Step-by-step explanation:
100% = X
50% = 100%/2 = X/2
X decreased by 50 means X - 50% = X - X/2 = X/2
now,
100% = X/2
50% = 100%/2 = X/2 / 2 = X/(2×2) = X/4
increasing the previous result by 50% means
X/2 + 50% = X/2 + X/4 = 2X/4 + X/4 = 3X/4
so, comparing this to the original X (= 4X/4), we are X/4 short.
<span>Your football team gained 4 yards on first down and 2 yards on second down during its last possession. Which number is the additive inverse of the yards gained?</span>
1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
Answer:
<em>The three angle bisector intersect at a point called the incenter</em> of the triangle, which is actually the center of the triangle. This center point is at equal distance from all sides of the triangle.
Also if a circle is inscribed in the triangle, the incenter will be located at the center of that circle.
