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sashaice [31]
3 years ago
9

three positive numbers are in Arithmetic Progression (A.P). the sum of the squares of the three numbers is 155. while the sum of

the numbers is 21. if the common difference is positive. find the values of x and y
Mathematics
1 answer:
Alecsey [184]3 years ago
6 0
Given:
Three numbers in an AP, all positive.
Sum is 21.
Sum of squares is 155.
Common difference is positive.

We do not know what x and y stand for.  Will just solve for the three numbers in the AP.
Let m=middle number, then since sum=21, m=21/3=7
Let d=common difference.
Sum of squares
(7-d)^2+7^2+(7+d)^2=155
Expand left-hand side
3*7^2-2d^2=155
d^2=(155-147)/2=4
d=+2 or -2
=+2  (common difference is positive)

Therefore the three numbers of the AP are
{7-2,7,7+2}, or
{5,7,9}


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Answer:

Part B: \displaystyle [1, 2]

Part A: Set both equation equal to each other by Substitution, since our <em>y-values</em> are already given to us.

Step-by-step explanation:

6x - 4 = 5x - 3

- 6x + 3 - 6x + 3

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\displaystyle -1 = -x; 1 = x

Plug this coordinate back into the above equations to get the <em>y-coordinate</em><em> </em>of 2.

<em>y</em><em> </em><em>=</em><em> </em><em>mx</em><em> </em><em>+</em><em> </em><em>b</em><em> </em>[where<em> </em><em>b</em><em> </em>is the y-intercept and the rate of change (slope) is represented by <em>m</em>]

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I am joyous to assist you at any time.

3 0
3 years ago
Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are
Galina-37 [17]

Answer:

B' = (-3,6)

Step-by-step explanation:

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A(4,5)

B(0,5)

C(3,-1)

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Required

Determine the new coordinates of B

Write out the coordinates of B

x = 0

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When a function is shifted to the left, we have to subtract the unit from the x value of the function;

<em>Shifting by 3 units left, the new x becomes </em>

<em />New\ x = 0 - 3<em />

<em />New\ x = -3<em />

<em />

When a function is shifted upward, we have to add the unit to the y value of the function;

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GarryVolchara [31]
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