Vertex of the polygon is (161, -329)
The new vertex is shifted 168 units to the right. A horizontal shift can be achieved be adding or subtracting the number from the x-coordinate. A change in the y coordinate brings the vertical shift. So in this case the x-component will change only and y component will be the same.
A shift towards right means, the value of x component is increase as x gets larger as we move towards right on the graph. So moving 168 units to the right, we will get the following vertex (329 , -329)
Thus, the new vertex of the polygon will be at the point (329, -329)
Answer:
f(3)=64
Step-by-step explanation:
f(3)=(1/8)(8 cubed)
f(3)= 8 to the negative one times 8 cubed
f(3)= 8 squared
f(3)=64
We have an triangle:
base=4 in
height=3 in,
This triangle can be dividided into two equal triangles, we need calculate the hypotenuse.
leg₁=4 in/2=2 in
leg₂=3 in
Pythagoras law:
hypotenuse²=leg₁²+leg₂²
hypotenuse²=(2 in)²+(3 in)²
hypotenuse²=4 in²+9 in²
hypotenuse²=13 in²
hypotenuse=√13 in.
Now, we can find the surface area.
Surface area=2 *(rectangle area)+base area + 2(triangle area)
rectangle area=10 in x √13 in=10√13 in²
base area=10 in x 4 in=40 in²
Triangle area=(4 in x 3 in)/2=6 in²
Surface area=2(10√13 in²)+40 in²+2(6 in²)=(20√13+52) in²≈124.11 in²
Answer: 124.11 in²
Step-by-step explanation:
2(2x + 1) = 3(x - 4)
4x+2=3x-12
4x-3x=--12-2
x=14
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
This is a exponential function of the form
where
a is the initial value
b is the base
b=(1+r)
r is the rate of growth or decay
In this problem
we have
a=2
b=2
1+r=2 -----> r=1 ----> r=100% (rate of growth)
using a graphing tool
The graph in the attached figure
The function initially increases slowly and then increases rapidly
