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posledela
3 years ago
6

The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card

Mathematics
1 answer:
gayaneshka [121]3 years ago
3 0
To set up an equation for this you must know what needs to be on the other side of the equals sign or what the answer is supposed to be. In this case, we know the answer should be the money remaining on the card. Since there is no number value for this, you must pick a variable to represent it. I am going to use variable R. So, since we know that you start with 100 dollars, and lose 4 dollars for each lunch, we can tell that there will be subtraction taking place. We also do not know how many lunches have been bought so we need a variable for that too. I will use variable x. That will leave you with an equation of:
R = 100 - 4x

x= number of lunches bought
R= remaining money on the lunch card

Hope this helps!
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elena-s [515]

The inverse of the function f(x) = 1/3x^2 - 3x + 5 is  f-1(x) = 9/2 + √[3(x + 7/4)], the sum of the arithmetic series is 1078 and the common ratio of the sequence is 2

<h3>The inverse of the function?</h3>

The function is given as:

f(x) = 1/3x^2 - 3x + 5

Next, we rewrite the function as in vertex form

Using a graphing calculator, the vertex form of the function f(x) = 1/3x^2 - 3x + 5 is

f(x) = 1/3(x - 9/2)^2 - 7/4

Express f(x) as y

y = 1/3(x - 9/2)^2 - 7/4


Swap x and y

x = 1/3(y - 9/2)^2 - 7/4

Add 7/4 to both sides

1/3(y - 9/2)^2 = x + 7/4

Multiply through  by 3

(y - 9/2)^2 = 3(x + 7/4)

Take the square root of both sides

y - 9/2 = √[3(x + 7/4)]

Add 9/2 to both sides

y = 9/2 + √[3(x + 7/4)]

Rewrite as an inverse function

f-1(x) = 9/2 + √[3(x + 7/4)]

<h3>Sum of arithmetic series</h3>

Here, we have:

5 + 18 + 31 + 44 + ... 161

Calculate the number of terms using:

L = a + (n -1)d

So, we have:

161 = 5 + (n - 1) * 13

This gives

(n - 1) * 13 = 156

Divide by 13

n - 1 = 12

Add 1

n = 13

The sum is then calculated as:

Sn = n/2 * [a + L]

This gives

Sn =13/2 * (5 + 161)

Evaluate

Sn = 1078

Hence, the sum of the arithmetic series is 1078

<h3>The common ratio of the sequence</h3>

Here, we have:

T11  = 32 * T6

The nth term of a geometric sequence is

Tn = ar^(n-1)

This gives

ar^10 = 32 * ar^5

Divide by ar^5

r^5 = 32

Take the fifth root

r = 2

Hence, the common ratio of the sequence is 2


Read more about sequence at:

brainly.com/question/7882626

#SPJ1

6 0
2 years ago
(WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST) Directed line segment is graphed below. Plot point R on the graph so that it spl
guajiro [1.7K]

Answer:

(0 , -1)

Step-by-step explanation:

WR = 4 + 2 = 6

WS = 1/3 x WR = 2   .... the point of 1:2 of WR

S (-2 + 2 , -4) i.e. (0,4)

The same reason: RQ = 1/3 x RY = 1/3 x (5 + 4) = 3

Q (-4 , -4 + 3) i.e. (-4, -1)

QP // RW

p (0 , -1)

4 0
3 years ago
Can someone help me with this! It would be much appreciated!!
love history [14]

Answer:

1. parallelogram

2. trapezoid

3.rectangle

4. parallelogram

5. trapezoid

6. rhombus

7.rectangle

8. rhombus

3 0
3 years ago
4/5G + 42 = 2.8G + 18<br> Plz solve with an explanation
inysia [295]

Answer:

12

Step-by-step explanation:

Simplify  \frac{4}{5}G

​5

​

​4

​​ G  to  \frac{4G}{5}

​5

​

​4G

​​ .

\frac{4G}{5}+42=2.8G+18

​5

​

​4G

​​ +42=2.8G+18

Multiply both sides by 5.

4g + 210 = 14g + 90

Simplify  

 14G + 90 - 4G to 10G + 90

Subtract 90 from both sides.

210-90=10G210−90=10G

Simplify  210-90210−90  to  120120.

120=10G120=10G

Divide both sides by 1010.

\frac{120}{10}=G

​10

​

​120

​​ =G

Simplify  \frac{120}{10}

​10

​

​120

​​   to  1212.

12=G12=G

Switch sides.

G=12G=12

SORRY ABOUT ALL THIS WORK...

3 0
3 years ago
Read 2 more answers
4/9 + 1/3 = ??<br><br> Simplify answer fully
galben [10]
Multiply the second fraction by three.

4/9 + 3/9 = 7/9
5 0
3 years ago
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