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aleksklad [387]
1 year ago
6

What is the y-value of the vertex of 4x^+ 8x - 8?

Mathematics
1 answer:
deff fn [24]1 year ago
5 0

Answer: The y-value of the vertex is

Step-by-step explanation: we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex of the parabola

In this problem we have

-----> this a vertical parabola open upward

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

The vertex is the point

The y-value of the vertex is

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Given the function with f(3) = 127 and f(1) = 95, determine the rate of change over the interval 1 <3 <3
Sonbull [250]

Answer:

When we have a function f(x) = y.

The rate of change between a and b (where a < b) is:

R = (f(b) - f(a))/(b - a)

In this case:

b = 3

a = 1

f(3) = 127

f(1) = 95

R = (127 - 95)/(3 - 1) = 16

The rate of change in that interval is 16.

3 0
3 years ago
Determine whether the statement is always true, sometimes true, or never true. Give an example. (a) Both sides of an equation ca
arsen [322]

Answer:

(A) Always true

(B) Seldom true

Step-by-step explanation:

(A) Both sides of an equation can be multiplied by the same number without this action changing the solution of the equation.

Keyword here is "number".

Multiplying both sides of an equation by an equal quantity (same number) will result in same solution after solving for the unknown in the equation. This is because that numeric quantity can always be removed by dividing both sides of the equation by it or by a factor (or multiple) of it.

EXAMPLE:

For a linear equation, 4x - 6 = 15x

let's find the solution, in other words solve for the unknown value X.

4x - 15x = 6

-11x = 6

x = -6/11

Now multiply both sides of the equation by 3.

3(4x - 6) = 3(15x)

12x - 18 = 45x   ___new equation

Solve for X

12x - 45x = 18

-33x = 18

x = -18/33

Reduce the fraction to its simplest form by looking for a number that can divide both numerator and denominator without remainder. In other words, think of a number that is a factor of 18 and a factor of 33.

That common factor or highest common factor (HCF) is 3.

Go ahead and reduce the fraction.

x will be reduced to -6/11

(B) Both sides of an inequality can seldom be multiplied by the same number, without such action changing the solution set of the equation.

Inequalities are more complex. Operational signs even change sometimes, in the course of finding the solution set of the inequality.

Sometimes, multiplying both sides of an inequality by a given numeric quantity will change its solution set and sometimes, it won't.

5 0
3 years ago
Did you hear the one about the acupuncture
Alecsey [184]

The answer is "It was A Jab Well Done" You have to finish the whole sheet to get the answer

8 0
3 years ago
Is 50.2 a rational or an irrational number, why?
Greeley [361]

Answer:

Rational.

Step-by-step explanation:

\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}

4 0
2 years ago
[Calculus, Derivatives] Can a function be differentiable at certain points even if the entire function is not differentiable?
koban [17]

A function is differentiable if you can find the derivative at every point in its domain. In the case of f(x) = |x+2|, the function wouldn't be considered differentiable unless you specified a certain sub-interval such as (5,9) that doesn't include x = -2. Without clarifying the interval, the entire function overall is not differentiable even if there's only one point at issue here (because again we look at the entire domain). Though to be fair, you could easily say "the function f(x) = |x+2| is differentiable everywhere but x = -2" and would be correct. So it just depends on your wording really.

5 0
3 years ago
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