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:
The amount in the account in the beginning of the 6th year is $6375 .
Step-by-step explanation:
Formula
As given
You invest $5000 in an account at 5.5% per year simple interest.
Principle = $ 5000
Rate = 5.5 %
Time = 5 years
(As calculate amount in the account for beginning of 6th year.)
Putting all the values in the formula
Simple interest = $ 1375
Amount = Principle + Simple interest
Putting values in the above formula
Amount = $5000 + $1375
Amount = $ 6375
Therefore the amount in the account in the beginning of the 6th year is $ 6375 .
Answer:
y=5x+(-19)
Step-by-step explanation:
Refer to the picture that given
Vertex coordinates: (h, k)
Vertex form: y = a(x-h)^2 + k
y = 2(x+3) + 2(x+4)
Use distributive property:
y = 2((x+3)+(x+4))
Simplify:
y = 2(2x+7)
y = 4x+14
This is slope - intercept form, not vertex form. Vertex form is for quadratic equations - this is a linear equation.
Answer (in slope - intercept form):
y = 4x+14
Answer: x exceeds y x - y r minus s r - s Multiplication Multiply, times, the product of, multiplied by, times as much, of × 7 times y 7y The product of x and y xy 5 multiplied by y 5y one-fifth of p 1 5 p Division Divide, divides, divided by, the quotient of, the ratio of, equal amounts of, per ÷ Divide x by 6 x 6 or x ÷6 7 divides x x 7 or x ÷7 7 ...
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Step-by-step explanation:
