Answer:
Step-by-step explanation:
To find the intercept with the x axis, we make h (x) = 0.
0 = (x + 1) ^ 2 - 4
0 = x ^ 2 + 2x + 1 -4
0 = x ^ 2 + 2x - 3
0 = (x +3) (x-1)
x = 1
x = -3
To find the intercept with the y axis, we make x = 0.
y = (0+1)^2 -4
y = -3
For a quadratic equation of the form ax ^2 + bx+ c
The vertex is calculated with the formula x = -b/2a
So:
x = -2/2(1)
x = -1
Finally the axis of symmetry of a quadratic function always passes through the vertex.
So:
x = -1
Below is a graph for this function, where you can see the cut points with the axes, the vertex and axis of symmetry
Answer:
53.3
Step-by-step explanation:
34^2=1156
41^2=1681
1156+1681=2837
Square root of 2837 is 53.26 which rounded to the nearest tenth is 53.3
<span> Two rectangles, one lying completely within the other. The area between the rectangles is shaded. Two adjacent sides of the larger rectangle are labeled sixty feet and forty feet. The shaded area is labeled four foot border.
Area of larger rectangle = 60 ft * 40 ft = 2400 ft</span>²
Area of smaller rectangle = (60-4)ft * (40-4)ft = 56 ft * 36 ft = 2,016 ft²
Area of the border = 2,400 ft² - 2,016 ft² = 384 ft²
Answer:
angle B is 38 degree
Step-by-step explanation:
In triangle ADC,
finding angle C
angle A + angle C = 110 degree (sum of two interior opposite angles are equal to the exterior angle formed)
46 + angle C = 110
angle C = 110 - 46
angle C = 64 degree
In triangle ABC
finding angle B
angle A + angle B + angle C = 180 degree (sum of interior angles of a triangle)
78 + angle B + 64 = 180
142 + angle B = 180
angle B = 180 - 142
angle B = 38 degree
