Let Tony's age = x
He is 4 years younger than his brother Josh, so Josh's age would be x + 4
He is 2 years older than his sister, so her age would be x - 2
He has a twin, which would be the same age, so the twins age is also x
They all add together to equal 66, so you get:
x + x + x+4 + x-2 = 66
Simplify:
4x +2 = 66
Subtract 2 from both sides:
4x = 64
Divide both sides by 4:
x = 64/4 = 16
Tony is 16 years old.
<span>The given function is ⇒⇒⇒ y = x² + 4x + 4
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To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i.e. make x as y and y as x)
y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation
y = (x+2)(x+2)
y = (x+2)² ⇒⇒⇒ take the square root to both sides
√y = x+2
x = √y - 2 ⇒⇒⇒ x becomes a function of y
final step:
∴ y = √x - 2 ⇒⇒⇒ the inverse of the given function
So, as a conclusion:
f(x) = y = x² + 4x + 4 ⇒⇒⇒ the given function
f⁻¹(x) = y = √x - 2 ⇒⇒⇒ the inverse of the given function
Answer:
1. The rectangular prism is a right prism with rectangular bases (check the picture)
2. It has 8 vertices, so we are looking for 3d figures with 4 vertices.
3. A face can have at least 3 vertices, and the 4th must be outside of the plane determined by the first 3 vertices. This makes 4 vertices in total.
4. The 3d figure described in step 3 is a pyramid.
so the answer is prism
Step-by-step explanation:
Answer:
1.734
Step-by-step explanation:
Given that:
A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles).
The fitted regression is Time = −7.126 + .0214 Distance
Based on a sample size n = 20
And an Estimated standard error of the slope = 0.0053
the critical value for a right-tailed test to see if the slope is positive, using ∝ = 0.05 can be computed as follows:
Let's determine the degree of freedom df = n - 1
the degree of freedom df = 20 - 2
the degree of freedom df = 18
At the level of significance ∝ = 0.05 and degree of freedom df = 18
For a right tailed test t, the critical value from the t table is :
1.734
Answer:
The equation is:
(2×π×r×4r)+(2×π×r^2)= A
The maximum radius of the can they will produce = 1.7 inches
Step-by-step explanation:
Please see the attached files for explanation