x² + 5x - 6 can be expressed as (x + 6)(x - 1).
9514 1404 393
Answer:
- tan(A) = 7/24
- sin(A) = 7/25
- cos(A) = 24/25
Step-by-step explanation:
The mnemonic SOH CAH TOA can help you remember the trig ratios:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
With respect to angle A, the sides are Adjacent = 24; Opposite = 7, Hypotenuse = 25. Then the desired trig ratios are ...
tan(A) = 7/24
sin(A) = 7/25
cos(A) = 24/25
9514 1404 393
Answer:
$2.50
Step-by-step explanation:
The question asks for the total cost of a notebook and pen together. We don't need to find their individual costs in order to answer the question.
Sometimes we get bored solving systems of equations in the usual ways. For this question, let's try this.
The first equation has one more notebook than pens. The second equation has 4 more notebooks than pens. If we subtract 4 times the first equation from the second, we should have equal numbers of notebooks and pens.
(8n +4p) -4(3n +2p) = (16.00) -4(6.50)
-4n -4p = -10.00 . . . . . . . . . . . simplify
n + p = -10.00/-4 = 2.50 . . . . divide by the coefficient of (n+p)
The total cost for one notebook and one pen is $2.50.
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<em>Additional comment</em>
The first equation has 1 more notebook than 2 (n+p) combinations, telling us that a notebook costs $6.50 -2(2.50) = $1.50. Then the pen is $2.50 -1.50 = $1.00.
One could solve for the costs of a notebook (n) and a pen (p) individually, then add them together to answer the question. We judge that to be more work.
<span>This is a very nice counting question.
Suggestion / Hint: Count how many ways he can get from (0,0) to (5,7) by going through the point (2,3). Then subtract that from ALL POSSIBLE ways he can get from (0,0) to (5,7).
Hint for the hint: How many ways he can get from (0,0) to (5,7) by going through the point (2,3)? Well, that's the SUM of how many ways he can get from (0,0) to (2,3) and how many ways he get get from (2,3) to (5,7).
Hope this helps! :)</span>
Answer:
4.0075017*10^7
Step-by-step explanation:
move the decimal place left 7
