the scale factor will be greater than 5 if the dilation enlargement
C.5
2.9%
because you have to divide 29/1000 then move the decimal place
- Hope that helps
The 1st equation can be factored into
you can apply the zero product rule now.
Answer: -185 (choice D)
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Explanation:
- x = first integer
- x+1 = second integer
Note how x+1 follows immediately after x. That's what "consecutive" means by definition. An example of consecutive integers would be 7,8,9,10.
Adding those two said integers will lead to -371
first+second = -371
x+(x+1) = -371
2x+1 = -371
2x = -371-1
2x = -372
x = -372/2
x = -186
x+1 = -186+1 = -185
Note how -186+(-185) = -371 to confirm the answer.
The two consecutive integers that add to -371 are -186, -185. The larger of the two is -185 since it's more to the right on the number line.
Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
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b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
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c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
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d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
