A triangle has an area of 40 square inches. It's base is written as (x + 2) and it's height is written as (x + 4). Calculate the
value of x and be sure to check for any extraneous (excluded) value.
1 answer:
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Answer: The correct option is (D) P″(9, -12) and Q″(15, -3).
Step-by-step explanation: Given that triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′. This triangle is then dilated by a scale factor of 2 to form triangle P″Q″R″.
The co-ordinates of vertices P and Q are (3, -4) and (5, -1) respectively.
We are to find the co-ordinates of the vertices P″ and Q″.
<u>Case I :</u> ΔPQR dilated to ΔP'Q'R'
The co-ordinates of P' and Q' are given by
<u>Case II :</u> ΔP'Q'R' dilated to ΔP''Q''R''
The co-ordinates of P'' and Q'' are given by
Thus, the co-ordinates of the vertices P'' and Q'' are (9, -12) and (15, -3).
Option (D) is CORRECT.
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Answer:
- <u><em>Option b. just below 30%</em></u>
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Explanation:
Please, see attached the <em>histogram that represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. </em>
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The<em> median</em> is the value that separates the lower 50% from the upper 50% of the data.
Since there are 25 business schools, the middle value is the number 13.
The height of each bar is the<em> frequency</em> or number of business school for that acceptace rate:
- The first bar has frequency of 1 school
- The second bar has frequency of 3 schools: cummulative frequency: 1+3=4.
- The third bar has frequency 5 schools: cummulative frequency 4 + 5 = 9.
- The fourth bar has frequency 3 schools: cummulative frequency: 9+3=12.
Then, the 13th value is on the next bar, the fifth bar.
The fifth bar has acceptance rates 25 ≤ rate < 30.
That means that the median acceptance rate is greater than or equal to 25 and less than 30.
Thus, the choice is the option <em>b. just below 30%.</em>
Answer:
The quadratic equation form is x² - 9 x + 14 = 0
Step-by-step explanation:
Given in the question as ,
The solution of quadratic equation are x = 2 and x = 7
The constant K is a non-zero number
Now , let the quadratic equation be , ax² + bx + c = 0
And sum of roots =
product of roots =
So, 2 + 7 =
Or, 2 × 7 =
I.e = 9 ,
= 14
Or, b = - 9 a And c = 14 a
Put this value of b and c in standard form of quadratic equation
I.e ax² + bx + c = 0
Or, ax² - 9 ax + 14 a = 0
Or , a ( x² - 9 x + 14 ) = 0
∴ a = 0 And x² - 9 x + 14 = 0
Hence , The quadratic equation form is x² - 9 x + 14 = 0 Answer