Two turtles come from opposite sides of the road, starting at the same time and moving at the same speed. When they met, they jvere 72 inches from the right hand edge of the road. How wide is the road?​

Answer:

its b

Step-by-step explanation:

i took the test

Answer: its b cause i took the test and got it right

The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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The number of more houses between the area 150m² and 200 m² than between 250m² and 300 m² is 8.

Histogram is a graphical representation of discrete or continuous data. In other words, it is a graphical representation of distribution of data.

Therefore, the histogram has number of houses on the y-axis and area on the x -axis,

The histogram relates the number of houses to the area of the houses in square metres.

Therefore, let's find how many more houses have an area between 150m² and 200 m² than between 250m² and 300 m²?

Hence,

Houses between 150m² and 200 m²  = 9

Houses between 250m² and 300 m² = 1

Finally,

difference between them = 9 - 1 = 8 houses

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The true statement is; II. Option D

From the information given, we have that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Note that;

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Answer:

Dimensions: 18.667 x 18.667 x 14 inches

Volume: 4878.22 in3

Step-by-step explanation:

If the length plus the girth does not exceed 84 inches, we have:

\(length + (2*width+2*height) = 84\)

The box has a square base, to length = width, then we have:

\(length + (2*length+2*height) = 84\)

\(3*length+2*height = 84\)

The volume of the box is given by the equation:

\(Volume = length * width * height = length^2*height\)

From the first equation, we have:

\(height = (84 - 3*length)/2\)

Using this height in the volume equation, we have:

\(Volume = length^2*(84-3*length)/2\)

\(Volume = 42length^2-1.5*length^3\)

To find the maximum volume, we can find the value of length that makes the derivative of the volume in relation to the length equal zero:

\(dV/dl = 84length - 4.5*length^2 = 0\)

\(84length = 4.5*length^2\)

\(length = 84/4.5 = 18.667\ inches\)

So the width, the height and the volume of the package are:

\(width = length = 18.667\ inches\)

\(height = (84 - 3*18.667)/2 = 14\ inches\)

\(Volume = 42*(18.667)^2-1.5*(18.667)^3 = 4878.22\ in3\)

Answer:

\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)

Answer:

y=-3x-1

Step-by-step explanation:

hope it helps.

\(\\ \tt\longmapsto Volume=Base\times Height\)

\(\\ \tt\longmapsto Height=\dfrac{Volume}{Base}\)

\(\\ \tt\longmapsto Height=\dfrac{2.9km^3}{339km^2}\)

\(\\ \tt\longmapsto Height=0.00079km\)

\(\\ \tt\longmapsto Height=7.9m\)

We know,

Volume:-

Base × Height

Height:-

Volume/Base

Now let's solve:-

Hgt-2.9km³/339km²

Hgt-0.00079 km

Height-7.9m

Note:

Hgt means Height.

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Answer:

Step-by-step explanation:

To find the left-hand derivative of f at x = 4, we need to evaluate:

f′−(4) = limh→0−f(4+h)−f(4)h

Since f(x) = 0 for x ≤ 0 and f(x) = 5 - x for 0 < x < 5, we have:

f(4 + h) = 0 for h < -4

f(4 + h) = 5 - (4 + h) = 1 - h for -4 < h < 1

f(4 + h) = undefined for h > 1

Therefore, we can rewrite the limit as:

f′−(4) = limh→0−f(4+h)−f(4)h = limh→0−(1 - h) - 0h = -1

To find the right-hand derivative of f at x = 4, we need to evaluate:

f′+(4) = limh→0+f(4+h)−f(4)h

Using the same reasoning as before, we can rewrite the limit as:

f′+(4) = limh→0+(5 - (4 + h)) - 0h = -1

Since the left-hand derivative and the right-hand derivative are equal, we can conclude that f'(4) exists and is equal to:

f'(4) = f′−(4) = f′+(4) = -1

Therefore, the derivative of f at x = 4 is -1.

Answer:

B

Step-by-step explanation:

7 > x  means what numbers are less than 7

A  and C are not correct because 7 = 7 is not less than 7

B is correct because 7 > -2, and 7 > 0

D is not correct because 8, 10, 20 are more than 7

The answer of the sum is D. 6(9 + 5).

To rewrite the sum 54 + 30 using the distributive property as a multiple of a sum whose addends have no common factors greater than 1, we need to factor out the greatest common factor from both numbers.

The greatest common factor of 54 and 30 is 6. By factoring out 6, we can rewrite the sum as:

54 + 30 = 6 * (9 + 5)

Now, let's examine the options given:

A. 2(27 + 15) does not have a common factor of 6.

B. 3(18 + 10) does not have a common factor of 6.

C. 5(11 + 6) does not have a common factor of 6.

D. 6(9 + 5) is the correct answer because it has a common factor of 6, which is the greatest common factor of 54 and 30.

Therefore, the answer is D. 6(9 + 5).

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Explanation

We are asked to get the probability of rolling either a 2 or 6 in a single dice

To do so, we will make use of the probability definition:

Probability simply means the ratio of possible outcomes to the total number of outcomes

In our case

we have a dice, so the total outcome will be {1,2,3,4,5,6}

to roll a 2, the possible outcome is {2}

to roll a 6, the possible outcome is {6}

Thus, the probability of rolling a 2 will be

The probability of rolling a 6 will be

Therefore, the probability of rolling a 2 or 6

In per cent, we will have

To the nearest whole number, we will have 33%

Answer:

x² + 10x + 25

Step-by-step explanation:

(x + 5)(x + 5)

using FOIL method

First x•x = x²

Outside x•5 = 5x

Inside 5•x = 5x

Last  5•5 = 25

add like terms together.

Answer:

x^2 + 25 + 10x

= x^2 + 10x + 25

Step-by-step explanation:

( x + 5 )^2

Formula : -

( a + b )^2 = a^2 + b^2 + 2ab

Here,

a = x

b = 5

( x + 5 )^2

= x^2 + 5^2 + 2 ( x ) ( 5 )

= x^2 + 25 + 10x

We have 5 balls, lets name each one:

Now, we want to take 2 balls at a time, wich means the the order that i take the ball doesnt matter, so lets see the possibilities:

So, we have 10 ways to take 2 balls from 5 balls.

If want to solve the formula, we just need to remember the formula for the combinations of 5 elements taking 2:

After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.

So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)

The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.

The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:

Midpoint of JK: (1, -4)

Midpoint of J'K': (4, 1)

The slope of the vector: 3/5

(x₁ + x₂)/2, (y₁ + y₂) /2

Point-slope formula: y - y₁ = m(x - x₁)

Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)

Applying simplification , we get: y = (- 3/5)x - 1.2

To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:

y - 1 = (7/3)( x - 4)

Apply simplification , we get: y = (7/3)x - 17/3

To evaluate the intersection point, we can solve the system of equations:

y =(- 3/5)x - 1.2 = (7/3)x - 17/3

Evaluating for x and y, we get x = -6 and y = -1.

Therefore, the center of rotation is (-6, -1).

√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)

Distance between image points and center of rotation

√( ( 6 - (-6))² + ( 3 - (-1))² = 13

The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).

The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':

Angle of vector: arctan(5/3) = 59.04 degrees

Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

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The outcomes that compose this event are the 13 cards in the deck that are clubs.

We have,

The event in this case is drawing a club from the deck.

In probability theory, an event refers to a subset of the sample space, which includes all possible outcomes of an experiment.

In this case,

Kristy's experiment is drawing a card randomly from a standard deck of 52 cards, and the sample space consists of all 52 cards.

Since Kristy is interested in knowing the probability of drawing a club card, the event in this case will be the subset of the sample space consisting of all the club cards.

There are 13 club cards in a standard deck, namely, ace of clubs, 2 through 10 of clubs, jack of clubs, queen of clubs, and king of clubs.

The event will consist of these 13 cards.

Thus,

The outcomes that compose this event are the 13 cards in the deck that are clubs.

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Answer:

the mid point is 6,3

Step-by-step explanation:

the mid point is 6,3

The graph of the function f(x) = 4(2/3)^x is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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Answer:

variable

Step-by-step explanation:

Answer:

Variable

Step-by-step explanation: In exponential functions the variable is in the exponent, like m = 2ˣ.

First, do 6 divided by 4

Then, do 2 x 3

Finally, subtract the two numbers you got from the equations before and that the answer.

The coordinates of the Triangle △DEF will be (-4,-5),(0,-1),(4,-5).

What is the definition of a triangle?

Triangles are polygons with three sides and three vertices in geometry. This figure is two-dimensional and has three straight sides. A triangle has three sides that is why it is also called polygon. The sum of a triangle's three angles equals 180°. A triangle is contained inside a single plane. The triangle may be divided into three types based on its sides.

Scalene Triangle - Each side is different in length.

Isosceles Triangle - A triangle with two sides that are equal in length and one side that is not.

A triangle with three equal sides in length is a equilateral triangle.

Now,

For triangle ABC coordinates are

(-2,-1), (0,1), (2,-1)

and we have to apply transformation (x,y)→(2x,2y)→(2x,2y−3) to get coordinates of △DEF

So, first apply  (x,y)→(2x,2y) we get (-4,-2), (0,2), (4,-2)

and then apply (2x,2y)→(2x,2y−3) to get coordinates of △DEF

(-4,-5),(0,-1),(4,-5)

Hence,

          The coordinates of the Triangle △DEF will be (-4,-5),(0,-1),(4,-5).

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The volumes of the right prism are, respectively:

Case 6: V = 703.72 mm³

Case 7: V = 57905.84 mm³

Case 8: V = 3744 ft²

Case 9: V = 475.20 mm³

The volume of the sphere is:

Case 10: V = 18816.57 cm³

In this problem we find four cases of right prisms, whose volumes must be computed. This can be done with the help of following formulas:

Volume

V = A · h

Area formula - Rectangle

A = w · l

Area formula - Triangle

A = 0.5 · w · l

Area formula - Circle

A = π · r²

In addition, we need to determine the volume of a sphere:

V = (4π / 3) · r³

Where:

Now we proceed to determine the volume for each case:

Case 6

V = π · (16 mm)² ·  (14 mm)

V = 703.72 mm³

Case 7

V = π · [(40 mm)² - (32 mm)²] · (32 mm)

V = 57905.84 mm³

Case 8

V = (12 ft) · (8 ft) · (39 ft)

V = 3744 ft²

Case 9

V = 0.5 · (11 mm) · (5.4 mm) · (16 mm)

V = 475.20 mm³

Case 10

V = (4π / 3) · (16.5 cm)³

V = 18816.57 cm³

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Answer:

Step-by-step explanation:

90.00 - 75.00 = 15.00

Using the graph,  it's cheaper to use Company B instead of Company A; when the number of miles is less than 5 miles.

For us to solve this question, we need to first create an equation;

If A company initially supplies $30 and then $2 per mile, then the equation here is:

y = 2x + 30

If B company initially supplies $20 and then $4 per mile, then the equation is expressed as:

y = 4x + 20

Due to the fact that the two wages are asked to be equalized, we equate these two equations with each other and find the result.

2x + 30 = 4x + 20

2x = 10

x = 10/2

x = 5

This is the number of miles that both companies will charge a customer the same amount.

Then the time for which it is cheaper to use company B is when number of miles is less than 5.

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Step-by-step explanation:

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Answer:

34/18 is greater than 1 5/6.

Step-by-step explanation:

hope this helps. . .<3

good luck!    uωu

Answer:

greater than

Step-by-step explanation:

1=6/6 and 6+5=11, so 1 5/6= 11/6

Next, you want to find a common denominator, in this case 18

11/6=x/18

x=33

11/6=33/18

34/18 > 33/18