What is the equation of the line which passes through A(0, 4) and B(2, 0)? ​

Answer:

2100

Step-by-step explanation:

The possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3,  cos θ = √3/3, sec θ = √3

The law of sines, also known as the sine rule, is a mathematical principle that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.

Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Each function represents a different ratio of two sides of a right triangle and can be used to solve problems in geometry, physics, engineering, and other fields that involve angles and triangles.

According to the given information,

Given that tan θ = -√(1/3) and 0 < θ < 180°, we can use the trigonometric identities to find the values of the other trigonometric functions of θ.

First, we can use the definition of the tangent function:

tan θ = opposite/adjacent

Since tan θ = -√(1/3), we can assign opposite = -1 and adjacent = √3 as their ratio equals -√(1/3). This means that the terminal side of the angle θ will lie in the fourth quadrant of the unit circle since the opposite is negative and the adjacent is positive.

Next, we can use the Pythagorean identity:

sin²θ + cos²θ = 1

to find the value of sin θ. Since we know that θ is in the fourth quadrant, we can assign sin θ = -1/√3, since sin θ is negative in the fourth quadrant and the ratio of opposite/hypotenuse of a 30-60-90 triangle is √3/2, which means the ratio of hypotenuse/opposite is 2/√3 = √3/3.

Then, we can use the definition of the cosine function:

cos θ = adjacent/hypotenuse

to find the value of cos θ. We know that adjacent = √3 and the hypotenuse is positive (since it is a length), so we can assign cos θ = √3/3.

Finally, we can use the reciprocal identity:

sec θ = 1/cos θ

to find the value of sec θ. We know that cos θ = √3/3, so we can assign sec θ = √3.

Therefore, the possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3

cos θ = √3/3

tan θ = -√(1/3)

sec θ = √3

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Answer:

I think its Yes!

Step-by-step explanation:

Hope this helps!!!

Answer:

3455/72

=47.9861111111

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

6 times 6 = 36, so 6 is the answer

Hope this helps. Please mark me brainliest!

The answer to the question 36/12=3

The perimeter of a rectangle is the sum of the lengths of its four sides. The perimeter is C. 28 units.

The perimeter of a two-dimensional shape is the total distance around its outer boundary. The formula for finding the perimeter depends on the shape you are dealing with.

Rectangle: Perimeter = 2(length + width)

The perimeter of a rectangle is the sum of the lengths of its four sides. In this case, the sides of the rectangle are 4 units, 10 units, 4 units, and 10 units. Therefore, the perimeter is:

= 4+10+4+10

= 28  units.

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The exercise above is one of the Discontinuous Initial Value Problems (DIVP) with a Discontinuous Function.

An Initial value problem

This topic is related to multivariable calculus. It is a standard differential equation with an initial condition that describes the unknown function's value at a selected point in the domain. IVP is often used in physics for modeling.

The solution for the IVP (Initial Value Problem) whose input function g(x) is discontinuous

y" + 4y = g(x),

y(0) =1, and

y' (0) = 2

Where

g(x) = [ sin x ,  0 ≤ x ≤ π /2 ]

         [  ,  x > / 2 ]

For the lower interval and use the result to solve the upper interval.

The homogeneous solution to (1) where (1) is

y′′ + 4y = g(x), y(0) = 1, y′(0) = 2

m² + 4 = 0 → m₁,₂ = ± 2i

From this derive:

y h = c₁ Cos 2x + c₂ sin 2x

To resolve the particular solution,

y p = a cos x + b sin x

Resolving the constants a and b, let's substitute back into equation 1 above to arrive at:

-a cos x - b sin x + 4a cos x + 4b sin x = sin x

From the above,

a = 0 and b= 1/3

Rewriting the equation,

y = y h + y p = c₁ cos 2x + c₂ sin 2x + 1/3sinx

Initiation constraints

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.

Using the Initiation constraints, we solve for c₁ and c₂:

c₁ = 1, c₂ = 5/6, this leaves us with the following:

y(x) =cos2x + 5/6sin 2x + 1/3sinx,

0 ≤ x ≤ π / 2                      (2)

From the above, we must proceed to calculate the upper half of the range so that we have, y" + 4y = 0.

Using the initial constraints in combination with (2), we get y  = -(2/3) and

y' (/2) = -(5/3)

Recall that solution 2 was:

y = c₁ cos 2x + c₂ sin 2x

With the new constraints, we can resolve this get:

c₁ = 2/3, c₂ = 5/6, so

y(x) = 2/3cos 2x + 5/6sin 2x, x > /3           (3)

Combining equations 2 and 3, we have:

y(x) = [ cos 2x + 5/6 sin 2x + 1/3 sin x , 0 ≤ x ≤ π / 2 ]

      = [ 2/3 cos 2x + 5/6 sin 2x,   x > π /2 ]

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Answer:

Graph 4)

Step-by-step explanation:

Absolute Value

The absolute value of x, written as |x| is a positive number that represents the distance from the origin and the number.

In practice, the absolute value is found writing the number without the negative sign, if present.

For example:

|-3| = 3

|12| = 12

|0| = 0

We are given the function:

y = - | x - 3 |

Since the absolute value is positive, the minus sign before the bars make this function always negative. All options except 4) are automatically discarded because they have positive values for y.

Give x some values: x={-1,0,3,4}

And evaluate y:

x=-1

y = - | -1 - 3 | = - | -4 | = -4

x=0

y = - | 0 - 3 | = - | - 3 | = -3

x=2

y = - | 2 - 3 | - | -1 | = -1

x=3

y = - | 3 - 3 | - | 0 | = 0

x=4

y = - | 4 - 3 | - | 1 | = -1

Plotting these points and drawing the graph, we get the graph shown in option 4)

Answer:

Step-by-step explanation:

Change in one year:

Change after 5 years:

Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.

A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.

y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.

y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.

y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.

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Answer:

15

Step-by-step explanation:

Let's call the number we try to find "\(x\)"

In the problem, we know that "26 is less than twice a number" is the same as "4". So we can write this as an equation:

\(2x - 26 = 4\)

Now we can solve for x by isolating it on one side of the equation.

First, we isolate "2x" by flipping "-26" to the other side, which will now be "26".

\(2x = 4 + 26\)

Then we add

\(2x = 30\)

finally, we isolate the x by dividing each side with 2

2x ÷ 2 = 30 ÷ 2
x = 15

Answer:

y < 4x + 3

Step-by-step explanation:

First find the equation represented by the graph...

using slope-intercept (y = mx + b where m = the slope and b = the y- intercept)

slope is 4

y- intercept is 3

Once you have the equation 4x + 3, determine whether y is greater than or equal to the point plotted.

I can explain more if you need but trust me the answer is y < 4x + 3

The inequality represented by the graph is y <1/4x + 3.

From the graph, the line of inequality cut the y axis at 3.

So, the y intercept is (0, 3).

and, the slope of the inequality is

= 1/4

Using slope-intercept form

y= mx+ b

y= 1/4x + 3

Since the inequality have the shaded area below the line to represent all the points that satisfy the inequality.

and, the inequality can be written as

y < 1/4x + 3

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We can see here that the probability that the password does not have repeated letters, expressed to the nearest tenth of a percent is = 9.8%.

Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

The probability of an event can be calculated using the following formula:

Probability = Favorable Outcomes / Total Outcomes

The number of possible passwords is:

26 × 26 × 26 × 26 × 26 × 26  = 308,915,776.

The number of passwords with no repeated letters is

26P6 = 30,260,000.

The probability of a password having no repeated letters is

= 30,260,000 / 308,915,776 = 0.09779 = 9.78%.

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Answer:

a:b = 1:2

Step-by-step explanation:

b/6=a/3

Answer:

Hope this helps

Step-by-step explanation:

The line segment starts at L ( -9,4) and goes through midpoint K (2,-1) and ends at M.  Thus M is twice the distance in x and y directions from L to K.  The x dimension goes up 11 and the y dimension goes down 5 from L to K.  Two times these are dimensions for x 22 and for y -10.  The endpoint = - 9 + 22 or 13 for x and 4 - 10 or -6 for y.  Thus the endpoint is 13, -6.

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The total amount of the emergency fund is $2280.82, with $1710.62 in the CD and $570.20 in the regular Savings account. The total interest earned between both accounts in 60 days is $48.96.

The total amount of the emergency fund, we first need to calculate the monthly deductions:

FICA deduction = 7.65% of $4520 = $345.78

Federal tax withholding = 11.75% of $4520 = $531.70

State tax withholding = 8.5% of $4520 = $384.20

Total deductions = $345.78 + $531.70 + $384.20 = $1261.68

Realized income = gross income - deductions = $4520 - $1261.68 = $3258.32

Fixed expenses = 30% of realized income = 0.3 x $3258.32 = $977.50

Amount saved in emergency fund = realized income - fixed expenses = $3258.32 - $977.50 = $2280.82

Amount placed in CD = 75% of $2280.82 = $1710.62

Amount placed in regular savings account = 25% of $2280.82 = $570.20

To calculate the total interest earned between both accounts in 60 days, we need to calculate the interest earned on each account separately and then add them together:

Interest earned on CD = ($1710.62 x 5.25% x 60 days) / 365 = $44.28

Interest earned on regular savings account = ($570.20 x 3.8% x 60 days) / 365 = $4.68

Total interest earned = $44.28 + $4.68 = $48.96

Therefore, the total amount of the emergency fund is $2280.82, with $1710.62 in the CD and $570.20 in the regular savings account. The total interest earned between both accounts in 60 days is $48.96.

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If the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that, a certain truck traveled 7,605 miles in 15 days.

The average number of miles traveled per day is obtained by dividing the total distance traveled by the total time taken as,

Suppose the average number of miles traveled per day is x,

x=76015 / 15

x=507 miles per day.

Thus, if the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

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Answer : 8$

you have 1$ left

Answer: The answer is 30

formulate the given
200 x 15%
= 200 x 0.15
= 30

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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Answer:

35 days

Step-by-step explanation:

Weight gain per day = 200 pounds

Weight gained by a whale since birth = \( 7*10^3 \) pounds

Number of days of the whale = \( \frac{7*10^3}{200} = \frac{7*10*10*10}{200} \)

\( = \frac{7*1000}{200} = \frac{7000}{200} = \frac{70}{2} = 35 \)

In standard notation form, the whale is 35 days old.

Answer:

66%

Step-by-step explanation:

Answer:

what questions need to be done? We need to know the problems before we answer them. :/

Step-by-step explanation:

y=k/x

The function A(x) = 100 + 4x describes the scenario of an ant colony that starts with an initial population of 100 and experiences a constant rate of increase of 4 ants per year.

We have,

The function A(x) = 100 + 4x represents a linear relationship between the variable x (representing time in this case) and the variable A(x) (representing the population of the ant colony).

The term 100 in the function represents the initial population of the ant colony.

It indicates that at the starting point (x = 0), the population is 100.

The term 4x in the function represents the rate at which the population increases over time. Since the coefficient of x is positive (4), it indicates that the population is increasing.

For every unit increase in x (in this case, for every year that passes), the population increases by 4.

Therefore,

The function A(x) = 100 + 4x describes the scenario of an ant colony that starts with an initial population of 100 and experiences a constant rate of increase of 4 ants per year.

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