They give us 2 pieces to the puzzle. Both are positive numbers...x and y.
1.) 1 number is 1 less than twice another number. (x = 2y -1)...and
2.) the sum of their squares is 106. (x^2 + y^2 = 106).
substitute the value for x into the second equation.
(2y-1)^2 + y^2 = 106
(2y-1) (2y-1) + y^2 = 106 (use distributive property)
4y^2 - 2y - 2y + 1 + y^2 = 106 (subtract 106 from both sides)
4y^2 - 2y - 2y + 1 + y^2 - 106 = 106 - 106 (combine like terms)
5y^2 - 4y - 105 = 0 (factor)
(y-5) (5y-21) = 0 (set to 0)
y - 5 = 0
y = 5
substitute the 5 into the equation for y (x = 2(5) - 1)
x = 9 if we square 9, we get 81.
subtracted from 106 we have 25...the square root of 25 is 5.
our answers are 5 and 9.
Answer: The pole is 17 feet long
Step-by-step explanation: If Matthew's shadow is 2 feet smaller than his actually size, the shadow of the pole will also be reduced. Since the pole's shadow is 15 feet long, adding 2 will give you its original size, 17 feet.
The x and y intercept for the equation 7x-2y= 14 is x=2 and y=7
<span>3•(x•y)=(3•x)•y
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answer
associative property of multiplication
Multiply each side of the given equation by <span>ax−2</span> (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:
<span><span><span><span>24 x ^2 </span>+ 25x </span>− 47 </span>= <span><span><span>(<span><span>−8x</span>−3</span>)</span><span>(<span>ax−2</span>)</span></span>−53</span></span>
You should then multiply <span>(<span><span>−8x</span>−3</span>)</span> and <span>(<span>ax−2</span>)</span> using FOIL.
<span><span><span><span>24 x ^2 </span>+ 25x </span>− 47</span>= <span><span><span><span><span>−<span>8ax^2 </span></span>− <span>3ax </span></span>+ 16x </span>+ 6 </span>− 53</span></span>
Then, reduce on the right side of the equation
<span><span><span><span>24 x ^2 </span>+ 25x </span>− 47</span>= (<span><span>−<span>8x </span></span>− <span>3(ax - 2) - 53</span></span></span>
Since the coefficients of the x^2-term have to be equal on both sides of the equation, <span><span>−8a</span>=24</span>, or <span>a=−3</span>.
Your answer would be <span>
B</span>
