the art museum charges $13 for each adult admission and $8 for each child the total bill for the 182 people from a achool trip w
as $1606 how many adults and children went to the museum?
1 answer:
Answer:
152 kids and 30 adults
Step-by-step explanation:
To solve this, we must create a system of equations
Suppose:
x = the number of adults
y = the number of children
We know that a total of 182 people attended the trip.
So:
x + y = 182
This equation represents the number of people attending the trip.
To find out the cost, look at the problem.
It costs 13$ for one adult and 8$ for a child.
So:
13x + 8y = 1606
This equation represents the total cost to attend the museum. Now, we must solve.
[There are two ways to solve a system of equations, substitution and adding/subtracting. I will use adding and subtracting. The steps to solving the system of equations is in the photos below]
The final answer is 152 kids and 30 adults
I hope this helps!!! :)
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Answer:
A. A reflection over the x-axis and a vertical stretch.
Step-by-step explanation:
Let , to obtain
, we need to use the following two operations:
(i) Vertical stretch
,
(ii) Reflection over the x-axis
Let prove both transformations in :
Step 1 - Vertical stretch ()
Step 2 - Reflection over the x-axis
Hence, correct answer is A.
Note that no diagram is drawn to scale.
If the diagram in the first picture is further worked upon, we have polygon ABCDE.
Note also that line AD = 18in and line MD = 10in.
This simply means the line Am = AD - MD = 8in.
We have the height of the triangle needed to solve for the area of the triangle. Area of Triangle = 1/2×b×h
Where b is length base of the triangle and h is the length of height of the triangle.
We still need b to find the Area.
Note also that two opposite sides of parallelograms are equal. This implies that line DC = line EB which is equal to 14in.
In the third image, you can see this. Half the length of the side of the parallelogram is needed. This means 14/2 = 7in.
We can now solve for the Area of the triangle.
We have the are of the triangle to be 28in. Multiply this by 3 to find the total area of all three triangles since the three triangles are identical. Thus,
Total Area of all Triangles = 28×3 = 76in
Now, find the area of the two parallelograms.
Area of parallelogram EBCD = bh
Where b is the length of the base side and h is the height.
Hence from the diagram,
Area of parallelogram EBCD is 140in.
Total Area of both Parallelograms will be 140 ×2= 280in since both are identical.
To find the Total Area of the tile pattern add the area of the triangles and the Parallelograms. This is 76 + 280 =356in.
Your answer is 356in.
If the diagram in the first picture is further worked upon, we have polygon ABCDE.
Note also that line AD = 18in and line MD = 10in.
This simply means the line Am = AD - MD = 8in.
We have the height of the triangle needed to solve for the area of the triangle. Area of Triangle = 1/2×b×h
Where b is length base of the triangle and h is the length of height of the triangle.
We still need b to find the Area.
Note also that two opposite sides of parallelograms are equal. This implies that line DC = line EB which is equal to 14in.
In the third image, you can see this. Half the length of the side of the parallelogram is needed. This means 14/2 = 7in.
We can now solve for the Area of the triangle.
We have the are of the triangle to be 28in. Multiply this by 3 to find the total area of all three triangles since the three triangles are identical. Thus,
Total Area of all Triangles = 28×3 = 76in
Now, find the area of the two parallelograms.
Area of parallelogram EBCD = bh
Where b is the length of the base side and h is the height.
Hence from the diagram,
Area of parallelogram EBCD is 140in.
Total Area of both Parallelograms will be 140 ×2= 280in since both are identical.
To find the Total Area of the tile pattern add the area of the triangles and the Parallelograms. This is 76 + 280 =356in.
Your answer is 356in.