60. An athletic field is a 100 yd-by-40 yd rectangle with asemicircle at each of the short sides. A running track 10 ydwide surrounds the field. Find the perimeter of the outsideof the running track to the nearest tenth of a yard.
Answers
The perimeter of the outside of the running track is the sum of the lengths A, B, C, and D.
Notice that A=B=100 yd, and D=C.
To find D we compute the semi perimeter of a circle with radius:
\(r_D=\frac{40yd}{2}+10yd=30yd\text{.}\)Then:
\(D=\frac{1}{2}\pi\cdot2r_D=\pi r_D=30\pi yd\text{.}\)Therefore the perimeter of the outside of the running track is:
\(A+B+C+D=(60\pi+200)yd\text{.}\)Answer: 388.5yd.
Related Questions
5. Identify the construction that the figure represents.
congruent segments
perpendicular bisector
congruent angles
angle bisector
Answers
The construction that the figure represents is perpendicular bisector
What is perpendicular bisector?A perpendicular bisector is a line that cuts through the intersection of two other line segments at a right angle.
So, a perpendicular bisector always splits a line segment through its middle, as we can see. By definition, the word "bisect" denotes an even or uniform division.
Perpendicular Bisector Properties for AB in the figure
It cuts AB in half, or into two equal halves.
It is perpendicular to AB or at right angles to it.
The distance between each point along the perpendicular bisector from points A and B is equal.
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The rule (x, y)→(x−1, y-3) represents a translation 1 unit ____ and 3 units ____
Answers
Answer: left, down
Hope this helps.
PLEAsSEEEEEEE I NEEEED IT
Answers
Answer:
Step-by-step explanation:
-4(2w+7) simply with distributive property
Answers
Answer:
\({ \tt{ - 4(2w + 7)}} \\ = { \tt{( - 4 \times 2w) + ( - 4 \times 7)}} \\ = { \tt{ - 8w - 28}}\)
4 and 3 half's divided by 2 and 7
halfs minus 8
Answers
Answer:
4/3/2/7-8= -7
Step-by-step explanation:
A school raised $4,589 in a magazine sale. Mr. Simmon's class raised 1 of the school's total. 100 How much money, in dollars, did Mr. Simmon's class raise? Enter the number in the box.
Answers
Answer:
Money raised by Mr. Simmons class = $ 45.89
in the form, y=a(1+r)^t PLEASEEEEEE
Answers
Answer:
y
a= ——
(r + 1 )t
Step-by-step explanation:
divide both sides
Simplify the variable expression by evaluating its numerical part, and enter
your answer below.
(48-17) - w
Answer here
SUBMIY
Answers
The simplified version of the expression would be 31-w
The numerical part of the expression given is :
48-17Simplifying using Subtraction operation:
48-17 = 31Adding the alphabetical part :
31 - wTherefore, the simplified form of the expression is 31-w.
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Here is a list of numbers:
8, 18, 10, 8, 15, 8, 9, 9, 4
State the median.
Answers
Answer:
The number 15 is the median..
Answer: 9
Step-by-step explanation:
8,18,10,8,15,8,9,9,4
Write out the numbers in accending order
4,8,8,9,9,10,15,18
Find the middle number
The coordinates of the turning point of the parabola whose
equation is y = x² - 6x + 8
Answers
Answer:
y=×2-6×+7 is the answer
Susan counted a total of 36 red and green cars in the parking lot. There were 8 times as many red cars as green cars. How many red cars did Susan count?
Answers
Answer:
32 red cars.
Step-by-step explanation:
Let the red cars be denoted by R
Let the green cars be denoted by G
Translating the word expression into an algebraic equation;
\( R + G = 36\) ...........equation 1
\( R = 8G\) ...........equation 2
Substituting equation 2 into equation 1;
\( 8G + G = 36\)
\( 9G = 36\)
\( G = \frac{36}{9}\)
G = 4
The number of green cars are 4.
From, \( R = 8G\)
\( R = 8*4\)
R = 32
Therefore, the number of red cars that Susan counted are 32.
Paul Curcio earns $7.45 per hour for regular time up to 40 hours, time-and-a-half for overtime, and double time for working on holidays. Find his gross pay (in $) if he worked 6 holiday hours for a total of 58 hours Monday through Saturday.
Answers
Answer: $521.50
Step-by-step explanation:
58 hours worked
40 hours regular x $7.45 = $298
6 hours holiday x $7.45 x 2 = $89.40
58 - 46 = 12 hours overtime x $7.45 x 1.5 = $134.10
$298 + $89.40 + $134.10 = $521.50
If the zeros of a quadratic functions are -2 and 4, which graph could represent the function? A. A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10). B. A parabola declines from (negative 5 point 8, 10), (negative 5, 7), (negative 4, 0), (negative 8, negative 2), (negative 1, negative 8 point 4) and rises through (2, 0), (3, negative 6) and (3 point 9, 10). C. A downward open parabola rises from (negative 6 point 2, negative 10), (negative 5 point 2, negative 6), (negative 4, 0), (negative 3, 1) and declines through (negative 1 point 4, negative 2), (1, negative 4), (0, negative 8), and (0 point 5, 10). D. A downward open parabola rises from (negative 0 point 5, negative 10), (0, negative 8), (1, negative 4), (2, 0), (3, 1), and declines through (5, negative 4), (6, negative 8), and (6 point 5, negative 10) on the x y coordinate plane.
Answers
Option A. The only graph that could represent the function with the zeros of -2 and 4 is the graph is : A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10).
How to determine the graphThe zeros of a quadratic function are the x-values where the function equals zero (where it crosses the x-axis). In this case, you mentioned that the zeros of the function are -2 and 4.
Looking at the provided options:
A. This graph crosses the x-axis at (-2, 0) and (4, 0), which are indeed the zeros of the function. Therefore, this could be a possible representation of the function.
B. This graph crosses the x-axis at (-4, 0) and (2, 0). These are not the zeros given for the function (-2 and 4), so this graph is not a possible representation of the function.
C. This graph crosses the x-axis at (-4, 0), but it never crosses at x=4. Instead, it crosses at x=2. Therefore, this is not a possible representation of the function.
D. This graph crosses the x-axis at (2, 0), but does not cross the x-axis at x=-2. Therefore, this is not a possible representation of the function.
So, the only graph that could represent the function with the zeros of -2 and 4 is the graph provided in Option A.
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The area of the circle is square
inches and the circumference is
inches.
16л, 8л
8л, 16
O 161, 641
o 640, 165
Answers
Answer:
16л, 8л
Step-by-step explanation:
r=4
area=4*4л
=16л
circumference= 2л*4
=8л
Geometry inscribed angle
find angle x
Answers
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
The arc subtended by the marked angle is ...
360° -226° = 134°
The measure of the marked angle is half this, so we have ...
15x -8 = 134/2
15x = 75 . . . . . . . add 8
x = 5 . . . . . . divide by 15
How would I graph this equation
Y+2=-4(x+1)
Answers
y = -4x -2
it’d look like this in a graph just make sure the line goes through -2 on the y axis and -2 is the y intercept.
if you do a table you can figure out what x is
Find the arc length AB
Answers
Answer :
34.56
I hope it helps
Not sure how I would see what quadrant this is
Answers
Answer: C) Quadrant 1
Step-by-step explanation:
Answer:
Quadrant 3
Step-by-step explanation:
A=1/2(B+b)h ; solve for h
Answers
First step is to divide both sides of the equation by h
\(\frac{A}{h}=\text{ }\frac{1}{2}(B+b)\)Now you have to invert the equation, to do so you have to power it by -1
\(\begin{gathered} (\frac{A}{h})^{(-1)}=(\frac{1}{2}(B+b))^{(-1)} \\ \frac{h}{A}=2(\frac{1}{B+b}) \end{gathered}\)Now you divide both sides by A
\(h=2(\frac{1}{B+b})(\frac{1}{A})\)Immediate help needed please.
Can you answer and explain please
Answers
The possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.
What is a quadratic equation?Any equation of the form \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)
We have a quadratic equation:
(k - 1)x² + (4k)x + k -3 = 0
Here,
a = k - 1
b = 4k
c = k - 3
As we know for distinct real roots:
D > 0
\(\rm {b^2-4ac}} > 0\)
(4k)² - 4(k-1)(k-3) > 0
\(\rm 16k^2-4\left(k-1\right)\left(k-3\right) > 0\)
\(\rm 12k^2+16k-12 > 0\)
\(\rm 3k^2+4k-3 > 0\)
\(\rm 3\left(k+\dfrac{2}{3}\right)^2-\dfrac{13}{3} > 0\)
\(\rm 3\left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{3}\)
\(\rm \left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{9}\)
\(\rm k < \dfrac{-\sqrt{13}-2}{3}\quad \mathrm{or}\quad \:k > \dfrac{\sqrt{13}-2}{3}\)
or
\(\rm k < -1.868 \quad \mathrm{or}\quad \:k > 0.535\)
Thus, the possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.
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The Jackson family has purchased dinner from a food truck in Austin TX.
They purchased one taco for $2.75 and four cheeseburgers.
If the Jacksons spent a total of $23. 75, how much was each cheeseburger?
Answers
Answer:
Each cheeseburger cost $5.25
Step-by-step explanation:
First, we must subtract the price of the taco, $2.75, from the total amount spent at dinner. This leaves us with 21 dollars.
Now, we must divide 21 by 4, this will show us the price of each cheese burger.
21 ÷ 4 = 5.25
So, each cheeseburger cost $5.25.
Help please!!!!!!!!!!!!!
Answers
Answer:
See below
Step-by-step explanation:
1. Here, we use the law of alternate interior angles. <3 and <6 are are alternate interior angles, meaning they have the same measure. We can solve x by using this equation:
3x-2=34
Add 2 to both sides
3x-2+2=34+2
3x=36
Divide both sides by 3
3x/3=36/3
x=12
2. Here, we use the law of consecutive interior angles. <4 and <6 are consecutive interior angles, meaning that the sum of their measures is equal to 180 degrees. We can solve x by using this equation:
-2x+20+6x+20=180
4x+40=180
Subtract both sides by 40
4x+40-40=180-40
4x=140
Divide both sides by 4
4x/4=140/4
x=35
3. Here, we use the law of alternate exterior angles. <7 and <2 are alternate exterior angles, meaning that their measures are the same. We can solve x by using this equation:
4x+3=x+15
Subtract both sides by 3
4x+3-3=x+15-3
4x=x+12
Subtract both sides by x
4x-x=x+12-x
3x=12
Divide both sides by 3
3x/3=12/3
x=4
4. Here, we use the law of alternate interior angles (again). <4 and <5 are alternate interior angles, meaning that they have the same measure. We can solve x by using this equation:
5x-3=3x+17
Add both sides by 3
5x-3+3=3x+17+3
5x=3x+20
Subtract both sides by 3x
5x-3x=3x+20-3x
2x=20
Divide both sides by 2
2x/2=20/2
x=10
5. Here, we use the law of consecutive interior angles (again). <3 and <5 are consecutive interior angles, meaning that the sum of their measures is equal to 180 degrees. We can solve x by using this equation:
5x-6+19=180
5x+13=180
Subtract both sides by 13
5x+13-13=180-13
5x=167
Divide both sides by 5
5x/5=167/5
x=33.4
I hope this helps!
Answer:
Here, we use the law of alternate interior angles. <3 and <6 are are alternate interior angles, meaning they have the same measure. We can solve x by using this equation:
3x-2=34
Add 2 to both sides
3x-2+2=34+2
3x=36
Divide both sides by 3
3x/3=36/3
x=12
2. Here, we use the law of consecutive interior angles. <4 and <6 are consecutive interior angles, meaning that the sum of their measures is equal to 180 degrees. We can solve x by using this equation:
-2x+20+6x+20=180
4x+40=180
Subtract both sides by 40
4x+40-40=180-40
4x=140
Divide both sides by 4
4x/4=140/4
x=35
3. Here, we use the law of alternate exterior angles. <7 and <2 are alternate exterior angles, meaning that their measures are the same. We can solve x by using this equation:
4x+3=x+15
Subtract both sides by 3
4x+3-3=x+15-3
4x=x+12
Subtract both sides by x
4x-x=x+12-x
3x=12
Divide both sides by 3
3x/3=12/3
x=4
4. Here, we use the law of alternate interior angles (again). <4 and <5 are alternate interior angles, meaning that they have the same measure. We can solve x by using this equation:
5x-3=3x+17
Add both sides by 3
5x-3+3=3x+17+3
5x=3x+20
Subtract both sides by 3x
5x-3x=3x+20-3x
2x=20
Divide both sides by 2
2x/2=20/2
x=10
5. Here, we use the law of consecutive interior angles (again). <3 and <5 are consecutive interior angles, meaning that the sum of their measures is equal to 180 degrees. We can solve x by using this equation:
5x-6+19=180
5x+13=180
Subtract both sides by 13
5x+13-13=180-13
5x=167
Divide both sides by 5
5x/5=167/5
x=33.4
I hope this helps!
Step-by-step explanation:
486 inches 162 inches 4 1/2 yards ?
Answers
Answer:
486 inches is 13.5 yards and 162 inches is 4.5 yards please mark brainlist thank you
What is the typical age of people shown in the frequency table?
Age Tallies Frequency
9 ll 2
10 llllllllllll 15
11 llll lll 8
12 ll 2
9
10
12
11
Answers
Answer:
Step-by-step explanation:
Answer:
I think the answer is ten but I don't know
Step-by-step explanation: from what I'm seeing, there aare more 10 yryes than any other age. Also meaning that ten is the typical age
I need help With this problem and D says (1,1) is the x- and y- intercept of the function
Answers
The statement which is true include the following: A. (0, 0) is the x- and y-intercept of the function.
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
By critically observing the graph (see attachment), we can reasonably infer and logically deduce that the x-intercept and y-intercept are located at the origin (0, 0).
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I need help asap thank you
Answers
Answer:
(x, -y)
Step-by-step explanation:
When you reflect across the x-axis, the point moves vertically up or down to the other side of the x-axis. The x-coordinate of the point remains the same. The y-coordinate of the point becomes the opposite of the original value.
x remains x. y becomes -y.
Answer: (x, -y)
What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
85 points -
Answers
Answer:
y ≥ -1/2x + 2y > 2x - 3Step-by-step explanation:
Find equations of each line using two points on each and then determine the inequalities.
Line 1Points
(0, 2) and (2, 1)The slope is:
m = (1 - 2)/2 = -1/2The y -intercept is 2.
The line is:
y = -1/2x + 2The shaded region is to the right and the line is solid, so the inequality is:
y ≥ -1/2x + 2Line 2Points:
(0, -3) and (2, 1)The slope is:
m = (1 - (-3))/2 = 2The y- intercept is -3The line is:
y = 2x - 3The shaded region is to the left and the line is not solid, so the inequality is:
y > 2x - 3Need ANSWER ASAP
Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid.
b) State the following for the transformed function
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
Answers
Answer:
See explanation below.
Step-by-step explanation:
Given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Part (a)The parent function of the given function is: y = sin(x)
The five key points for graphing the parent function are:
3 x-intercepts → (0°, 0) (180°, 0) (360°, 0)maximum point → (90°, 1)minimum point → (270°, -1)(See attachment 1)
Part (b)Standard form of a sine function:
\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shift (axis of symmetry: y = D)Therefore, for the given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Amplitude = -2Period = 2π/2 = πPhase shift = 45° to the rightEquation of axis of symmetry: y = 1Part (c)See attachment 2.
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/rHmvQCSFzLuN7xkVIxhNC3hToKfYa2ZX.png)
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/RTeQ1nKnPwOJZpxZH6e5ecn6PqRfr3g0.png)
At an amusement park, riders must be at least 48 inches tall to ride the Night Eagle roller coaster. Keenan has grown 1.5 inches since last summer, but he is still too short to ride. Let x represent how tall Keenan was last summer. Which inequality describes the problem?
Answers
The inequality that describes the given word problem is;
x + 1.5 < 48
How to solve Inequality word problems?Let x represent how tall Keenan was last summer. Thus;
x = Keenan's height last summer in inches
If he was x inches last summer, and has since grown an additional 1.5 inches up to date, then it means that his total height now is;
x + 1.5 inches.
The conditons state "riders must be at least 48 inches tall to ride the Night Eagle roller coaster". So it means that his height must be equal to 48 inches, or larger than 48 inches, to make him eligible to ride the roller coaster.
But since he is still too short to ride, this means the expression x+1.5 is smaller than 48 and as such the inequality of this problem is;
x + 1.5 < 48
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A health club charges a one-time sign-up fee and a monthly membership fee. The
equation y = 28x + 50 represents what the health club charges. Find the rate of
change.
Answers
Answer:
The rate of change is 28.
Step-by-step explanation:
The equation is in slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept.