The graph of a function f(x) passes through the following points:
(0,2), (1, 0), (-1,-4)
Which of the following could be f(x)?
O f(x) = 2x - 2
O f(x) = 2x² - 2
○ f(x) = - 2x - 2
○ f(x) = 2√x-2

Rewriting the left hand side,

csc²t - cost sec t

= (1/sin²t)-(cost)(1/cost)

= 1/sin²t - 1

= 1/sin²t - sin²t/sin²t

= (1-sin²t)/sin²t

= cos²t/sin²t

= cot²t

The regression equation is y = 3.231x + 10.138

The regression model that fits the data is a linear model.

This is so because as x increases by 1, the y value increases by an almost constant rate

To determine the regression equation, we make use of a graphing calculator

From the graphing calculator, we have the following summary:

The regression equation is then calculated as;

y = bx + a

Where

b = SP/SSX = 56.55/17.5 = 3.23143

a = MY - bMX = 18.22 - (3.23*2.5) = 10.1381

So, we have:

y = 3.23143x + 10.1381

Approximate

y = 3.231x + 10.138

Hence, the regression equation is y = 3.231x + 10.138

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The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.

A real root of a polynomial function is the point where the graph crosses the x-axis (also known as a zero or solution). For example, the root of y=x^2 is at x=0.

Roots can also be complex in the form a + bi (where a and b are real numbers and i is the square root of -1) and not cross the x-axis. Imaginary roots of a quadratic function can be found using the quadratic formula.

A root can tell you multiply things about a graph. For example, if a root is (3,0), then the graph crosses the x-axis at x=3. The complex conjugate root theorem states that if there is one complex root a + bi, then a - bi is also a complex root of the polynomial. So if you are given a quadratic function (must have 2 roots), and one of them is given as complex, then you know the other is also complex and therefore the graph does not cross the x-axis.

So, The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.

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The measure of each interior angle of a regular polygon is [tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides.

Question 1

[tex]144=\frac{180(n-2)}{n}\\\\144n=180(n-2)\\\\144n=180n-360\\\\-36n=-360\\\\n=10 \text{ sides}[/tex]

Question 2

[tex]\frac{180(n-2)}{n}=135\\\\180(n-2)=135n\\\\180n-360=135n\\\\-360=-45n\\\\n=8 \text{ sides}[/tex]

Answer:

78.5

Step-by-step explanation:

pi(r^2)

3.14(5^2)

3.14(25)

78.5

pls kindly see the attached picture for the answer and explanation thank you

Answer:

185 when we subtract 212-127 it gives 185 thanks for the seeing image

the quadratic equation is:

y = 0.2*x*(x - 28)

If we know that the roots are J and K, and the leading coefficient is a, then the quadratic equation is:

y = a*(x - K)*(x - J)

Here we know that the roots are at x = 0 and x =28, then:

y = a*(x - 0)*(x - 28).

We also know that the vertex is a minimum, so a is positive, and we know that the vertex is (14, -40), then we have:

-40 = a*(14)*(14 - 24) = -a*196

a = 40/196 = 0.20

Then the quadratic equation is:

y = 0.2*x*(x - 28)

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Answer:

a=223.57

c=181.43

Step-by-step explanation:

a=405-c

substitute for a in the equation :

12a+5c=3590

12(405-c)+5c=3590

4860-12c+5c=3590

-7c=3590-4860

-7c=-1270

c=1270/7=181.43

a=405-1270/7

a=1565/7=223.57

The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

When a linear equation is represented as:

Ax + By = C

The slope (m) is:

m = -A/B

When the linear equation is represented as:

y = mx + c

The slope is m

A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m

Using the above highlights, the equations of the lines are:

6. y = -2x + 5; (2, 7)

The slope is:

m = -2

The perpendicular slope is:

n = 1/2

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/2(x - 2) + 7

Evaluate

y = 1/2x - 1 + 7

This gives

y = 1/2x + 6

7. y = -5; (11, 15)

The slope is:

m = 0

The perpendicular slope is:

n = 1/0 = undefined

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 15

8. Graph ; (-12, 10)

The slope is:

m = (y2 - y1)/(x2 - x1)

Using the points on the graph, we have:

m = (2 - 3)/(3 - 4)

m = 1

The perpendicular slope is:

n = -1

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = -1(x + 12) + 10

y = -x - 12 + 10

Evaluate

y = -x - 2

9. y = -1/6x + 1; (-2, -9)

The slope is:

m = -1/6

The perpendicular slope is:

n = 6

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 6(x + 2) - 9

Evaluate

y = 6x + 12 - 9

This gives

y = 6x + 3

10. 6x + 2y = 14; (12, 0)

The slope is:

m = -6/2

m = -3

The perpendicular slope is:

n = 1/3

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/3(x - 12) + 0

Evaluate

y = 1/3x - 4

Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

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Answer:

b. The graph of g(x) is a translation 10 units right and 8 units up from the graph of f(x).

Step-by-step explanation:

See attached image.

Answer:

4 units

Step-by-step explanation:

Answer:

The number of ways in which the digits can be assigned in the color wheel can be determined by the permutation of 8 taken 4 since it is in circular formation and whichever comes first is not important.

number of ways = 9P4 = 3024 ways

Current year's debt ratio is 2.50

Last year's debt ratio is 2.44

Compute Dan's Dependable Delivery debt ratio for two consecutive years?

The debt ratio is the total liabilities divided by the total assets

The debt ratio for the current year =  2.50

The debt ratio for last year =2.44(find attached excel file and formula sheet)

Debt ratio means the portion of the firm's total assets funded using borrowing(external funding), the lower the ratio, the better since having a higher debt means a higher interest would be paid, the higher the debt, the higher the chance of the firm defaulting on paying interest and repaying the principal borrowed.

The fact that the debt ratio has increased in the current year, means that the ratio has worsened because more debt has been taken.

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Answer:

-70x, 26y^3, -3z

Step-by-step explanation:

The way to solve this is by combining like terms. The terms we have given to us include x, y^3, and z. As a result, we will group terms based on these variables.

1. Find all the terms with each variable.

* -35x, -35x

* 23y^3, 3y^3

* -3z

2. Combine like terms.

* -35x + (-35x) = -35x - 35x = -70x

* 23y^3 + 3y^3 = 26y^3

* -3z + 0 = -3z

Answer:

Hello! The answer is: [tex]-70x - 3z + 26y^3[/tex]

Step-by-step explanation:

First, rearrange to combine like terms:

[tex]-35x - 35x - 3z + 23y^3 + 3y^3[/tex]

Now, combine like terms:

[tex]-70x - 3z + 26y^3[/tex]

The y-intercept of the line is 0.75 or 3/4

The given parameters are:

Slope, m = 1/4

Point (x, y) = (0.2, 4/5)

A linear equation is represented as:

y = mx + b

This gives

4/5 = 1/4 * 0.2 + b

Evaluate the product

4/5 = 0.05 + b

Subtract 0.05 from both sides

b = 0.75

Hence, the y-intercept of the line is 0.75 or 3/4

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There are 50-50 chances that you will get a head or a tail

Answer:

The table that has the y-value as 2 for each input

Step-by-step explanation:

The table that has the y-value as 2 for each input. This is because as x increases by 1, the y-value is increasing by 0, so the slope is 0/1 or 0. The vertical line doesn't have a zero slope, since it's undefined,  because if you take any two points the "run" is 0, thus you would be dividing by 0, the slope cannot be defined.

The system of linear equations that represents this scenario is: q + d = 16

0.25q + 0.10d = 3.10

To represent the scenario described, we can set up a system of linear equations using the given variables:

Let q represent the number of quarters.

Let d represent the number of dimes.

We are given two conditions:

1) The total number of coins is 16:

q + d = 16

2) The total value of the coins is $3.10:

0.25q + 0.10d = 3.10

Therefore, the system of linear equations that represents this scenario is:

q + d = 16

0.25q + 0.10d = 3.10

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Answer:

∠ 3 = 105°

Step-by-step explanation:

∠ 3 and ∠ 6 are same- side interior angles and sum to 180° , that is

∠ 3 + ∠ 6 = 180°

∠ 3 + 75° = 180° ( subtract 75° from both sides )

∠ 3 = 105°

The diameter of the milky way is given as 4.3 x 10¹¹m while the diameter of the radius of the earth is 0.00276

The transformed system is given as 23.18 x 10⁸ in real length

Hence the diameter is

10 x 10²⁰ / 23.18 x 10⁸

= 4.3 x 10¹¹ m

Distance from the sun to the earth = 1.496 x 10¹¹m

Transformed system = 1.496 x 10¹¹m/23.18 x 10⁸

= 64.5 m

Actual radius = 6.4 x10⁶ / 23.18 x 10⁸

= 0.00276

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Answer:

angle angle theorem.

Step-by-step explanation:

If you want to determine whether a few angles are similar you can use formulas such as SAS AAA ASA etc.

this means

side angle side

angle angle anlge

angle side angle

Answer:

For the function [tex]$f(x)=4 x-3$[/tex] the average rate change from x is equal 1 to x is equal 2 is 4 .

Step-by-step explanation:

A function is given f(x)=4x-3.

It is required to find the average rate change of the function from x is 1 to x is 2 . simplify.

Step 1 of 2

A function f(x)=4 x-3 is given.

Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x=1 in the given function.

[tex]$$\begin{aligned}&f(1)=4(1)-3 \\&f(1)=1\end{aligned}$$$$f(1)=1$$[/tex]

Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x is 2 in the given function.

[tex]$$\begin{aligned}&f(2)=4(2)-3 \\&f(2)=5\end{aligned}$$[/tex]

Step 2 of 2

According to the formula of average rate change of the equation [tex]$\frac{\Delta y}{\Delta x}=\frac{f\left(x_{2}\right)-f\left(x_{2}\right)}{x_{2}-x_{1}}$[/tex]

Substitute the value of [tex]$f\left(x_{1}\right)$[/tex] with, [tex]$f\left(x_{1}\right)$[/tex] with [tex]$3, x_{2}$[/tex] with 2 and [tex]$x_{1}$[/tex] with 1 .

[tex]$$\begin{aligned}&\frac{\Delta y}{\Delta x}=\frac{5-1}{1} \\&\frac{\Delta y}{\Delta x}=4\end{aligned}$$[/tex]

The side of the edge of the cube is 9. 9cm

Given that the diagonal of a cube measures the square root of 294cm and the diagonal of a face measures 14cm

To find the edge of the face, we know that the face of the cube is a square

Formula for diagonal of a square = [tex]\sqrt{2a}[/tex]

Where is the side of the square

We then have,

[tex]\sqrt{2a} = 14[/tex]

Make 'a' the subject

a = [tex]\frac{14}{\sqrt{2} }[/tex]

Simplify the surd

a = [tex]\frac{14}{\sqrt{2} }[/tex] × [tex]\frac{14}{\sqrt{2} }[/tex]

a = [tex]\frac{14\sqrt{2} }{2}[/tex]

a = [tex]7\sqrt{2}[/tex]

a = 9. 9cm

Therefore, the side of the edge of the cube is 9. 9cm

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Answer: Its 9.8 cm

Step-by-step explanation: I said so

The equation of the hyperbola with foci (-2, 0), (2, 0), and vertices, (-1, 0), (1, 0) is [tex] \underline{\frac{ {x}^{2} }{ {1}^{2} } - \frac{ {y}^{2} }{ 3} } = 1[/tex]

The general form of the equation of an hyperbola is presented as follows;

[tex] \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

Where a is obtained from the vertex written as (-a, 0), (a, 0)

The given vertex are (-1, 0), (1, 0), which gives;

a = 1

The general form of the foci of a hyperbola are; (-c, 0), (c, 0)

The given foci of the hyperbola are; (-2, 0), (2, 0)

Where;

Therefore;

By comparison, we have;

c² = 2²

Which gives;

The equation of the hyperbola is therefore;

[tex] \underline{\frac{ {x}^{2} }{ {1}^{2} } - \frac{ {y}^{2} }{ 3} } = 1[/tex]

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[tex]m = \frac{ - 5 - 4}{3 - 0} = \frac{ - 9}{3} = - 3[/tex]

[tex]g(x) = - 3x + 4[/tex]

[tex]g(x) \: ha s \: a \: steeper \: slope[/tex]

The chocolate will last for 1 day, if she gets 4 more dragons

The expression can be represented using the following ratio:

Ratio = Dragons : Days : Chocolate

For the 2 dragons she has, we have:

Ratio = 2 : 12 : 300

When she gets 4 more dragons, we have:

Ratio = 6 : days : 300

Equate both ratios

6 : days = 12 : 2

Express as fraction

days/6 = 2/12

Multiply both sides by 6

days = 6 * 2/12

Evaluate

days = 1

Hence, the chocolate will last for 1 day

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Answer:

<C = 45 degrees.

Step-by-step explanation:

This is a right triangle (indicated by the square representing <A). All angles in a triangle add up to 180 degrees

180 - 90 is 90. Knowing that there are only two angles left, you can divide 90 by 2, resulting in 45.

<C = 45.

Answer:

probably c

Step-by-step explanation:

Hello!

d₁ = distance covered in Part 1

d₂ = distance covered in Part 2

d₃ = distance covered in Part 3

Distance in Part 2 :

⇒ d₃ = 15 x 300 = 4500 m

⇒ d₂ = 2/5d₃

⇒ d₂ = 2/5 x 4500

⇒ d₂ = 1800 meters

Speed in Part 2 :

⇒ v₂ = 1800 m / 12 min

⇒ v₂ = 150 meters per minute