The factored form of the quadratic equation x² - 2x - 3 = 0 is (x - 3)(x + 1)
<h3>How to factor quadratic equation?</h3>
The quadratic equation can be factored as follows;
x² - 2x - 3 = 0
Therefore, let's find the numbers we can multiply to get -3 and add to get -2.
x² + x - 3x - 3
x(x + 1) - 3(x + 1)
Therefore,
(x - 3)(x + 1)
Therefore, the factored form of x² - 2x - 3 = 0 is (x - 3)(x + 1)
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Let's assume
the price of each train ticket is x
we are given
total number of family members =5
so, total cost of ticket = total number of family members*the price of each ticket
so, total cost of ticket =5*x
so, total cost of ticket =5x
now, we have
each family member buys a boxed lunch for $6.50
so, total cost of lunch box = total number of family members*price of each lunch box
so, total cost of lunch box = 5*6.50
total cost of trip = total cost of ticket+total cost of lunch box
we are given
total cost of trip is $248.50
now, we can plug values
and we get

now, we can solve for x





so,
the price of each train ticket is $43.2..........Answer
Answer:
- same: 30×40 = 1200
- different: 20×50 = 1000
Step-by-step explanation:
Same: 30×40 = 1200 . . . . . 2 zeros in the factors; 2 in the product
Different: 20×50 = 1000 . . . 2 zeros in the factors; 3 in the product
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Same: 0.3×0.4 = 0.12 . . . . no zeros in the factors; no zeros in the product
Different: 0.2×0.4 = 0.08 . . . no zeros in the factors; 1 zero in the product after the decimal point
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For a product, the number of zeros will be different if the combined factors of the numbers increase the number of factors of 10 beyond the sum of the factors of 10 of the numbers being multiplied.
<u>Example</u>: neither 2 nor 5 has a factor of 10, but their product does.
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For a product that is a decimal fraction, the number of leading zeros will increase if the product of the mantissas of the numbers is less than 10. The number of trailing zeros will increase under the conditions discussed above. (0.25×0.4 = 0.100)
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<em>Additional comment</em>
Here, the term "mantissa" is used to refer to the portion of the number written in scientific notation that multiplies the power of 10.
Answer:
1.88 inches
Step-by-step explanation:
The volume is the product of length, width, and height. If w represents the width of the box, then its length is 4w and its height is w+7. The volume is then ...
V = (4w)(w)(w+7)
We want to find the value of w that makes V=126. It is convenient to use the graphing calculator to look for zeros of a function, so we can write the equation as ...
V - 126 = 0
4w·w·(w+7) -126 = 0
The only positive solution to this equation is near w ≈ 1.883.
The width of the box is about 1.88 inches.
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Attached is output from the DESMOS free graphing calculator. The ALEKS calculator requires a subscription. The method of solution is substantially the same, but requires a little more work on the ALEKS calculator to find the zero-crossing.