Answer: They will travel about 131.18 yards.
Step-by-step explanation:
Given : A football field is 120 yards long by 53 yards wide.
We know that a football field is rectangular in shape.
Each interior angle in a rectangle is a right angle.
Then, by Pythagoras theorem, we have
(Diagonal)² = (Length)² + (Width)²
If a player runs diagonally from one corner to the opposite corner, then the length of the diagonal is given by :-
[tex](\text{Diagonal})=\sqrt{(120)^2+(53)^2}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{14400+2809}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{17209}\\\\\Rightarrow\ (\text{Diagonal})=131.183078177\approx131.18\text{ yards}[/tex]
Hence, they will travel about 131.18 yards.
Final answer:
The distance a player would travel running diagonally across a football field that is 120 yards long and 53 yards wide is approximately 131.183 yards.
Explanation:
The student asked about the distance a player would travel if they ran diagonally from one corner to the opposite corner of a football field that is 120 yards long and 53 yards wide.
To solve this, we need to apply the Pythagorean theorem in which the length and width of the football field will be the legs of the right triangle and the diagonal the player runs will be the hypotenuse.
The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.
Therefore, the calculation will be as follows:
(120 yd)² + (53 yd)² = c².
Simplifying,
14400 yd² + 2809 yd² = c².
Adding these together gives us 17209 yd², and taking the square root of that gives us the length of the diagonal, which is the distance the player will travel.
Thus, c = √17209 yd2 ≈ 131.183 yards.
The sum of Rodney and his sister is 31 his sister is five years less than three times Rodney’s age what is the difference in age between Ronnie and his sister
Answer: The difference in their ages is 13.
Step-by-step explanation: We shall start by assigning letters to represent the age of each one of them, that is the unknown variables. So, we shall call Rodney’s age r, and his sister’s age we shall call t. If the sum of Rodney and his sister’s age is 31, then we can write this as an expression,
r + t = 31
Also three times Rodney’s age can be written as 3 times r, or simply put, 3r. So five years less than three times Rodney’s age is equal to 3r - 5. Hence his sister’s age is equal to 3r - 5, or simply put,
t = 3r - 5
What we now have is a pair of simultaneous equations
r + t = 31 ————(1)
t = 3r - 5 ————(2)
We shall use the substitution method here. From equation (2), t = 3r - 5. So we shall substitute for the value of t into equation (1).
r + t = 31 now becomes
r + 3r - 5 = 31
4r - 5 = 31
Add 5 to both sides of the equation
4r -5 + 5 = 31 + 5
4r = 36
Divide both sides of the equation by 4
r = 9.
That means Rodney’s age is 9.
If from equation (1) r + t = 31, we can now insert the value of r in order to find t.
r + t = 31
9 + t = 31
Subtract 9 from both sides of the equation
t = 22.
That means his sister’s age is 22 while Rodney’s age is 9.
Therefore the difference in age between Rodney and his sister is
22 - 9 which equals 13.
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots
are located
x2 + 3x -4 = 0
Answer:
x = 1 and x = -4
Step-by-step explanation:
Step 1: Factor and find the roots
x^2 + 3x - 4 = 0
(x - 1)(x + 4)
x - 1 + 1 = 0 + 1 and x + 4 - 4 = 0 - 4
x = 1 and x = -4
Answer: x = 1 and x = -4
Graph Below:
Fabio has run 5/8 of the race what fraction of the race remains?
Answer:
3/8
Step-by-step explanation:
The total race is equal to 1. Rewriting this as 8/8. We subtract the part of the race that as already been run from the total and that is the part that remains
8/8 - 5/8 = 3/8
3/8 remains
If A varies directly as b and A=6, when b=1/3, find the equation that relates A and b.
Answer:
A = 18b
Step-by-step explanation:
A = kb
6 = k(⅓)
k = 6×3
k = 18
A = 18b
Answer:
a = 18b
Step-by-step explanation:
Given that a varies directly as b then the equation relating them is
a = kb ← k is the constant of variation
To find k use the condition that a = 6 when b = [tex]\frac{1}{3}[/tex] , thus
k = [tex]\frac{a}{b}[/tex] = [tex]\frac{6}{\frac{1}{3} }[/tex] = 18
a = 18b ← equation of variation
Colton has math and reading homework tonight. Colton can solve each math problem in 3 minutes and he can read each page in 1.5 minutes. The number of pages Colton read is twice the number of math problems he solved. and it took him 54 minutes to complete all of his homework. Determine the number of math problems Colton solved and the number of pages he read.
Answer:
12 math problems and 12 pages.
Step-by-step explanation:
Reading=1.5x
Soling math=3x
1.5x+3x=4.5 minutes. Add like terms together.
4.5x=54 minutes. Divide both sides by 4.5 to get x. So x=12 minutes.
1.5x=18 minutes. 3x=36 minutes
If 1 problem took him 3 minutes,what about 36 minutes??
Now divide 36 by 3. The answer is 12 problems.
If 1 page took 1.5 minutes, what about 18 minutes?? So divide 18 by 1.5 and you will get 12 pages .
Colton solved 9 math problems and read 18 pages.
Since Colton has math and reading homework tonight, and he can solve each math problem in 3 minutes and he can read each page in 1.5 minutes, and the number of pages Colton read is twice the number of math problems he solved, and it took him 54 minutes to complete all of his homework, to determine the number of math problems Colton solved and the number of pages he read, the following calculation must be performed:
3X + 2 x 1.5X = 54 3X + 3X = 54 6X = 54 X = 54/6 X = 9 3 x 9 + 1.5 x 9 x 2 = X 27 + 27 = X 54 = X
Therefore, Colton solved 9 math problems and read 18 pages.
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Simplify the difference. (–7x – 5x4 + 5) – (–7x4 – 5 – 9x)
A) –14x4 + 10x + 10
B) 2x4 + 2x + 10
C) –14x4 – 10x + 10
D) 2x4 + 2x + 8
What points names the ordered -4 -2
Do any students own bicycles a statistical question?
Answer:
yes
Step-by-step explanation:
Answer:
yes it is because a in statistical question, you need to collect data. A non statistical question is where you don't need any data to find out the answer.
I hope this helped!!!
create a pattern for the rule a x +2
What is the algebraic way to solve 2000 (X -0.03)= 6000 by using the dividing each side first method
To solve the equation 2000 (X - 0.03) = 6000, divide both sides by 2000 to get X - 0.03 = 3, and then add 0.03 to each side to find X = 3.03.
Explanation:To solve the algebraic equation 2000 (X - 0.03) = 6000 using the divide each side method, we can follow these steps:
Divide both sides of the equation by 2000 to isolate the term with the variable X.This simplifies the equation to X - 0.03 = 3.Add 0.03 to both sides to solve for X.This gives us X = 3.03 as the solution.Now X has been isolated, and we have found the value that satisfies the equation.
What is the perimeter of an isosceles trapezoid whose base 1 is 39ft, base 2 is 27ft and height is 12ft
Step-by-step explanation:
Given one is an isosceles trapezoid. Hence its non-parallel sides are equal.
In order to find the Perimeter of trapezoid, we need to find the length of non-parallel sides
Length of non-parallel sides can be obtained using Pythagoras theorem as given below:
[tex]Length \: of \: non-parallel \: sides \\ = \sqrt{ {(diff. \: of \: bases)}^{2} + ({height)}^{2} } \\ = \sqrt{ {(39 - 27)}^{2} + {(12)}^{2} } \\ = \sqrt{ {12}^{2} + {12}^{2} } \\ = \sqrt{2 \times {12}^{2} } \\ = 12 \sqrt{2} \\ = 12 \times 1.414 \\ = 16.968 \\ = 16.97 \: ft \\ \\ perimeter \: of \: trapezoid \\= 39 + 27 + 2 \times 16.97 \\ = 66 + 33.94 \\ = 99.94 \: ft[/tex]
Suppose a population of 50 crickets doubles in size every 4 months. How many crickets will there be after 5 years?
1,500 crickets
1,600 crickets
2,000 crickets
1,638,400 crickets
Answer:
Starting population of crickets is 50. It doubles in size every 4 months.
5 years = 60 months
60 : 4 = 15
The equation is:
f ( x ) = 50 * 2^x ( an exponential function )
f ( 15 ) = 50 * 2^15 = 50 * 32,768
f ( 15 ) = 1,638,400
Answer: A ) 1,638,400
how many solutions does this system of Equations have x-2y=2 y=-2x+5
Answer:
One solution: x=2.4, y=0.2
Step-by-step explanation:
x-2y=2
y=-2x+5
x-2(-2x+5)=2
x+4x-10=2
5x=2+10=12
x=12:5=2.4
y=-2x+5=-2*2.4+5=-4.8+5=0.2
Find the area of this parallelogram. Be sure to include the correct unit in your answer
Area of the parallelogram = 96 yd²
Solution:
The formula to calculate area of the parallelogram = Base × Height
Base of the parallelogram = 8 yd
Height of the parallelogram = 12 yd
To find the area of the parallelogram:
Area of the parallelogram = Base × Height
= 8 yd × 12 yd
= 96 yd²
Area of the parallelogram = 96 yd²
Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s?
units
Answer: Line s = 17 units
Step-by-step explanation: Please refer to the attached diagram.
The triangle ACD is drawn and labeled such that line BD extends from point D and forms a right angle at point D. A careful observation shows that we now have two right angled triangles. One is DAB and the other is DCB. The unknown side ‘s’ lies on triangle DAB, hence we shall use the available dimensions in DAB. Line AD or a, is the hypotenuse (side facing the right angle). We can now apply the Pythagoras theorem since we have been given the other two sides.
The theorem states that,
AD^2 = DB^2 + AB^2
AD^2 = 15^2 + 8^2
AD^2 = 225 + 64
AD^2 = 289
Add the square root sign to both sides of the equation
AD =17.
Therefore, s measures 17 units
The line BD drawn perpendicular to side AC forms two right triangles with
the side s being of the hypotenuse side.
The value of s is 17Reasons:
The given parameters are presented ;
The given triangle = ΔACD
The points on the line BD are; Point B on side AC and point D
Line BD forms a right angle
Line AD = s
Length AB = 8
Length BC = 5
Line BD = 15
According to Pythagorean theorem, we have;
[tex]\overline{AD}[/tex]² = [tex]\overline{BD}[/tex]² + [tex]\overline{AB}[/tex]²
Which gives;
[tex]\overline{AD}[/tex]² = 15² + 8² = 289
[tex]\overline{AD}[/tex] = √289 = 17
Therefore;
[tex]\overline{AD}[/tex] = s = 17
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-2x+y=5
-7x+9y=56
I don't know the answer, and I don't understand the material.
Answer:
what do you need to do plz give the question
Step-by-step explanation:
9. Jady got a job at Yogurt land. She makes $17 per hour as a store manager. On Friday she worked 6 hours, on Sunday
she worked 4 hours and on Wednesday she worked 5 hours. When she picked up her paycheck her mom reminded her
that she owed her $65 for a pair of shoes she bought her. How much money did she have left after paying back her
mom (before taxes)?
steps ?
Answer:
190$
Step-by-step explanation:
6+4+5=15 (Hours per day she worked)
15*17=255 (The money Jady got from her paycheck)
255-65=190 (The money Jady owes her mom)
what value of x makes the equation true?
x+41=-90
i need help
Answer:
Step-by-step explanation:
x+41=-90 (original problem)
-41 -41 (you must get rid of the common factors by doing the opposite on both sides)
x= -132 (add -90 and -41 to get -132)
A manufacturing plant is looking at units shipped for a 3-year period. In 2005, the plant shipped 12,500 units. In 2008, the
plant shipped 16,000 units. Find the rate of change of units shipped over the 3-year period.
A. 3,500/
2,008
B. 3,500/
2,005
C. 3,500/3
D. 9,500
Option C - 3500/3
Step-by-step explanation:
Step 1 :
Number of units shipped in the year 2005 = 12,500 units
Number of units shipped in the year 2008 = 16,000 units
Time period = 3 years
We have to determine the rate of change of units over the 3 year period. This is obtained by dividing the difference in units by the time period.
Step 2:
The difference in units over the 3 year period = 16000 - 12,500 = 3500 units.
Hence the required change rate over the 3 year period = 3500/3
Option C is the answer.
If u is inversely proportional to the square of v and u is 4/9 when v is 3, find u when v is 8
Answer:u=1/16
Step-by-step explanation:
u is inversely proportional to v^2
u=k× 1/v^2
u=k/v^2
When U=4/9 when v=3
4/9=k×1/3^2
4/9=k×1/9
4/9=k/9
Cross multiply
4×9=k×9
36=9k
Divide both sides by 9
36/9=9k/9
4=k
When v= 8, u=?
u=k/v^2
Recall k=4
u=4/8^2
u=4/64
u=1/16
16k + 24, can you show work?
Answer:yes
Step-by-step explanation:
Answer:
k = -1.5
Step-by-step explanation:
Step 1: Solve for k
16k + 24 - 24 = 0 - 24
16k / 16 = -24 / 16
k = -3/2
k = -1.5
Answer: k = -1.5
Before lunch, Carol hiked 3 5/8 miles. After lunch, she hiked another 2 7/8 miles. How far did she hike altogether?
6 6/8 or 6 3/4 simplified
Step-by-step explanation:
First, add 5/8 and 7/8
Next, divide the sum of 5/8 and 7/8 (which is 1 4/8)
Lastly, add the wholes and 1 from 4/8
A data set consists of the following data points:
(2,4),(4,7), (5, 12)
The line of best fit has the equation y = 2.5x - 1.5. What does this equation
predict for a value of x = 7?
0
O A. 16
O B. 19
O C. 20.5
O D. 175
0 0 0
Answer: when x=7 the answer is 16
Step-by-step explanation:
The intensity I of a light a distance x meters beneath the surface of a lake decreases exponentially. From the illustration, find the depth at which the intensity will be 60%. (Round your answer to the nearest meter.)
Answer:
6m is the answer
Step-by-step explanation: We have rounded numbers down and the correct answer is 6.25 =60% in the illustration it measures 70% =6m rounded up from 5.6
If we refer to reduction r to find meters and input m in the equation to find percent at 6m shown. We can re-arrange at point 6(6m)100 = 36 (6m)100=36/6 =6m 1/100 = 0.6. or 0.6/6 =1 To find ?r we can show 0.6 as 6r = 0.6 x 100 6r=10 6/10= 4r reduction etc.. 60% to work this out. Based on isolated data of only 6ft being shown and compare the relation with that 0-30%. and 0-40% in change of data with 6= 30% decrease = r = 6.25 as 6ft is r4 within reduction to 1dp. =3.2 which could be 3.2x 100=+30 etc rearrange and 3.2 x100 =32 +30 is 6.2
The requried depth at which the intensity will be 60% is 9 meters.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
Let the y be the intensity at distance x below the surface,
Now, exponential function representing the scenario is given as,
y = abˣ
Where,
a = 100%,
b = constant of variability.
Now,
for x = 0, y = 100%,
a = 100% - - - - (1)
And x = 6, y = 70%,
70 = ab⁶ - - - (2)
Dividing equation 1 by 2,
Gives b = 0.9423
Now,
y = 100(0.9423)ˣ
Put y = 60
60 = 100(0.9423)ˣ
x = 8.69
x≈ 9 meters
Thus, the requried depth at which the intensity will be 60% is 9 meters.
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i will mark as brainliest whoever gets this question
The division axiom states that both sides of an equation can be divided by the same number except 0, without changing the value of the equation
Answer:
This is true
Step-by-step explanation:
Take for example 10=5x, you would divide both sides by 5 without changing anything to the equation.
In a case like 5=0x, you can't divide both sides by 0, so the solution is undefined.
Answerrrrrrrr nowwww
Answer:
a is equal to 22 because 11 times 2 is 22
Answer:
A is 22
Step-by-step explanation:
1/2 = 0.5
0.5×22=11
Averi was trying to factor 4x2 + 20x - 16. She found
that the greatest common factor of these terms was 4
and made an area model:
What is the width of Averi's area model?
Answer:
The width will be [tex]x^{2} +5x-4[/tex]
Step-by-step explanation:
Thinking process:
Let the model be:
[tex]4x^{2} +20x-16[/tex]
factoring out 4 gives:
[tex]4(x^{2} +5x-4)[/tex]
Factorizing the expression in the parentheses gives:
[tex]4(x^{2} +5x-4)[/tex]
Therefore, since the expression in the parentheses cannot be factorized further, the expression is:
[tex]length = 4 units\\width = x^{2} +5x-4[/tex]
The width of the area model is x^2 + 5x - 4
How to determine the width?The area model is given as:
Area = 4x^2 + 20x - 16
Factor out 4 from the expression
Area = 4(x^2 + 5x - 4)
Express as product
Area = 4 * (x^2 + 5x - 4)
4 represents the length.
So, the width of the area model is x^2 + 5x - 4
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Melissa Sartini's gross pay is $52,000 a year. The state income tax rate is 3% of taxable wa
a married exemption for herself and her husband. Using Figure 2.3. how much is withheld a year for state
income tax?
After accounting for exemptions, Melissa's tax is calculated by multiplying her taxable income by the state income tax rate. Due to missing information regarding the value of exemptions, we've assumed Melissa's entire gross pay is taxable. Therefore, she pays $1,560 per year in state income tax.
Explanation:Based on the information presented in your question, we're to determine state income tax withholdings for an individual named Melissa Sartini. First, we need to subtract any allowable exemptions from Melissa's annual gross pay. In this question, the figures for the married exemptions are not provided so we'll have to assume that Melissa's taxable income is still $52,000.
To calculate the tax, we simply multiply her taxable income by the state income tax rate. The state income tax rate is given as 3%, so we convert 3% to a decimal (0.03) and multiply by $52,000. This gives us:
$52,000 * 0.03 = $1,560
Therefore Melissa has $1,560 withheld each year for state income tax.
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Order this fraction from largest to smallest
1/4, 1/2, 1/5, 2/3, 1/6
For the same numerator, bigger denominators mean smaller fractions (if everything's positive). 2/3 is bigger than all the other ones , which are 1/2 or less.
Answer: 2/3, 1/2, 1/4, 1/5, 1/6
Simplest form of 7/10 and 2/10
Answer:
7/10 can't be simplified, 2/10->1/5
Step-by-step explanation:
7/10 cannot be simplified as 7 and 10 don't have any common factors other than 1
2/10 can be simplified by a factor of 2 to get 1/5
Answer:
Simplest form of 7/10=7/10
Simplest form of 2/10=1/5
Step-by-step explanation:
7/10 is 7/10 because it cannot be simply none has the same factors.