Answer:
- 100
- 489.190
- 10,000
- 48,919,000
Step-by-step explanation:
Each factor of 10 in the divisor causes the decimal point to move 1 place to the left.
a) The decimal point has moved 2 places to the left. The divisor is 10^2 = 100.
b) The divisor is 10^3, so the decimal point will move 3 places to the left.
489.190
c) The decimal point has moved 4 places to the left, so the divisor is 10^4 = 10,000.
d) The divisor is 10^5, so the decimal point in the quotient if 5 places to the left of where it is in the dividend. Moving the quotient's decimal point 5 places to the right gives ...
48,919,000
_____
<em>Additional comment</em>
An exponent signifies repeated multiplication. Here, we're concerned with repeatedly multiplying (or dividing) by factors of 10. The exponent indicates the number of factors: 10·10 = 10^2 = 100. It also matches the number of zeros following the 1 in the product. 1000 = 10^3 has 3 zeros after the 1, for example.
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola will lie at (-3,2).
<h3>What is the Equation of a parabola?</h3>
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Comparing the given equation with the equation of a parabola, we will get,
y = a(x -h)² + k
y = -4(x+3)² + 2
Hence, the vertex of the parabola will lie at (-3,2).
Learn more about Parabola:
brainly.com/question/8495268
#SPJ1
We need Pythagoras theorem here
a^2+b^2 = c^2
a, b = legs of a right-triangle
c = length of hypotenuse
Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 + S^2+4S+4 = 100 cm^2 [collect terms and isolate]
2S^2+4S = 100-4 = 96 cm^2
simplify and form standard form of quadratic
S^2+2S-48=0
Solve by factoring
(S+8)(S-6) = 0 means (S+8)=0, S=-8
or (S-6)=0, S=6
Reject nengative root, so
Shorter leg = 6 cm
Longer leg = 6+2 cm = 8 cm
Hypotenuse (given) = 10 cm
Answer:
7.5 miles
Step-by-step explanation:
Half of 5 equals 2.5. Bobby already walked 5 miles so you add the 2.5 since he walked another half of that distance. 5 + 2.5 = 7.5
