Answer:
3,7/6
Step-by-step explanation:
The answer is <span>c. 16x2 + 24xy + 9y2.
Since we need trinomial (three term expression) choices a and b are incorrect because they have only two terms.
So, our square trinomial is a</span>² + 2ab + b² or a² - 2ab + b²
a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²
Let's check choices c and d:
c) 16x² + 24xy + 9y²
a² = 16x²
a² = (4x)²
a = 4x
b² = 9y²
b² = (3y)²
b = 3y
a² + 2ab + b² = (4x)² + 2 * 4x * 3y + (3y)² = 16x² + 24xy + 9y²
CORRECT
d) 49x² - 70xy + 10y²
a² = 49x²
a² = (7x)²
a = 7x
b² = 10y²
b² = (y√10)²
b = y√10
a² + 2ab + b² = (7x)² + 2 * 7x * y√10 + (y√10)² = 49x² + 14xy√10 + 10y²
INCORRECT
So, c) is correct answer
Answer:
Any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.
Step-by-step explanation:
<u>Interpreting Box Plots</u>
A box plot is used to present the 5-Number summary of a set of data.
The 5-Number summary consists of the following in their order of appearance on the box plot.
- Minimum Value
- First Quartile,
- Median,
- Third Quartile,
- Maximum Value
In the box plot, the following rules applies
- The whisker starts from the minimum value and ends at the first quartile.
- The box starts at the first quartile and ends at the third quartile. There is a vertical line inside the box which shows the median.
- The end whisker starts at the third quartile and ends at the maximum value.
Using these, we interpret the given box plot
A left whisker extends from 1 to 6.
- Minimum Value=1
- First Quartile =6
The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12.
- Median=12
- Thrid Quartile=16
The right whisker extends from 16 to 19.
Therefore any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.
Answer:
a)
d)
Step-by-step explanation:
It's easiest to reduce each statement to its simplest form for comparison
Our test statement can be reduced by combining like terms
16x - 12 -24x + 4 = -8x - 8
this becomes our new gold standard
a) 4 + 16x - 12(1 + 2x)
apply the distributive property by multiplying terms in parenthesis by -12
4 + 16x - 12 - 24x
combine terms
-8x - 8 Yeaah, We have a winner as it exactly matches our gold standard.
b) 40x - 16 is already in simplest terms and does NOT match the gold standard.
c) 16x - 24x - 4 + 12
has the same cardinal values as the original, but differing signs, reducing gives -8x + 8
Not quite the same as a plus sign occurs where a negative exists in our gold standard.
d) -8x - 8 is already in simplest terms and exactly matches our gold standard. Yeah!
e) 10(1.6x - 1.2 - 2.4x + 4)
apply distributive property by multiplying each term in parenthesis by 10
16x - 12 - 24x + 40
combine like terms
-8x + 28 does NOT match our gold standard
<span>So we want to know the difference between a= 126 1/4 and b= 78 2/3. Lets turn them into a fraction: a = 124*4 + 1/4 = 496/4 + 1/4 = 495/4. b= 78*3 + 2/3 = 234/3 + 2/3 = 236/3. Now we find the common denominator of a and b: and that is 12. so lets multiply a by 3/3 and b by 4/4: (495/4)*(3/3)=1485/12. (236/3)*(4/4)=944/12. Now the difference is: 1485/12 - 944/12=541/12 and that is: 45 1/12 </span>
