9514 1404 393
Answer:
y = 3x^2 +30x +69
Step-by-step explanation:
Transformations work this way:
g(x) = k·f(x) . . . . vertical stretch by a factor of k
g(x) = f(x -h) +k . . . . translation (right, up) by (h, k)
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So, the translation down 2 units will make the function be ...
f(x) = x^2 ⇒ f1(x) = f(x) -2 = x^2 -2
The vertical stretch by a factor of 3 will make the function be ...
f1(x) = x^2 -2 ⇒ 3·f1(x) = f2(x) = 3(x^2 -2)
The horizontal translation left 5 units will make the function be ...
f2(x) = 3(x^2 -2) ⇒ f2(x +5) = f3(x) = 3((x +5)^2 -2)
The transformed function equation can be written ...
y = 3((x +5)^2 -2) = 3(x^2 +10x +25 -2)
y = 3x^2 +30x +69
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The attachment shows the original function and the various transformations. Note that the final function is translated down 6 units from the original. That is because the down translation came <em>before</em> the vertical scaling.
<h2>HOW TO: SOLVE AN APPLICATION</h2>
Step 1. Identify what you are asked to find and choose a variable to represent it.
Step 2. Write a sentence that gives the information to find it.
Step 3. Translate the sentence into an equation.
Step 4. Solve the equation using good algebra techniques.
Step 5. Check the answer in the problem and make sure it makes sense.
Step 6. Write a complete sentence that answers the question.
Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.
Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item. See Figure 6.7. The sales tax is determined by computing a percent of the purchase price.
To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays.
Answer:
75%
Step-by-step explanation:
48 of 64 times 100
48/64 × 100
0.75 × 100
75
So 75% of the bottle of orange juice is water
Hope this helps!!
For the reaction,
Initial concentration:
<u>0.1M</u> , <u>0.1M</u> , <u>0</u> , <u>0</u>
Let 'x' mole per litre of each of theproduct be formed.
At equilibrium:
<u>(0.1 – x)M</u> , <u>(0.1 – x)M</u> , <u>xM</u> , <u>xM</u>
where x is the amount of Carbon dioxide and Hydrogen, at equilibrium.
Hence, equilibrium constant can be written as,
→ x² = 4.24 (0.01 + x² – 0.2x)
→ x² = 0.0424 + 4.24 x² - 0.848x
→ 3.24x² - 0.848x + 0.0424 = 0
<em>a = 3.24, b = -0.848, c = 0.0424</em>
(for quadratic equation ax² + bx+c=0)
Here, the value 0.194 should be neglected because it will give concentration of the reactant which is more than initial concentration.
∴ The equilibrium concentrations are :-
![[CO_2] [H_2] = x = 0.067M](https://tex.z-dn.net/?f=%5BCO_2%5D%20%5BH_2%5D%20%3D%20x%20%3D%200.067M)
![[CO] [H_2 O] = 0.1 - 0.067 = 0.033M](https://tex.z-dn.net/?f=%5BCO%5D%20%5BH_2%20O%5D%20%3D%200.1%20-%200.067%20%3D%200.033M)
