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3 years ago

The sum of two numbers is 33. The sum of the smaller and 3 times the larger is 81. Find the numbers.

2 answers:

6 0

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Define x and y :
-------------------------------------------
Let the small number be x.
And the big number be y.

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Construct equations :
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The sum of the 2 numbers is 33.
⇒ x + y = 33

The sum of the smaller number and 3 times the larger number is 81.
⇒x + 3y = 81

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Find x and y :
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x + y = 33 ---------------- (1)
x + 3y = 81 .---------------- (2)

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Equation (2) - (1) :
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2y = 48
y = 24

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Sub y = 24 into equation (1) :
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x + y = 33
x + 24 = 33
x = 33 - 24
x = 9

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Find the two numbers :
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Smaller number = 9
Bigger number = 24

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Answer: The two numbers are 9 and 24.
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posledela3 years ago

4 0

The two numbers are 9and 24

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3 years ago

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A. 55°

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Step-by-step explanation:

A. 180 - (90 + 35) = 55°

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3 years ago

Determine the scale factor for the following points: (4, 2) to (16, 8)

hammer [34]

Answer:

The rule of dilation by a scale factor 4 is:

(x, y) → (4x, 4y)

P(4, 2) → (4x, 4y) = (4(4), 4(2)) = P'(16, 8)

Therefore, 4 will be the scale factor.

Step-by-step explanation:

Given the point

(4, 2)

As the image coordinates of (4, 2) are (16, 8) after the scale factor, we need to determine what could be the scale factor.

Let P(4, 2) is the original point, and P'(16, 8) is the image of the point P(4, 2).

It is clear that the coordinates of the image P'(16, 8) are 4 times the coordinates of the original point P(4, 2), which means the point P(4, 2) is dilated by a scale factor of 4.

Thus, the rule of dilation by a scale factor 4 is:

(x, y) → (4x, 4y)

P(4, 2) → (4x, 4y) = (4(4), 4(2)) = P'(16, 8)

Therefore, 4 will be the scale factor.

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3 years ago

One term of a geometric sequence is a4=135. The common ratio is r=3. Write an explicit rule for the nth term.

Anni [7]

Answer:

$a_{n} = 5 * 3^{n-1}$

Step-by-step explanation:

To find the nth term of a geometric sequence, you have the general formula:

$a_{1} *r^{n-1}$

where a1 is the first term and r is the common ratio. In order to find the 4th term, we can substitute what we have(n is 4 because we are looking for the fourth term):

135 = $a_{1} * 3^{4 - 1}$

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Now, we can substitute the first term back in:

$a_{n} = 5 * 3^{n-1}$

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3 years ago