1.) 3124
2.) 3214
3.) 3412
4.) 1432
5.) 1342
6.) 1234
7.) 1423
I hope I helped
Answer:
90°
Step-by-step explanation:
The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.
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The slope to point 'a' is y/x = 2/1 = 2.
The slope to point 'b' is y/x = (-1/2)/1 = -1/2.
The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.
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We can also use the trig formula for the tangent of the difference of angles.
tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))
The tangents are the slopes, calculated above, so we have ...
tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = <em>undefined</em>
The tangent is <em>undefined</em> for angles that are odd multiples of 90°. The angle between the vectors is 90°.
Answer:
i)
0.79m
ii)
1.21m
iii)
7/5m
iv)
3/5m
Step-by-step explanation:
i)
The price of a USB memory stick selling at a 21% discount off its marked price (m)
The marked price m represents 100% of the value of the USB memory stick. Offering a 21% discount off the marked price will mean that the USB will be selling at;
(100 - 21)% of the marked price m
=79% of m
= (79/100)*m
= 0.79m
ii)
The price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD.
The amount (m) needed to manufacture the CD would represent 100% of the value of the CD. Selling the CD for 21% more than the amount (m) needed to manufacture the CD will imply that the selling price is;
(100+21)% of m
= 121% of m
= (121/100)*m
= 1.21m
iii)
The final value of a painting after its initial value, m, increases by 2/5.
The initial value of the painting is given as m. The value of the painting is said to increase by 2/5 which means that the increase in its value would be;
2/5 of m
=2/5 * m
=2/5m
The final value of the painting will thus be;
initial value + increase in value
=m + 2/5m
= m(1+2/5)
=7/5m
iv)
The total number of markers that Nancy has if she gives away 2/5 of her m markers to Amy.
Initially, Nancy had a total of m markers. By giving away 2/5 of her markers to Amy, her markers reduced by;
2/5 of m
=2/5*m
=2/5m
The new number of her markers will be given by;
initial numbers - total given to Amy
= m - (2/5m)
= m(1 - 2/5)
=m(3/5)
=3/5m
Answer:
68 texts per day
Step-by-step explanation:
The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).
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Substitute the number (15) for the variable (a) and do the arithmetic:
t = -1.63a +92.14
t = -1.63(15) +92.14 = -24.45 +92.14
t = 67.69
Keiko's trend line estimates a 15-year-old would send about 68 texts per day.
Answer:
i don't know
Step-by-step explanation:
get a tutor
