The figure is the right triangle DEF.
In it, E is the 90° angle, D is the corner over E (this is, DE is the vertical segment or height from the base) and F is the corner to the right of E (f, is the angle and EF is the horizontal segment or base of the triangle).
Then EF is the adjacent leg to the angle f, DE is the opposite leg to the angle f, and DF is the hypotenuse of the triangle.
Given that the angle f is 45°, you know that the triangle is isosceles (45-45-90) and then the two legs have the same length and you can use Pytagorean theorem:
DF^2 = x^2 + x^2 = 2x^2 => x^2 = (DF)^2 / 2
Taking square roots from both sides:
=> x = DF / √2 = 22 / √2 = [22√2] / [(√2)(√2)] = [22√2] / 2 = 11√2
Remember, both legs have the same length.
Answer: 11√2
Answer:
The answer is x=4
1.Move 7 to the other side (which makes it become a negative)
2.solve 19 -7=12
3.12 divided by 3=4
x=4
<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:
B. The student incorrectly calculated the scale factor to be –2
Step-by-step explanation:
Given that :
After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y).
The student determined y to be -2
If a figure dilated with a center of (0, 0) and scale factor k, then
(x , y) → (kx , ky)
(4, -6) → (12, y)
k = 3
Thus; the scale factor is 3
Now; the y-coordinate can now be calculated as;
ky = (3 × -6)
ky = -18
Therefore; the value of y = -18 and the student incorrectly calculated the scale factor to be -2.
