Let x be larger integer so x-3 is the smaller
so x^2+ x-3 = 87
x^2 +x -90=0 and factor
(x-9)(x+10)=0
x=9 or x=-10 but x must be positive
so x=9 and smaller number is 6

6 0

3 years ago

Graph the system of equations.

Marat540 [252]

You can soustracte the first or the second one

and y cancel

x = 6

now you put 6 in x
you can take the first or the second one

6 - y = -2
6 - y = -2
y = -8

8 0

3 years ago

Please someone help me out

Aneli [31]

Answer: maximum height of the football = 176 feet

Step-by-step explanation:

We want to determine the maximum height of the football from the ground. From the function given,

h(t) = -16t^2+96t +32, it is a quadratic function. Plotting graph if h will result to a parabolic shape. The maximum height of the football = the vertex of the parabola. This vertex is located at time, t

t = -b/2a

b = 96 and a= -16

t = -b/2a = -96/2×-16= 3

Substituting t = 3 into the function if h

h(t) = -16×3^2+96×3 +32

=-16×9 + 96×3 +32

= -144+ 288+32

=176 feet

6 0

3 years ago

The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:

denis23 [38]

Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)

Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is $f(x)=-0.03x^{2}+3x$ .
Plugging 15 and 35 in x, we can find the values of the function, i.e.
$f(15)=38.25$ and $f(35)=68.25$ .
Then, the average change is $\frac{68.25-38.25}{35-15}=1.5$

4 0

3 years ago

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