Answer:
Step-by-step explanation:
You are to assume in both problems that the two triangles are similar. That is a very dangerous assumption -- especially in later math classes. But in this case, there is no other way to do the problem. The two sets of triangles look like they are proportional. So set up two ratios that are = to each other
On the left
long side small triange / long side large triangle = base small triangle / base large triangle
On the right
hypotenuse/longest leg = hypotenuse / longest leg.
Problem A
Set up the similar Proportion
5/40 = x/20 Cross Multiply
40x = 20*5
40x = 100 Divide by 40
x = 100/40
x = 2.5
Problem B
Again set up the similar triangle proportion
15/10 = x/2 Multiply by 2
15*2/10 = x
3 = x
1.
k = 1
J = 7(1) + 5
J = 12
k = 1 + 2 = 3
J = 7(3) + 5
J = 26
26 - 12 = 14
J increases by 14.
2.
1/6 = 0.16 false (1/6 = 1.67)
0.08 = 4/5 false (0.08 = 8/100 = 2/25)
0.25 = 1/4 true (0.25 = 25/100 = 1/4)
<span>1/3 = 0.3 true (if rounded)</span>
<span>
3.
12 candles in 3 hours
12 </span>÷ 3 = 4
4 candles in 1 hour
4 × 8 = 32
32 candles in 8 hours
4.
$3.45 for 64 ounces
3.45 ÷ 64 = 0.05
$0.05 or 5 cents per ounce
5.
75 is what percent of 250?
75 ÷ 250 = 0.3
0.3 × 100 = 30
30%
Answer: 0.023 is twenty-three thousandths written in standard form!
Answer:
I think you mean: x^2 + 3x - 10, then
x^2 + 3x - 10
= x^2 + 5x - 2x - 10
=x(x + 5) - 2(x + 5)
=(x - 2)(x + 5)
Hope this helps!
:)
6. The lengths of two tangent lines to a circle are equal, which can be proved using similar triangles. The perimeter is 2*(3+2+5)=10.
14. c=40 degrees, since c and the given 40 angle correspond to the same arc on the circle. b=40, since b and the given angle are alternate interior angles of two parallel lines. d=180-40-40=100 degrees. a=180-d=180-100=80 degrees.
18. a is two times the given angle according to the inscribed angle theorem. a=2*20=40. b=180-a=140. c=90 since the tangent line is perpendicular to the diameter of the circle.
19. b=85, a=95. Connect the two points on the circle near 45 degrees on the diagram. b is the sum of the two angles formed (b is the exterior angle of the small triangle), and the sum is half the central angles they correspond to, which is 360-145-45=170. So b=170/2=85, and a=180-85=95 degrees.
20. Use power of a triangle. 5*(10+5)=6(6+x), x=6.5.
