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galina1969 [7]
3 years ago
15

Tommy has a pet monkey. Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana th

at tommy eats. Write an equation to describe this situation where x is the number of bananas tommy eats and y is the total number of peices of fruit the monkey eats
Mathematics
2 answers:
Licemer1 [7]3 years ago
4 0

Answer:

Step-by-step explanation:

Let x represent the number of bananas that Tommy eats.

Let y represent the total number of pieces of fruit that the monkey eats.

Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that tommy eats. This means that the number of bananas that the monkey eats is 2x. The expression for the total number of fruits eaten by the monkey becomes

y = 2x + 4

jeka57 [31]3 years ago
3 0

Answer:

Step-by-step explanation:

Y=2X+4

Where y is the the total no of fruits the monkey eats and x is the no of bananas the Tommy eats... 4 represents the 4 apples eaten every morning by the monkry

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If this particular arithmetic sequence, a7=34 and a15=74. What is the value of a21
Ilya [14]
This is an arithmetic sequence, meaning, to get the next term, you simply add some value to the current one, namely the "common difference" "d".

now, we know the 17th term is 34, let's go to the 15term then

34 + d
34 + d + d
34 + d + d + d
34 + d + d + d + d
34 + d + d + d + d + d
34 + d + d + d + d + d + d
34 + d + d + d + d + d + d + d
34 + d + d + d + d + d + d + d + d

now, notice, we got to the 15th term, which is 34  + d + d + d + d + d + d + d + d, or namely 34 + 8d, it just so happen we know is 74, therefore,

\bf 34+8d=74\implies 8d=40\implies d=\cfrac{40}{8}\implies \boxed{d=5}

ok, now that we know what the common difference is, let's find the first term in the sequence using the 7th term of 34,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=7\\
d=5\\
a_7=34
\end{cases}
\\\\\\
a_7=a_1+(7-1)5\implies 34=a_1+(7-1)5
\\\\\\
34=a_1+30\implies \boxed{4=a_1}

and now let's use those 2 found folks, to get the 21st term,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=4\\
d=5\\
n=21
\end{cases}
\\\\\\
a_{21}=4+(21-1)5\implies a_{21}=4+100\implies a_{21}=104
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3 years ago
Simplify: -1-(-10x-10)​
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Answer:

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Step-by-step explanation:

-1 - (-10x - 10)

Distribute.

-1 + 10x + 10

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Simplify the expression: 5 x t x 5
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I think it would be 25t but correct me if i’m wrong
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For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x
Alla [95]
The <u>correct answer</u> is:

D) \left \{ {{2x-y=7} \atop {2x+7y=31}} \right..

Explanation:

We solve each system to find the correct answer.

<u>For A:</u>
\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.

Since we have the coefficients of both variables the same, we will use <u>elimination </u>to solve this.  

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. &#10;\\&#10;\\6x=23

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is <u>not the x-coordinate</u> of the answer we are looking for, so <u>A is not correct</u>.

<u>For B</u>:
\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.

For this equation, it will be easier to isolate a variable and use <u>substitution</u>, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
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Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
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This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>B is not correct</u>.

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Since the coefficient of x in the second equation is 1, we will use <u>substitution</u> again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
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Now substitute this in place of x in the first equation:
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Using the distributive property, we have:
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Combining like terms:
22+3y=-13

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Divide both sides by -8:
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The y-coordinate is correct; next we check the x-coordinate  Substitute the value for y into the first equation:
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2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so <u>D is the correct answer</u>.
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