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3 years ago

Help me please don't understand geometry and I have a test tomorrow

Mathematics

1 answer:

abruzzese [7]3 years ago

8 0

41. Make it into two triangles. After splitting the shape into two equal parts, you need to divide 89 by two and divide 42 by two in order to come up with the angles of the triangle that you made. 89/2=44.5 and 42/2=21. After that just add both the angles, and subtract it from 180. When you add the angles you get 65.5 and when you subtract that from 180, you get the answer, which is 114.5.

42. Set both of the terms equal to each other. 1/2x+15=2x-15. Solve for x. subtract 15 from both sides, and then you have 1/2x=2x-30. Then subtract 2x from both sides. That gives you -3/2x=30. Then you divide both sides by -3/2, which gives you x=20.

43. This one is a square since all sides are congruent. All of the angles in a square must be 90 degrees, therefor you set 2x=90. This gives you x=45

45. Make 60+60+8x+8x=360. After that make solve for x. Combine like terms first. Do 60+60=120 and 8x+8x=16x. Now we have 120+16x=360. Subtract 120 from both sides. That gives you 16x=240, and then divide both sides by 16 and you get x=15.

46. Set one parallel side equal to the one it is parallel with to find x. We can start with 3x+12=18. First subtract 12 from both sides. You get 3x=6 and then divide both sides by 3 to get x=2. Plug x into both equations to see if the answer is correct.

47. Make two congruent triangles. After that, to find the angles of the triangles, divide 95 by 2and divide 35 by 2. Your new triangle has the angles 17.5 and 47.5. To find x, in other words, the missing angle, add the two together and subtract it from 180. By adding 47.5 and 17.5 you get 65. That means x is equal to 180-65 which equals 115.

49. Add all the sides and set them to 360. Do 3x+2x+44+86=360. Combine like terms and get 5x+130=360. Subtract 130 from 360 and get 5x=230. Then divide 5 from both side and get x=46. To find what the angles equal, just plug x into it. The one on the left is 138 and the one on the right is 92.

50. I am not sure what the terms are corresponding to. From what I am assuming, the answer would be x=29. This is from adding the two together and solving for x. You would do that if the terms were corresponding to angles that would add to be a total of 180. Don't take my word on this one. If you know what they are corresponding to, then please message me. I'd love to help you out (:

51. To find x, just use a^2+b^2=c^2. Basically square 2 and square 4 and add them together. By squaring them, you get 4+16=c^2. To solve you need to do 4+16=20, and then take the square root of 20, which is approximately 4.472

In most of these I was teaching you how to solve for x, if you need further help, please let me know.

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3 years ago

"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the

STALIN [3.7K]

Answer:

$\\ P(z>-2) = 0.97725$ or P(x>49) is about 97.725% (or being less precise 97.5% using the empirical rule).

Step-by-step explanation:

We solve this question using the following information:

We are dealing here with normally distributed data, that is "the frequency distribution of the life length data is known to be mound-shaped".
The normal distribution is defined by two parameters: the population mean ( $\\ \mu$ ) and the population standard deviation ( $\\ \sigma$ ). In this case, we have that $\\ \mu = 55$ months, and $\\ \sigma = 3$ months.
To find the probabilities, we have to use the standard normal distribution, which has $\\ \mu = 0$ and $\\ \sigma = 1$ . The probabilities for this distribution are collected in the standard normal table, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
For most cases, we need to use the cumulative standard normal table, and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: $\\ z = \frac{x - \mu}{\sigma}$ [1]. A z-score tells us the distance from the mean that a raw score is from it in standard deviations units. If this value is negative, the raw score is below the mean. Conversely, a positive value indicates that it is above the mean.
The cumulative standard normal table is made for positive values of z. Since the normal distribution is symmetrical around the mean, we can find the negative values of z using this formula: $\\ P(z$ [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

First Step: Use formula [1] to find the z-score of the raw score x = 49 months.

$\\ z = \frac{49 - 55}{3}$

$\\ z = \frac{-6}{3}$

$\\ z = -2$

This means that the raw score is represented by a z-score of $\\ z = -2$ , which tells us that it is two standard deviations below the population mean.

Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.

For a z = 2, the probability is 0.97725.

Then

$\\ P(z$

$\\ P(z2)$

But we are not asked for P(z<-2) but for P(z>-2) = P(x>49). This probability is the complement of the previous result, that is

$\\ P(z>-2) = 1 - P(z$

$\\ P(z>-2) = 1 - 0.02275$

$\\ P(z>-2) = 0.97725$

That is, the "percentage of the manufacturer's grade A batteries will last more than 49 months" is

$\\ P(z>-2) = 0.97725$ or about 97.725%

A graph below shows this result.

Notice that if we had used the 68-95-99.7 rule (also known as the empirical rule), that is, in a normal distribution, the interval between one standard deviation below and above the mean contains, approximately, 68% of the observations; the interval between two standard deviations below and above the mean contains, approximately, 95% of the observations; and the interval between three standard deviations below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last less than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the symmetry of the normal distribution, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

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4 years ago

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y=4x^2+5x-1

Ivanshal [37]

Answer:

Axis of symmetry: $x=-\frac{5}{8}$

Vertex: $(-\frac{5}{8},-2\frac{9}{16})$

Step-by-step explanation:

The given quadratic equation is

$y=4x^2+5x-1$

By comparing to the general quadratic function; $y=ax^2+bx+c$

We have a=4,b=5,c=-1

The equation of the axis of symmetry is given by the formula;

$x=-\frac{b}{2a}$

We got this formula by completing the square on the general quadratic function.

We substitute a=4 and b=5 to obtain;

$x=-\frac{5}{2(4)}$

$x=-\frac{5}{8}$
is the axis of symmetry.

To find the y-value of the vertex, we put $x=-\frac{5}{8}$ into the function to obtain;

$y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1$

$y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1$

$y=-\frac{41}{16}$

The vertex of the given function is $(-\frac{5}{8},-2\frac{9}{16})$

4 0

4 years ago