Answer:
a ≥ 18
p ≤ 275
Step-by-step explanation:
a. The inequality for the minimum age for voting in the United States is:
a ≥ 18
This inequality states that a person's age (represented by 'a') must be greater than or equal to 18 years in order to be eligible to vote in the United States.
b. The inequality for the maximum number of people that can attend a performance in the theater is:
p ≤ 275
This inequality states that the number of people (represented by 'p') attending a performance in the theater must be less than or equal to 275 in order to accommodate all attendees within the seating capacity of the theater.
Calcular el área bajo la curva de la función x^3-5x^2+2x+8 en el intervalo (1,5)
The area under the curve of the given function from x=1 to x=5 is -64.17.
The area under a curve is the area between the curve and the x-axis in a certain range. To calculate the area under a curve, we will use the definite integral of the function. The definite integral of a function f(x) from x=a to x=b is defined as
[tex]∫baf(x)dx[/tex]
For the given function f(x) = x^3 - 5x^2 + 2x + 8, the definite integral from x=1 to x=5 is
[tex]∫51(x^3 - 5x^2 + 2x + 8)dx = [x^4/4 - 5x^3/3 + x^2 - 8x]5[/tex]
Substituting x=1 and x=5 gives
[54 - 5(125)/3 + 25 - 8(5)] = -64.17
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Jake built a skateboard ramp, if the distance of the ramp is 10 ft. The ramp rises a
total of 3. 5ft. What angle does the ramp make with the ground? Round to the
nearest degree.
As per the given distance, the angle that is made by the ramp with the ground is 19.1 degrees
Let's call the angle we're trying to find theta (θ). We can use the tangent function to calculate θ, as follows:
tan(θ) = opposite / adjacent
We know the opposite side (height of the ramp) is 3.5ft, and the adjacent side (distance along the ground) is 10ft. Plugging these values into the tangent equation, we get:
tan(θ) = 3.5 / 10
We can solve for θ by taking the inverse tangent (also known as arctan) of both sides:
θ = arctan(3.5 / 10)
Using a calculator, we find that θ is approximately 19.1 degrees. Therefore, the ramp makes an angle of 19.1 degrees with the ground.
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1. Calculate the mean for each sample.
Sample #
1
234
2
3
5
6
7
8
9
O ACCESS Virtual Learning 2022
Sample Items
(1, 1, 2, 0)
(2, 2, 0, 1)
(1, 1, 1, 2)
(2,0, 1, 0)
(2, 2, 0, 1)
(1, 1, 2, 3)
(3, 2, 0, 0)
(1, 1, 1, 1)
(3, 1, 1, 1)
x
Step-by-step explanation:
1. Calculate the mean for each sample.
Sample #
1
234
2
3
5
6
7
8
9
O ACCESS Virtual Learning 2022
Sample Items
(1, 1, 2, 0)
(2, 2, 0, 1)
(1, 1, 1, 2)
(2,0, 1, 0)
(2, 2, 0, 1)
(1, 1, 2, 3)
(3, 2, 0, 0)
(1, 1, 1, 1)
(3, 1, 1, 1)
x
Company ABC is offering bonds to investors to pay for its corporate
expansion.
• Par value: $1,000 per bond
Coupon rate: 5 percent per year (fixed rate)
• Maturity: 10 years
Each year the bond would pay the bondholder the following amount:
$500.
$50.
$5.
$1,500.
$1,000.
The bond would pay the bondholder the following sum of $1,000 annually.
The bond being offered by Company ABC has a par value of $1,000, a fixed coupon rate of 5% per year, and a maturity of 10 years.
The coupon rate of 5% per year means that for each $1,000 bond, the bondholder will receive an annual interest payment of $50 (5% of $1,000).
Therefore, out of the given options, the correct amount that the bondholder would receive each year is $50.
It's important to note that this interest payment is fixed and does not change over the 10-year term of the bond. At maturity, the bondholder would receive the par value of $1,000 back from the company.
So, over the course of 10 years, the bondholder would receive a total of $500 ($50 per year) in interest payments, in addition to the return of the $1,000 par value at maturity.
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A study investigated if cell phone use impacted student drivers' reaction times. There were two groups: 27 students were assigned to the cell phone group while 27 students were assigned to the control group. The experiment measured the response time to traffic lights; for the cell phone group, the mean was 585. 3 with a standard deviation of 85. 2 and for the control group, the mean was 537. 9 with a standard deviation of 66. 3. Construct a 90% confidence interval for the difference in mean response times between the cell phone and control groups
The 90% confidence interval for the difference in mean response times between the cell phone and control group is given as follows:
(12.6, 82.2).
How to construct the confidence interval?The estimate of the differences is given as follows:
585.3 - 537.9 = 47.4.
The standard error for the distribution of each sample is given as follows:
Cell phone group: 85.2/sqrt(27) = 16.4.Control group: 66.3/sqrt(27) = 12.8.Hence the standard error for the distribution of differences is given as follows:
sqrt(16.4² + 12.8²) = 20.8.
The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 27 + 27 - 2 = 52 df, is t = 1.6747.
The lower bound of the interval is given as follows:
47.4 - 1.6747 x 20.8 = 12.6.
The upper bound of the interval is of:
47.4 + 1.6747 x 20.8 = 82.2.
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select the two values of x that are roots of this equation 2x²-11x+15=0
Answer:
[tex]x=\frac{5}{2},\:x=3[/tex]
Step-by-step explanation:
[tex]\mathrm{Factor\:}2x^2-11x+15[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]
[tex]\left(2x^2-5x\right)+\left(-6x+15\right)[/tex]
[tex]\mathrm{Factor\:out}\:x\:\mathrm{from}\:2x^2-5x:\quad \:x\left(2x-5\right)[/tex][tex]\mathrm{Factor\:out}\:-3\:\mathrm{from}\:-6x+15:\quad \:-3\left(2x-5\right)[/tex]
[tex]x\left(2x-5\right)-3\left(2x-5\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}2x-5[/tex]
[tex]\left(2x-5\right)\left(x-3\right)[/tex]
[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0[/tex]
[tex]2x-5=0\quad \mathrm{or}\quad \:x-3=0[/tex]
[tex]\mathrm{Solve\:}\:2x-5=0:\quad x=\frac{5}{2}[/tex]
[tex]\mathrm{Solve\:}\:x-3=0:\quad x=3[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=\frac{5}{2},\:x=3[/tex]
Use Pythagorean theorem to find perimeter What is the perimeter of the triangle? in units PLS HELP
Answer:
30. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
The following data represent a random sample of the number of shares of a pharmaceutical company's stock traded for 20 days in 2000. Use a normal probability plot to asses whether the sample data could have come from a population that is normally distributed. Start 4 By 5 Matrix 1st Row 1st Column 4. 78 2nd Column 9. 7 3rd Column 11. 2 4st Column 8. 32 5st Column 14. 64 2nd Row 1st Column 6. 09 2nd Column 10. 49 3rd Column 9. 74 4st Column 12. 9 5st Column 14. 05 3rd Row 1st Column 5. 04 2nd Column 9. 34 3rd Column 12. 39 4st Column 7. 55 5st Column 28. 34 4st Row 1st Column 8. 51 2nd Column 10. 94 3rd Column 5. 08 4st Column 8. 04 5st Column 11. 68 EndMatrix 4. 78 9. 7 11. 2 8. 32 14. 64 6. 09 10. 49 9. 74 12. 9 14. 05 05. 04 09. 34 12. 39 7. 55 28. 34 8. 51 10. 94 5. 08 08. 04 11. 68
we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.
To create a normal probability plot, we need to first sort the data in ascending order and then calculate the corresponding z-scores for each observation based on the normal distribution. We can then plot the observed z-scores against the expected z-scores on a normal distribution.
Here is the sorted data:
5.04 5.08 6.09 7.55 8.04 8.32 8.51 9.34 9.7 9.74
10.49 10.94 11.2 11.68 12.39 12.9 14.05 14.64 28.34
And here are the corresponding z-scores calculated based on the normal distribution:
diff
-1.77 -1.74 -1.53 -1.17 -1.04 -0.96 -0.90 -0.72 -0.67 -0.65
-0.41 -0.29 -0.24 -0.17 0.06 0.21 0.48 0.65 3.09
The plot appears to be fairly linear, which suggests that the data could have come from a population that is normally distributed. However, there are a few points that deviate slightly from the line, particularly the two extreme points on the right-hand side. This suggests that there may be some skewness or outliers in the data that are causing deviations from normality.
Overall, we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.
the complete question is :
"The following data represent a random sample of the number of shares of a pharmaceutical company's stock traded for 20 days in 2000. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.
4.78 9.7 11.2 8.32 14.64
6.09 10.49 9.74 12.9 14.05
5.04 9.34 12.39 7.55 28.34
8.51 10.94 5.08 8.04 11.68
Please create a normal probability plot and interpret your findings."
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Calculate the pressure if the force is 270N/m2 and the area is 0.03m2
If the force is 270 Newton and the area is 0.03 square meter, the pressure is equal to 9,000 N/m².
What is pressure?In Mathematics, pressure can be defined as a measure of the force exerted per unit area of an object or physical body. This ultimately implies that, it is usually measured in Newton per meter square.
How to calculate the pressure of an object?Mathematically, the pressure of a physical object can be calculated by using this formula:
P = F/A
Where:
P represents the pressure.F represents the force.A represents the area.By substituting the given parameters, we have:
Pressure, P = 270/0.03
Pressure, P = 9,000 N/m².
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Help PLEASE( HELP WITH BOTH)
Check the picture below.
[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JN}{\sin(65^o)}\implies \cfrac{39\sin(65^o)}{\sin(53^o)}=JN\implies 44.3\approx JN \\\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JS}{\sin(62^o)}\implies \cfrac{39\sin(62^o)}{\sin(53^o)}=JS\implies 43.1\approx JS[/tex]
Make sure your calculator is in Degree mode.
Milan is driving to Memphis. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Milan has 45 miles to his destination after 39 minutes of driving, and he has 26.3 miles to his destination after 61 minutes of driving. How many miles will he have to his destination after 79 minutes of driving?
The distance after 79 minutes is 11 miles.
How many miles will he have to his destination after 79 minutes of driving?We know that the distance can be modeled with a linear equation like:
y = ax + b
Where a is the slope and b is the y-intercept.
We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know the points (39, 45) and (61, 26.3)
Then we can write:
a = (26.3 - 45)/(61 - 39) = -0.85
So we can write:
y = -0.85*x + b
To find the value of b we can replace the values of one of the points, i will use (39, 45) to get.
45 = -0.85*39 + b
45 + 0.85*39 = b
78.15 = b
So the line is:
y = -0.85*x + 78.15
The distance after 79 minutes is.
y = -0.85*79 + 78.15
y = 11
The distance left is 11 miles.
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Which point represents (3, negative StartFraction 5 pi Over 3 EndFraction) ?
WILL GIVE BRAINLIEST
The point (3, -5π/3) can be represented by the formula x = 3, y = -5π/3.
The point (3, -5π/3) can be represented by the formula x = 3, y = -5π/3. To calculate this, we first find the x-coordinate, which is simply 3. To find the y-coordinate, we must first multiply 5 and π. 5π = 15.78. We then divide 15.78 by 3, which gives us 5.26. To make this a negative number, we add a negative sign, giving us -5.26. We can then convert this to fraction form by dividing the numerator and denominator by the greatest common factor, which is 1. This gives us -5π/3.
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Complete question:
What point represents (3, negative StartFraction 5 pi Over 3 EndFraction)?
Answer:
A
Step-by-step explanation:
Hind a formula that expresses the fact thet f(x,y) is a distance 8 from the origin.
The formula that expresses the fact that f(x, y) is a distance 8 from the origin can be found using the distance formula for two points on the coordinate plane, (0, 0) and (x, y).
The distance formula is given by d = √(x2−x1)2+(y2−y1)2where (x1, y1) = (0, 0) and d = 8. Thus, we have8 = √(x2−0)2+(y2−0)2Squaring both sides gives8^2 = (x2−0)2+(y2−0)2which simplifies to64 = x2+y2
Therefore, the formula that expresses the fact that f(x, y) is a distance 8 from the origin isx2+y2= 64.
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The following graph represent the cost of Nolan's
retirement party :
a.
Complete the following table that represent the cost of Nolan's
party
Guests :x
Cost :y
10
20
b.
Find the unit rate.
c. Write the relation between x and y
30
$100
$90
500
$70
$60
$40
$30
$20
$10
0
Cost of Nolan's retirement party
10 20 30 40 50 60 70 80 90 100
Guests
Answer:
See below.
Step-by-step explanation:
Please check the assumptions. I did not see a graph, so made assumptions in the calculations,
Given that for 10 guests, the total cost is $20, we can calculate a rate of $2/guest ( the unit rate). This seems too inexpensive, even for a hot dog and soft drink. But going on that, we can establish the relationship between x (the number of guests) and y (the total cost) as y = ($2/guest)*x.
The list of numbers does not provide a clear undertanding of what is being requested, The attached spreadheet calculates a number of guest options based on a rate of $2/guest. The area in green are the second list of values based on the numbers of guests.
In 2022, a customer buys 5 GE 10% debentures, M '41. The interest payment dates are Feb 1st and Aug 1st. The current yield on the bonds is 11. 76%. The bonds are callable as of 2032 at 103. The bond is trading:
The current yield of the bond is 11.76% and the yield to call is 19.51%.
The current yield of the bond can be calculated using the following formula:
Current Yield = (Annual Interest Payment/Bond Price) * 100
In this case, the annual interest payment is 10% of the face value of the bond (5 * $100 = $500). The bond price is $41, so the current yield is 11.76%:
Current Yield = ($500/$41)*100 = 11.76%.
The bond is callable at 103 as of 2032, so the call premium is 103 – 41 = 62. This means that if the bond is called, the investor will receive an additional payment of $62 per bond (5 * $62 = $310). The yield to call is the total annual return the investor will receive if the bond is called:
Yield to Call = (Annual Interest Payment + Call Premium)/Bond Price * 100
In this case, the yield to call is:
Yield to Call = ($500 + $310)/$41 * 100 = 19.51%.
This means that if the bond is called in 10 years, the investor will receive an annual return of 19.51%.
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I neeeddd this answerrr asppp plsssss
Answer: the very top answer -> A
In OH, IR = jk, mik = (11x + 2)", and mjk = (12x - 7).
What is the measure of ik)?
mik) =
Intro
Done
The measure of ik in the given equation can be calculated by subtracting the sum of IR (which is equal to jkh) and mjk from 180e degrees.
In order to calculate the measure of ik in the given equation, we must use the formula for interior angles of a triangle which is the sum of all angles in a triangle is 180 degrees. In this equation, we are given the measures of two of the angles, IR and mjk. Therefore, the measure of ik can be calculated by subtracting the sum of IR and mjk from 180 degrees.
Given that IR = jk, we can calculate the measure of ik by first calculating the measure of jk. We are given that mik = (11x + 2), so we can solve for x and use that value to calculate jk. If we solve for x, we find that x = (mik-2)/11. We can then use that value to calculate jk, which equals mik-mjk. In this equation, we are given that mjk = (12x - 7), so jk = (11x + 2) - (12x - 7). Simplifying, we find that jk = 9x + 9.
Now that we have the measure of jk, we can calculate the measure of ik by subtracting the sum of jk and IR from 180 degrees. Since IR = jk, we can substitute jk in for IR, so ik = 180
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Fill in the table so that every row and every column sums to zero.
Answer:
Step-by-step explanation:
wheres the table
A DVD club charges nonmembers $20. 50 to purchase a DVD. With a $25 one-time membership fee, members pay $18 per DVD. For what number of DVDs is the cost the same for members and nonmembers on the first purchase? Write an equation that models the situation. Let d represent the number of DVDs. Solve the equation. For what number of DVDs is the cost the same for members and nonmembers’ first purchase from the DVD club?
A DVD club charges nonmembers $20. 50 to purchase a DVD. Members pay $18 per DVD for a one-time membership cost of $25. The cost is the same for members and nonmembers on the first purchase is 10.
Let's call the number of DVDs "d". For non-members, the cost of purchasing d DVDs is:
Cost for non-members = 20.50d
For members, the cost of purchasing d DVDs is:
Cost for members = 25 + 18d
We want to find the value of d for which the cost is the same for members and non-members. In other words, we want to find the value of d that satisfies the equation:
20.50d = 25 + 18d
To solve for d, we can start by subtracting 18d from both sides of the equation:
2.50d = 25
Then, we can divide both sides by 2.50:
d = 10
Therefore, the cost will be the same for members and non-members on the first purchase if the number of DVDs purchased is 10.
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two step equations -6+x/4=-5
Answer:
x = 4
Step-by-step explanation:
- 6 + [tex]\frac{x}{4}[/tex] = - 5 ( add 6 to both sides )
[tex]\frac{x}{4}[/tex] = 1 ( multiply both sides by 4 to clear the function )
x = 4
Factor completely
72w^2-50w^4
hm, dunno.
2w^2(5w + 6)(-5w + 6)
Answer:
2w^2(6 + 5w)(6 - 5w)
Step-by-step explanation:
A certain radioactive material is decaying at a rate proportional to the amount present. If a sample of 50 grams of the material was present initially and after 2 hours the sample lost 10% of its mass, find: An expression for the mass of the material remaining at any time t. The mass of the material after 4 hours. The half-life of the material.
The Half-Life of the material is 13.86 hours. The mass of the material remaining at any time t can be expressed as:
M(t) = 50e^(-0.05t), where t is measured in hours.
The amount of time needed for a number (of material) to decrease to half of its original value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long steady atoms last.
The mass of the material after 4 hours is M(4) = 50e^(-0.2) ≈ 31.4 grams. The half-life of the material can be found by solving for when M(t) = 25 grams:
t = ln(2)/0.05 ≈ 13.86 hours.
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Two schools are investigating whether there is a difference in the proportion of students who attend the homecoming football game. Both schools have over 2,000 students. School A selected a simple random sample of 100 students and found that 98 attended the homecoming football game. School B selected a simple random sample of 150 students and found that 142 attended the homecoming football game. Have the conditions for statistical inference for testing a difference in population proportions been met
All four conditions have been met, the conditions for statistical inference for testing a difference in population proportions have been satisfied. The conditions for statistical inference for testing a difference in population proportions are:
Random samples: Both schools have selected simple random samples of their respective student populations, which satisfies this condition.
Large sample size: Both schools have over 2,000 students, which satisfies the large sample size condition.
Independent samples: The samples from schools A and B are independent, as the students from one school do not affect the students from the other school.
Success-failure condition: The sample sizes are large enough to satisfy the success-failure condition, which states that there should be at least 10 successes and 10 failures in each sample. Both schools have well over 10 successes and failures in their respective samples.
Since all four conditions have been met, the conditions for statistical inference for testing a difference in population proportions have been satisfied.
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(find the slope of each line)
help—
Write the LCM of the following A=a^3× b^2×c and B=a^5 ×b×c^4×d , giveyour answer in exponential form
The LCM of A = a^3× b^2×c and B=a^5 ×b×c^4×d in exponential form is a^5 × b^2 × c^4 × d^1.
To find the LCM (Least Common Multiple) of two numbers, we need to find the greatest power of each prime factor that occurs in either number.
The prime factors in the given expressions are a, b, c, and d. For each prime factor, we need to find the greatest power that occurs in either A or B.
For a: The highest power of a that occurs in A is a^3, and the highest power that occurs in B is a^5. Therefore, the LCM must include a^5.
For b: The highest power of b that occurs in A is b^2, and the highest power that occurs in B is b^1. Therefore, the LCM must include b^2.
For c: The highest power of c that occurs in A is c^1, and the highest power that occurs in B is c^4. Therefore, the LCM must include c^4.
For d: The highest power of d that occurs in A is d^0, and the highest power that occurs in B is d^1. Therefore, the LCM must include d^1.
Putting all of this together, we have:
LCM(A,B) = a^5 × b^2 × c^4 × d^1
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solve the quadratics attached using at least two different methods (factoring, completing the square or the quadratic formula)
[tex]m^2+7m+10\\\\n^2\:+9n+18\\\\\\p^2-6p+8[/tex]
Method 1: Factoring
m^2 + 7m + 10
We need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5.
m^2 + 2m + 5m + 10
(m + 2)(m + 5)
n^2 + 9n + 18
We need to find two numbers that multiply to 18 and add up to 9. These numbers are 3 and 6.
n^2 + 3n + 6n + 18
(n + 3)(n + 6)
p^2 - 6p + 8
We need to find two numbers that multiply to 8 and add up to -6. There are no such numbers, so we cannot factor this quadratic.
Method 2: Quadratic Formula
m^2 + 7m + 10
a = 1, b = 7, c = 10
m = (-b ± sqrt(b^2 - 4ac)) / 2a
m = (-7 ± sqrt(7^2 - 4(1)(10))) / 2(1)
m = (-7 ± sqrt(9)) / 2
m = -5 or -2
n^2 + 9n + 18
a = 1, b = 9, c = 18
n = (-b ± sqrt(b^2 - 4ac)) / 2a
n = (-9 ± sqrt(9^2 - 4(1)(18))) / 2(1)
n = (-9 ± sqrt(9)) / 2
n = -3 or -6
p^2 - 6p + 8
a = 1, b = -6, c = 8
p = (-b ± sqrt(b^2 - 4ac)) / 2a
p = (6 ± sqrt(6^2 - 4(1)(8))) / 2(1)
p = (6 ± sqrt(16)) / 2
p = 2 or 4
Therefore, the solutions to the quadratics are:
m^2 + 7m + 10 = (m + 2)(m + 5) or m = -5 or -2
n^2 + 9n + 18 = (n + 3)(n + 6) or n = -3 or -6
p^2 - 6p + 8 = (p - 2)(p - 4) or p = 2 or 4
a survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. undergraduate major graduate school business engineering other total yes 35 44 64 143 no 92 101 64 257 total 127 145 128 400 what percentage of the students' undergraduate major is engineering?
The percentage of college seniors' undergraduate major that is engineering is 36.25%.
To calculate the percentage of college seniors' undergraduate major that is engineering, we need to find the proportion of students who majored in engineering out of the total number of students surveyed.
We see that out of the 400 college seniors surveyed, 145 majored in engineering. Therefore, the proportion of students who majored in engineering is 145/400. To convert this proportion to a percentage, we multiply it by 100. So, (145/400) x 100 = 36.25%.
Therefore, 36.25% of the college seniors surveyed had an undergraduate major in engineering.
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Consider the expression . Which of the following is an equivalent expression ?
Answer:
4 th option bcoz [tex]x^{y+2}=x^{y}x^{2[/tex]
The length of the smallest side (or leg) of a right triangle is 18. The lengths of the
other two sides are consecutive even integers. Use the Pythagorean theorem to solve
tor the smaller of the two missing sides (the second leg).
Length οf the smaller οf the twο missing sides (the secοnd leg) is 80
What is Pythagοrean theοrem?In mathematics, the Pythagοrean theοrem οr Pythagοras' theοrem is a fundamental relatiοn in Euclidean geοmetry between the three sides οf a right triangle. It states that the area οf the square whοse side is the hypοtenuse (the side οppοsite the right angle) is equal tο the sum οf the areas οf the squares οn the οther twο sides.
Let x be the length οf the smaller οf the twο missing sides (the secοnd leg). Then the length οf the larger missing side (the hypοtenuse) is (x + 2), since the twο sides are cοnsecutive even integers.
By the Pythagοrean theοrem, we have:
[tex]18^2 + x^2 = (x + 2)^2[/tex]
Simplifying and expanding the right side, we get:
[tex]324 + x^2 = x^2 + 4x + 4[/tex]
Subtracting x^2 frοm bοth sides, we get:
324 = 4x + 4
Subtracting 4 frοm bοth sides, we get:
320 = 4x
Dividing bοth sides by 4, we get:
x = 80
Therefοre, the length οf the smaller οf the twο missing sides (the secοnd leg) is 80.
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Liam is making a stone walkway. The rectangular walkway is 6 feet wide and 24 feet long. Each stone measures 2 feet by 2 feet and covers an area of 4 square feet.
What is the area, in square feet, of the walkway?
How many stones will Liam need to make the walkway?
Show your work.
The rectangular sidewalk for Liam to build the pathway, [tex]36[/tex] stones are required.
What is a rectangle shape?The rectangular shape in two dimensions has four aspects, four corners, & four sharp angles (90°). Equal and equal opposing sides make form a rectangle. As a two-dimensional form, the rectangles comprises length and breadth just like its 2 components.
What about a square?Because a square is indeed a parallelogram with all specific corners at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all have the same length, hence not all rectangles are squares.
Area of the walkway [tex]=length * width[/tex]
[tex]24*6=144[/tex] square feet
Area of each stone [tex]= length of each side * width of each side[/tex]
[tex]=2ft*2ft=4[/tex] square feet
Number of stones needed [tex]=\frac{Area of walkway }{Area of each stone}[/tex]
Number of stones needed [tex]=\frac{144}{4}=36[/tex] stones
Therefore, Liam will need [tex]36[/tex] stones to make the walkway.
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