Find all the possible values of tan^-1 1

Answer:

The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as [tex]$y=\frac{4}{5} x+4$[/tex].

Step-by-step explanation:

A condition is given that a line has an x- intercept at (-5,0) and y- intercept at (0,4).

It is asked to find a linear equation satisfying the given condition.

To do so, first determine the slope of the line using coordinates of the given intercepts. Then write the equation in the slope-intercept form using the slope and the y- intercept.

Step 1 of 2

Determine the slope of the line.

The points of the intercepts of the line are given as (-5,0) and (0,4). Next, the formula for the slope is given as,[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute 4&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex]respectively, and 0&-5 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]$$\begin{aligned}m &=\frac{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$$[/tex]

Step 2 of 2

Write the equation in the slope-intercept form.

The slope-intercept form of a line is given as follows,

[tex]$$y=m x+b$$[/tex]

The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.

So, substitute 4 for b and [tex]$\frac{4}{5}$[/tex] for m in the equation y=mx+b, as follows,

[tex]$y=\frac{4}{5} x+4$$[/tex]

This is the required linear equation.

There are 16 red counters there.

If one-quarter of the counters in a tub are red and the rest are green, then there are three-quarter of the counter in the tub.

Let the total counter be x such that

3/4x = 48

3x = 4 * 48

x = 4 * 16

x = 64

Determine the amount of red counter

Red counter = 64 - 48

Red counter = 16

Hence there are 16 red counters there.

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Answer:

The solution to the inequality |x-2|>10 in interval notation is given by -8<x<12

Step-by-step explanation:

An absolute value inequality |x-2|>10 is given.

It is required to solve the inequality and write the solution in interval form.

To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.

Step 1 of 2

The given absolute value inequality is $|x-2|>10$.

The inequality can be written as

x-2<10 and x-2>-10

First solve the inequality, x-2<10.

Add 2 on both sides,

x-2<10

x-2+2<10+2

x<12

Step 2 of 2

Solve the inequality x-2>-10.

Add 2 on both sides,

x-2>-10

x-2+2>-10+2

x>-8

The solution of the inequality in interval notation is given by -8<x<12.

Answer:

F = 2

Step-by-step explanation:

Answer:6

Step-by-step explanation:i did the quiz

The volume of the square pyramid is: B. One-third s^2h units^3.

An example of a square pyramid is given in the image attached below. It has a square base and 4 triangular faces.

A right pyramid that has a square base has a volume that can be calculated using the following volume formula, given as: 1/3(a² × h), where "a" is the length of the edge of the square base, and "h" is the height of the square pyramid.

Given the following parameters for a square pyramid:

The length of the edge of the square base (a) = s units

The height of the square pyramid = h units.

Plug in the values into 1/3(a² × h) to find the expression that represents the volume of the pyramid:

Volume of the square pyramid = 1/3(a² × h) = 1/3(s² × h)

Volume of the square pyramid = 1/3s²h units ³.

The expression that represents the volume of the square pyramid is: B. One-third s^2h units^3.

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Answer:

Step-by-step explanation:

Using the triangle midsegment theorem, x = 5; BC = 10 units.

According to the triangle midsegment theorem, ED = 1/2(BA).

Given the following:

ED = x + 2

BA = 4x - 6

x + 2 = 1/2(4x - 6)

2(x + 2) = 4x - 6

2x + 4 = 4x - 6

2x - 4x = -4 - 6

-2x = -10

x = 5

BC = 2(BE)

BC = 2(x)

BC = 2(5)

BC = 10 units

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Answer:

D

Triangle Midsegment

5

10

Step-by-step explanation:

E2020 Geometry B!!:3

The value of the angle m∠4 is 105 degrees.

The sum of angles in a quadrilateral is 360 degrees.

Therefore,

m∠1 + m∠2  + m∠3 + m∠4 = 360°

Hence,

x + x + 10 + x + 20 + x + 30 = 360

4x + 60 = 360

4x = 360 - 60

4x = 300

x = 360 / 4

x = 75

Therefore,

m∠4 = 75 + 30 = 105°

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[tex] - 4y = v - 4x \\ y = \frac{ - v}{4} + x[/tex]

[tex]\\ \rm\dashrightarrow V=-4y+4x[/tex]

[tex]\\ \rm\dashrightarrow -4y=V-4x[/tex]

[tex]\\ \rm\dashrightarrow y=\dfrac{V-4x}{-4}[/tex]

[tex]\\ \rm\dashrightarrow y=x-\dfrac{V}{4}[/tex]

Answer:

680π dm² = 2136.28 dm²

Step-by-step explanation:

Recall:

lateral area of cone = πrs; where s = slant height = 17 dm

area of circle = πr²

lateral area of cylinder = πdh

Lateral area of cone: (3.14159)(8 dm)(17 dm) = 427.26 dm²

Area of base of cylinder: (3.14159)(8 dm)² = 201.06 dm²

Lateral area of cylinder: (3.14159)(16 dm)(30 dm) = 1507.96 dm²

Total surface area = 427.26 dm² + 201.06 dm² + 1507.96 dm²

Total surface area = 680π dm² = 2136.28 dm²

Answer:

Your answer is ∠PQR=(1/2)* m arc PR.

Step-by-step explanation:

The Angle Described is one that has its vertex in the circumference. The inscribed angle measures half of the arc it comprises.

So, in this problem, The inscribed angle=∠PQR

The arc it comprises=m arc PR too.

So therefore:

∠PQR=(1/2)* m arc PR is the answer

Answer:

-3.7

Step-by-step explanation:

1.  More = Addition

2. 0.65 + -4.35 = -3.7

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

0.65 more than -4.35

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The word more means addition, thus

-4.35+0.65=

[tex]\bf{-3.7}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=-3.7}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Step-by-step explanation:

Combine common terms

(3x²+5x²)+(7x-4x)+(-5+11)

8x²+3x+6

The polynomial that represents the total area of both plots of land will be;  8x²+3x+6

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

We are given that ;

The area of Plot A can be represented by 3x² +7x - 5, and the area of Plot B can be represented by 5x² - 4x + 11.

So the polynomial that represents the total area of both plots of land

Now Combine common terms;

(3x²+5x²)+(7x-4x)+(-5+11)

Then we get;

8x²+3x+6

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Answer:

13

Step-by-step explanation:

cos17 = x/14

x = 14cos17

x= 13.38826658

to the nearest hundredth

x=13

Quinn needs to save another $275.

The money that she needs will be equal to the difference between the amount that she wants to save, and the amount that she already has.

The difference is:

D = $300 - $25 = $275

This means that, to reach her goal this year, Quinn needs to save another $275.

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Answer:

144

Step-by-step explanation:

Base:16

Height: 18

Triangle area formula: (bxh)/2

16x18=288

288/2=144

Answer:

Length equals 16 and Width equals 4

Step-by-step explanation:

First let us create an equation. We can use L and W for length and width.

If the length is 4 times the width, then we end up with: L = 4W

It then says, " If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square."

Since a square has an equal length and width then we end up with:

L - 6 = W + 6

Knowing this we can just substitute the first equation into the second one leaving us with: 4W - 6 = W + 6

We then remove a W from both sides so that the right side is left with a 6, and add 6 to both sides to remove the -6 from the left one.

This leaves us with 3W = 12

W = 4, and if we put that into our first equation, L = 4W, then Length equals 16, and Width equals 4. We can check this by putting it into the 2nd equation. 16 - 6 = 4 + 6.

Answer:

she would be 20 years old if lily is 22

Answer:

(2,3),(4,3),(-2,-3),(-4,-3)

Step-by-step explanation:

A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).

This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.

The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.

A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.

In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:

(5,1),(5,2),(5,3),(5,4)

Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.

Answer:

3

Step-by-step explanation:

9 divided by 3 is 3...

hope this helped

Answer:

its 3

Step-by-step explanation:

im doing summer school rn lol

Answer:

-2

Step-by-step explanation:

The solution to the system of equations is (x, y) = (-2, 1).

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The second equation tells us that x = -2.

Substituting this value into the first equation, we get:

y = -2 + 3

Simplifying, we get:

y = 1

Therefore,

The solution to the system of equations is (x, y) = (-2, 1).

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Answer:

15/17

Step-by-step explanation:

The true statements are :

the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.

The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.

A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers and a box. The whiskers represents the minimum and maximum scores. The difference between the minimum and maximum scores is the range.

On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.

Range for New Orleans = 85 - 50 = 35

Range for Indianapolis = 75 - 25 = 50

Median for New Orleans = 70

Upper quartile for  Indianapolis = 70

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From the given graph, and using the scatter plot function of a graphing calculator, the residuals are;

-0.08693, -0.019376, -0.518, -0.183, -0.083, 0.135, 0.318, and 0.578

From the diagram, the given points are;

(14, 4), (15, 4), (16.5, 3.5), (18, 4), (18, 3.9), (19.5, 3.85), (20, 4), (26.8, 3.8)

Utilizing a graphing calculator, using the scatter plot function we have the following predicted values;

Best fit line; y = 5.032 - 0.0676•x

Residuals = Actual - Predicted from equation

The residuals are;

y1 = 4 - 4.08693 = -0.08693

y2 = 4 - 4.019376 = -0.019376

y3 = 3.5 - 3.918 = -0.518

y4 = 4 - 3.817 = -0.183

y5 = 3.9 - 3.817 = -0.083

y6 = 3.85 - 3.715 = 0.135

y7 = 4 - 3.682 = 0.318

y8 = 3.8 - 3.222 = 0.578

The residuals are therefore;

The residuals are;

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The number of zeros are; Positive; 2 or 0; Negative: 4 or 2 or 0; Complex; 0, 2, 4, 6  

We are given the polynomial function as;

f(x) = x⁶ + x⁵ + x⁴ + 4x³ - 12x² + 12

Use Descartes Rule rule of signs allows us to determine the possible number of positive, negative, and complex roots.

For the function f(x), the number of sign changes that occur from term to term will give us the number of positive possible roots.

For the function f(-x), the number of sign changes that occur from term to term will give us the number of negative possible roots.

The numbers of complex roots is the difference between the degree of function and total number of positive and negative roots.

For f(x), the signs change 2 times.  Thus, there can only be a possibility of 2 positive roots

For f(-x), we have;

x⁶ - x⁵ + x⁴ - 4x³ - 12x² + 12

Thus, the sign changes 4 times and so we have a possibility of 4 negative roots.

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Answer:

The rate of growth of the population is -400, this means the growth of the population from year 1960 to 1989 has dropped by 400 per city.

Step-by-step explanation:

It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .

It is required to compute the rate of growth of population and make a statement about the population rate of 1989 with the year 1989 and the time taken to change the population.

Step 1 of 1

It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .

To find the rate of growth of population and make a statement about the population rate of change in people per year.

Now let f(x) be the number of population and x be the year and use formula of rate of change to find the change in population,

[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$[/tex]

Now substitute, 275900 for [tex]$f\left(x_{2}\right)[/tex], 287500 for  then,

[tex]$$\begin{aligned}m &=\frac{275900-287500}{1989-1960} \\&=\frac{-11600}{29} \\&=-400\end{aligned}$$[/tex]

The rate of growth of population -400, so there is a drop in the population by 400 per city.

Answer:

The answer would be C

Answer:

1136/295 cm

Step-by-step explanation:

Corresponding lengths of similar figures are proportional.

If we let the radius of the second cylinder be x,

x/6.4 = 7.1/11.8

x = 6.4(7.1/11.8) = 1136/295 cm

The hypothesis which can be used to show whether data provide strong evidence or not are: [tex]H_{0}:p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1}:p_{1}=p_{2}[/tex] where [tex]p_{1} and p_{2}[/tex] are the proportions of Americans and chinese  people who use mobile phones to access internet.

Given proportion of Americans uses mobile phones is 17%. Proportion of chinese uses mobile phones is 38%.

Hypothesis are the statements which can be tested through its validity.  There can be  null hypothesis and alternate hypothesis.

The hypothesis which can be used are as under:

[tex]H_{0} :[/tex][tex]p_{1}[/tex]≠[tex]p_{2}[/tex]

[tex]H_{1}:p_{1} =p_{2}[/tex]

We have used equal to signs because we have to check whether they are different or not.

We cannot check hypothesis as we don't have standard deviation.

Hence the hypothesis for this test are: [tex]H_{0} :p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1} :p_{1} =p_{2}[/tex].

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