Cot^2x+1 please simplify

Answers

Answer 1

Answer:
csc^2(x)

Explanation:
We have:
cot
2
(
x
)
+
1

This expression can be simplfiified by applying one of the Pythagorean identities:
1
+
cot
2
(
x
)
=
csc
2
(
x
)
=
csc
2
(
x
)

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If a line crosses the y-axis at (0,1) and has a slope of 4/5 what is the equation of the line

Make a conjecture. How could the distance formula and slope be used to classify triangles and quadrilaterals in the coordinate plane? Check all that apply. Use the distance formula to measure the lengths of the sides. Use the slope to determine whether opposite sides are parallel. Use the slope to check whether sides are perpendicular and form right angles. Use the distance formula to compare whether opposite sides are congruent. Use the slope to check whether the diagonals are perpendicular to each other. Use the distance formula to compare whether diagonals are congruent.

Answers

Answer:

1. Use the distance formula to measure the lengths of the sides.

3. Use the slope to check whether sides are perpendicular and form right angles.

5. Use the slope to check whether the diagonals are perpendicular to each.

Step-by-step explanation:

We know that, the distance formula given by

$d = \sqrt{ ({y_(2)-y_(1)}) ^(2)+({x_(2)-x_(1)}) ^(2)}$ ,

gives the length of the line joined by $(x_(1),y_(1))$ and $(x_(2),y_(2))$ .

Now, after using this formula, if:

1. The length of the opposite sides are equal, then the quadrilateral could be a rectangle or a parallelogram.

2. The length of all sides are equal, then the quadrilateral could be a square or a rhombus.

So, this gives us option 'Use the distance formula to measure the lengths of the sides' is correct.

Now, we use slope to find the angles i.e. If:

1. The product of two slopes is -1, then the lines are perpendicular and so, forms right angle between them.

2. The slope of two lines are equal, then the lines are parallel.

So, this gives us that the option 'Use the slope to check whether sides are perpendicular and form right angles' is correct.

Since, some quadrilaterals have the property that the diagonals are perpendicular bisector of each other.

So, the option 'Use the slope to check whether the diagonals are perpendicular to each other' is also correct.

Hence, option 1, 3 and 5 are correct.

Using a limited selection from among the options, a quadrilateral, or

triangle can be classified into one of the eleven classes.

The correct options are;

Use the distance formula to measure the lengths of the sides

Use the slope to determine whether the sides are perpendicular and form right angles

Use the slope to check whether the diagonals are perpendicular

Reasons:

The classification of triangles are;

Right triangles; Having two legs that are perpendicular

Isosceles triangles; Having two sides equal

Equilateral triangles; Having all sides equal

Scalene triangle; Have all sides of different dimensions

Classification of quadrilaterals are;

Kite, rhombus, rectangle, parallelogram, square, trapezoid, isosceles trapezoid

Use the distance formula to measure the lengths of the sides;

The above process can be used to classify parallelograms, equilateral triangles, isosceles trapezoids, kite

The process can be used to classify all triangles

Use the slope to determine whether the sides are perpendicular and form right angles;

The above process can be used to differentiate parallelogram from squares and rectangles, kite trapezoid

The process can be used to determine if the triangle is a right triangle

Use the slope to check whether the diagonals are perpendicular;

The above process can be used to differentiate squares from rectangles, kite, and rhombus

Learn more about slope, distance formula, triangles and quadrilaterals here:

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Warehouse Club A charges its members $55 to join plus $25 Warehouse Club B charges a $10 to join plus $40 each month.

Answers

Warehouse Club A: y= $25x + $55
Warehouse Club B: y= $40x + $10

Which if the following quartic functions has x = 1 and x =

Answers

Answer:

y = x⁴ +4x³ +4x² +4x +3

Step-by-step explanation:

The coefficients of the offered quartics (in order) have 1, 1, 1, and 0 sign changes, respectively. Descartes' rule of signs tells you this means the first three choices all have one (1) positive real root, so the negative real roots -1 and -3 are not the only ones.

The only possible polynomial is the last one. Synthetic division of that polynomial by roots -1 and -3 leave the remaining factor as x²+1, which has only complex zeros.

The appropriate choice is ...

... y = x⁴ +4x³ +4x² +4x +3

Consider the following hypothesis test:H 0: = 17H a: 17A sample of 40 provided a sample mean of 14.12. The population standard deviation is 4.a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus "-" sign.)b. What is the p-value (to 4 decimals)?c. Using = .05, can it be concluded that the population mean is not equal to 17? SelectYesNoItem 3Answer the next three questions using the critical value approach.d. Using = .05, what are the critical values for the test statistic (to 2 decimals)? ±e. State the rejection rule: Reject H 0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the upper critical value.f. Can it be concluded that the population mean is not equal to 17?

Answers

Answer:

We conclude that the population mean is not equal to 17.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 17

Sample mean, $\bar{x}$ = 14.12

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 4

First, we design the null and the alternate hypothesis

$H_(0): \mu = 17\nH_A: \mu \neq 17$

We use Two-tailed z test to perform this hypothesis.

a) Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$

Putting all the values, we have

$z_(stat) = \displaystyle(14.12 - 17)/((4)/(√(40)) ) = -4.5536$

b) P-value can be calculated from the standard z-table.

P-value = 0.0000

c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17

d) Now, $z_(critical) \text{ at 0.05 level of significance } = \pm 1.96$

e) Rejection Rule:

We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value

If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.

f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.

Final answer:

The test statistic is -1.78 and the p-value is 0.0761, indicating that we fail to reject the null hypothesis. Therefore, it cannot be concluded that the population mean is not equal to 17.

Explanation:

The test statistic can be calculated using the formula:

test statistic = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the given values, we get:

test statistic = (14.12 - 17) / (4 / sqrt(40))

Calculating this gives us a test statistic value of -1.78.

The p-value can be calculated using the test statistic. We need to find the probability that a test statistic at least as extreme as -1.78 would occur assuming the null hypothesis is true. Using a standard normal distribution table or software, we find the p-value to be approximately 0.0761.

Since the p-value is greater than the significance level (alpha = 0.05), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the population mean is not equal to 17.