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Doss [256]
3 years ago
12

Solve using completing the square x^2 – 8x + 16 = 25

Mathematics
1 answer:
lisov135 [29]3 years ago
5 0

First we need to factor the left side. Since it is a perfect square (as is the process with completing the square, we know we can take half of the middle number along with x to be in the two parenthesis.

(x - 4)(x - 4) = 25

Now we simplify to show it as a square.

(x - 4)^2 = 25

Next we take the square root of both sides

x - 4 = +/- 5

Note that we have plus or minus 5. This is because either square would give us positive 25. Now we add 4 to both sides

x = 4 +/- 5

4 + 5 = 9

4 - 5 = -1

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Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units
Yakvenalex [24]

Answer:

a) positive direction: t < 2s & t>6s   ; negative direction: 2s < t < 6s

b) 7 m

c) 71 m

Step-by-step explanation:

Given:

v(t) = 3t^2 -24t +36   [0 , 7]

Find:

a) The value of time when particle is moving in positive direction:

The change in direction of the particle can be determined by v(t) > 0

Hence,

                                    0 < 3t^2 -24t +36

                                    0 < t^2 - 8t + 12

                                    0 < (t - 2)*(t - 6)

                                    t < 2s  , t  > 6s  

The particle travels in positive direction in the interval t < 2s and t > 6s , While it travels in negative direction when 2s < t < 6s.

b) The displacement ds over the given interval [ 0 , 7 ]

                                  ds = integral (v(t)).dt

                                  ds = t^3 -12t^2 +36t

                                  ds = 7^3 -12*7^2 +36*7

                                  ds = 7 m

c) Total distance traveled in the interval:

                                 Total distance= ds(0-2) + ds(2-6) + ds(6-7)

                                 D = 2*(2^3 -12*2^2 +36*2) - 2*(6^3 -12*6^2 +36*6) + 7

                                 D = 2*32 - 2*0 + 7

                                 D = 71 m          

     

6 0
3 years ago
What is the area of a regular heptagon with side length of 6 meters and a distance from the to the vertex of 6 meters? round you
Ahat [919]
Apothem = side length / 2*tan(180 / number of sides)
apothem = side length / 2*tan (180 / 7)
apothem = 6 / (2*tan( <span> <span> <span> 25.7142857143</span></span></span>))
apothem = 6 / 2*0.48157
<span><span><span>apothem = 6.2296239384 </span> </span> </span>

Polygon area = (# of sides * side length * apothem) / 2
Polygon area = ( 7 * 6 * <span>6.2296239384) / 2
</span><span><span><span>Polygon area = 130.8221027064 </span> </span> </span> 



8 0
3 years ago
A candy manufacturer claims that the average weight of their individually wrapped candy is 3 grams. Sixty-four candy pieces were
Anon25 [30]

Answer:

t=\frac{2.8-3}{\frac{0.5}{\sqrt{64}}}=-3.2    

p_v =P(t_{(63)}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 3 grams at 5% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=2.8 represent the sample mean

s=0.5 represent the sample standard deviation for the sample  

n=64 sample size  

\mu_o =3 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is lower than 3 grams, the system of hypothesis would be:  

Null hypothesis:\mu \geq 3  

Alternative hypothesis:\mu < 3  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{2.8-3}{\frac{0.5}{\sqrt{64}}}=-3.2    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=64-1=63  

Since is a one sided test the p value would be:  

p_v =P(t_{(63)}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 3 grams at 5% of signficance.  

8 0
3 years ago
ABCD is a rhombus. Fill in the missing steps in the two column proof to explain why ABC is congruent to CDA.
White raven [17]
1)Opposite sides of a rhombus are have the same length. 
2)Same thing as statement 1: Opposite sides of a rhombus have the same length.
3) The side AC is common to the two triangles ABC and CDA. 
4)The two angles ABC and CDA are congruent   by the SSS theorem of 
congruent triangles 
8 0
3 years ago
Least common multiples are most helpful for ________.
Nady [450]

Answer:

The answers is C I think

6 0
2 years ago
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