Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
_____
<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5
<h3>How to find the equation of a line?</h3>
The equation of a line can be represented as follows:
y = mx + b
where
Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4
Hence,
perpendicular lines follows the rule below:
m₁m₂ = -1
Hence,
5x - 3y = 4
5x - 4 = 3y
y = 5/ 3 x - 4 / 3
m₁ = 5 / 3
5/3 m₂ = -1
m₂ = - 3 / 5
Hence,
using (-4, 5)
5 = - 3 / 5 (-4) + b
5 = 12 / 5 + b
b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5
Therefore,
y = -3 / 5 x + 13 / 5
learn more on equation of a line here: brainly.com/question/10727767
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Answer:
<h2>In this particular case,the target population of interest to the university administration constitutes the university students.</h2>
Step-by-step explanation:
- The university administration is interested to conduct a statistical study to identify the average or mean time taken by the students to find a vacant parking spot.
- Therefore,the research topic here is the average time taken by the university students to find parking spot. The administrator collects an inconspicuous sample of 240 samples from the target population of the study,which is the overall student population of the university.
- The sample collected by the university administration is used to observe the average or mean parking time by the university students.
Answer:
4 ft by 2 ft
Step-by-step explanation:
4*2=8
4+4+2+2=12
Answer:
Step-by-step explanation
Hello!
Be X: SAT scores of students attending college.
The population mean is μ= 1150 and the standard deviation σ= 150
The teacher takes a sample of 25 students of his class, the resulting sample mean is 1200.
If the professor wants to test if the average SAT score is, as reported, 1150, the statistic hypotheses are:
H₀: μ = 1150
H₁: μ ≠ 1150
α: 0.05
![Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } ~~N(0;1)](https://tex.z-dn.net/?f=Z%3D%20%5Cfrac%7BX%5Bbar%5D-Mu%7D%7B%5Cfrac%7BSigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D%20~~N%280%3B1%29)
The p-value for this test is 0.0949
Since the p-value is greater than the level of significance, the decision is to reject the null hypothesis. Then using a significance level of 5%, there is enough evidence to reject the null hypothesis, then the average SAT score of the college students is not 1150.
I hope it helps!
