, 0) and (2, 6) is different than 3 units, meaning that the point is not in the circle.
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To find the missing value?
Answers
Answer:
To fine the missing value JUST transpose
___ -(-5) = -7 {- * - = +}
___ +5 = -7
___ = -7-5
___= -12
so the missing place is -12
Answer:
-12
Step-by-step explanation:
can someone plz make a histogram for the numbers 60,60,65,71,72,75,80,88,92,95,100,152
Answers
Answer:
lol sorry i don't know. but i would try my best to find your answer
pls solve fast pls help
Answers
Answer:
The Answer should be 6%
Step-by-step explanation:
Given,
MP =1500 and Discount =10%
So, SP = 1500 × 90% =1350
We know, profit = [tex]\frac{sp-cp}{cp}[/tex] × 100%
=>20 =[tex]\frac{1350-cp}{cp}[/tex] × 100
=>CP = 1125
Now, if profit =12%
then, SP' = 1260 ;(using previous equation for profit and CP=1125)
So, SP' = MP × (100 -Discount )
∴ Discount = 16% ;(SP' = 1260 and MP = 1500)
So, Discount should be increased = 16% - 10% = 6%
Pls mark this as the brainliest
Find the slope of the line that contains (-1, 9) and (9, 9).
Answers
Step-by-step explanation:
using the slope formula, we can see that the slope is 0
Ethan sells e candy bars for $2.50 apiece and Chloe sells c candy bars for $2.00 apiece to raise
money for a school trip. Ethan sold 15 fewer candy bars than Chloe, but he also got a $6.00
donation. If Chloe and Ethan raised the same amount of money, which of the following systems
could be used to find how many candy bars each sold?
Answers
The system that could be used to find how many candy bars each sold is given is option B.
What is the candy bar about?Since Ethan sold 15 fewer candy bars than Chloe, as portrayed in the question, so:
e = C - 15
Based on the fact that Chloe and Ethan raised the same amount of money, the equation will be:
2C: 2.5e + 6
Therefore, The system that could be used to find how many candy bars each sold is given is option B.
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Paul found a job listed in the classified ads that pays a yearly salary of $76K. What is the
weekly salary based on this annual salary? Round to the penny.
*
Answers
Divide 76,000 by the number of weeks in a year (52) and you get 1,461.538 round up and you get $1,461.64
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IUF YOU KNOW THE ANSWER PLS GIVE ME A STEB BY STEP EXPLANATION!!
A sample in which each individual in the population has an equal chance to be selected is a ________________.
A. probability sample
B. determined sample
C. random sample
D. selected sample
Answers
Answer:
c random sample
Step-by-step explanation:
I may be wrong but When random sampling is used, each element in the population has an equal chance of being selected (simple random sampling) or a known probability of being selected (stratified random sampling).
find the value of x and y..
Answers
Answer:
x=30° y=110°
Step-by-step explanation:
80+70=150
180-150=30° 》》》》 angles in a triangle add up to 180°
x=30° opposite angles are equal
180-140=40° angles on a straight line add up to 180°
30+ 40=70
180-70=110°
y=110°
For which of the following intervals is the graph decreasing?
O A. -2
OB.-4
C. -8 < X <-5
OD. 6
Answers
Sixteen blocks are needed to build a four-step double staircase like
the one on the right. How many blocks will be needed to build a
double staircase of similar shape with 50 steps?
Snacks:
Answers
x blocks = 50 steps
(16 blocks x 50 steps)/4 steps
= 200 blocks
. f(x) = Square root of quantity x plus nine. ; g(x) = 8x - 13 Find f(g(x)). (1 point)
f(g(x)) = 2 Square root of quantity two x minus one.
f(g(x)) = 8 Square root of quantity x minus four.
f(g(x)) = 2 Square root of quantity two x plus one.
f(g(x)) = 8 Square root of quantity x plus nine - 13
Answers
Answer:
2 sqrt(2x-1)
Step-by-step explanation:
f(x) = sqrt( x+9)
g(x) = 8x-13
f(g(x))
place the function g(x) in for x in f(x)
f(g(x)) = sqrt(8x-13+9)
Combine like terms
f(g(x)) = sqrt(8x-4)
Factor out 4
f(g(x)) = sqrt(4*(2x-1)
2 sqrt(2x-1)
[tex]\\ \sf\longmapsto f(x)=\sqrt{x+7}[/tex]
[tex]\\ \sf\longmapsto g(x)=8x-11[/tex]
g(x) will be put on the place of x[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-11+7}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-4}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{4(2x-1)}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=2\sqrt{2x-1}[/tex]
What is the solution to the system of equations graphed below?
Answers
Answer:
A
Step-by-step explanation:
The solution to a system of equations is the point of intersection of the 2 lines.
The lines intersect at (6, 9 ) ← solution
Answer:
A(6, 9)
Step-by-step explanation:
The intersecting points of the two lines gives the solution of the equation.
what is a possible solution to the inequality?
1/4a +1 > 9
Answers
Answer:
a > 32 is one possible solution to the inequality 1/4a +1 > 9.
Step-by-step explanation:
anyone help me, please I need help
[tex] \sqrt{x - 5} = 8 \sqrt[]{x - 2} [/tex]
Answers
Answer:
No Real Solutions.
Step-by-step explanation:
√(x-5)=8√(x-2)
Square on both sides,
(√(x-5))^2=(8√(x-2))^2
or,(x-5)=64(x-2)
or,x-5=64x-128
or,-5+128=64x-x
or,123/63=x
Therefore, x=41/21
If you plug x=41/21 in √(x-5)=8√(x-2) you do not get equals, so the problem has no real solutions.
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인도
한국 사람이에요?
Chase plans to repaint some classroom bookcases. He has 1 4/7 gallons of paint. All of the bookcases are the same size and each requires 1/3 gallon of paint. How many bookcases will the custodian be able to repaint with that amount of paint?
