Answer:
Step-by-step explanation:
<u>We know that:</u>
<u>Solution:</u>
- 3 miles = 45 minutes
- => 1 mile = 45/3 minutes
- => 5 miles = 45/3 x 5
- => 5 miles = 15 x 5
- => 5 miles = 75 minutes
Hence, it takes 75 minutes for Jim to walk 5 miles.
Answer: the function g(x) has the smallest minimum y-value.
Explanation:
1) The function f(x) = 3x² + 12x + 16 is a parabola.
The vertex of the parabola is the minimum or maximum on the parabola.
If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.
The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.
When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).
Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.
Then, finding the minimum value of the function is done by finding the vertex.
I will change the form of the function to the vertex form by completing squares:
Given: 3x² + 12x + 16
Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4
That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).
Then the minimum value is 4 (when x = - 2).
2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>
The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.
When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2
Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.
Sin OH Cosin AH Tangent OA search "SOCAHTOA"
Answer:
A
Step-by-step explanation: just divide 71 into 2 which gives you 35.5 making a your answer.
Answer:
Width=4, and Length=17
Step-by-step explanation:
first you will make a variable for the width which i will say is x
now make it an equation (3x+5) (x) = 68
then solve 3x^2+5x=68
then 3x^2+5x-68=0
then x=4
then you have to substitute so 3(4)+5= 17 and 4
