Tanya is training a turtle for a turtle race. For every 1/3 of an hour that the turtle is crawling, he can travel 2/23 of a mile. At what unit rate is the turtle crawling?

The region enclosed by the given curve is integrated with respect to y and the area is 21.33 square units.

In this question,

The curves are x = 4 - y^2 -------- (1) and

x = y^2 - 4 ------- (2)

The limits of the integral can be found by solving these two curves simultaneously.

On equating (1) and (2),

[tex]4 - y^2 = y^2 - 4[/tex]

⇒ [tex]4 +4 = y^2 +y^2[/tex]

⇒ [tex]8= 2y^2[/tex]

⇒ [tex]y^2=\frac{8}{2}[/tex]

⇒ [tex]y^2=4[/tex]

⇒ y = +2 or -2

The limits of y is {-2 < y +2} or 2{0 < y < 2}

The diagram below shows the region enclosed by the two curves.

The region enclosed by the given curves can be integrated with respect to y as

[tex]A=2\int\limits^2_0 {[(4-y^{2})-(y^{2}-4 )] } \, dy[/tex]

⇒ [tex]A=2\int\limits^2_0 {[4-y^{2}-y^{2}+4 ] } \, dy[/tex]

⇒ [tex]A=2\int\limits^2_0 {[8-2y^{2} ] } \, dy[/tex]

⇒ [tex]A=2[8y-\frac{2y^{3} }{3} ]\limits^2_0[/tex]

⇒ [tex]A=2[8(2)-\frac{2(2)^{3} }{3} ][/tex]

⇒ [tex]A=2[16-\frac{16}{3} ][/tex]

⇒ [tex]A=2[\frac{48-16}{3} ][/tex]

⇒ [tex]A=2[\frac{32}{3} ][/tex]

⇒ [tex]A=\frac{64}{3}[/tex]

⇒ [tex]A=21.33[/tex]

Hence we can conclude that the region enclosed by the given curve is integrated with respect to y and the area is 21.33 square units.

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The maximum area is achieved when the rectangle is a square of side 6 feet, with a domain, 0 < x < 12.

The perimeter available with Brayden is 24 feet.

The width of the rectangle is assumed to be x feet.

The length can be calculated using the formula:

2(length + width) = perimeter,

or, 2length + 2width = perimeter,

or, 2length = perimeter - 2width,

or, length = (1/2)(perimeter - 2 width).

Substituting the values, we get:

length = (1/2)(24 - 2x).

The area can be calculated using the formula:

Area = length*width.

Substituting the values, we get:

Area = (1/2)(24 - 2x)x = (1/2)x(24 - 2x).

Now, we need to maximize the area for the given perimeter.

For that, we differentiate the area function, with respect to its width x.

d(Area)/dx = (1/2)(24 - 2x) + (1/2)x(-2),

or, d(Area)/dx = 12 - x - x = 12 - 2x ... (i).

To check for the point of inflection, we equate this to zero, to get:

12 - 2x = 0,

or, 2x = 12,

or, x = 6.

To check whether this is maximum or  minimum, we differentiate (i) with respect to x to get:

d²(Area)/dx² = -2 which is less than 0, implying area is maximum at x = 6.

Thus, the maximum area is achieved when the width is 6 feet.

Length = (1/2)(24 - 2x) = (1/2)(24 - 2*6) = (1/2)12 = 6.

Thus, the maximum area is achieved when the length is 6 feet.

The area function is, area = (1/2)x(24 - 2x).

We know that the area is always greater than 0, thus, we can show that:

(1/2)x(24-2x) > 0,

or, x(24 - 2x) > 0,

or, x(12 - x) > 0, which is true when 0 < x < 12.

Thus, the domain of the area function is 0 < x < 12.

Thus, the maximum area is achieved when the rectangle is a square of side 6 feet, with a domain, 0 < x < 12.

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Answer: 170 marbles

Step-by-step explanation: Rani had 20 more marbles than Seema and Seema had 150. 150+20 is 170.

Answer:

5.5

Step-by-step explanation:

For the first fold, we cut the 11-inch side in half, resulting in an 8.5-by-5.5-inch piece. After the second fold, we have a 4.25 by 5.5 piece after halving the 8.5 inch side. The length is 5.5 inches.

Answer:

sub -2 into 12x^3 - 15

h(-2) = 12(-2)^3 -15

        = -111

hope this helps!!!! If it's incorrect I'm sorry :(

Answer:

[tex]h(-2) =\boxed{ \bf -111}[/tex]

Step-by-step explanation:

The function [tex]h(x)[/tex] is defined as:

[tex]h(x) = 12x^3 - 15[/tex]

To calculate the value of [tex]h(-2)[/tex], we have to replace the [tex]x[/tex] in the definition of [tex]h(x)[/tex] with -2:

[tex]h(-2)[/tex] = [tex]12(-2)^3 - 15[/tex]

       ⇒ [tex]12(-8) -15[/tex]

       ⇒ -96 - 15

       ⇒ -111

Answer:

The y-intercept is (0, 0).

Step-by-step explanation:

The y-intercept is where the line passes through the y-axis.

Please see attachment.

Hope this helps!

The function f(x) = ∛x - 3 is positive at the interval (3, oo)

The function is given as:

f(x) = ∛x - 3

The function is positive when the function value is greater than 0

This is represented as:

f(x) > 0

So, we have the following inequality expression

∛x - 3 > 0

Take the cube of both sides

x - 3 > 0

Add 3 to both sides

x > 3

Express as an interval notation

(3, oo)

Hence, the function f(x) = ∛x - 3 is positive at the interval (3, oo)

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If the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

Given that the arc of a circle measures 250 degrees.

We are required to find the range of the central angle.

Range of a variable exhibits the lower value and highest value in which the value of particular variable exists. It can be find of a function.

We have 250 degrees which belongs to the third quadrant.

If 2π=360

x=250

x=250*2π/360

=1.39 π radians

Then the radian measure of the central angle is 1.39π radians.

Hence if the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

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Answer:

Simplified: 2x/15 + 5y/8

Step-by-step explanation:

Simplify the expression.

Answer:

Answer: 2x/15 + 5y/8

Step-by-step explanation:

Just Simplify the expression dude.

(A) Algorithms are mathematical formulas placed in software that performs an analysis on a data set.

Therefore, (A) algorithms are mathematical formulas placed in software that performs an analysis on a data set.

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Answer:

TRUE

Since , Angle ABD is congruent or equal to Angle CBD

we know that sides opposite to equal angles are also equal.

i.e AD and CD are opposite sides to angles ABD and CBD respectively.

So, AD = CD

The ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10.

A ratio is a number representing a comparison between two named things.

StartFraction 2 Over 5 EndFraction = StartFraction 6 Over 10 EndFraction = StartFraction 8 Over 20 EndFraction = StartFraction 12 Over 30 EndFraction

2/5 = 6/10 = 8/20 = 12/30

2/5 = 0.4

6/10 = 0.6

8/20 = 0.4

12/30 = 0.4

Therefore, the ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10

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Answer:

[tex]x = 3.5[/tex]

[tex]y\approx1.666666667[/tex]

Step-by-step explanation:

To solve simultaneous equations, at least one of our variables must have the same coefficient. We can easily multiply the first equation by 4 to get 12y on both sides, so let's do that:

[tex]8x + 12y = 8[/tex]

No let's subtract the second equation from the first equation to get the third equation:

[tex]2x = 7[/tex]

Solve:

[tex]x = 3.5[/tex]

Now, we can substitute this value into one of the original equations - let's use the second one:

[tex]21 + 12y = 1[/tex]

Solve:

[tex]12y = - 20[/tex]

[tex]y = - \frac{ - 20}{12} = \frac{ - 10}{6} = - \frac{5}{3} \approx - 1.66666666667[/tex]

Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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Transforming the function using f(x - h) shifts its graph h units to the right. Here, we have h = -4, so the graph exists shifted 4 units to the left.

The transformations of functions describe how to graph a function that exists moving and how its shape exists being changed. There exist basically three kinds of function transformations: translation, dilation, and reflection.

Let f(x) = x³ be the original function.

When -5 exists added to the y-value, it moves the point on the graph down 5 units. Compared to f(x), g(x) exists 5 units down.

f(x) = (x + 4)³ - 5

= [x- (- 4) ]³ - 5 (shift 4 units in the negative x direction that exists 4 units left)

Transforming the function using f(x - h) shifts its graph h units to the right. Here, we have h = -4, so the graph exists shifted 4 units to the left.

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His body temperature in the evening is 102.6 °F

The given parameters are:

Temperature in the morning = 99.2°F.

Temperature increase = 3.4°F.

His body temperature in the evening is calculated as:

New = Temperature in the morning + Temperature increase

So, we have

New = 99.2°F +  3.4°F

Evaluate the sum

New = 102.6 °F

Hence, his body temperature in the evening is 102.6 °F

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His average rate of speed for the entire trip is 12.8 miles per hour.

Marty's speed is =V

[tex]\frac{3}{4} V+\frac{1}{2} V=8*2[/tex]

         [tex]\frac{5}{4} V=16[/tex]

           [tex]V=12.8[/tex]

The average rate of speed for the entire trip is 12.8 miles per hour.

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The solutions using the relevant theorems are:

13. x = −3 or x = 4

14. x = 12

15. x = 12

16. x = 1/2 or x = 4

17. x = 5

18. x = −1 or x = 6

The midsegment of a triangle that joins two sides of a triangle divides the two sides proportionally based on the triangle midsegment theorem.

The angle bisector of a triangle, according to the angle bisector theorem divides the opposite angles sides in a proportional manner.

The theorem states that when three or more lines that are parallel is cut across by two transversals, they are divided by the transversal proportionally.

13. Apply the angle bisector theorem:

x/3 = (x + 4)/(x + 2)

Cross multiply

x(x + 2) = 3(x + 4)

x² + 2x = 3x + 12

x² + 2x - 3x - 12 = 0

x² - x - 12 = 0

Factorize

x = −3 or x = 4

14. Apply the angle bisector theorem:

16/x = 12/9

x(12) = (16)(9)

12x = 144

x = 12

15. Apply the angle bisector theorem:

(x - 4)/6 = x/9

9(x - 4) = 6x

9x - 36 = 6x

9x - 6x = 36

3x = 36

x = 12

16. Apply the triangle midsegment theorem:

3x/(x + 4) = (x - 1)/(x - 2)

Cross multiply

3x/(x + 4) = (x - 1)/(x - 2)

(x - 1)(x + 4) = 3x(x - 2)

x² + 3x - 4 = 3x² - 6x

x² + 3x - 4 - 3x² + 6x = 0

-2x² + 9x - 4 = 0

Factorize

x = 1/2 or x = 4

17. Apply the Parallel Lines and Proportionality Theorem:

(x + 3)/(2x + 2) = (2x + 2)/(4x - 2)

Cross multiply

4x² + 10x - 6 = 4x² + 8x + 4

4x² + 10x - 6 - 4x² - 8x - 4 = 0

2x - 10 = 0

2x = 10

x = 5

18. Apply the angle bisector theorem:

(2x + 3)/x = (x + 4)/(x - 2)

Cross multiply

(2x + 3)(x - 2) = x(x + 4)

2x² - x - 6 = x² + 4x

2x² - x - 6 - x² - 4x = 0

x² - 5x - 6 = 0

Factorize

x = −1 or x = 6

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Answer:

Trapezoidal prism

Step-by-step explanation:

As long as only two sides of two of the faces are parallel, and the other four faces have two sets of parallel sides, this is a trapezoidal prism.

Answer:

it is a Trapezoidal prism

The coordinates of F is (8.5, 7)

The coordinates of the points are given as:

D = (-2, -5)

F = (5, 3)

DF : FE = 4 : 2

Rewrite the ratio as

m = 4 : 2

The coordinate of the partition is calculated as:

F = 1/(m + n) * (mx2 + nx1, my2 + ny1)

This gives

(5, 3) = 1/(4 + 2) * (4 * x + 2 * -2, 4 * y + 2 * -5)

Evaluate the sum and the product

(5, 3) = 1/6 * (4x - 4, 4y - 10)

Multiply both sides by 6

(30, 18) = (4x - 4, 4y - 10)

By comparison, we have:

4x - 4 = 30

4y - 10 = 18

Solve the equations

x = 8.5

y = 7

So, we have:

F = (8.5, 7)

Hence, the coordinates of F is (8.5, 7)

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Answer:

12.5%

Step-by-step explanation:

27-24=3

3/24=1/8

1/8=0.125

0.125 in percent is 12.5%

The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.

First, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.

The word more will be represented for the add symbol (+). Thus,

the algebraic expression is 6+7x.

The expression 3*(n+8) can be represented for the sentence:

The triple of the sum between the numbers n and 8.

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Using a quadratic regression equation, it is found that the prediction of y when x = 6 is of -154.70.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(-1, -2.75), (0, 2.15), (1, -1.60), (2, -13.85), (3, -34.55).

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = -4.721428571x² + 1.482857143x + 3.201428571

Hence, when x = 6, the prediction is:

y = -4.721428571 x 6² + 1.482857143 x 6 + 3.201428571

y = -154.70

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The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.

In this case we have a quadratic equation whose domain is stated. The domain of a function is the set of x-values associated to only an element of the range of the function, that is, the set of y-values of the function. We proceed to evaluate the function at each element of the domain and check if the results are in the choices available.

x = - 9

y = (2 / 3) · (- 9)² - 6

y = 48

x = - 6

y = (2 / 3) · (- 6)² - 6

y = 18

x = - 3

y = (2 / 3) · (- 3)² - 6

y = 0

x = 0

y = (2 / 3) · 0² - 6

y = - 6

x = 3

y = (2 / 3) · 3² - 6

y = 0

x = 6

y = (2 / 3) · 6² - 6

y = 18

x = 9

y = (2 / 3) · 9² - 6

y = 48

The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.

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Answer:

5) 26

6) 18

Step-by-step explanation:

Substitute the value of the variables in the expression and evaluate.

x = 2 ; y = -3 and z = 1

Absolute value:  Absolute value of a real number is the non negative a value of x without regard its sign.

Example: I-3I = 3

               I 3I = 3

5) 24 + Ix - 4I =24 + I 2 - 4I

                      = 24 + I-2I

                      = 24 + 2

                      = 26

6) 13 + I 8 +y I = 13 + I 8 + (-3)I

                       = 13 + I 5 I

                       = 13 + 5

                       = 18

Answer:

8km  5mi

Step-by-step explanation:

20x400=8000meters a km = to 1000meters

8000/1000=8km

A mile is a kilometer/ 1.6  8/1.6=5 miles

Sanford ran approximately 8 kilometers and about 4.97 miles.

Given that a coach made someone run 20 laps on a 400 m track.

We need to find the number of mile he ran as well as number of kilometers he ran.

To find out how many kilometers Sanford ran, we can use the fact that 1 kilometer is equal to 1000 meters.

Similarly, to find out how many miles he ran, we'll use the conversion factor of 1 mile being equal to approximately 1609.34 meters.

Let's calculate it:

1 lap = 400 meters

20 laps = 20 x 400 = 8000 meters

Kilometers:

8000 meters ÷ 1000 meters/kilometer = 8 kilometers

Miles:

8000 meters ÷ 1609.34 meters/mile ≈ 4.97 miles

So, Sanford ran approximately 8 kilometers and about 4.97 miles.

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TRUE

The safety triangle tries to predict safety performance.

The accident triangle, also known as Heinrich's triangle or bird's triangle, is a theory of occupational injury prevention. Indicates the relationship between serious accidents, minor accidents, and near misses. The idea is that the fewer minor accidents, the fewer serious accidents.

The process safety triangle is used to illustrate the different actions that can lead to an accident. This tool has a bottom up flow where each layer can be thought of as a preventative measure to the layer above it.

One of the main purposes of the process safety triangle is to explain how unsafe actions can lead to serious accidents. The Process Safety Triangle is also used to visualize different layers of protection and redesign systems to ensure better preventive practices. The lowest level of unsafe actions is categorized as the primary metric. A leading indicator is a preventive action taken to prevent an incident from occurring. Dangerous behavior by employees. B. Not wearing personal protective equipment or missing a system layer of protection is a major cause of process safety incidents. The wider the base of the process safety triangle, the wider the top level. This triangle shows that the more unsafe your actions are, the more likely you are to die in a process safety incident.

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Answer:

(2,4)

Step-by-step explanation:

1. Add the 2 x-values together, then divide. The resulting number is the x-value of the midpoint. -4+8=4 and 4/2=2, so the x-value is 2

2. Do the above steps (add & divide) for the two y-values. 6+2=8 and 8/2=4, so the y-value is 4

3. put the two values together in a coordinate pair & you have your midpoint! so if x=2 and y=4, then the midpoint is (2,4)

hope this helps :)

Answer:

0

Step-by-step explanation:

A 0 horas, la temperature era 9.

Answer:

x=1 and y=−5

Step-by-step explanation:

Problem:

Solve y=−5x;y=x−6

Steps:

I will solve your system by substitution.

y=−5x;y=x−6

Step: Solve y=−5x for y:

Step: Substitute −5x for y in y=x−6:

y=x−6

−5x=x−6

−5x+−x=x−6+−x (Add -x to both sides)

−6x=−6

−6x/−6=−6/−6 (Divide both sides by -6)

x = 1

Step: Substitute 1 for x in y=−5x:

y=−5x

y=(−5)(1)

y=−5(Simplify both sides of the equation)

Answer:

x=1 and y=−5

Thank you,

Eddie