Let θ be an angle in standard position, with its terminal side in quadrant IV such that tanθ = -7/9. Find the exact values of sinθ and cosθ.

The discriminant, D of the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex] when calculated is 64/9

The quadratic equation is given as

[tex]3x\² + 3 \frac 13x + \frac 13[/tex]

The discriminant of a quadratic equation of the form ax² + bx +c = 0 is given by the expression b² - 4ac

In this case, we have the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex], which can be written in the standard form as

[tex]3x\² + \frac {10}3x + \frac 13[/tex]

Comparing with the standard form ax² + bx + c = 0,

we have a = 3, b = 10/3 and c = 1/3

The discriminant of this quadratic equation is therefore:

D = b² - 4ac

[tex]D = (\frac{10}{3})\² - 4 \cdot 3 \cdot \frac{1}{3}[/tex]

D = 64/9

Hence, the discriminant of [tex]3x\² + 3 \frac 13x + \frac 13[/tex] is 64/9

Read more aboit discriminant at

https://brainly.com/question/29594745

#SPJ1

Answer:

  f(-3) = 6

Step-by-step explanation:

You want the value of f(-3) given a graph of f(x).

To find the value of f(-3), locate -3 on the x-axis. Follow the vertical grid line to where it intersects the graph of f(x). Follow the horizontal grid line from there to the axis marked f(x), and read the value on the vertical scale.

The attachment shows this process, and that the value of f(-3) is 6.

__

Additional comment

Unless there is information to the contrary, the usual assumption is that each grid line represents one unit. Positive is to the right of the vertical axis, and up from the horizontal axis. Then x=-3 is 3 grid lines left of the vertical axis.

The notation f(x) means the value of function f depends on the value x. The expression f(-3) is the function value when x=-3. Here, it is found by reading the graph. In other situations, it might be found from a table or by evaluating an algebraic expression.

Answer:

Step-by-step explanation: 55 i think

Answer:

2%?

Step-by-step explanation:

The slope of the linear function that represents the cost of plan B is $0.17.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Since Plan B has the same monthly base charge as plan A, we can logically deduce that the data points (0, 14.45) and (45, 22.10) lie on the linear function.

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (22.10 - 14.45)/(45 - 0)

Slope (m) = $0.17

Read more on slope here: https://brainly.com/question/17460142

#SPJ1

Complete Question:

Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table. Monthly Charge for Plan A Minutes used, x Monthly charge ($), y 0 14.45 3 14.84 6 15.23 9 15.62 12 16.01 Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?

The distance the plane traveled from point A with measures an angle of elevation of 16°, to point B with measures an angle of elevation of 28°, is equals to the 11,728.6feet.

Jaya spots an airplane on radar that is currently approaching in a straight line start from point O in above figure, and that will fly directly overhead.

Altitude that plane maintain,h = 7300 feet

Initially, measure an angle of elevation to the plane at point A = 16°

Measure an angle of elevation to the plane at point B = 28°

Now, Let the distance between point A and point B be equal to 'x feet' and distance between point B and point C ( base) be equal to 'y feet'. So, distance between point A to point C = (x + y ) feet. We have to calculate the distance the plane traveled from point A to point B, i.e., x feet. See the above figure carefully, we see in right angled triangle BOC, tan 28° = 7300/y --(1)

In right angled triangle AOC,

tan 16° = 7300/(x + y) --(2)

Cross multiplication in equation (2)

=> tan 16° ( x + y ) = 7300

=> x + y = 7300/tan 16° --(3)

from equation (1), y = 7300/tan 28°

=> y = 7300/0.5317 = 13,729.55

so, x = 7300/tan 16° - y = 7300/0.287 - 13,729.55

= 25,458.12 - 13,729.55

= 11,728.58 ~ 11,728.6

Hence, required distance is 11,728.6feet.

For more information about angle of elevation, visit :

https://brainly.com/question/88158?utm

#SPJ4

Thus, to the closest dollar, the total sales revenue included in the master budget for September was as follows: master budget sales income = $11.71 multiplied by 40,000 Sales master budget.

Let's first get the precise variable cost per unit:

Real variable cost is $7.43 per unit.

Let's next determine the revenue from the flexible budget:

$400 000 in flexible budget revenue

Let's now determine the actual sales revenue:

$383,000 was the actual sales revenue.

Let's figure out the overall variance for the flexible budget:

Overall variance for the flexible budget is $17,000.

Given that the flexible-budget variance is unfavourable (U), we can infer that actual revenue was lower than anticipated.

a... a.. a.. a.. a

Variance in sales volume is 40,000 x ($9.58 - $10.00 + $7.43)

Variance in sales volume = 40,000 x $6.01

Variance in sales volume = $240,400

Let's figure out the overall flexible-budget variation for variable costs:

Variance in the flexible budget for all variable costs is $-106,800.

Let's now determine the precise number of units sold using the sales volume variance.

The budgeted amount of units sold that were sold:

With the actual number of units sold compared to the projected amount (34,132.94), we can determine the budgeted price per unit as follows:

$11.71 is the planned price per unit (rounded to nearest cent)

Thus, to the closest dollar, the total sales revenue included in the master budget for September was as follows:

master budget sales income = $11.71 multiplied by 40,000

Sales master budget

Learn more about the master budget here:

https://brainly.com/question/13059911

#SPJ4

1. The sequence is an arithmetic sequence with a common difference of d = -200.

2. The sequence is not an arithmetic sequence.

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

For item 1, each term is the previous term subtracted by 200, hence the sequence is in fact an arithmetic sequence with a common difference of -200.

For item 2, the difference between consecutive terms is difference, hence the sequence is not an arithmetic sequence.

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

#SPJ1

(a) (f∘g)(x) and the domain of f∘g are defined for real numbers and (b) (g∘f)(x) and the domain of g∘f is defined for real numbers.

The given functions are:f(x) = −x² + 1g(x) = x

Exer. 21-34: To Find

(a) (f ∘ g)(x) and the domain of f ∘ g and (b) (g ∘ f)(x) and the domain of g ∘ f.(a) (f ∘ g)(x) and the domain of f ∘ gTo find the composite of the two functions, substitute the value of g(x) into f(x). Now, (f ∘ g)(x) is given by:f(g(x)) = f(x) = f(x) = f(x) = -x² + 1. The domain of (f ∘ g)(x): Since g(x) is defined for all real numbers, the domain of (f ∘ g)(x) is also defined for all real numbers.

(b) (g ∘ f)(x) and the domain of g ∘ f

To find the composite of the two functions, substitute the value of f(x) with g(x). Now, (g ∘ f)(x) is given by:g(f(x)) = g(-x² + 1) = -x² + 1

The domain of (g ∘ f)(x): The domain of f(x) is defined for all real numbers. However, the domain of g(x) is also defined for all real numbers. Therefore, the domain of (g ∘ f)(x) is defined for all real numbers.

You can learn more about domain at: brainly.com/question/13113489

#SPJ11

m = 532 - (57 * h) represents the number of miles remaining after h hours of traveling at an average speed of 57 miles per hour.

The equation m = 532 - (57 * h) is used to represent the number of miles remaining, m, after h hours of traveling at an average speed of 57 miles per hour. The equation works by taking the total distance, 532 miles, and subtracting the product of the average speed, 57 miles per hour, and the amount of hours traveled, h. The result of the equation is the number of miles remaining, m. For example, if the family has been traveling for four hours, the equation would be m = 532 - (57 * 4). Solving the equation, m = 344, meaning the family has 344 miles left to travel. This equation allows the family to easily determine how many miles they have left to travel, given the average speed and amount of time traveled.

Learn more about hours here

https://brainly.com/question/13533620

#SPJ4

Mila should receive 44.44% of the profit.

An equation is a statement that asserts the equality of two expressions, typically with one or more variables. Equations are used to represent relationships between different quantities, such as the relationship between the length and width of a rectangle or the relationship between the time and distance traveled by an object.

Profit is the financial gain that is earned by a business or an individual after all expenses and costs have been subtracted from revenue or income. It is the difference between the amount earned from sales or services and the costs incurred to produce or provide those goods or services.

In the given question,

Let's begin by determining the amount of money each person invested in the project.

Let Sydney's investment be x.

Roy's investment is twice Sydney's, so Roy invested 2x.

Mila's investment is twice Roy's, so Mila invested 2(2x) = 4x.

Taniya's investment is half of Mila's, so Taniya invested 0.5(4x) = 2x.

The total amount invested is x + 2x + 4x + 2x = 9x.

Now, we need to find the percentage of profit Mila should receive. Since the profit is shared in proportion to the amount invested, Mila should receive a fraction of the profit equal to her investment divided by the total investment.

Mila's share = (Mila's investment) / (Total investment) x (Total profit)

Mila's share = (4x / 9x) x 27000

Mila's share = 12000

So Mila should receive $12,000 of the profit. To find the percentage of profit Mila should receive, we can divide her share by the total profit and multiply by 100:

Percentage of profit Mila should receive = (Mila's share / Total profit) x 100%

Percentage of profit Mila should receive = (12,000 / 27,000) x 100%

Percentage of profit Mila should receive = 44.44%

Therefore, Mila should receive 44.44% of the profit.

To know more about equations, visit:

https://brainly.com/question/14686792

#SPJ1

The measures in the circles are calculated as:

2. FD = 22; 4. US = 58

6. MN = 11; 8. YZ = 34

The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

2. 12(3x - 5) = 15(8) [based on the Intersecting Chords Theorem]

36x - 60 = 120

36x = 120 + 60

36x = 180

x = 5

FD = 3x - 5 + 12 = 3(5) - 5 + 12

FD = 22

4. 30(3x + 1) = 42(x + 11) [based on the Intersecting Chords Theorem]

90x + 30 = 42x + 462

90x - 42x = -30 + 462

48x = 432

x = 9

US = 3x + 1 + 30 = 3(9) + 1 + 30 = 58

6. (2x - 7 + 9)(9) = (8 + 10)(10) [based on the intersecting secants theorem]

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 9

MN = 2x - 7 = 2(9) - 7

MN = 11

8. (2x + 12 + 6)(6) = (x + 3 + 10)(10) [based on the intersecting secants theorem]

12x + 108 = 10x + 130

12x - 10x = -108 + 130

2x = 22

x = 11

YZ = 2x + 12 = 2(11) + 12

YZ = 34

Learn more about the intersecting chords theorem on:

https://brainly.com/question/30994417

#SPJ1

The work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.

A particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. With the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx(t) = (2.6 N) sin(2.2t)where t is in seconds.

The work done by the force as the particle moves from x = 0 m to x = 2.2 m: For a sinusoidal force that changes with time, the work done is given by W = ∫F dx where F is the force, and dx is the displacement. For this problem, the force is given by fx(t) = (2.6 N) sin(2.2t)dx is the displacement, which is given by dx = x2 – x1 where x2 = 2.2 m, and x1 = 0 m.

Substituting for F and dx, we get W = ∫02.2(2.6 sin(2.2t)) dx= 2.6 ∫02.2 sin(2.2t) dx= 2.6 [(-1/2.2) cos(2.2t)]02.2= 1.18 (cos(4.84) – 1)≈ -0.53 J. So, the work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.

To know more about force and work, refer here:

https://brainly.com/question/758238#

#SPJ11

Answer:The coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2).

What do you mean by reflection of coordinates?

A reflection on the coordinate plane is a type of transformation. It takes a geometric figure such as a point, line segment, or shape and transforms it into a congruent geometric figure called the image.

Given is a point (-3, 2) reflected across the y - axis.

Now, when any given coordinate is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.

As given, the coordinates of the point are - P(-3, 2)

Now, after reflection across the y - axis, the new coordinates of the image of this point will be -

x' = - (- 3) = 3

y' = y = 2

P'(3, 2)

Therefore, the coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2)

Answer:

3,2

Step-by-step explanation: Just took the test

Answer: Tazi-D

Bugsy-B: 0.16 per ounce

Tazi-D: 0.14 per ounce

Step-by-step explanation:

divide the $ by the ounce for both.

Answer:  this equals 100

Step-by-step explanation:

Answer:

3x³- 8x² + 2x +3

Step-by-step explanation:

All you need to do is multiply everything in the second bracket with the first bracket like you would normally do with double brackets.

3x³-3x²-5x²+5x-3x+3=

3x³-8x²+2x+3

Answer:

Step-by-step explanation:

2/3*6

6*6

12

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For [tex]0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.[/tex] Hence, the correct option is (a) P(X ≤ 1).

Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:

[tex]cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x[/tex]

To use the cdf to obtain the following.P(X ≤ 1)

So, the probability distribution function is the derivative of the cumulative distribution function.

∴ f(x) = d/dx(F(x))

Also, from the cdf, we know that:

[tex]f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.[/tex]

f(x) = 1 when x ≥ 2.

Using the above conditions, we have to calculate the following:

(a) P(X ≤ 1)

Here, P(X ≤ 1) = F(1).

When[tex]0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)[/tex]

Thus, for[tex]0 ≤ x ≤ 2, F(x) = (x^3/12).[/tex]

for such more question on Time

https://brainly.com/question/26862717

#SPJ11

Answer: The area of each slice of pizza can be calculated by finding the area of the whole pizza and dividing it by the number of slices.

The radius of the pizza is half of the diameter, so the radius is 20/2 = 10 inches.

The area of the whole pizza can be calculated using the formula for the area of a circle:

Area = π × radius^2

Area = π × 10^2

Area = 100π square inches

Since there are 8 slices, each slice has an area of:

100π square inches / 8 = 12.5π square inches

Therefore, the area of the 5 slices that Chris ate is:

5 × 12.5π square inches = 62.5π square inches

This is approximately equal to 196.35 square inches, when rounded to two decimal places.

Step-by-step explanation:

The probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.

A mathematical technique called the Bayes theorem enables us to revise our views or probability regarding an occurrence in light of fresh data or evidence. It has the name of the reverend Thomas Bayes, a statistician and philosopher active in the 18th century. According to the Bayes theorem, the likelihood of an event A given that an event B has already happened is equal to the likelihood of an event B given that an event A has already occurred, multiplied by the prior likelihood of an event A, divided by the previous likelihood of an event B.

The Baye's Theorem is given as:

P(B|A) = P(A|B) × P(B) / P(A)

Here,

P(A) is the probability that a customer ordered a small drink = 0.22.

P(B) is the probability that a customer ordered a hot drink, regardless of whether it was small or medium or large = 0.05.

P(A|B) is the probability that a customer ordered a small drink, given that they ordered a hot drink = 0.2.

Substitute the value we have:

P(B|A) = P(A|B) × P(B) / P(A) = (0.2 × 0.05) / 0.22 ≈ 0.045

Therefore, the probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.

Learn more about Baye's Theorem here:

https://brainly.com/question/28096770

#SPJ1

The rent of the apartment during the 8th year would be approximately $2491.4.

To calculate the rent of the apartment during the 8th year, we need to apply the 11% increase per year for a total of 7 years (from the 2nd to the 8th year). Here's the calculation:

Rent for the 2nd year:

$1200 + (11% of $1200) = $1200 + ($132) = $1332

Rent for the 3rd year:

$1332 + (11% of $1332) = $1332 + ($146.52) = $1478.52

Rent for the 4th year:

$1478.52 + (11% of $1478.52) = $1478.52 + ($162.64) = $1641.16

Rent for the 5th year:

$1641.16 + (11% of $1641.16) = $1641.16 + ($180.53) = $1821.69

Rent for the 6th year:

$1821.69 + (11% of $1821.69) = $1821.69 + ($200.39) = $2022.08

Rent for the 7th year:

$2022.08 + (11% of $2022.08) = $2022.08 + ($222.43) = $2244.51

Rent for the 8th year:

$2244.51 + (11% of $2244.51) = $2244.51 + ($246.90) = $2491.41

Therefore, the rent of the apartment during the 8th year would be approximately $2491.4.

For more such questions on rent , Visit:

https://brainly.com/question/28693274

#SPJ11

Step-by-step explanation:

False, it is 3 units to the left

For any function,

[tex]f(x)[/tex]

the function transformation of

[tex]f(x - h)[/tex]

implies a transformation h units to the left

If h is the positive, this implies a transformation to the right

If h is negative, this implies a transformation to the left.

Here's since

[tex](x + 3[/tex]

can be written as

[tex](x - ( - 3))[/tex]

Our h is negative, therefore we move 3 units to the left

Answer:

8 degrees

Step-by-step explanation:

Given in the picture, hope it helps.

Therefore , the solution of the given problem of unitary method comes out to be in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.

The task can be completed by multiplying the data gathered using this type of nanosection along with two variable individuals who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.

Here,

1.1. The statement omits details about the truck's loan term. Therefore, without more details, we are unable to respond to this query.

1.2. Assume that the truck's loan period is n years and that the contractor borrowed P dollars at an annual interest rate of r to buy the water tanker.

M is calculated as (r * P * (1 + r)n) / ((1 + r)n - 1)

5 years + 60 months Equals n

r = 5% / 12 = 0.004166667 (weekly interest rate) (monthly interest rate)

P = $100,000

=> M = (0.004166667 * $100,000 * (1 + 0.004166667)^60) / ((1 + 0.004166667)^60 - 1)

≈> $1,870.24

As a result, the total monthly payments made for the water tanker, including the insurance protection, came to about $1,870.24.

1.3

(Total Amount Borrowed - Amount Paid) / 2

=>  ($100,000 - $1,870.24 * 6) / 2 = $47,259.52 is the sum that is owed.

Therefore, in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.

To know more about unitary method visit:

https://brainly.com/question/28276953

#SPJ1

The simplest form of the ratio 2m : 8cm : 40mm is

50mm : 2mm : 1mm

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

For we to simplify the ratio , we have to convert the unit to the least form. The least form of the unit is millimeter

2m = 2× 1000mm = 2000mm

8cm = 8 × 10 = 80mm

40mm = 40mm

therefore the ratio will be in form of

2000mm : 80mm ; 40mm

divide through by 10

200mm : 8mm : 4mm

divide through by 4

50mm : 2mm : 1mm

therefore the simplest form of the ratio 2m: 8cm : 40mm is 50mm : 2mm : 1mm

learn more about ratio from

https://brainly.com/question/2328454

#SPJ1

The time needed to paint 3 rooms together is given as follows:

308.4 minutes.

The time needed is obtained applying the proportions in the context of the problem.

First we use the together rate, which is the sum of each separate rate, for the time needed to paint a single wall, hence:

1/x = 1/45 + 1/60

1/x = 7/180

7x = 180

x = 180/7

x = 25.7 minutes per wall.

The number of walls in 3 rooms is given as follows:

3 x 4 = 12 walls.

Thus the time needed to paint the 3 rooms is given as follows:

25.7 x 12 = 308.4 minutes.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

y = 4x + 15

Step-by-step explanation:

Using 'y=mx+c' form,

Since m = 4,

y = 4x + c

Substituting (-5, -5) into the above equation:

-5 = -20 + c

c = 15

Hence,

y = 4x + 15

Feel free to mark this as brainliest! :)