The school track has eight lanes. Each lane is 1.25 meters wide. The arc at each end of the track is 180. The distance of the home straight and the radii for the arcs in the 1st 4 lanes are given.

S=85m

r1=36.5m

r2=37.75m

r3=39m

r4=40.25m


Part one: Find the radii of lanes 5 through 8 of the track. Show your work.


Part two: If Max ran around lane one, how far did he run? Show your work and explain your solution.


Part three: Max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. Show your work and round to the hundredths.


Part 4: Based on your lane choices in part three, what was the total distance Max ran in the three laps around the track?

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> the number of solved puzzles

y -----> the number of solved riddles

we know that

[tex]2x+y \geq 4[/tex]

The solution of the inequality is the shaded area above the solid line [tex]2x+y=4[/tex]

The slope of the solid line is negative [tex]m=-2[/tex]

The y-intercept of the solid line is the point (0,4)

The x-intercept of the solid line is the point (2,0)

therefore

The graph in the attached figure

Answer:

The graph that representss this scenario is attached.

Explanation:

You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.

1. Determine the expression that relates the variables.

a) The name of the variables is given:

x: number of solved puzzles

y: number of solved riddles

b) Point rules:

Each solved puzzle is worth two points: 2x

Each solved riddle is worth 1 point: 1y = y

Sum of points: 2x + y

The video game requires at least 4 points to advance: this means that the number of points must grater than or equal to 4 ⇒ 2x + y ≥ 4 .

In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.

2) Building the graph

Solve algebraically for y: y ≥ 4 - 2x

You want to draw the border line of the function, that is y = 4 - 2x

You have a linear function, so you need only two points to draw it. It is generally easier to work with the intercepts.

x-intercept (y = 0) ⇒ 2x + 0 = 4 ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)

y-intercept (x = 0) ⇒ 2(0) + y = 4 ⇒ y = 4 ⇒ point (0, 4).

In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.

Addtional constrains: x and y cannot be negative, so add the constrains:

       x ≥ 0 and y ≥ 0

The set of solutions of y ≥ 4 - 2x is the same line y = 4 - 2x and the region over the line, so you have to shade that portion of the graph, but only in the first quadrant (since x and are greater than or equal to zero).

plz give brainliest

Answer:

Step-by-step explanation:

|a| = a for a ≥ 0

|a| = -a for a < 0

============================================

|c² + b²|

Put b = -3 and c = -2 to the expression:

|(-2)² + (-3)²| = |4 + 9| = |13| = 13

Answer:

-.1

Step-by-step explanation:

The common difference in the arithmetic sequence can be found by doing term minus a previous term.

So 0.26-0.36=-.1

or 0.16-0.26=-.1

or 0.06-0.16=-.1

or -0.04-0.06=-.1

or -0.14-(-0.04)=-.1

Answer:

Area=512 square inches

Step-by-step explanation:

According to the given data;

A side of a square = (8)³/² inches.

Area of a square = ?

To find the area of a square we use the formula:

Area = s²

Area=(8)³/²)²

Area = 8³

Area= 8*8*8

Area=512 square inches....

Answer:

Step-by-step explanation:

[tex]\dfrac{10x^3 + 40x^2 + 15x}{5x}\\ \dfrac{10x^3}{5x} +\dfrac{40x^2}{5x}+\dfrac{15x}{5x}[/tex]

2x^2 + 8x + 3 is your final answer.

Answer:

18+8=26

Step-by-step explanation:

Their sum would be 18 and * because they have  difference of ten. In order o get this you would have to multiply 1 X144 and so on.

Answer:

Step-by-step explanation:

Its 134 hope this helos

Answer:

2(x-2y)/(4x-y)  =  dy/dx

Step-by-step explanation:

2x^2+y^2=8xy

Take the derivative of each term, remembering that we take the 8xy as derivative by parts)

2 * 2x dx +  *2y dy = 8 ( x dy + dx *y)

4x dx +2y dy = 8x dy + 8y dx

Subtract 2y dy from each side

4x dx +2y dy -4y dy = 8x dy - 2y dy + 8y dx

4x dx  = 8x dy - 2y dy + 8y dx

Subtract 8y dx from each side

4x dx -8y dx  = 8x dy - 2y dy + 8y dx-8y dx

4x dx -8y dx  = 8x dy - 2y dy

(4x-8y) dx = (8x-2y) dy

Factor out a 4 from the left side and a 2 from the right side

4(x-2y) dx = 2( 4x-y) dy

Cancel a 2

2(x-2y) dx = ( 4x-y) dy

Divide each side by (4x-y)

2(x-2y)/(4x-y) dx = ( 4x-y)/(4x-y) dy

2(x-2y)/(4x-y) dx =  dy

Divide by dx

2(x-2y)/(4x-y) dx/dx =  dy/dx

2(x-2y)/(4x-y)  =  dy/dx

Answer with Step-by-step explanation:

Bev earns $2 a week for taking out her neighbor’s trash cans.

Number of Weeks     Money Earned ($)

1                                      2

2                                      4

3                                      6

4                                     8

As we can see the domain is the number of weeks which is:

{1,2,3,4,...}

and Range is the money earned in dollars which is:

{2,4,6,8,...}

Step-by-step explanation:

1 * (-5) = -5     a = -5

6 + (-5) = 1      b = 1

1 * (-5 ) = -5     c = -5

-7 + -5 = -12     d = -12

The divisor of the polynomial in the synthetic long division is linear factor

The correct values are;

Reason:

[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex]

The divisor in the division is (x - (-5)) = (x + 5)

By synthetic long division, we have;

Carry down the 1 representing the leading coefficient

Multiply the 1 brought down by the zero value of x which is -5, and take the result into the second line of the division symbol

-5 × 1 = -5

Add the coefficient 6 to -5, and bring down the result

Repeat the above steps again to get;

-5 × 1 = -5

-5 × (-12) = 60

By comparison to the given synthetic long division, [tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex], we have;

a = -5, c = -5, b = 1, and d = -12

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Answer:

5/6

Step-by-step explanation:

There are 6 possible rolls

1 2 3 4 5 6

Only one of 6 is a five

Answer:

2/3

Step-by-step explanation:

To find the slope based off of two points, use the following formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in your values and simplify.

[tex]\frac{-7-1}{-3-9} \\\\\frac{-8}{-12}[/tex]

[tex]\frac{8}{12}[/tex]

[tex]\frac{2}{3}[/tex]

Answer:

2/3

Step-by-step explanation:

I like the line up and subtract strategy. At the end you just put 2nd number over 1st.

This is the slope formula; just a different way to think about the formula.

(9,1)

-(-3,-7)

=======

12, 8

So the slope is 8/12=2/3.

Answer:

q=0

r=2

s=3

t=-3

Step-by-step explanation:

q represents the value we should get from evaluating d(-8).

[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]

To find d(-8) we use this function here labeled d and replace x with -8:

[tex]d(-8)=-\sqrt{\frac{1}{2}(-8)+4}[/tex]

[tex]d(-8)=-\sqrt{-4+4}[/tex]

[tex]d(-8)=-\sqrt{0}[/tex]

[tex]d(-8)=0[/tex]

So q is 0 since d(-8)=0.

r represents the value we should get from evaluating f(0).

[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]

To find f(0) we use this function labeled f and repalce x with 0:

[tex]f(0)=\sqrt{\frac{1}{2}(0)+4}[/tex]

[tex]f(0)=\sqrt{0+4}[/tex]

[tex]f(0)=\sqrt{4}[/tex]

[tex]f(0)=2[/tex]

So r is 2 since f(0)=2.

s represents the value we should get from evaluating f(10).

[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]

To find f(10) we use this function labeled f and replace x with 10:

[tex]f(10)=\sqrt{\frac{1}{2}(10)+4}[/tex]

[tex]f(10)=\sqrt{5+4}[/tex]

[tex]f(10)=\sqrt{9}[/tex]

[tex]f(10)=3[/tex]

So s is 3 since f(10)=3.

t represents the value we should get from evaluating d(10).

[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]

To find d(10) we use the function labeled d and replace x with 10:

[tex]d(10)=-\sqrt{\frac{1}{2}(10)+4}[/tex]

[tex]d(10)=-\sqrt{5+4}[/tex]

[tex]d(10)=-\sqrt{9}[/tex]

[tex]d(10)=-3[/tex]

So t is -3 since d(10)=-3

q=0

r=2

s=3

t=-3

Answer:

(7, 3), (–1, –1) and (2, 8) are at a distance of  units from (2, 3).

Step-by-step explanation:

We know that the formula of distance is given by:

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

So substituting the given points points to check which points are at a distance of 5 units from [tex](2,3)[/tex].

1. (2, 3) and (7, 3):

[tex]\sqrt{(7-2)^2+(3-3)^2} =\sqrt{25} = 5[/tex]

2. (2, 3) and (–1, –1):

[tex]\sqrt{(-1-2)^2+(-1-3)^2} =\sqrt{25} = 5[/tex]

3. (2, 3) and (0, 3):

[tex]\sqrt{(0-2)^2+(3-3)^2} =\sqrt{4} = 2[/tex]

4. (2, 3) and (2, 8):

[tex]\sqrt{(2-2)^2+(8-3)^2} =\sqrt{25} = 5[/tex]

5. (2, 3) and (-7, 6):

[tex]\sqrt{(-7-2)^2+(6-3)^2} =\sqrt{90} =9.5[/tex]

Answer:

Step-by-step explanation:

The correct answer are A B and D

I just took the test

Answer with Step-by-step explanation:

Let ?=x

We have to find the value of x in:

[tex](-b^3+3b^2+8)-(x-5b^2-9)=5b^3+8b^2+17[/tex]

Adding [tex]b^3[/tex] on both sides, we get

[tex]-b^3+3b^2+8-x+5b^2+9+b^3=5b^3+8b^2+17+b^3[/tex]

[tex]3b^2+8-x+5b^2+9=5b^3+8b^2+17+b^3[/tex]

Combining the like terms on both side, we get

[tex]8b^2+17-x=6b^3+8b^2+17[/tex]

Subtracting both sides by 8b², we get

[tex]8b^2-x+17-8b^2=6b^3+8b^2+17-8b^2[/tex]

[tex]-x+17=6b^3+17[/tex]

subtracting both sides by 17, we get

[tex]-x+17-17=6b^3+17-17[/tex]

[tex]-x=6b^3[/tex]

Dividing both sides by -1, we get

[tex]x=-6b^3[/tex]

Hence, ? = [tex]-6b^3[/tex]

Answer:

Option C (d = 14n + 50).

Step-by-step explanation:

The observations for Year 1, 2, 3, and 4 are 64, 78, 92, and 106 respectively. It can be observed that the difference between second term and the first term is 78 - 64 = 14. This is also true for the third term and the second term. In fact, the difference between the terms is fixed. This means that the sequence is an arithmetic sequence, in which the difference between the terms is fixes for all the terms. The nth term in this case is defined as:

S = a + (n-1)*d; where S is the output at a given n, a is the first term, n is the position, and d is the common difference. In this question, S = ducks (d), a = 64, and d = 14. Therefore, plugging in the values in the above formula gives:

d = 64 + (n-1)*14.

d = 64 + 14n - 14.

d = 14n + 50.

Therefore, the model which best describes the amount of ducks that will be in the pond during the nth year is d = 14n + 50, i.e. Option C!!!

Answer: Third Option

[tex]a_n =14n+50[/tex]

Step-by-step explanation:

By subtracting consecutive terms from the number of ducks each year you will get a common difference of 144.

[tex]78-64 = 14\\92-78 = 14\\106-92 = 14[/tex]

This means that the data can be modeled by the equation of an arithmetic sequence

The arithmetic sequences have the following form:

[tex]a_n = a_1 + d(n-1)[/tex]

Where [tex]a_1[/tex] is the first term and d is the common difference between the consecutive terms.

So :

[tex]a_1 = 64[/tex]

[tex]d = 14[/tex]

Then the equation is:

[tex]a_n = 64 + 14(n-1)[/tex]

[tex]a_n = 64 + 14n-14[/tex]

[tex]a_n =14n+50[/tex]

Answer:

43.75 liters.

Step-by-step explanation:

125% = 1.25 as a decimal fraction.

number of liters of milk = 35 * 1.25

= 43.75 liters.

Answer:

96

Step-by-step explanation:

64 -[16 x (-3) – 2 x{17 – 25 }]​   I'm going to take a couple of steps that are very small and they can be combines along with other steps. Combine 16*-3

64 - [-48 - 2*(17 - 25)]            Combine what is inside (17 - 25)

64 - [-48 - 2*(-8)]                    Combine -2*-8

64 - [-48 + 16]                         Combine what is in the brackets.

64 - [-32]                                 Remove the brackets

64 + 32                                    Combine

96

The trick in this question is the signs.

Answer: [tex]x=129\°[/tex]

Step-by-step explanation:

By definition, it is important to remember that:

[tex]Angle\ formed\ by\ two\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex])

You can observe in the figure that "x" is an Angle formed by two chords, therefore, you can find its value applying the formula.

Therefore, the value of "x" is this:

[tex]x=\frac{1}{2}(204\°+54\°)\\\\x=\frac{1}{2}(258\°)\\\\x=129\°[/tex]

Answer:

75 dollars

Step-by-step explanation:

If an item is 50 and you want to markup 50%, you must find 50% of 50 to find how much the item will go up by from 50.

So 50% of 50 means 50% times 50.

50%=.5 or 1/2

So .5(50)=25.

The item is going up by 25 dollars.

So we started at 50 dollars.

So 50+25 is going to be the new amount.

50+25=75 is the new amount.

$75

In this question, it's asking you to find the selling price of an item after the markup.

We know that:

With the information above, we can find the answer.

A markup is pretty much an increase in a price. This means that in this context, the item's price increased by 50%

We're going to need to find how much the selling price is after the markup.

We would multiply 50 by 1.5 to find the selling price.

[tex]50*1.5=75\\\\\text{Or you can do it this way}\\\\50*0.5=25\\\\50+25=75[/tex]

With either method, you're still going to get 75.

This means that the selling price of the item after applying the markup value is $75

Answer:

62 DEGREES

Step-by-step explanation:

TWO ANGLES=2A

LARGEST ANGLE=A+3

2A+A+3=180

3A=180-3=177

A=177/3=59

LARGEST ANGLE=59+3=62

Answer:

The Largest Angle angle has a measure of 62 degrees.

Step-by-step explanation:

In triangle ABC, angle ABC equals to angle ACB.

and BAC is the largest angle.

Let angle measure of ABC and ACB angles be "x" degree.

then, measure of third angle i.e BAC will be "x + 3" degrees.

Since sum of all angles of any triangle is 180 degree.

so,  first angle + second angle + third angle = 180

       x  + x + (x + 3) = 180

        3x  = 180 - 3

         3x = 177

          x = 59 degrees

So, First angle = 59 degree

     Second angle = 59 degree

     Third Angle = 62 degree.

The Largest Angle angle has a measure of 62 degrees.

     Measure of angle 'x' given in the picture will be 36°.

  From the picture attached,

In ΔABD,

m∠DAB = x° [Given]

AB ≅ BD [Isosceles triangle]

Therefore, opposite sides of the given triangles will measure the same.

m∠BAD = m∠BDA = x°

m∠BAD + m∠BDA + m∠ABD = 180° [By triangle sum theorem]

x° + x° + m∠ABD = 180°

m∠ABD = 180°- 2x°

m∠DBC + m∠ABD = 180° [Linear pair of angles]

m∠DBC + (180° - 2x) = 180°

m∠DBC = 2x°

In isosceles ΔBCD,

BD ≅ CD

Therefore, m∠DBC = m∠BCD = 2x°

In isosceles ΔACD,

Since, AC ≅ AD,

Therefore, m∠ACD = m∠ADC = 2x°

By applying triangle sum theorem in ΔACD,

m∠ACD + m∠DAC + m∠CDA = 180°

2x° + x° + 2x° = 180°

5x° = 180°

x = 36°

   Therefore, measure of 'x' will be 36°.

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Answer:

-1/100

Step-by-step explanation:

-(10)^-2

Exponents first

We need to make the negative in the exponent positive, which means move it to the denominator

-1

--------

10^2

-1

---------

100

Answer:

-1/100

Step-by-step explanation:

10^(-2) becomes 1/100.

-(10)^(-2) is -1/100.

Answer:

You might want to see if I read your ordered pairs right because it was really hard to see for me:

f(2,6)=14

f(-1,3)=5

f(6,4)=14

Step-by-step explanation:

I assume they meant to write f(x,y)=x+2y.

Doing f(2,6) now.  This means replace x with 2 and y with 6:

f(2,6)=2+2(6)=2+12=14

f(2,6)=14

Doing f(-1,3) now.  This means replace x with -1 and y with 3:

f(-1,3)=-1+2(3)=-1+6=5

f(-1,3)=5

Doing f(6,4) now. This means replace x with 6 and y with 4:

f(6,4)=6+2(4)=6+8=14

f(6,4)=14

Tha values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively

Give the function expressed as:

f(x, y) = x + 2y

If the coordinate point is (2, 6), then;

f(2, 6) = 2 + 2(6)

f(2, 6) = 2 + 12

f(2, 6) = 14

If  the coordinate point is (-1, 3), then;

f(-1, 3) = -1 + 2(3)

f(-1, 3) = -1 + 6

f(-1, 3) = 5

If the coordinate point is (6, 4), then;

f(6, 4) = 6 + 2(4)

f(6, 4) = 6 + 8

f(6, 4) = 14

Hence the values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively

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Answer:

Dependent would be the number of times she rides because it would add up to how many times she could ride. 6.75= x(.45)

Step-by-step explanation:

In Jewels' ferry ride scenario, the independent variable is the number of rides taken, and the dependent variable is the total cost incurred based on the rides. This follows the general rule where the dependent variable's outcome is determined by the choice made in the independent variable.

In the scenario described, Jewels has a certain amount of money to spend on ferry rides, and each ride costs a fixed amount. Here, the number of ferry rides she can take is the independent variable, as it can be chosen freely by Jewels. The total cost of the ferry rides is the dependent variable, as it depends on the number of rides she takes.

Therefore, the correct answer is that the number of rides is the independent variable and the total cost is the dependent variable.

As for the given reference information, in the vacation resort case, the number of hours the equipment is rented is the independent variable, and the total fee is the dependent variable. This is similar to Jewels' scenario because the basic principle in both instances is about the relationship between a variable you can control (number of rides or hours) and a variable that depends on this control (total cost or total fee).

For example, if Jewels decides to ride the ferry 5 times, the total cost would be 5 rides × $0.45 per ride = $2.25. This demonstrates how the dependent variable (total cost) changes in response to a change in the independent variable (number of rides).

Answer:

the amount of green blocks = X then you'll end up with the amount of yellow blocks

Answer:

so x can be either yellow or green

Step-by-step explanation:

Ryan has total 57 blocks (total yellow and green)

if x is either of yellow or green

then 57 -x will be either green or yellow (According to x is green or yellow)

x can be either yellow or green .

To find the cost of 4 ounces of pecans, we set up a proportion comparing the cost to weight, resulting in $2.25 after rounding to the nearest cent.

To determine the cost of 4 ounces of pecans when a one-pound (16 ounces) canister costs $8.99, we set up a proportion where the cost is directly proportional to the weight.

The proportion is $8.99/16 ounces = $X/4 ounces, where X represents the cost of 4 ounces of pecans.

Multiplying both sides by 4 to solve for X gives us $X = (4 ounces × $8.99) / 16 ounces.

Simplifying this, we find that $X = $2.2475, which, when rounded to the nearest cent, gives us an answer of $2.25.

Answer:

[tex]\large\boxed{B.\ \left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+3y=7&(1)\\4x-2y=4&(2)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+3y=7\\4x-2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad6x+y=11\qquad(3)\\\\\text{Make the system of equation with (1) and (3):}\\\\\left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right[/tex]

The equivalent system of equations for the given system of equations is

option (B)

[tex]2x+3y=7\\6x+y=11[/tex]

This is obtained by adding the given equations.

Given the system of equations as

[tex]2x+3y=7\\4x-2y=4[/tex]

Adding the two equations,

[tex]2x+3y+4x-2y=7+4\\6x+y=11[/tex]

Therefore, the system of equations

[tex]2x+3y=7\\6x+y=11[/tex]

are equivalent to the given set of equations.

Thus, option (B) is correct.

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Answer:

Your grade point average would be 2.75(B- or C+)

Step-by-step explanation:

[tex]\frac{3+4+3+1}{4} \\\frac{11}{4} \\2.75[/tex]

Final answer:

Explaining the calculation of GPA based on given grades, resulting in an approximate value rounded to the hundredths place.

Explanation:

The grade point average (GPA) for the given grades can be calculated as follows:

English: 3.0 credits, B, which is 3.0 in GPA scale

Biology: 4.0 credits, B, which is 3.0 in GPA scale

Communications: 3.0, F, which is 0.0 in GPA scale

New student seminar: 1.0, A, which is 4.0 in GPA scale

Calculating the GPA:

(3.0 + 3.0 + 0.0 + 4.0) / 11 = 10.0 / 11 = 0.91

Therefore, the grade point average would be approximately 0.91 rounded to the hundredths place.

Answer:

Step-by-step explanation:

Answer "A"

Dodecahedron

Dodecahedron does not have triangular faces.

The dodecahedron is also known as pentagonal dodecahedron which is composed of 12 regular pentagonal faces, 30 edges, and 20 vertices.

A  regular icosahedron is a 3D polyhedron having 20 triangular faces, 30 edges, and 12 vertices.

A regular octahedron has 8 triangular faces, 6 vertices, and 12 edges.

A tetrahedron has 4 triangular faces, 4 vertices, and 6 edges.

All of these 3 have triangular faces.

But Dodecahedron has 12 faces which are pentagonal in shape.

Therefore Dodecahedron does not have triangular faces.

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Answer:

Vertical shift of 3 units down ⇒ last answer

Step-by-step explanation:

* Lets revise the translation of a function

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ The parent function y = √x

∵ There is a translation by k = -3

- From the rules above k is for the vertical translation

∵ k = -3

- That means the parent function translated 3 units down

∴ The value of k = -3 makes the graph of the parent function translated

   3 units down

- For more understand look to the attached graph

# y = √x ⇒ the red graph

# y = √x - 3 ⇒ the blue graph