Given:
Last year Lira earned $12,000 less than her husband Todd.
Together they earned $75,000.
To find:
The amount earned by Lira in last year.
Solution:
Let x be the amount earned by Lira's husband inn last year.
Last year Lira earned $12,000 less than her husband Todd.
Amount earned by Lira = 
Total amount earned by Lira and her husband = 
= 
Together they earned $75,000.
Now,
Amount earned by Lira =
= 
= 
Therefore, the amount earned by Lira in last year is $31500.
Answer:
w > -3
Step-by-step explanation:
2w<9+5w
Subtract 5w from each side
2w-5w<9+5w-5w
-3w <9
Divide each side by -3 remembering to flip the inequality
-3w/-3 > 9/-3
w > -3
Answer:
3
Step-by-step explanation:
3/5 x 6 = 3 3/5
Answer:
137 m²
Formula's:
- area of rectangle: length + width
- area of triangle: 1/2 * base * height
Explanation:
⇒ area of rec + area of rec + area of rec + area of triangle
⇒ 2 * 4 + 7 * 6 + 8 * 9 + 1/2 * 6 * 5
⇒ 8 + 42 + 72 + 15
⇒ 137 m²
Answer:
a) maximum; the parabola opens downward
b) positive; it must lie above the x-axis
c) x = 1.5
Step-by-step explanation:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.
The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When <em>second differences are negative</em>, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the <em>curvature</em> of the function is <em>negatve</em>, and that it <em>opens downward</em>.
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<h3>a, b.</h3>
If the graph of the parabola opens downward, and it crosses the x-axis, it must have a <em>maximum</em> that is a <em>positive value of y</em>.
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<h3>c.</h3>
The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:
x = (-2 +5)/2 = 3/2
The x-coordinate of the vertex is x = 1.5.
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<em>Additional comment</em>
The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.
