What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
we know that
The equation of the line in slope-intercept form is equal to
where
m is the slope of the line
b is the N-intercept
In this problem we have
Find the slope
Let
substitute the values
The correct answer is: [A]: "69° <span>" .
</span>______________________________________________________
m∠1 = 69° .
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Explanation:
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180 - (39 + 30) = 180 - 69 = 111. This is the measurement of the third angle in the triangle. Note that all angles in a triangle add up to 180° . All triangles have 3 (three) sides and 3 (three) angles.
To find m∠1 :
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The only single angle that exists that is supplementary to ∠1 is 69.
So: m∠1 = 180 - 111 = 69 . (Note: since all angles on a straight line are supplementary angles; and supplementary angles add up to 180° .
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The answer is: 69° .
m∠1 = 69° .
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Answer:
1
Step-by-step explanation:
