Given the next quadratic function:
to sketch its graph, first, we need to find its vertex. The x-coordinate of the vertex is found as follows:
where <em>a</em> and <em>b</em> are the first two coefficients of the quadratic function. Substituting with a = 2 and b = 3, we get:
The y-coordinate of the vertex is found by substituting the x-coordinate in the quadratic function, as follows:
The factorization indicates that the curve crosses the x-axis at the points (-2, 0) and (1/2, 0). We also know that the curve crosses the y-axis at (0,-2). Connecting these points and the vertex (-0.75, -3.125) with a U-shaped curve, we get:
Step-by-step explanation:
first collect terms, while the < remains unchange
<u>P</u><u> </u><u> </u>< 1-2
9
cross examine and get the answer
<u>P</u><u> </u>< <u>-</u><u>1</u>
9 1
<em>P</em><em> </em><em>=</em><em> </em><em>-</em><em>9</em>
Answer:
Two options:
5,6, and 7
-1,0,and 1
Step-by-step explanation:
Three consecutive natural numbers can be represented as n, n+1, and n+2.
The product of the smaller two would be n(n+1). The less than 5 times the larger is 5(n+2)-5.
Set them equal and solve by factoring:
Set each factor equal to 0.
n-5==0 so n=5.
n+1=0 so n=-1.
This means the 3 consecutive numbers would be 5,6, and 7
OR
-1, 0 or 1.
B) 6, 8, 10
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Answer:
75min or 1 hour 15min
Step-by-step explanation:
45/12 = 3.75min per problem
3.75 x 20 = 75min or 1 hour 15min
