The velocity of a car on the highway is given by v(t) where 0 ≤ t ≤ 10 in minutes. Which of the following represents the rate at which the velocity is changing at 2 minutes?

D. I and IV are the quadrants the cosine function is positive

To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.

The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.

Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.

Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.

Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.

It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.

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Answer:

d = 13 and n = 52

Step-by-step explanation:

Number of dimes:  d

Number of nickels:  n

Then d + n = 65, and n = 4d

Substituting 4d for n in the first equation, we get:

d + 4d = 65, or 5d = 65.  Then d = 13 and n = 52

Answer:

The answer would be the first one.

Step-by-step explanation:

5.50 x n which n=4 so its actually 5.50 x 4 which equals 22 then you add the 22 to the 78 to get the result of exactly 100 dollars.

Using relations in a right triangle, the secant of angle θ is given by:

D. 5/4.

The relations in a right triangle are given as follows:

Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 9² + 12²

h = sqrt(9² + 12²)

h = 15.

The secant of an angle is 1 divided by the cosine, hence:

Which means that option D is correct.

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Answer:

30 Nickels and 188 Pennies

Step-by-step explanation:

okay, so to set up the equation first, we have to assign each coin a variable, let's call them p and n:

P= number of pennies

N= number of nickels

the value of a penny is 1 cent, so 1P, and the value of a nickel is 5 cents, so 5N

The problem states that he has 218 coins, meaning that the total number of pennies and nickels adds up to 218:

P + N = 218

the total value of the coins is $3.38, so that would mean that 1P + 5N has to equal $3.38:

1P + 5N = 338

Okay, so now that we have our equations let's solve them using elimination:

we have to get a common coefficient between both equations, so let's multiply our first equation by 5:

P x 5 = 5P

N x 5 = 5N

218 x 5 = 1090

so, now we can solve by elimination:

5P + 5N = 1090

1P + 5N = 338

the N's cancel out:

4P = 752

divide both sides by 4:

P = 188

okay, so if theres a total of 218 coins, subtract 188 from 218:

218 - 188 = 30

so, there are 30 nickels and 188 pennies.

check our work:

5 x 30 = 150

1 × 188 = 188

150 + 188 = 338

338 = 338

I hope this helps! :)

Answer:

.aabc=amn0#1211

Step-by-step explanation:

nosascoOsasco n=12.8

Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

 (f(g)) = √x - 2 is the value of function .

What does a math function mean?

f(x) = x - 2

g(x ) = \(\sqrt{x}\)

(f(g))  = f ( g(x) ) =  √x - 2

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Answer:

Step-by-step explanation:

In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.

Using this information, we can set up equations to solve for the variables.

From the given information, we have -

AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)

BE = x + 2

DE = BE = (x + 2) = g (since diagonals bisect each other at point E)

We also know that opposite sides of a parallelogram are parallel.

Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -

10/1 = 2y/1

10 = 2y

y = 5

Now we can use equation (1) to solve for x -

2x - 5 = 5x - 17

12 = 3x

x = 4

Finally, we can use x to solve for g -

(x + 2) = g

(4 + 2) = g

g = 6

Therefore, the values of x, y, and g are 4, 5, and 6, respectively.

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76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or

Answer:

2

Step-by-step explanation:

p3 = 8

square root of 64 = 8

q = 8

so that means that the equation is > 8+8 / 8 = 2

plz mark brainliest!

A.) 9

Original Equation: p³ + √64 ÷ q

Substitute: ⇒2³ + √64 ÷ 8

Solve for Each Value:

⇒ (p³ or 2³) = 8

⇒ (√64) = 8

⇒ (q or 8) = 8

Now, Solve the Equation Using the Order of Operations ( or P.E.M.D.A.S (perenthesis, exponents, multiplication, division, addition, subtraction)):

New equation: 8 + 8 ÷ 8

Using P.E.M.D.A.S.:

(8 ÷ 8) = 1

8 + (1) = 9

Answer: 5 hours

Step-by-step explanation: 161$/7h= 23 per hour, therefore, 115$/23 per hour= 5 hours.

Answer: Point G is obtained by using the same compass width and drawing an arc from point F, intersecting the arc drawn from A

Step-by-step explanation:

I took the test and got the right answer

The steps for constructing a parallel line require steps for constructing

angles of equal measures.

Reasons:

The steps to construct the AG parallel to PQ, passing through the point A

outside of PQ are as follows;

Step 1; A line is drawn from point A to intersect PQ at point B.

Step 2; From point B on PQ, an arc is drawn intersecting segment BQ of PQ at  D and segment BA at point E.

Step 3; To construct the angle equal to angle ∠DBE at point A, an arc is drawn from Point A with radius BD, that intersects the segment BA extended in point F

Therefore;

To construct an angle equal to the angle ∠DBE to point A, we have;

The points A and G can then be joined with a straight line and extended to form the line AG.

The correct option is therefore;

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Step-by-step explanation:

12/14= 85.7143% 19/24= 79.1667%

Answer:

44

Step-by-step explanation:

20+36+40+80= 176

176/4= 44

Answer:

explanation provided in the picture

Step-by-step explanation:

the answer is x= 55°

hopefully this helps ! :)

Answer:

c

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

43.55

Step-by-step explanation:

1. Use the distance formula on both points AC and AB.

Distance formula is this:

\(d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(1--5)^2+(8--7)^2} \\\\d=\sqrt{(6)^2+(15)^2} \\\\d=\sqrt{36+225} \\\\d=\sqrt{261} \\\\\)

Distance for AC  is  16.16

Now do the same with the numbers for AB and get the distance of 5.39

2. To get the area, use the formula 1/2 x base x height

AB is the base and AC is the height.

1/2 x 16.16 x 5.39 = 43.55

The area of triangle ABC is 43.5 square units.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The shape ABC is a triangle.

Where,

AB = Base

AC = Height

A = (1, 8)

B = (6, 6)

C = (-5, -7)

First, let's find the length of AB using the distance formula:

AB = √((6-1)² + (6-8)²)

= √(25 + 4)

= √(29)

Next, let's find the length of AC using the distance formula:

AC = √((1-(-5))² + (8-(-7))²)

= √(36 + 225)

= √(261)

The area of the triangle ABC can be found using the formula:

Area = (1/2) x base x height

We know that AB is the base and AC is the height,

Area = (1/2) x AB x AC

Area = (1/2) x √(29) x √(261)

Area = (1/2) x √(7569)

Area = (1/2) x 87

Area = 43.5

Therefore,

The area of triangle ABC is 43.5 square units.

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The equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is 16 = 2 1/2 + 2 1/4b (option b)

To start with, we know that the farmer picks 16 quarts of berries. Out of those, 2 1/2 quarts cannot be used, which means the farmer has 16 - 2 1/2 quarts of berries that can be used to make jam.

Now, the recipe requires 2 1/4 quarts of berries to make one batch of jam. Let's represent the number of batches of jam the farmer can make with the remaining berries as "b".

Therefore, the equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is written as,

=> 16 = 2 1/2 + 2 1/4b

Hence the correct option is (b).

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Answer:

The statement that is a claim that cannot be supported is **D. Smith Delivery Service will improve a person's business**. This statement is a claim because it asserts that using Smith Delivery Service will have a positive impact on a person's business. However, there is no evidence provided in the advertisement to support this claim.

Answer:

60

Step-by-step explanation:

let X be the total number of students.

48÷x *100 = 80

4800= 80x

X = 60 students

Answer: -36

Step-by-step explanation:

when k=6

-6(6)

-36

Answer:

-36

Step-by-step explanation:

\(-6k\\k=6\)

Since we know that the value of 'k' is 6, we can replace 'k' with 6.

\(-6k\) ⇒ \(-6*6\)

\(=-36\)

----------------------------------------

Reminders:

- Remember, whenever there is a variable next to a number, this means that you should multiply the value of the variable by the coefficient.

- Coefficient: the number in front of a variable.

- Variable: a symbol (usually a letter) standing in for an unknown value.

- Do not get confused by the word "evaluate." This simply means to solve.

- A negative number multiplied by a positive number will always equal a negative number.

Problem

Henry purchased compact disks for $112. The compact discs cost $16 each.

Which of the following equations could you use to find how many compact disks, x, Henry purchased?

Solution

We can set up the following notation:

x= number of disks

total cost = (number of disks)* (unitary price)

Total cost = $112

number of disks =x

unitary price = $16

Replacing we got:

112 = x*16

For this case the correct equation would be given by:

$112 = $16x

Answer:

25.1 cm

Step-by-step explanation:

4 * 2 * 3.142 = 25.136 = 25.1 cm

yes, he is right all distance is the same from the origin point to any side of the circle same as radius which is half a line starts at any side of the circle and ends at the origin point.

Mason is correct.

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

A circle centered at the origin with a radius of 4 units can be represented by the equation:

x² + y² = r²

Substituting the coordinates of the point (4, 4), we have:

4² + 4² = r²

16 + 16 = r²

32 = r²

Taking the square root of both sides, we get:

r = 4√2

Therefore,

The circle centered at the origin with a radius of 4 units has an equation of x^2 + y^2 = 32.

Point (4, 4) satisfies this equation since:

4² + 4² = 32

16 + 16 = 32

32 = 32

Thus,

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

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a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Answer:

Length = 12 inches

Width = 14 inches

Step-by-step explanation:

Formula for perimeter of a rectangle is;

P = 2(L + W)

Where;

L is length

W is width

We are told that the length is 2 inches shorter than its width. Thus;

L = (W - 2)

Thus,perimeter is now;

P = 2(W - 2 + W)

P = 2(2W - 2)

P = 4W - 4

We are told that the perimeter is 52. Thus;

4W - 4 = 52

4W = 52 + 4

4W = 56

W = 56/4

W = 14 inches

From L = (W - 2) ;

L = 14 - 2

L = 12 inches