PLEASE help me answer this!!!

Consider the following system of equations:

jenyasd209 [6]

Y=-x+10
2x+3(-x+10)=45
2x+-3x+30=45
2x+-3x=15
-x=15
X=15

4 0

3 years ago

Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to f

Marina86 [1]

The linear approximation to $f(x)$ centered at $x=a$ is

$f(x)\approx f(a)+f'(a)(x-a)$

What this means is that you can use the tangent line to $f(x)$ at $x=a$ to get a decent approximation of $f(x)$ at some other value of $x$ to within a certain degree of accuracy depending on how close this value $x$ is close to $a$ . (Note that when $x=a$ , the approximation is exact; $f(a)=f(a)$ .)

So what you're asked to do is find an approximate value of a zero of $f(x)$ near $a=3$ . That is to say, you're looking for some value $c$ such that $f(c)=0$ , but all you have at your disposal is the linear approximation to the function.

$f(x)\approx f(3)+f'(3)(x-3)$
$f(x)\approx2+5(x-2)$
$f(x)\approx5x-8$

You know that if $c$ is a zero of $f$ , then $f(c)=0$ , so you get

$f(c)=0\approx5c-8$

Solving for $c$ , you find

$0=5c-8\implies 5c=8\implies c=\dfrac85=1.6$

This means that an approximate zero of $f(x)$ is $x=1.6$ .

5 0

3 years ago

Please help! acellus

ch4aika [34]

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
$\displaystyle a^2 + b^2 = c^2$

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

[Pythagorean Theorem] Square root both sides [Equality Property]:
$\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}$

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

[Equation] Substitute in variables:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}$

∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.

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Learn more about Trigonometry: brainly.com/question/27707750

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Topic: Trigonometry

3 0

2 years ago

15. Suppose a car gas tank holds 21 gallons of gas. On a trip it uses 2/3 of a tank of gas on a trip. Then it uses 1/3 of what i

Eduardwww [97]

Answer:

4 2/3 gallons of gas

Step-by-step explanation:

Step 1

Suppose a car gas tank holds 21 gallons of gas.

On a trip it uses 2/3 of a tank of gas on a trip.

= 2/3 × 21 gallons of gas

= 14 gallons of gas

Step 2

Then it uses 1/3 of what is left in the tank.

The number of gallons of gas left =

21 gallons of gas - 14 gallons of gas

= 7 gallons of gas

Hence, this is calculated as:

1/3 × 7 gallons of gas

= 2 1/3 gallons of gas

Step 3

How many gallons of gas are left in the tank?

This is calculated as:

7 gallons of gas - 2 1/3 gallons of gas

= 7/1 - 7/3

Lowest common denominator =

= 21 - 7/3

= 14/3

= 4 2/3 gallons of gas is left

Therefore, 4 2/3 gallons of gas is left.

5 0

3 years ago

If half of a box of candy weighs 3/5 of a pound, how much would 4 full boxes weigh?

Reil [10]

So we want to know what a full box is. We have the weight of half a box. So we can use the formula: (2 x 3/5) and you want to know the outcome of four full boxes. So (2x3/5)4
Or: 6/5 x 4

And the answer is 24/5. But if you want to simplify it, it’s 4 4/5

7 0

3 years ago