Answer: D) -2 |x| - 2
<u>Step-by-step explanation:</u>
A v-shaped graph is an absolute value graph.
The general form of an absolute value equation is: y = a |x - h| + k
where (h, k) represents the vertex and "a" represents the vertical stretch (aka slope).
The vertex of the given graph is (0, 2), however the graph is inverted (upside-down) which is a reflection across the x-axis. Therefore,
<h2> --> y = -2 |x| - 2</h2>
The diameter of under the magnifying glasses is 6cm, so the actual size is 6÷5cm, the diameter is 1.2 cm
In general to be able to add or subtract fractions you need to have the same denominator so that you can add the numerators.
The easiest way to find the same denominator is to identify the lowest common denominator (LCD).
You can find the LCD by finding the prime factors of the denominators in question and multiplying them all together. If the denominators share a prime factor, only multiply it once.
Sometimes you can just eyeball the numbers to find the LCD, which might be faster.
For #W we need to find the LCD of 10 and 6, so prime factorize:
10 = 2 x 5
6 = 2 x 3
LCD = 2 x 5 x 3 = 30
The LCD is 30, so we need to change the fraction to reflect that. Remember, what you do to the denominator you need to do to the numerator as well. So:
-9/10 becomes -27/30 (both multiplied by 3)
-1/6 becomes -5/30 (both multiples by 5)
Now you can easily add:
-27/30 + (-5/30) = -32/30
In summary:
Step #1: find LCD (prime factor or eyeball)
Step #2: multiply the numerator of each fraction by the factor needed to obtain the LCD in that denominator
Step #3: add the fractions now that they have the LCD
Here’s the solution to #G:
-¾ + (-7/12)
Step #1:
4 = 2 x 2
12 = 2 x 2 x 3
LCD = 2 x 2 x 3 (count each unique prime factor once)
Step #2:
-¾ becomes -9/12 (both multiplied by 3)
-7/12 stays the same (it already has the LCD)
Step #3:
-9/12 + (-7/12) = -16/12
Let me know if you have any questions. Try to work though the others!
Answer: A ≈ 271.7 square inches
Answer:
C. 10y^4(3y^4 + 1)
Step-by-step explanation:
The GCF of 30 and 10 is 10.
The GCF of y^8 and y^4 is y^4.
The GCF is 10y^4
Answer: C. 10y^4(3y^4 + 1)