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Savatey [412]
3 years ago
12

A positive number is 5 less than 3 times another. The sum of the smaller number and 4 times the larger is 97. Find the smaller n

umber
Mathematics
1 answer:
Gre4nikov [31]3 years ago
5 0

Answer:

  9

Step-by-step explanation:

The first sentence of the problem can be interpreted two ways. The way that makes the second sentence work out correctly is ...

  'a larger number is 5 less than 3 times a smaller number'

Using x for the smaller number, the two equations that can be written are ...

  • 3x -y = 5
  • x +4y = 97

Adding 4 times the first equation to the second, we get ...

  4(3x -y) + (x +4y) = 4(5) +(97)

  13x = 117 . . . . . simplify

  x = 9 . . . . . . . . divide by 13

The smaller number is 9.

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Triangle QRS has been rotated 90° to create triangle TVU. Using the image below, prove that lines RS and VU have the opposite an
Zanzabum

Answer:

If the line RS has been rotated 90 degrees, then VU will be perpendicular to RS and the two slopes must be opposite and reciprocal, i.e. product of the two slopes will equal -1.

As a verification, we find the locations of V and U from rotations of R & S.

(actually, the triangle had been rotated -90°, 90 ° clockwise)

Step-by-step explanation:

Slope RS, m1:

Slope VU, m2

Hence m1*m2=1*-1=-1, meaning that m1 and m2 are opposite (in sign) and are reciprocal to each other, as expected

6 0
3 years ago
The proportion of households in a region that do some or all of their banking on the Internet is 0.31. In a random sample of 100
Alenkasestr [34]

Answer:

Approximate probability that the number of households that use the Internet for banking in a sample of 1000 is less than or equal to 130 is less than 0.0005% .

Step-by-step explanation:

We are given that let X be the number that do some or all of their banking on the Internet.

Also; Mean, \mu = 310/1000 or 0.31   and  Standard deviation, \sigma = 14.63/1000 = 0.01463 .

We know that Z = \frac{X-\mu}{\sigma} ~ N(0,1)

Probability that the number of households that use the Internet for banking in a sample of 1000 is less than or equal to 130 is given by P(X <= 130/1000);

 P(X <=0.13) = P( \frac{X-\mu}{\sigma}  <= \frac{0.13-0.31}{0.01463} ) = P(Z <= -12.303) = P(Z > 12.303)

Since this value is not represented in the z table as the value is very high and z table is limited to x = 4.4172.

So, after seeing the table we can say that this probability is approximately less than 0.0005% .

4 0
3 years ago
The Layer of the upper mantle that can flow is called the what?
inna [77]
Your answer is the athenosphere.

5 0
3 years ago
Which expression is equivalent to -9x^-1y^-9/-15x^5y^-3? Assume x is not equal to 0,y is not equal to 0
VladimirAG [237]
I am going to assume that "v" is meant to be a "y"
the answer is b. (3)/(5x^6 y^6)
7 0
3 years ago
Read 2 more answers
What is pi times 3?<br> Thank you!!!
natta225 [31]
The correct answer is 9.42477796077 because pi 3.14ect you would just multiply it by 3 so the answer would be 9.42477796077
4 0
3 years ago
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