Is (-3,2) a solution to the system of equations below ?

The perimeter of the composite shape is approximately 55.1 feet

The area of the composite shape is approximately 236.7 square feet

The area of a composite shape is the sum of the area of the components of the shape

The diameter of the semicircle, D = 15 feet

The width of the rectangle, W = 4 feet

The length of the rectangle, L = The diameter of the semicircle = 15 feet

The area of each of the semicircle, A = π·D²/8

The area of the two semicircle, 2·A = 2 × π·D²/8

Therefore;

2·A = 2 × π ×15²/8

Area of a rectangle = Length × Width

Area of the rectangle = W × L

Therefore;

Area of the rectangle = 4 × 15 = 60

Area of the composite shape = 2 × π ×15²/8 + 60 ≈ 236.7

Area of the composite shape = 236.7 ft²

The perimeter of the semicircular parts, \(P_s\) = π × D

Therefore; \(P_s\) = π × 15 = 15·π

The exposed perimeter of the rectangle = 2 × 4 = 8

Perimeter of the composite shape = 15·π + 8 ≈ 55.1

The perimeter of the composite shape is approximately 55.1 feet

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Answer:

1. No solution.

2. (-1,3)

3. (2,0)

4. (1,0)

Step-by-step explanation:

Hope it helps.

To determine the rate at which the angle θ, between the ladder and the ground is changing, we need to establish a relationship between the angle θ and the given variables.

Let's assume the ladder is leaning against a wall, forming a right triangle with the ground. The ladder acts as the hypotenuse, and the angle θ is the angle opposite to the height of the wall.

Given that the length of the ladder is decreasing at a constant rate of 2 ft/s, we can express this as dh/dt = -2 ft/s, where h represents the height of the wall.

Using trigonometry, we know that sin θ = h/l, where l represents the length of the ladder. Taking the derivative of this equation with respect to time t, we get:

d/dt(sin θ) = d/dt(h/l)

Differentiating both sides using the chain rule, we have:

cos θ * dθ/dt = (dl/dt * h - dh/dt * l) / l²

Since dl/dt is given as -2 ft/s and dh/dt is given as -2 ft/s, we can substitute these values into the equation:

cos θ * dθ/dt = (-2 * h - (-2) * l) / l²

Simplifying further:

cos θ * dθ/dt = (-2h + 2l) / l²

Now, to find the rate at which the angle θ is changing (dθ/dt), we need to know the values of h and l at a specific point in time. Without additional information or specific values for h and l, we cannot determine the exact rate at which θ is changing.

In summary, the rate at which the angle θ is changing (dθ/dt) depends on the specific values of h and l at a given time.

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Answer:

13

Step-by-step explanation:

\(Sin = \frac{opp}{hyp} \\cos= \frac{adj}{hyp} \\tan = \frac{opp}{adj}\)

=> get the length of the diag on bottom

\(tan x = \frac{3}{4} x = 36.87\) degree

\(sin(36.87)=\frac{3}{y}\)

y is about 5

=> calculate max length of stick

\(tan\left(x\right)\:=\frac{5}{12}, x= 22.62degree\)

\(sin\left(22.62\right)\:=\:\frac{5}{x}\)

which is 13

Answer:

9hours

Step-by-step explanation:

The total temperature would be decreased by 18°C.

18/2 =9

The final displacement of Jane is approximately 11.281 miles in the direction of approximately 88.8 degrees clockwise from the positive x-axis.

To solve this problem, we can use vector addition to find the final displacement of Jane.

Step 1: Determine the components of each displacement.

The southwest direction can be represented as (-5.0 miles, -45°) since it is in the opposite direction of the positive x-axis (west) and the positive y-axis (north) by 45 degrees.

The direction 70 degrees north of the west can be represented as (8.0 miles, -70°) since it is 70 degrees north of the west direction.

Step 2: Convert the displacement vectors to their Cartesian coordinate form.

Using trigonometry, we can find the x-component and y-component of each displacement vector:

For the southwest direction:

x-component = -5.0 miles * cos(-45°) = -3.536 miles

y-component = -5.0 miles * sin(-45°) = -3.536 miles

For the direction 70 degrees north of west:

x-component = 8.0 miles * cos(-70°) = 3.34 miles

y-component = 8.0 miles * sin(-70°) = -7.72 miles

Step 3: Add the components of the displacement vectors.

To find the total displacement, we add the x-components and the y-components:

x-component of total displacement = (-3.536 miles) + (3.34 miles) = -0.196 miles

y-component of total displacement = (-3.536 miles) + (-7.72 miles) = -11.256 miles

Step 4: Find the magnitude and direction of the total displacement.

Using the Pythagorean theorem, we can find the magnitude of the total displacement:

\(magnitude = \sqrt{(-0.196 miles)^2 + (-11.256 miles)^2} = 11.281 miles\)

To find the direction, we use trigonometry:

direction = atan2(y-component, x-component)

direction = atan2(-11.256 miles, -0.196 miles) ≈ -88.8°

The final displacement of Jane is approximately 11.281 miles in the direction of approximately 88.8 degrees clockwise from the positive x-axis.

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Answer:

i would say 62 but im not completely sure. but i THINK its 62. sorry if its wrong

1)

a. 4

b. 9

c. -7

d. -23

2)

a. F

b. F

c. T

d. F

3)

a. 100 -66 =34

b. 78 x 3 = 234

c. 36 + 24 = 60

d. 4 x 17 x 3 = 204

21)

a. -9 + (-12)

= - 9 - 12

= - 21

b. -17 + (3)

= -17 + 3

= - 14

c. 24 + ( -11 )

= 24 - 11

= 13

d. - 15 + (-10)

= - 15 - 10

= - 25

e. - 63 + ( -42) + 8

= - 63 - 42 + 8

= - 97

f. 101 + ( -11 ) + ( -100 )

= 101 -11 - 100

= - 10

To ensure that each of the three friends has a fair chance of being selected to drive first on their road trip, they can use the method of flipping a coin. Here's a step-by-step explanation:
1. Mark, Anthony, and Derek can gather together and agree to use a coin flip method to determine who will drive first.
2. They can designate one person to be the flipper, who will toss the coin into the air.
3. Before flipping the coin, they should establish what each side of the coin represents. For example, they can agree that heads means Mark drives first and tails means Anthony drives first.
4. The flipper then tosses the coin into the air, allowing it to spin and fall back down.
5. Once the coin lands, they can check the result and determine who will drive first based on the agreed-upon assignment for each side of the coin.
6. If Mark and Anthony are not selected to drive first, it automatically means that Derek will be the one to drive first.

Using the coin flip method ensures fairness because it provides an equal chance for each friend to be selected. It relies on chance rather than personal preferences or biases, making it an unbiased way to decide who will drive first on their road trip.

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Answer:

\(\Large \boxed{\mathrm{E}}\)

Step-by-step explanation:

The x-intercept is when y = 0.

\(y = 3x + 1\)

Let y = 0.

\(0=3x+1\)

Subtracting 1 from both sides.

\(-1=3x\)

Dividing both sides by 3.

\(\frac{-1}{3} =x\)

The x-intercept is negative.

A measurement scale in which respondents are asked to rank items based on their preferences is called an ordinal scale, not a nominal scale. the answer is False.

A statement is a declarative sentence that expresses a complete thought or idea and can be either true or false. In other words, a statement is an assertion or a claim that can be evaluated based on its factual accuracy or logical validity.

False.

A measurement scale in which respondents are asked to rank items based on their preferences is not a nominal scale. It is called an ordinal scale.

Nominal scales are used to categorize data into groups or classes based on their attributes or characteristics, such as gender, race, or color. In nominal scales, the categories do not have an inherent order or ranking.

Therefore, A measurement scale in which respondents are asked to rank items based on their preferences is called an ordinal scale, not a nominal scale. the answer is False.

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Since candy costs $6 per pound, it implies that p pounds of candy costs:

So $6p will be spent on candy.

Since less than $44 will be spent on candy. it follows the required inequality is:

Solve for p in the inequality:

Note that the number of pounds, p should be a positive number hence, the possible number of pounds that can be bought will be non-negative:

Answer:

\(x\textdegree = 120\textdegree\)

Step-by-step explanation:

Because alternate exterior angles (of a transversal that intersects parallel lines) are congruent, the bottom left interior angle of the triangle is 55º.

Using this information, we can solve for the bottom right interior angle of the triangle (denoted θ) by setting the sum of the measures of the triangle's interior angles to 180º.

\(55\textdegree + 65\textdegree + \theta = 180\textdegree\)

↓ subtract 55º and 65º from both sides

\(\theta = (180-55-65)\textdegree\)

↓ simplify

\(\theta = 60\textdegree\)

Now that we have the measure of the triangle's bottom right interior angle, we can solve for xº because an interior angle of a triangle and its corresponding exterior angle are supplementary (their angle measures add to 180º).

\(\theta + x\textdegree = 180\textdegree\)

↓ plug in the solved value for θ

\(60\textdegree + x\textdegree = 180\textdegree\)

↓ subtract 60º from both sides

\(x\textdegree = (180 - 60)\textdegree\)

↓ simplify

\(x\textdegree = 120\textdegree\)

Answer:

4000 meters

Step-by-step explanation:

Shortest run was 5 laps (2000 meters), and longest was 15 (6,000 meters)

Answer:

25% or 1/4 chance

Step-by-step explanation:

The coin has 2 possibilities. The dice has 6 but since we’re using evens and odds we can split into 2 possibilities.

Heads + even number = 25%

Heads + odd number = 25%

Tails + even number = 25%

Tails + odd number = 25%

Answer:

20 in^2

Step-by-step explanation:

(base 1 + base 2) * height

then divide that by two

The expression (x - 10)(60 - 3x) represents Elliot's profit based on the price per key chain, where x is the price in dollars that Elliot charges for each key chain.

The expression can be interpreted as follows:

x - 10 represents the revenue Elliot makes from each key chain, as it's equal to the price per key chain minus the cost of materials for each key chain.

60 - 3x represents the number of key chains Elliot can make and sell, as it's equal to the maximum amount of money Elliot has minus the total cost of materials for all key chains.

So, (x - 10)(60 - 3x) represents Elliot's total profit, which is equal to the revenue from each key chain multiplied by the number of key chains Elliot can make and sell.

In other words, Elliot's profit is proportional to both the price he charges per key chain and the number of key chains he can sell at that price. The expression captures this relationship and can be used to determine Elliot's profit for different prices.

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The expression (x - 10)(60 - 3x) represents Elliot's profit based on the price per key chain, where x is the price in dollars that Elliot charges for each key chain.

The expression can be interpreted as follows:

x - 10 represents the revenue Elliot makes from each key chain, as it's equal to the price per key chain minus the cost of materials for each key chain.

60 - 3x represents the number of key chains Elliot can make and sell, as it's equal to the maximum amount of money Elliot has minus the total cost of materials for all key chains.

So, (x - 10)(60 - 3x) represents Elliot's total profit, which is equal to the revenue from each key chain multiplied by the number of key chains Elliot can make and sell.

In other words, Elliot's profit is proportional to both the price he charges per key chain and the number of key chains he can sell at that price. The expression captures this relationship and can be used to determine Elliot's profit for different prices.

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At t = 1.5 the height is 119 feet.

Distance is the measurement of an object from a specific point in the horizontal direction, and height is the measurement of an object in the vertical direction.

Without actually measuring the distances, heights, or angles, one of the principal applications of trigonometry is to determine the angles subtended by any object at a particular position, the height of the object, or both.

Given:

A window washer drops a tool from their platform 155 ft high.

and, polynomial =  -16t² + 155 tells us the height, in feet.

Now, the height after after t = 1.5 seconds.

h(t) = -16r² + 155

h(1.5) = -16t² + 155

h(1.5) = -16(1.5)² + 155

h(1.5) = -16(2.25) + 155

h(1.5) = -36 + 155

h(1.5) = 119 feet

Hence, the height is 119 feet.

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Answer:

y = 60x + 20

Step-by-step explanation:

The number of hours that we ski is a variable cost where each hour costs $60. On top of that, we have a fixed cost of $20 which stays the same no matter how long we ski.

So we can use an equation to find the totla cost C given the number of hours t as follows:

C(t) = 60t + 20

We can use this equation to find the cost of a skiing session by plugging in some value for t. For example, if we ski for 3 hours:

C(3) = 60(3) + 20 = $200

The equation can also be written using x and y and mean the same thing.

Answer:

Step-by-step explanation:

First of all 3^2 is equal to 3*3 NOT 3*3*3

3^2 means "3 raised to the power of 2," which is equal to 3 multiplied by itself 2 times:

3^2 = 3 x 3 = 9

Therefore, 3^2 is equal to 9.

Your welcome

Answer:

4.375cm

Step-by-step explanation:

You have to look at what volume equals Volume= l×w×h so 3/2 × 5/4 × 7/3

In parallelogram LMNP,

The measure of angle N in degrees is 50°

Now, According to the question:

Let's know:

What is parallelogram?

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

The given data is :

In parallelogram LMNP, m∠L = 6x-40, m∠M = 4x+10

We know that, sum of the interior angles of parallelogram is 360°.

Here, m∠M=m∠P=4x+10

and, Here, m∠L=m∠N=6x - 40

m∠L+m∠M+m∠N+m∠P=360°

6x - 40 + 4x + 10 + 6x - 40 + 4x +10 = 360°

20x - 80 + 20 = 360°

20x - 60 = 360°

20x = 360° - 60

20 x = 300

x = 15°

Now, To find the measure of angle N in degrees.

where, m∠N = 6x - 40

Put the value of x

m∠N = 6 × 15 - 40

m∠N = 50°

Hence,  The measure of angle N in degrees is 50°

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Answer:

8 and 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

What are the factors of 40? 8 * 5

8 + 5 = 13

To do it algebraically gives you a quadratic:

A + B = 13

AB = 40

A(13 - A) = 40

A2 - 13A + 40 = 0

(A - 8)(A - 5) = 0

A = 8 and B = 5

Answer:

h = (3×V)/ (pi×r²)

Step-by-step explanation:

\(v = \frac{\pi {r}^{2} h}{3} \)

\(3 \times v = \pi {r}^{2} h\)

\(h = \frac{3v}{\pi {r}^{2} } \)

Answer:

Step-by-step explanation:

mean : added up the values and divide the result by the number of the values

Mr Jones = (5 + 6.25 + 5.75 + 6.50 + 8)/5 = $6.30

Mrs Jones = (5.50 + 7 + 6.25 + 5.75 + 7.75)/5 = $6.45

The difference between the two mean is 15 cents or $0.15

The value of set of side lengths can be used to construct a triangle are,

⇒ 3, 5, 7

We have to given that;

To find the set of side lengths can be used to construct a triangle.

Now, We know that;

The sum of two side of a triangle is always greater than third side.

Hence, We can check all options as;

⇒ 3, 4, 9

Since, 3 + 4 = 7 < 9

Hence, It does not form a triangle.

⇒ 3, 5, 7

Since, 3 + 5 = 8 > 7

Hence, It form a triangle.

⇒ 3,5, 8

Since, 3 + 5 = 8 = 8

Hence, It does not form a triangle.

⇒ 2, 6, 8

Since, 2 + 6 = 8 = 8

Hence, It does not form a triangle.

Thus, The value of set of side lengths can be used to construct a triangle are,

⇒ 3, 5, 7

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Answer:

-4 and 9

Step-by-step explanation:

-4 + 9 = 5

-4 x 9 = -36