The predicted population of the school in 2012 is P = 1060 + 78.14(12) = 2002.68 students. We can round this up to 2003 students.
1. The population grew by _____students.
The population in 2001 was 1138 students, and in 2008, it had risen to 1691 students. Therefore, the population increased by 1691-1138 = 553 students.
2. The population took _____ years to grow from 1138 students to 1691 students.
From the year 2001 to the year 2008, the population increased from 1138 to 1691 students. The number of years it took for this growth is 2008-2001 = 7 years.
3. The average population growth per year is _____ students per year.
To obtain the average growth rate per year, divide the total growth in the population by the number of years between the starting year and the ending year. Therefore, the average population growth per year = (1691 - 1138) / 7 = 78.14 students per year.
4. The population in the year 2000 was _____ students.
Since the population was given for the year 2001, we'll have to work our way backward to find the population in the year 2000. It took 7 years for the population to increase from 1138 to 1691, so if we go back another year, we'll have to subtract the average yearly growth rate, which is 78.14 students. Therefore, the population in 2000 = 1138 - 78.14 = 1059.86 students, which we can round up to 1060 students.
5. An equation for the population P of the school t years after 2000 is P = _____.
We can use the formula for linear growth to determine the population of the school t years after 2000. The formula is P = P0 + rt, where P0 is the initial population (in the year 2000), r is the average annual growth rate, and t is the number of years. Therefore, the equation for the population P of the school t years after 2000 is P = 1060 + 78.14t.
6. The predicted population of the school in 2012 is _____ students.
To predict the population of the school in 2012 using the equation, we need to substitute t = 12 - 2000 = 12 into the equation we derived in part 5. Therefore, the predicted population of the school in 2012 is P = 1060 + 78.14(12) = 2002.68 students. We can round this up to 2003 students.
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Solve the equation for x.
2(5x + 3) = 26
Answer:
x=2
Step-by-step explanation:
2(5x+3)=26
expand the bracket first
10x+6=26
take away 6 from both sides
10x=20
divided by 10 on each side
x=2
Answer:
You would use the PEDMAS rule for this equation.
First, distribute 2 inside the parentheses so the equation is 10x + 6 = 26
Then, subtract 6 from both sides 10x = 20
The answer is x = 2.
Step-by-step explanation:
how many solutions does the system of equations 4x+2y=6 and y=-2x+6 have?
The system of equations 4x + 2y = 6 and y = -2x + 6 have infinite many solutions
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Given the system of equation:
4x + 2y = 6
Divide through by 2:
2x + y = 3
y = -2x + 6 (1)
The second equation is:
y = -2x + 6 (2)
Since both equations are the same hence the system of equations have infinite many solutions
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Bashir walked 10 miles in 4 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The missing values are 2 and 35 respectively. The points plotted have been attached below. The solution has been obtained by using equivalent ratio.
What is an equivalent ratio?When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another.
We are given that Bashir walked 10 miles in 4 hours and the table is of equivalent ratios.
The ratio comes out to be 2.5.
So, he will walk 5 miles in 2 hours.
Similarly, in 14 hours he will walk 35 miles.
The points have been plotted on the coordinate axes and has been attached below.
Hence, the missing values are 2 and 35 respectively.
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Which methods for "thinking out computalion" Gie, mental arithmetic) are correct
a)7+8 Think: 7 plus 7 is 14, plus 1 more is 15
b) 38 - 17
Think: 38 minus 10 is 28, minus 7 more is 21
c) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997
d) 150 ÷ 3 Think: what equals 150 x 3, that's 450
The correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.
The correct methods for "thinking out computation" (mental arithmetic) are a, b, and c.
a) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15. This method is correct because it breaks down the calculation into smaller, easier-to-manage parts.
b) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21. This method is also correct because it simplifies the calculation by subtracting 10 first, and then subtracting the remaining 7.
c) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997. This method is correct because it simplifies the calculation by multiplying 1000 by 3 first, and then subtracting 1 three to get the correct answer.
d) 150 ÷ 3 Think: what equals 150 x 3, that's 450. This method is incorrect because it is actually doing the opposite operation (multiplication instead of division) and therefore does not result in the correct answer. The correct method would be to think about how many times 3 can go into 150, which is 50.
In conclusion, the correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.
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The correct methods for "thinking out computation" (mental arithmetic) are:
A) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15
B) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21
C) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997
D) 150 ÷ 3 Think: what equals 150 x 3, that's 450
All four methods of "thinking out computation" provided in the question are correct and valid.
Method (a) is using the "doubles" method, which is a common mental arithmetic technique. By recognizing that 7+7 is 14, it is easy to add 1 more to get 15.
Method (b) is using the "subtracting by tens" method. By recognizing that 38 minus 10 is 28, it is easy to subtract 7 more to get 21.
Method (c) is using the distributive property of multiplication. By recognizing that 999 is very close to 1000, we can multiply 3 by 1000 and then subtract 3 to get 2997.
Method (d) is using the inverse operation of multiplication. By recognizing that 150 is a multiple of 3, we can think of 150 as 3 times some unknown number, and then determine that number by dividing 150 by 3. The answer is 50, which is the same as thinking of what equals 150 times 3 (450).
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What is the simplified form of StartRoot 400 x Superscript 100 Baseline EndRoot ?
The simplified root of the given root i.e. √(400x¹⁰⁰) is 20x⁵⁰. The solution has been obtained by using the law of indices.
What is the law of indices?
The guidelines for simplifying expressions containing powers of the same base number are known as index laws.
We are given an expression as √(400x¹⁰⁰).
Using law of indices,
⇒ √(400x¹⁰⁰) = √400 * √(x¹⁰⁰) ( as √ab = √a * √b)
⇒ √(400x¹⁰⁰) = 20 √(x¹⁰⁰)
⇒ √(400x¹⁰⁰) = 20 √(x⁵⁰ * x⁵⁰) ( as a⁴ = a² + a²)
⇒ √(400x¹⁰⁰) = 20x⁵⁰
Hence, the simplified root of the given root i.e. √(400x¹⁰⁰) is 20x⁵⁰.
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Write the following radical expressions in simplest form: a)−72x4y122x8y2(
b)7z21128x14t8y6
The simplified form of the radical expressions are:
a) −12x2y6
b) 284x7t4y3
To simplify the following radical expressions, we need to factor the radicand and then use the properties of radicals to simplify.
For a) −72x4y122x8y2, we can factor the radicand as follows:
−72x4y12 = −(2*2*2*3*3)x4y12 = −(2*2*2*3*3)(x4)(y12)
Now we can use the properties of radicals to simplify:
√−(2*2*2*3*3)(x4)(y12) = √−(2*2)(2*2)(3*3)(x4)(y12) = −(2*2*3)(x2)(y6) = −12x2y6
For b) 7z21128x14t8y6, we can factor the radicand as follows:
1128x14t8y6 = (2*2*2*2*71)(x14)(t8)(y6)
Now we can use the properties of radicals to simplify:
√(2*2*2*2*71)(x14)(t8)(y6) = √(2*2)(2*2)(71)(x14)(t8)(y6) = (2*2*71)(x7)(t4)(y3) = 284x7t4y3
So the simplified form of the radical expressions are:
a) −12x2y6
b) 284x7t4y3
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For each of the following, find the formula for an
exponential function that passes through the two points
given.
a. (-1,2) and (4,64)
f(x)=?
b. (-3,9) and (2,1)
g(x)=?
The exponential function that passes through the two points given is (a) f(x) = 4(2ˣ) and (b) g(x) = (9^(2/5)) ((1/9)^(1/5))ˣ.
To find the formula for an exponential function that passes through two points, we can use the following steps:
1. Use the general form of an exponential function: f(x) = abˣ
2. Plug in the x and y values from the first point into the equation and solve for b.
3. Plug in the x and y values from the second point and the value of b into the equation and solve for a.
4. Substitute the values of a and b back into the general equation to get the formula for the function.
For point a:
1. f(x) = abˣ
2. 2 = ab⁻¹
3. 64 = ab⁴
4. Divide the equations to eliminate a: (64/2) = (ab⁴)/(ab⁻¹) = b⁵
5. Solve for b: b = 2
6. Substitute b back into one of the equations and solve for a: 2 = a(2)⁻¹ = a/2, a = 4
7. Substitute a and b back into the general equation: f(x) = 4(2)ˣ
For point b:
1. g(x) = abˣ
2. 9 = ab⁻³
3. 1 = ab²
4. Divide the equations to eliminate a: (1/9) = (ab²)/(ab⁻³) = b⁵
5. Solve for b: b = (1/9)^(1/5)
6. Substitute b back into one of the equations and solve for a: 9 = a((1/9)^(1/5))⁻³ = a(9^(3/5)), a = 9^(2/5)
7. Substitute a and b back into the general equation: g(x) = (9^(2/5))((1/9)^(1/5))ˣ
So the formulas for the exponential functions are:
f(x) = 4(2)ˣ
g(x) = (9^(2/5)) ((1/9)^(1/5))ˣ
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Evaluate the following algebraic expression under the given conditions. b^(2)-4ac for a=-4,b=-2,c=6
The value of the algebraic expression [tex]b^(2)-4ac for a=-4,b=-2,c=6[/tex] is 100.
An algebraic expression is an expression that consists of constants, variables, and some algebraic operations. To solve it, simply use multiplication, division, addition, and subtraction when necessary to isolate the variable and solve.
To evaluate the given algebraic expression, we will substitute the given values of a, b, and c into the expression and simplify.
Step 1: Substitute the given values into the expression.
[tex]b^(2)-4ac = (-2)^(2)-4(-4)(6)[/tex]
Step 2: Simplify the expression.
[tex]= 4+96= 100[/tex]
Therefore, the value of the algebraic expression [tex]b^(2)-4ac[/tex] for [tex]a=-4,b=-2,c=6 is 100.[/tex]
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There are approximately 7. 48 liquid gallons in a cubic foot. If a cylindrical water tank holds 1,600 liquid gallons and has a radius of 2. 2 feet, what is the approximate height of the water tank? Approximate using π = 3. 14 and round to the nearest tenth. 213. 9 feet
44. 2 feet
14. 1 feet
4. 8 feet
Answer:
14.1 feet
Step-by-step explanation:
Amount of liquid gallons in 1 cubic foot= 7.48
Radius of the cylindrical water tank= 2.2 feet
Amount of liquid gallons it can hold= 1,600
Volume of the cylindrical water tank to carry 1,600 liquid gallons= [tex]\frac{1600}{7.48}[/tex]
= 213.90 ft³
Volume of the cylinder= [tex]\pi r^{2} h[/tex]
213.9= 3.14 x 2.2 x 2.2 x h
213.9= 3.14 x 4.84 x h
213.9= 15.2 x h
h= [tex]\frac{213.9}{15.2}[/tex]
h= 14.07
h= 14.1 feet
∴ height of the water tank is 14.1 feet.
suppose 8x + 16 ice cream cones were sold on saturday and 7x - 9 were sold on sunday. what is the total number of ice cream cones sold?
Answer:
this is right.....
Step-by-step explanation:
15x + 6
Hi so my question is what are all of the expressions equivalent to 11x + 10 ? I am very confused..
There are infinitely many expressions equivalent to 11x + 10, including 22x + 20, 11(x+1)-1, -11(-x)-10, and 11(x+2)-12.
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and/or variables that are put together in a meaningful way, usually to represent a quantity or a mathematical relationship.
There are infinitely many expressions that are equivalent to 11x + 10, because you can add or subtract any expression to both sides of the equation to get a new equivalent expression. Here are some examples:
22x + 20: This is equivalent to 11x + 10 because if you distribute 11 to x and 10, you get 11x + 10.
11(x + 1) - 1: This is also equivalent to 11x + 10 because if you distribute 11 to x and 1, you get 11x + 11 - 1, which simplifies to 11x + 10.
-11(-x) - 10: This is equivalent to 11x + 10 because if you distribute -11 to -x, you get 11x + 10.
11(x + 2) - 12: This is also equivalent to 11x + 10 because if you distribute 11 to x and 2, you get 11x + 22 - 12, which simplifies to 11x + 10.
In general, any expression of the form 11x + k, where k is a constant, is equivalent to 11x + 10.
Therefore, there are infinitely many expressions equivalent to 11x + 10, including 22x + 20, 11(x+1)-1, -11(-x)-10, and 11(x+2)-12.
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Consider the time it takes in minutes, for police officers to respond to a 911 call, where a life- threatening crime (an armed robbery, an assault, a shooting) is in progress. For a particular police jurisdiction, the average response time is 26 minutes with a standard deviation of 3 minutes Assuming the data is symmetric and using the Empirical rule, what % of the response times fall between 20 to 32 minutes a. 68% b. 95% c. 86% d. 99.7% e. 50% f. none of the above
The correct answer is b. 95%.
According to the Empirical rule, for a symmetric data set, 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations of the mean, and 99.7% falls within 3 standard deviations of the mean.
In this particular case, the mean response time is 26 minutes and the standard deviation is 3 minutes. Therefore, 1 standard deviation from the mean is 23 to 29 minutes, 2 standard deviations from the mean is 20 to 32 minutes, and 3 standard deviations from the mean is 17 to 35 minutes.
Since the question asks for the percentage of response times that fall between 20 to 32 minutes, we are looking for the percentage of data that falls within 2 standard deviations of the mean. Therefore, the correct answer is 95%.
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Simplify: 18+7/10 -16+26/6 A. -25/6 B. -5/6 C. 5/6 D. 25/6
Step-by-step explanation:
[tex]18 + \frac{7}{10} - 16 + \frac{26}{6}\\ 30(18) + 30 \times \frac{7}{10} - 30(16) + 30 \times \frac{26}{6} \\ 540 + 21 - 480 + 130 \\ = 211[/tex]
The Lcm of 10 and 6
is 30
sorry but I got my answer to be 211
Jonah is a baker who specializes in wedding cakes. He would like to calculate the
cost of decorating a 3-tiered circular cake with fresh flowers around the base of each level. The bottom cake has a 14-inch diameter, the middle layer has a 10-inch diameter, and the top layer has a 6-inch diameter. All three layers are stacked on top of each other without spacers. He wants to place red roses without their stems around the bottom of each layer. The roses are 1½ inches wide and are sold for $0.99 each. How much will it cost Jonah to decorate the cake with the roses?
It wiII cοst Jοnah $63.36 tο decοrate the 3-tiered circuIar wedding cake with fresh red rοses arοund the base οf each IeveI.
Tο caIcuIate the cοst οf decοrating the cake with rοses, we need tο first determine the circumference οf each tier, which wiII teII us hοw many rοses are needed fοr each tier.
The circumference οf a circIe can be caIcuIated using the fοrmuIa C = πd, where C is the circumference, π is the mathematicaI cοnstant pi (apprοximateIy 3.14), and d is the diameter.
Fοr the bοttοm tier with a diameter οf 14 inches, the circumference is C = πd = 3.14 x 14 = 43.96 inches.
Fοr the middIe tier with a diameter οf 10 inches, the circumference is C = πd = 3.14 x 10 = 31.4 inches.
Fοr the tοp tier with a diameter οf 6 inches, the circumference is C = πd = 3.14 x 6 = 18.84 inches.
Nοw, we need tο determine hοw many rοses are needed fοr each tier. Tο dο this, we need tο caIcuIate hοw many rοses wiII fit arοund the circumference οf each tier. We can dο this by dividing the circumference οf each tier by the width οf the rοses, which is 1.5 inches.
Fοr the bοttοm tier: 43.96 inches / 1.5 inches per rοse = 29.3, rοunded up tο 30 rοses.
Fοr the middIe tier: 31.4 inches / 1.5 inches per rοse = 20.9, rοunded up tο 21 rοses.
Fοr the tοp tier: 18.84 inches / 1.5 inches per rοse = 12.6, rοunded up tο 13 rοses.
Nοw that we knοw hοw many rοses are needed fοr each tier, we can caIcuIate the tοtaI cοst οf the rοses. Each rοse cοsts $0.99, sο the cοst οf the rοses fοr each tier is:
Bοttοm tier: 30 rοses x $0.99 per rοse = $29.70
MiddIe tier: 21 rοses x $0.99 per rοse = $20.79
Tοp tier: 13 rοses x $0.99 per rοse = $12.87
The tοtaI cοst οf decοrating the cake with rοses is the sum οf the cοsts fοr each tier:
$29.70 + $20.79 + $12.87 = $63.36
Therefοre, it wiII cοst Jοnah $63.36 tο decοrate the 3-tiered circuIar wedding cake with fresh red rοses arοund the base οf each IeveI.
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PLEASE HELP ME IF CORRECT I WILL FRIEND AND GIVE BRAINLIEST
Answer:
see below
Step-by-step explanation:
(6x-1)(3x-2)= 6x*(3x-2) - 1*(3x-2)
=6x*3x - 6x*2 -1*3x - (-1)*2
= 18x² - 12x - 3x + 2
=18x² - 15x + 2
Answer:
18x²-15x+2
Step-by-step explanation:
please let me know if i got brainliest
A)
Discuss the main quality standards and provide some examples to
show where these standards are effective.
B) Why is translation quality so critical? Select an industry
and show how translation qual
A) In the technology industry, usability and security are essential for creating user-friendly and secure software and hardware. Without these quality standards, products and services may not function properly or may even pose risks to consumers.
B) In the legal industry, translation quality is also crucial for ensuring that contracts and other legal documents are accurately translated and understood by all parties involved. Without high-quality translation, there is a risk of miscommunication and misunderstandings, which can have serious consequences.
The main quality standards include reliability, validity, usability, and security. These standards are effective in various industries and settings. For example, in the medical field, reliability and validity are crucial in ensuring that medical devices and treatments are safe and effective for patients. In the technology industry, usability and security are essential for creating user-friendly and secure software and hardware. Without these quality standards, products and services may not function properly or may even pose risks to consumers.
Translation quality is critical because it ensures that information is accurately conveyed across different languages and cultures. This is especially important in industries such as healthcare, where accurate translation of medical information can be a matter of life or death. In the legal industry, translation quality is also crucial for ensuring that contracts and other legal documents are accurately translated and understood by all parties involved. Without high-quality translation, there is a risk of miscommunication and misunderstandings, which can have serious consequences.
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Exercise - 4.4 f mathematical induction, prove that, for n>=1 1^(3)+2^(3)+3^(3)+cdots +n^(3)=((n(n+1))/(2))^(2)
The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.
Proof by mathematical induction:
Base case: n = 1
1^(3) = ((1(1+1))/(2))^(2)
1 = ((2)/(2))^(2)
1 = 1^(2)
1 = 1
The base case is true.
Inductive step:
Assume that the statement is true for n = k, that is:
1^(3)+2^(3)+3^(3)+...+k^(3) = ((k(k+1))/(2))^(2)
Now we need to prove that the statement is also true for n = k+1:
1^(3)+2^(3)+3^(3)+...+k^(3)+(k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)
Substituting the assumption into the left-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)
Expanding the right-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)(k+2))/(2))^(2)
Simplifying the equation:
(k^(2)(k+1)^(2))/(2^(2)) + (k+1)^(3) = ((k+1)^(2)(k+2)^(2))/(2^(2))
Multiplying both sides of the equation by 2^(2):
(k^(2)(k+1)^(2)) + 2^(2)(k+1)^(3) = (k+1)^(2)(k+2)^(2)
Expanding the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = (k+1)^(2)(k^(2)+4k+4)
Simplifying the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = k^(2)(k+1)^(2) + 4k(k+1)^(2) + 4(k+1)^(2)
Subtracting k^(2)(k+1)^(2) from both sides of the equation:
2^(2)(k+1)^(3) = 4k(k+1)^(2) + 4(k+1)^(2)
Factoring out (k+1)^(2) from the right-hand side of the equation:
2^(2)(k+1)^(3) = (k+1)^(2)(4k+4)
Simplifying the equation:
2^(2)(k+1)^(3) = 4(k+1)^(2)(k+1)
Dividing both sides of the equation by (k+1)^(2):
2^(2)(k+1) = 4(k+1)
Simplifying the equation:
2^(2)(k+1) = 2^(2)(k+1)
The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.
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Simplify 3x to the power of 2 x 4x to the power of 5
Answer:
I found this
Step-by-step explanation:
To simplify 3x² * 4x⁵, we can multiply the coefficients (numbers in front of the variables) and add the exponents of x:
3x² * 4x⁵ = (3 * 4) x^(2+5) = 12x^7
Therefore, the simplified expression is 12x^7.
Find the point(s) of intersection, if any, between the circle and line with the equations given. (x+4)^2+(y−3)^2=25; y=x+2
The intersection points between the two equations are (1, 3) and (-4, 2)
How to find the intersection points?Here we have the system of equations:
(x+4)^2+(y−3)^2=25
y=x+2
We can replace the second equation into the first one to get:
(x+4)^2+(x + 2−3)^2 = 25
(x + 4)^2 + (x - 1)^2 = 25
Now let's solve that:
x^2 + 8x + 16 + x^2 - 2x + 1 = 25
2x^2 + 6x + 17 - 25 = 0
2x^2 + 6x - 8 = 0
x^2 + 3x - 4 = 0
Using the quadratic formula:
[tex]x = \frac{-3 \pm \sqrt{3^2 - 4*1*-4} }{2} \\\\x = \frac{-3 \pm5 }{2}[/tex]
So the two solutions are:
x = (-3 + 5)/2 = 1
x = (-3 - 5)/2 = -4
Evaluating the line in these values:
y = 1 + 2 = 3 ----> we have the point (1, 3)
y = -4 + 2 = -2 ----> we have the point (-4, -2)
These are the intersection points.
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What is the perimeter of kite FGHJ? Round to 2 decimal places.
The perimeter of kite FGHJ is 39. Rounded to 2 decimal places, the answer is 39.00.
What is the perimeter?
The perimeter is the total distance around the boundary of a two-dimensional shape. It is calculated by adding up the lengths of all the sides of the shape.
First, we need to find the length of the other two sides of the kite:
Since FH = 17 and FT = 10, we can find the length of TH by subtracting: TH = FH - FT = 17 - 10 = 7.
Similarly, since GJ = 10 and TJ = 5, we can find the length of GT by subtracting: GT = GJ - TJ = 10 - 5 = 5.
Now we can find the perimeter of the kite by adding up the lengths of all four sides:
Perimeter = FH + TH + GJ + GT
Perimeter = 17 + 7 + 10 + 5
Perimeter = 39
Therefore, the perimeter of kite FGHJ is 39. Rounded to 2 decimal places, the answer is 39.00.
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Complete question:
What is the 'perimeter of kite FGHJ? Round to 2 decimal places?
Use the formula for future value, A - P(1 + rt), to find the missing quantity. P = $1800; r = 8%; t = 5 years A = $1080 O A = $4320 O A = $9720 O A = $2520 Use the formula for future value, A=P(1 + rt
Option d) The missing quantity A is $2520. The formula for future value is A=P(1+rt), where A is the future value, P is the principal amount, r is the interest rate, and t is the time period.
We are given the values of P, r, and t, and we need to find the value of A.
P = $1800
r = 8% = 0.08
t = 5 years
Plugging these values into the formula, we get:
A = P(1 + rt)
A = $1800(1 + 0.08*5)
A = $1800(1 + 0.4)
A = $1800(1.4)
A = $2520
Therefore, the future value of the investment is $2520. The correct answer is A = $2520.
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Which numbers below are ratonal? (Select all that apply)
A. -7
B. 36.545454....
C. 9.149278643
D. 7/11
E. 10√
F. 25√+ 3
G. 2√+9√
Answer:
a,b,c,d
Step-by-step explanation:
all are rational except efg
Find the HCF. 6. ( 26, 32)=
What is the volume (in cubic units) of a sphere with a radius of 15 units?
Answer:
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.
Substituting r = 15, we get:
V = (4/3)π(15)^3
V = (4/3)π(3375)
V = 4π(1125)
V = 4500π
Therefore, the volume of the sphere with a radius of 15 units is 4500π cubic units. This can also be approximated as 14,137.17 cubic units by using a value of 3.14 for π and rounding to the nearest hundredth.
Step-by-step explanation:
4 PQ and RS are two chords of a circle meeting at point T.if T is the midpoint of each of the chord,show that PQ and RS are the diameter of the circle.
Since TB = TS and OT is perpendicular to RS, it follows that BO is also perpendicular to RS, and hence RS is the diameter of the circle.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the out trace.
Since T is the midpoint of both chords PQ and RS, it follows that the perpendicular bisectors of these chords pass through the centre of the circle. Let O be the centre of the circle.
Consider the perpendicular bisector of PQ passing through T. Let it intersect the circle at point A. Since TA = TP and OT is perpendicular to PQ, it follows that AO is also perpendicular to PQ, and hence PQ is the diameter of the circle.
Similarly, consider the perpendicular bisector of RS passing through T. Let it intersect the circle at point B. Since TB = TS and OT is perpendicular to RS, it follows that BO is also perpendicular to RS, and hence RS is the diameter of the circle.
Therefore, PQ and RS are both diameters of the circle.
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Find all integer values of k such that [18]25 is equal to
[7]k
25?
(Explain and/or show work.))
The integer values of k such that [18]25 is equal to [7]k are 4, 11, 18, 25
To find all integer values of k such that [18]25 is equal to [7]k, we need to use the following steps:
Start with the given equation: [18]25 = [7]k
Use the definition of modular arithmetic to write the equation in a different form: 25 ≡ k (mod 7)
Simplify the equation: 4 ≡ k (mod 7)
Find all integer values of k that satisfy the equation. The smallest positive integer value of k that satisfies the equation is 4. We can add multiples of 7 to find other integer values of k: 4 + 7 = 11, 4 + 14 = 18, 4 + 21 = 25, etc.
The integer values of k that satisfy the equation are 4, 11, 18, 25, etc.
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the class survayed 100 other students and found that 23% chose in-line skating as their favorite. Estimate how many students in both surveys combined chose in-line skating as their favorite.
An estimated 46 students in both surveys combined chose in-line skating as their favorite.
To estimate how many students in both surveys combined chose in-line skating as their favorite, we can use the given percentage and the total number of students surveyed.
First, we need to calculate the number of students who chose in-line skating in the first survey. We can do this by multiplying the percentage by the total number of students surveyed:
23% × 100 = 23
So, 23 students in the first survey chose in-line skating as their favorite.
Next, we need to add this number to the number of students who chose in-line skating in the second survey. Since we don't have information about the second survey, we can assume that the same percentage of students chose in-line skating:
23% × 100 = 23
Finally, we can add the two numbers together to get the total number of students who chose in-line skating in both surveys:
23 + 23 = 46
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If the coordinates of point a are (-2,,3) what is the image of a after reflection over the y axis followed by dilation with a scale factor of 3 centered at the orgin
The image of point a after reflection over the y axis followed by dilation with a scale factor of 3 centered at the origin is,
⇒ (6, 9)
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The coordinates of point a are,
⇒ a = (-2,3)
Now, We can multiply by 3 in the point;
⇒ (- 2, 3) = (- 2 × 3, 3×3)
= (- 6, 9)
Now, After reflection over the y axis,
Image of the point are,
⇒ (6, 9)
Thus, The image of point a after reflection over the y axis followed by dilation with a scale factor of 3 centered at the origin is,
⇒ (6, 9)
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Which is the correct factorization for the Difference of Squares or a^(2)-b^(2) ?
The correct factorization for the Difference of Squares or a²-b² is (a+b)(a-b). This is because when you multiply (a+b)(a-b), you get a²- ab + ab - b², which simplifies to a²-b².
Here is a step-by-step explanation of how to factor the Difference between Squares:
Step 1: Identify the two terms that are being squared. In this case, a and b are the terms being squared.
Step 2: Write the two terms with a plus sign in between them in one set of parentheses and with a minus sign in between them in another set of parentheses. This will give you (a+b)(a-b).
Step 3: Multiply the two sets of parentheses together to check your answer. You should get a²-b².
So, the correct factorization for the Difference of Squares or a²-b² is (a+b)(a-b).
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Given z^(2)+2z-15=(z-3)(z+5), write another polynomial in general form that has a factored form of (z-3)(z+5) with different values for z.
Another polynomial with the same factored form of (z-3)(z+5) but different values for z is 2z^(2)+4z-30.
To find another polynomial with the same factored form, we can simply multiply the given factored form by a constant. This will change the values of z, but the factored form will remain the same.
For example, let's multiply the factored form by 2:
2(z-3)(z+5) = 2z^(2)+4z-30
In general form, this polynomial is 2z^(2)+4z-30.
We can see that the factored form is still (z-3)(z+5), but the values of z have changed. In the original polynomial, z^(2)+2z-15, the values of z were 3 and -5. In the new polynomial, 2z^(2)+4z-30, the values of z are 3/2 and -5/2.
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