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Aleks04 [339]
3 years ago
8

.4(2X+1/2)=3[.2X+(-2)]-4 can u also show the check

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
8 0
0.4(2x+1/2)=3(.2x-2)-4
0.8x + 0.2 = 0.6x - 6 - 4
0.8x + 0.2 = 0.6x - 10
0.2x = -10.2
2x = -102
x = 51
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Prove that every integer greater than 7 can be written by using 3's and 5's only. that is, for every n > 7 there exist non-ne
Taya2010 [7]
An integer may be a multiple of 3.
An integer may be 1 greater than a multiple of 3.
An integer may be 2 greater than a multiple of 3.

It is redundant to say an integer is 3 greater than a multiple of 3 (that's just a multiple of 3, we've got it covered).  Same for 4, 5, 6, 7...

Let's consider a number which is a multiple of 3.  Clearly, we can write 3+3+3+3+... until we reach the number.  It can be written as only 3's.

Let's consider a number which is 2 greater than a multiple of 3.  If we subtract 5 from that number, it'll be a multiple of 3.  That means we can write the number as 5+3+3+3+3+...  Of course, the number must be at least 8.

Let's consider a number which is 1 greater than a multiple of 3.  If we subtract 5 from that number, it'll be 2 greater than a multiple of 3.  If we subtract another 5, it'll be a multiple of 3.  That means we can write the number as 5+5+3+3+3+3+...  Of course, the number must be at least 13.

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Beautiful question.
4 0
3 years ago
A drawer contains quarters and nickels. There are 200 total coins valuing $30.00. Think about a system of equations that can be
Margaret [11]

Answer:

100

Step-by-step explanation:

Let n and q represent the numbers of nickels and quarters, respectively. A suitable system of equations is ...

  n + q = 200 . . . . . . there are 200 coins in the drawer

  5n +25q = 3000 . . .their value is $30.00

For mixture problems like this, it is often a good idea to substitute for the variable representing the contributor of lower value. That is, we want to write an expression for n that we can use for substitution.

Using the first equation to solve for n, ...

  n = 200 - q

Substituting this into the second equation gives ...

  5(200 -q) +25q = 3000

  1000 +20q = 3000 . . . . . . simplify

  20q = 2000 . . . . . . . . . . . . subtract 1000

  q = 100 . . . . . . . . . . . . . . . . divide by 20

  n = 200 -q = 100 . . . . . . . . the number of nickels, as we want

_____

<em>Comment on the solution</em>

We solved for q, then had to do an extra step to find the value of n that the problem asks for. Had we written q = 200-n and used that for substitution, we would have ended with the equation -20n = -2000. This would give the answer for n directly (with no additional steps required).

Sometimes working with negative numbers is uncomfortable or results in errors, so we chose to use the solution method that would avoid negative numbers.

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<em>Comment on the problem statement</em>

We are told about coins in a <u>drawer</u>, and we are asked about coins in a <u>jar</u>. There is not enough information to answer the question asked. We have had to assume that both refer to the same quantity of coins—an assumption that is not supported by anything in the problem statement.

8 0
3 years ago
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What is the y-intercept of the line y = 20x?
OlgaM077 [116]

Answer:

0

Step-by-step Explanation

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7 0
3 years ago
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Qual a altura máxima atingida por um projétil cuja trajetória pode ser descrita pela função: h(x) = –4x² + 5, sabendo que h é a
masya89 [10]

Answer:

A altura máxima é 5

Step-by-step explanation:

Matematicamente, a altura máxima pode ser obtida

A altura máxima é simplesmente o vértice da parábola

Começamos diferenciando a função Isso será -8x

Agora, defina -8x como 0

Isso significa que x = 0

Agora, substitua x = 0 de volta na equação temos

f (0) = -4 (0) ^ 2 + 5

f (0) = 5

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6 0
3 years ago
A book claims that more hockey players are born in January through March than in October through December. The following data sh
denis-greek [22]

Complete question :

Birth Month Frequency

January-March 67

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Yes, There is significant evidence to conclude that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

Step-by-step explanation:

Observed value, O

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The test statistic :

χ² = (O - E)² / E

E = Σx / n = (67+56+30+37)/4 = 47.5

χ² = ((67-47.5)^2 /47.5) + ((56-47.5)^2 /47.5) + ((30-47.5)^2/47.5) + ((37-47.5)^2/47.5) = 18.295

Degree of freedom = (Number of categories - 1) = 4 - 1 = 3

Using the Pvalue from Chisquare calculator :

χ² (18.295 ; df = 3) = 0.00038

Since the obtained Pvalue is so small ;

P < α ; We reject H0 and conclude that there is significant evidence to suggest that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

5 0
3 years ago
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