Answer:
Choice 3 is your answer
Step-by-step explanation:
The format of the function when you move it side to side or up and down is
f(x) = (x - h) + k,
where h is the side to side movement and k is up or down. The k is easy, since it will be positive if we move the function up and negative if we move the function down from its original position.
The h is a little more difficult, but just remember the standard form of the side to side movement is always (x - h). If our function has moved 3 units to the left, we fit that movement into our standard form as (x - (-3)), which of course is the same as (x + 3). Our function has moved up 5 units, so the final translation is
g(x) = f(x + 3) + 5, choice 3 from the top.
given :
volume = 115 yd³
Dimensions are :
We know,
Therefore Length of the prism is 8 yards.
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Answer:
In 10 seconds, the garden hose will emit 15 quarts of water.
Step-by-step explanation:
The amount of water emitted by the garden hose over time can be expressed as a ratio: 9/6, or 9 quarts of water for every 6 seconds of time. We can then simplify this ratio to 3/2, or 3 quarts of water for every 2 seconds of time. Since the ratio will remain constant, or the same, over time, we can set up an equivalent ratio, or fraction to find the amount of water emitted in 10 seconds: 3/2 = x/10. We look at the denominators and see that 2 x 5 = 10. In order to make the ratios equivalent, we would also multiply the numerator by 5: 3 x 5 = 15, which gives us the amount of water emitted in 10 seconds.
Answer:
2x - 10 = 10 - 3x
Simplifying
2x + -10 = 10 + -3x
Reorder the terms:
-10 + 2x = 10 + -3x
Solving
-10 + 2x = 10 + -3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '3x' to each side of the equation.
-10 + 2x + 3x = 10 + -3x + 3x
Combine like terms: 2x + 3x = 5x
-10 + 5x = 10 + -3x + 3x
Combine like terms: -3x + 3x = 0
-10 + 5x = 10 + 0
-10 + 5x = 10
Add '10' to each side of the equation.
-10 + 10 + 5x = 10 + 10
Combine like terms: -10 + 10 = 0
0 + 5x = 10 + 10
5x = 10 + 10
Combine like terms: 10 + 10 = 20
5x = 20
Divide each side by '5'.
x = 4
Simplifying
x = 4
Answer:
x = √53
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
We are given a right triangle. We can use PT to solve for the missing length.
<u>Step 2: Identify Variables</u>
Leg <em>a</em> = 6
Leg <em>b</em> = <em>x</em>
Hypotenuse <em>c</em> = √89
<u>Step 3: Solve for </u><em><u>x</u></em>
- Set up equation: 6² + x² = (√89)²
- Isolate <em>x</em> term: x² = (√89)² - 6²
- Exponents: x² = 89 - 36
- Subtract: x² = 53
- Isolate <em>x</em>: x = √53
