Answer:
The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.
Step-by-step explanation:
Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.
Two algebraic expressions are said to be equivalent if their values obtained by substituting any values of the variables are same.
Two expressions 3f+2.6 and 2f+2.6 are not equivalent, because when f=1,
Method of substitution can only help her to decide the expresssions are not equivalent, but if she wants to prove the expressions are equivalent, she must prove it for all values of f.
This is true only when f=0.
Hence,
The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.
Answer:
12 < x < 16
What we know:
- The longest side of the triangle is 20, another side length is 'x + 4'
- Since the triangle is acute, we know that the value of 'x' will have to be <u>greater than its right triangle value</u> because whatever 'x' equals will result in a <em>right </em>triangle, not an acute one
- We must solve for the <em>right </em>triangle first in order to determine the acute triangle
Solving for 'x' in the right triangle:
- a^2 + b^2 = c^2
- (x+4)^2 + x^2 = 20^2
- x^2 + x^2 + 8x + 16 = 400
- 2x^2 + 8x - 384 = 0
- simplify x^2 + 4x - 192 = 0
- factor (x + 16) (x - 12) = 0
- solve for each 'x' x + 16 = 0 & x - 12 = 0
- x = -16 & x = 12
- check the value of 'x' cannot be negative, so it is not -16. this means the value of 'x' is 12
- the value of 12 for 'x' makes a <em>right triangle, </em>so that is not the answer. this means the the value of 'x' needs to be <em>greater</em> than 12
<u>Checking your answer:</u>
- original equation (x + 4)^2 + x^2 = 20^2
- with answer (12 + 4)^2 + (12)^2 = 20^2
- (16)^2 + (12)^2 = 20^2
- 256 + 144 = 400
- 400 = 400 this is true, so the answer of 'x = 12' is <em>correct </em>for making it into a <em>right triangle</em>
<em></em>
Solving for 'x' in the acute triangle:
- x = 12 makes a right triangle
- x > 12 minimum for an acute triangle
- what is the maximum value for 'x' in the acute triangle? take the two other side lengths --> (x + 4) < 20 (longest side, so it will be the greater number)
- simplify x < 16
- x < 16 maximum for an acute triangle
Conclusion:
- if 'x = 12' makes a right triangle, then 'x > 12' and 'x < 16' are the values that will make it acute
- answer 12 < x < 16
<span>Slope is calculate by dividing the change in y-values by the change in x-values between a pair of points.
For 7: (7-1)/(1-10) = 6/-9 = -2/3
For 8: (6.1-3.1)/(-5.5 - -2.5) = 3/-3 = -1
For 9: (5/2 - -3) / (-5 - -7/3) = 11/2 / -8/3 = -33/16. This is not an answer option, so double check the problem.</span>
X=30
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Answer:
u
Step-by-step explanation:
the endpoint will be the last one to the right
