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Alona [7]
3 years ago
12

The sum of two numbers is 57 and the difference is 13 what are the numbers

Mathematics
2 answers:
Sergio [31]3 years ago
6 0
Guess and Check!
N1=Number 1
N2=Number 2

n1 + n2 = 57

<span>n1 - n2 = 13</span>

<span>2n2 = 70</span>

n2 = 35

n1 = 57 - 35 = 22

<span> 22 and 35=number</span>

Rainbow [258]3 years ago
5 0
Let the numbers be x and y

x  + y  =  57          ........(i)
x  -  y  =  13          ........(ii)

Add equations (i) and (ii)  to eliminate y

x  + y  + x  -  y   =  57 + 13
x + x  + y - y =   57 +13
2x  =     70
x  =  70/2 = 35

From (i)  x  + y  =  57
              35 + y = 57
                      y = 57 - 35
                      y  =   22

The numbers are 35 and 22.
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Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the orig
gayaneshka [121]

Answer:

The correct option is;

A dilation by a scale factor of Two-fifths and then a translation of 3 units up

Step-by-step explanation:

Given that the coordinates of the vertices of square S are

(0, 0), (5, 0), (5, -5), (0, -5)

Given that the coordinates of the vertices of square S' are

(0, 1), (0, 3), (2, 3), (2, 1)

We have;

Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices

When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;

s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5

For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)

Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2

Therefore;

The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5

The after the dilation (about the origin),  the coordinates of S becomes;

(0, 0) transformed to (remains at) (0, 0) ....center of dilation

(5, 0) transformed to (5×2/5, 0) = (2, 0)

(5, -5) transformed to (2, -2)

(0, -5) transformed to (0, -2)

Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;

For (0, 0), (2, 0), (2, -2), (0, -2) we have;

(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)

(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)

For (0, 1), (0, 3), (2, 3), (2, 1) we have;

(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)

(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)

Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)

That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up

The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.

7 1
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If a car can travel 435 miles on 25 gallons of gas how many miles per gallon does the car get?
nirvana33 [79]

Answer:17.4

Step-by-step explanation:435 Divided by 25

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Lera25 [3.4K]

Answer:

B

Step-by-step explanation:

180-130=50

180-50=130

130:2=65

4 0
3 years ago
Follow the steps to find the value of x 1/5(x)5/1=6/3(5/1)
german

Answer: x=10

This is the answer I got.

6 0
3 years ago
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