4/5/10/11/16/18/19/35 percent difference

Serena has attached a 10 inch ribbon to the corners of a frame to hang it on the wall. The frame 9 inches wide. How far above th

kherson [118]

Answer: The hook would be 2.2 inches (approximately) above the top of the frame

Step-by-step explanation: Please refer to the picture attached for further details.

The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse (longest side) and AB and BC are the other two sides

5^2 = 4.5^2 + BC^2

25 = 20.25 + BC^2

Subtract 20.25 from both sides of the equation

4.75 = BC^2

Add the square root sign to both sides of the equation

2.1794 = BC

Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches

4 0

3 years ago

Find the quadratic function y=f(x) whose graph has a vertex (−3,4) and passes through the point (−7,0). Write the function

olganol [36]

Answer:

Step-by-step explanation:

This is a parabola since a quadratic is a parabola. The standard form for a parabola is y = ax² + bx + c

but before we do that, we will use the vertex form, since it will make our work easier at the beginning.

First and foremost, when we plot the vertex and the given point, the vertex is higher up than is the point; that means that this parabola opens upside down, and its vertex form will be

y=-|a|(x - h)² + k

The absolute value is out in front of the a, so we know that the value of a is positive, but the quadratic itself is negative (upside down) and we will find that math takes care of that negative that needs to be out front. So we need to solve for a by filling in the x, y, h, and k values from the point and the vertex: x = -7, y = 0, h = -3, k = 4

0 = a(-7 - (-3))² + 4 and

0 = a(-7 + 3)² + 4 and

0 = a(-4)² + 4 and

0 = a(16) + 4 and

0 = 16a + 4 and

-4 = 16a so

$a=-\frac{1}{4}$