Answer:
<h2>Number of solutions: 3</h2><h2>Type: -10, -2, 2.8</h2>Step-by-step explanation:
f(x) = 0 - the solutions are the x-intercepts.
Look at the picture.
<em>Unit: 2 : 5 = 0.4</em>
What is the value of x? Enter your answer in the box.
1 answer:
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Answer:
The original length was 41 inches and the original width was 16 inches
Step-by-step explanation:
Let
x ----> the original length of the piece of metal
y ----> the original width of the piece of metal
we know that
When squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box
The dimensions of the box are
The volume of the box is equal to
so
simplify
-----> equation A
Remember that
The piece of metal is 25 in longer than it is wide
so
----> equation B
substitute equation B in equation A
solve for y
Solve the quadratic equation by graphing
using a graphing tool
The solution is y=16
see the attached figure
Find the value of x
therefore
The original length was 41 inches and the original width was 16 inches
Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
. That is, 
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
and replace 
and 
using expressions that contain an expression in terms of x from the first two equations we came up with.
That gives us:
which we solve for x as follows:
Now that we know x we can substitute 36 for x into the equation
and solve for z as follows:
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
That gives us:
Now that we know x we can substitute 36 for x into the equation
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.