So we have the system of equations:
equation (1)
equation (2)
To use substitution, we are going to solve for one variable in one of our equations, and then we are going to replace that value in the other equation:
Solving for
in equation (2):
equation (3)
Replacing equation (3) in equation (1):
equation (4)
Replacing equation (4) in equation (3):
We can conclude that the solution of our system of equations is <span>
(7/5, 21/10)</span>
Answer:
y=70°
z= 60°
w= 70°
Step-by-step explanation:
Since the two triangles are similar, we know that all of the corresponding angles must be the same. On the triangle on the left, we can see that the angle formed between sides AB and AC is 60°. This means that the same angle is formed at Z, which is in the same location on the triangle to the right. From there, we can find the missing angle, W, from the difference of 180°.
180°-50°-60°=70°.
The same way we found Z, we can also find Y, since it has to be the same as W.
Answer:
54 feet
Step-by-step explanation:
We can use proportions
1 inch 27 inches
--------- = ------------
2 feet x feet
Using cross products
1x = 54
The building is 54 feet
Answer:
Step-by-step explanation:
Let the side of the square base be x
h be the height of the box
Volume V = x²h
13500 = x²h
h = 13500/x² ..... 1
Surface area = x² + 2xh + 2xh
Surface area S = x² + 4xh ...... 2
Substitute 1 into 2;
From 2; S = x² + 4xh
S = x² + 4x(13500/x²)
S = x² + 54000/x
To minimize the amount of material used; dS/dx = 0
dS/dx = 2x - 54000/x²
0 = 2x - 54000/x²
0 = 2x³ - 54000
2x³ = 54000
x³ = 27000
x = ∛27000
x = 30cm
Since V = x²h
13500 = 30²h
h = 13500/900
h = 15cm
Hence the dimensions of the box that minimize the amount of material used is 30cm by 30cm by 15cm
Option B
i(x) = 2x - 4 is the equation of the new function
<em><u>Solution:</u></em>
Given that the function h(x) = 2x-9 is translated up 5 united to become a new function, i(x)
To find: Equation of new function
The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input.
Adding to the output of a function moves the graph up
Therefore,
Given function is:
h(x) = 2x - 9
Translated up by 5 units
<em><u>Therefore, new function is:</u></em>
i(x) = h(x) + 5
i(x) = 2x - 9 + 5
i(x) = 2x - 4
Thus Option B is correct
