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tigry1 [53]
2 years ago
5

PLEASE help me answer this!!!

Mathematics
1 answer:
tia_tia [17]2 years ago
8 0

Check the picture below.

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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 <em>in</em> the green box is equal to 909.

General Formulas and Concepts:
<u>Algebra I</u>

Equality Properties

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

<u>Trigonometry</u>

[<em>Right Triangles Only</em>] 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:

<u>Step 1: Define</u>

<em>Identify given variables</em>.

<em>a</em> = 30

<em>b</em> = 3

<em>c</em> = <em>x</em>

<em />

<u>Step 2: Find </u><u><em>x</em></u>

Let's solve for the <em>general</em> equation that allows us to find the hypotenuse:

  1. [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 <em>formula</em> to solve for the hypotenuse, let's figure out what <em>x</em> is equal to:

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

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

___

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

___

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
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