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aniked [119]
3 years ago
11

(PLEASE HELP!!!) Two cooks purchased plates and cups at the same store. The first cook bought 4 plates and 5 cups for a total of

$25.25. The second cook bought 7 plates and 3 cups for a total of $25.50.
What is the price of a plate?

Mathematics
2 answers:
ANTONII [103]3 years ago
8 0

If "a" will be "plate" and "c" will be "cup" it's going to be like this:
4a + 5c = 25.25
7a + 3c = 25.50

Then we multiply first equation by +3 and the second one by -5 the it's going to be like this:
12a + 15c = 75.75
-35a - 15c = -127.5

So we can say:
-23a = -51.75

Then:
a = 2.25
c = 3.25

Advocard [28]3 years ago
4 0
The price of the cups would be 2.75

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olga2289 [7]
13.525 is greater then 13.255
7 0
3 years ago
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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.
Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have S_1=3\times2^{1-1}+2(-1)^1=3-2=1, which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}

and

S_k=3\times2^{k-1}+2(-1)^k

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}

From the given recurrence, we know

S_{k+1}=S_k+2S_{k-1}

so that

S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)

S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}

S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)

S_{k+1}=3\times2^k-2(-1)^k

S_{k+1}=3\times2^k+2(-1)(-1)^k

\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}

which is what we needed. QED

6 0
3 years ago
I need help pls no wronge answers this is for a test
VashaNatasha [74]

Answer:

I think the answer is

Step-by-step explanation:

(D) OR (B)

4 0
3 years ago
Use the given map to find the coordinates of a point that lies on the directed line segment from c to d and partitions the segme
Lelechka [254]

Given:

The line segment is passing through the points (-9,-3) and (8,5),

Divide the segment in the ratio of 1:4.

Use the formula,

\begin{gathered} (\frac{mx_2+nx_1}{m+n},\frac{my_2-ny_1}{m+n}) \\ (x_1,y_1)=(-9,-3) \\ (x_2,y_2)=(8,5) \\ m\colon n=1\colon4 \end{gathered}

It gives,

\begin{gathered} (\frac{1(8)+4(-9)}{1+4},\frac{1(5)+4(-3)}{1+4}) \\ (-\frac{28}{5},-\frac{7}{5}) \end{gathered}

Answer:

(-\frac{28}{5},-\frac{7}{5})

8 0
1 year ago
Please help with 1 and 2 :)
nordsb [41]

Answer:

1. The domain for the number of fruit cups is 0 minimum and 20 maximum.

   [0 < x < 20].

2. [10 < y < 70]

Step-by-step explanation:

1. The domain is 0 to 20 because there are 20 people total who will each have a fruit cup

2. The range is $10 to $70 because the minimum price is $10 without any fruit cups and $70 when there are 20 fruit cups.

4 0
3 years ago
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