Two sailboats are traveling along the same path away from
a dock, beginning from different locations at the same
time. John's boat begins 15 miles from the dock and is 45
miles from the dock after 5 hours. The distance of
Roberta's boat from the dock is represented by the
function y = 5x + 20, where x represents time, in hours, and
y represents the distance, in miles, from the dock.

Answer:

2352

Step-by-step explanation:

You just multiply them

Answer:

6.2 < x < 26.6

Step-by-step explanation:

The length of a side of a triangle is between the difference and the sum of the lengths of the other two sides.

16.4 - 10.2 = 6.2

16.4 + 10.2 = 26.6

Let x = length of third side.

6.2 < x < 26.6

Answer:

non living are computer baseball phone bear  living are tree human fern and bacteria the rest i.d.k

Step-by-step explanation:

Answer:

Living: Penguin, Bear, Human, Bacteria, Tree

Nonliving: Baseball,Phone,Aluminium Can, computer

Unicellular: Euglena, Amoeba, Bacteria

Multicellular: Fern, Human, Bear, Tree,  Penguin

Answer:

I think it is the first one as you add the 4 like from the other

Answer:

154 feet squared

Step-by-step explanation:

1. Divide 14 by 2

2. Use the equation pie times radius squared

3. Answer is 153 foot squared

Answer:

The answer is x < 9

Step-by-step explanation:

The graph shows an open circle pointing to the left, which means that x is less than 9

Answer:

x is less than or equal to 9

Step-by-step explanation:

the arrow/ray is indicating that everything on and before nine is valid.

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer:

About 55.9 degrees

Step-by-step explanation:

The cosine of an angle is equivalent to the length of the adjacent side divided by the length of the hypotenuse. Therefore:

\(\cos x= \dfrac{14}{25} \\\\x=\cos^{-1}\left( \dfrac{14}{25}\right) \approx 55.9\)

Hope this helps!

Answer: 418.7

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/geometry-solids/cone.php

Answer:

A≈6163.05

Step-by-step explanation:

the formula is A=2πrh+2πr2

The area of the shaded square is 4 square centimeters, and the radius of the circle is approximately 1.41 cm.

To find the area of the shaded square and the radius of the circle, we will follow these steps:
Step 1: Identify the dimensions of the square.
From the student question, we know that the square has sides of 2 cm each.
Step 2: Find the area of the square.
The area of a square can be calculated using the formula:

Area = side × side.
In this case, the area of the square is:

2 cm × 2 cm = 4 square centimeters.
Step 3: Find the diagonal of the square.
The diagonal of a square can be found using the Pythagorean theorem:

diagonal² = side² + side².
In this case, the diagonal² = 2 cm² + 2 cm² = 4 cm² + 4 cm² = 8 cm².
Taking the square root of both sides, we get: diagonal = √8 cm ≈ 2.83 cm.
Step 4: Find the radius of the circle.
Since the circle is inscribed in the square, its diameter is equal to the diagonal of the square.

Thus, the radius of the circle is half the diagonal.
Radius = diagonal ÷ 2 ≈ 2.83 cm ÷ 2 ≈ 1.41 cm.

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(a) A total of 66 students were surveyed

(b) Those who are Math majors and not biology majors were 7

(c) Those who were neither math nor biology majors were 47

(d) Those who majored in both math and biology were 4

Step-by-step explanation:

2x + 4y = 36

2 × 4 + 4y = 36

8 + 4y = 36

4y = 36 - 8

4y = 28

y = 28 ÷ 4

y = 7

Answer:

40

Step-by-step explanation:

The middle dot of the box is the median.

Answer:

the median is 44.75

Step-by-step explanation:

first i add up all the numbers

40+37+48.5+53.5=175

then i divide them by how 4

179 divided by 4=44.75

Answer:

10 to the 4th power

Step-by-step explanation:

the decimil point was moved four spaces to the right resutiong to the 4th power.

Answer:

10 to the 4th power

Step-by-step explanation:

Explanation:

The x coordinates are -4 and 14. They add up to -4+14 = 10. Then this cuts in half to get 10/2 = 5. This is the x coordinate of the midpoint.

We'll follow this same idea for the y coordinates as well.

10+0 = 10 which cuts in half to 10/2 = 5, and this is the y coordinate of the midpoint.

Therefore, the midpoint is (5,5).

Coincidentally, the x and y coordinates are the same for the midpoint (both are 5). This won't always happen.

Answer:

A 3.14159.......

Step-by-step explanation:

We need a non rational number

3.14159 is pi which is an irrational number

1/7, .27(repeating) and .83333(repeating) can be written in the form

a/b where a and b are integers, which makes them rational

Answer:

its a

Step-by-step explanation:

....

Answer:

4x - 43

Step-by-step explanation:

7x - 28 - 3x - 15

7x - 3x - 28 - 15

4x - 43

The simplified expression is 4x - 43.

The correct option is A.

A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.

As per the information provided, it is given that,

7(x - 4) - 3(x + 5)

Expanding the brackets and simplifying, we get:

7(x - 4) - 3(x + 5)  = 7x - 28 - 3x - 15

7(x - 4) - 3(x + 5)  = 4x - 43

Therefore, the expression is 4x - 43.

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Answer:

A

Step-by-step explanation:

Answer:

-14

Step-by-step explanation:

Given -x+5y=7

Now we substitute x+5y into -2(-x+5y)

-2(-x+5y) = (-2)(7)

= - 14

Answer:

The resulting image is neither congruent or similar.

Step-by-step explanation:

Congruent triangles are the same size and shape. Because of the operations conducted on the coordinates of the triangle, it can be easily seen that the size changes. If one were to investigate further, one would see that the shape changes as well, however we only need to know that the size changes. Therefore, the triangles cannot be congruent.

Because the operations on the \(x\) and \(y\) of each point are not the same, the triangle cannot be similar. When adding to the coordinates of the first point, multiplying the coordinates of the second point, and negating the \(x\)-value of the third point the result cannot be similar. This, as mentioned earlier, is the further investigation that reveals that the triangles are not the same shape and therefore not similar.

To plant 10 acres of land, the farmer should plant 6.25 acres of corn and 3.75 acres of soybeans. This allocation maximizes the farmer's profit given the assumptions of the problem.

To determine how much of each crop to plant on 10 acres of land, we need to consider the profit per acre for each crop and the total profit that can be obtained by planting a combination of the two crops.

From the problem statement, we know that the profit per acre for corn is $300 and the profit per acre for soybeans is $200. We also know that the total amount of money available to the farmer is $2500.

Let x be the number of acres of corn to plant, and y be the number of acres of soybeans to plant. Then we have the following constraints:

x + y = 10 (the total area planted is 10 acres)

300x + 200y ≤ 2500 (the total profit cannot exceed $2500)

To solve this problem, we can use linear programming techniques. We want to maximize the objective function:

P = 300x + 200y

subject to the constraints above. We can graph the feasible region determined by the constraints, and then find the corner points of this region. The maximum value of P occurs at one of these corner points.

The feasible region is a triangle with vertices at (0, 0), (8.33, 1.67), and (10, 0). Evaluating the objective function at each of these vertices gives:

P(0, 0) = 0

P(8.33, 1.67) = $2416.67

P(10, 0) = $3000

Therefore, the maximum profit of $3000 occurs when the farmer plants 10 acres of corn and 0 acres of soybeans.

However, this requires planting more than the available land. The next best option is to plant 6.25 acres of corn and 3.75 acres of soybeans, which yields a profit of:

P(6.25, 3.75) = $2125

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The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

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The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

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The value of x in the given diagram is x = 20

From the question, we are to determine the value of x in the given diagram

In the given diagram,

We have a right angle

Thus,

The angles sum up to a right angle

That is,

x° + 2x° + (x + 10)° = 90°

x° + 2x° + x° + 10° = 90°

4x° + 10° = 90°

Subtract 10° from both sides of the equation

4x° + 10° - 10° = 90° - 10°

4x° = 80°

Divide both sides by 4

4x°/4 = 80°/4

x° = 20°

Hence, x = 20

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Answer:

X : Z = 6 : 5

Step-by-step explanation:

X : Y      =  3 :  1

Double both sides

X : Y      =  6 : 2

     Y : Z=        2 :  5

Combined

X : Y : Z     =  6 : 2 : 5

Therefor

X : Z = 6 : 5

Answer:

10 people didn't answer the servey

Step-by-step explanation:

servey=80 people

70= answered the servey

so we should take the difference:-

80–70= 10

Hope I got the right answer!