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skelet666 [1.2K]
2 years ago
10

Rosie needs to buy balloons and tablecloths for her party. Each balloon costs $1.50 and each tablecloth costs $2.25. She cannot

spend more than $30.00 on balloons and tablecloths for the
party. Write an inequality to represent the possible number the balloons and tablecloths that Rosie can buy. Let'x' represent balloons and and represent the tablecloths
Mathematics
2 answers:
sammy [17]2 years ago
7 0

Answer: The inequality can be written as 1.5x + 2.25y ≤ 30

Step-by-step explanation: What Rosie needs is an expression that shows  the highest she can spend on tablecloths and balloons. If the question states that she cannot spend more than 30 dollars, then it simply means she can either spend a maximum of 30 dollars, OR any amount below 30 dollars. So what she needs is an inequality that shows her spending as being less than or equal to 30.

Let the balloons be represented by letter x and the tablecloths be represented by the letter y. If each balloons cost 1.50 dollars, then the total cost of balloons equals 1.5 times x or simply 1.5x. Likewise, if each tablecloth cost 2.25, then the total cost of tablecloths shall be 2.25y.

The possible number of balloons and tablecloths that she can buy based on the conditions given can be expressed as follows;

1.5x + 2.25y ≤ 30

Snezhnost [94]2 years ago
3 0

Answer:

1.50x + 2.25y ≤ 30

Step-by-step explanation:

Hi, let’s say that 'y' represent the tablecloths.

So, we have to write an inequality:

The product of the number of balloons (x) and the cost of each one (1.50) plus the product of the number of tablecloths (y) and the cost of each tablecloth (2.25) must be less or equal to Rosie's budget (30)

Mathematically speaking:

1.50x + 2.25y ≤ 30

Feel free to ask for more if needed or if you did not understand something  

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-4x-15y=-17<br>-x+5y=-13<br><img src="https://tex.z-dn.net/?f=%20-%204x%20-%2015y%20%3D%20%20-%2017%20%20%5C%5C%20%20-%20x%20%2B
salantis [7]
To solve this system of linear equations we need a little trick called elimination steps are below

we are given the following system of equations
- 4x - 15y = - 17
- x + 5y = - 13
if you look at the x variables in both equations you can see that we can easily eliminate them by multiplying the bottom equation by -4 as so
- 4x - 15y = - 17
- 4( - x + 5y = - 13)
simplify and we get
- 4x - 15y = - 17
4x - 20y = 52
now we can combine like terms on each side with the x's cancelling and get

- 35y = 35
now divide off -35
y = - 1
great now we can go back to our original system and pick a equation and substitute y back in to find x lets use

- x + 5y = 13
so now we substitute y and get
- x + 5( - 1) = 13
- x - 5 = 13
- x = 17
x = - 17

now we put x and y into one coordinate (x,y)
so now our FINAL ANSWER IS
(-17,-1)
6 0
2 years ago
Determine whether the series is convergent or divergent. 1 2 3 4 1 8 3 16 1 32 3 64 convergent divergent Correct:
Vanyuwa [196]

Answer:

This series diverges.

Step-by-step explanation:

In order for the series to converge, i.e. \lim_{n \to \infty} a_n =A it must hold that for any small \epsilon>0, there must exist n_0\in \mathbb{N} so that starting from that term of the series all of the following terms satisfy that  |a_n-A|n_0 .

It is obvious that this cannot hold in our case because we have three sub-series of this observed series. One of them is a constant series with a_n=1 , the other is constant with a_n=3 , and the third one has terms that are approaching infinity.

Really, we can write this series like this:

a_n=\begin{cases} 1 \ , \ n=4k+1, k\in \mathbb{N}_0\\ 2^{k}\ , \ n=2k, k\in \mathbb{N}_0\\3\ , \ n=4k+3, k\in \mathbb{N}_0\end{cases}

If we  denote the first series as b_n=1, we will have that \lim_{k \to \infty} b_k=1.

The second series is denoted as c_k=2^k and we have that \lim_{k \to \infty} c_k=+\infty.

The third sub-series d_k=3 is a constant series and it holds that \lim_{k \to \infty} d_k=3.

Since those limits of sub-series are different, we can never find such n_0\\ so that every next term of the entire series is close to one number.

To make an example, if we observe the first sub-series if follows that A must be equal to 1. But if we chose \epsilon =1, all those terms associated with the third sub-series will be out of this interval (A-1, A+1)=(0, 2).

Therefore, the observed series diverges.

5 0
2 years ago
Solve the linear equation for x <br><br> -4.8(6.3x-4.18) =-58.56<br><br> X=
lyudmila [28]

Answer:

x= 2.6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

4 0
2 years ago
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -1
Ludmilka [50]
The zeros are the values of t for which f(t) = 0.
i.e. <span>-16t^2 + 96t = 0
16</span>t^2 - 96t = 16t(t - 6)
16t = 0 or t - 6 = 0
t = 0 or t = 6
Therefore, the zeros are 0, 6

The time taken for the ball to hit the ground is the value of t when f(t) = 0.
i.e. t = 6.
3 0
2 years ago
Jane builds a ramp made of a triangular prism and a rectangular prism. What is the volume
Alex787 [66]

Answer:

Correct option: third one ->  11.5 m3

Step-by-step explanation:

To find the volume of the ramp, first we need to find the volume of the rectangular prism and the volume of the triangular prism:

V_rectangular = 4m * 2m * 1m = 8 m3

V_triangular = (2m * 3.5m * 1m) / 2 = 3.5 m3

Now, to find the volume of the ramp, we just need to sum both volumes:

V_total = V_rectangular + V_triangular = 8 + 3.5 = 11.5 m3

Correct option: third one.

6 0
2 years ago
Read 2 more answers
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