The measure of the smallest possible sector angle possible is 8°.
Let [tex]$a_1$[/tex] be the first term of the arithmetic progression and [tex]$a_{12}$[/tex] be the last term of the arithmetic progression.
From the formula of the sum of an arithmetic progression, we have -
[tex]$12*\frac{a_1+a_{12}}{2}=360$[/tex]
simplifying we get,
[tex]$a_1 + a_{12} = 60$[/tex]
[tex]$a_{12}$[/tex] is the largest term of the progression and it can also be expressed as-
[tex]a_{12} = $a_1+11d$[/tex]
where d is a common difference.
Since each angle measure must be an integer, d should also be an integer.
[tex]$a_{12}-a_1=a_1+11d-a_1=11d$[/tex]
Since d is an integer, the difference between the first and last terms, 11d, must be divisible by 11.
Since the total difference should be less than 60, let's start checking multiples of 11 less than 60 for the total difference between [tex]$a_1$[/tex] and [tex]$a_{12}$[/tex].
Let us take the largest multiple because the maximum difference will give us the minimum value of the first term.
If the difference is 55, [tex]$a_1=\frac{60-55}{2}=2.5$[/tex], is not an integer.
If the difference is 44, [tex]$a_1=\frac{60-44}{2}= 8[/tex] . It satisfies the given conditions.
Hence, the measure of the smallest possible sector angle possible = 8°.
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Pablo draws rectangle p he says that the area is greater than 50 square units what could the missing side length be
Any pair of positive numbers x and y that satisfy the inequality x * y > 50 will be the sides of rectangle.
If the area of rectangle P is greater than 50 square units, then the product of its length and width must be greater than 50. Let the length of the rectangle be x and the width be y. Then, we have:
x * y > 50
Since the missing side length is unknown, we cannot solve for a specific value. But we can say that any pair of positive numbers x and y that satisfy the inequality will represent a rectangle with an area greater than 50 square units.
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Two circle of radii 8cm with centre p and q are given the chord AB of circle with centre P and the chord CD of the circle with centre Q are equal if angle PAB=40 then find angle CQD
The angle PAB is given as 40 degrees so we can use the sine rule to calculate the lengths of the chords is CQD = 17.7 degrees.
The sine rule states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal to the ratio of any other side to the sine of its opposite angle.
Let us denote the length of chord AB by x and the length of chord CD by y.
Therefore x/sin 40 = y/sin (180-40)
=> x/0.766 = y/0.939
=> x = 0.766*0.939 = 0.723
y = 0.939*0.766 = 0.723
Since AB=CD, x=y=0.723.
We can now use the cosine rule to calculate the angle CQD.
The cosine rule states that the square of the length of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides times the cosine of the included angle.
Therefore CQ^2 = 8^2 + 8^2 - 2(8^2)cosCQD
=> CQ^2 = 64 - 64cosCQD
=> 64 - 64cosCQD = 0.723^2
=> 64 - 64cosCQD = 0.521
=> 64cosCQD = 63.479
=> cosCQD = 63.479/64
=> cosCQD = 0.988
Therefore CQD = cos^-1(0.988)
=> CQD = 17.7 degrees.
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I dont understand what the question is, i need help
equations of the line in slope intercept form:
y = -2x - 3y =-1/2xWhat is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given two linear function,
For first equation:
2x +y = -3
in slope intercept form
y = -2x - 3
For second equation:
Given second line passes through the origin
thus, equation of the line.
y = mx
where m is slope
m = (y₂ - y₁)/(x₂ - x₁)
in our case,
m = (0 -2)/(0-(-4))
m = -1/2
Thus, equation of second line;
y =-1/2x
Therefore, equations of the line in slope intercept form:
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HURRY PLEASE!!!!!
Which statements about the factors of the terms in the expression 20 a + 15 a b + 24 b are true? Select three options.
Group of answer choices
a) The GCF of the expression is 1
b) The factors common to 20a and 24b are 1, 2, and 4.
c) The GCF of the expression is ab.
d) The factors common to 20a and 15ab are 1, 5, a, and b.
e) The factors common to 20a and 15ab are 1, 5, and a.
Answer: A, B, E
Step-by-step explanation:
For A:
None of the factors have one same factor they can be divided by besides 1.
For B:
Both 20a and 24b can be divisible by 1,2,4.
For E:
Both 20a and 15ab are divisible by 1,5 and a.
Consider the two equations below. Explain completely the similarities and differences in how you would solve each equation. Be clear and complete.
The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:
x = log3(12)
The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:
x = ∛12
How does the equation compare?The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.
The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.
As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.
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What fraction names the equal parts of the whole pizza? Enter your answer in the boxes. Circle is divided into 4 equal parts. Line
If the pizza is divided in to four equal parts , then each equal part is named as "one fourth" .
The fraction is defined as a numerical value that is part of a whole. Fraction is evaluated by dividing a whole into number of parts.
For Example : 1/2 represents the half part of the whole .
The pizza is divided into four equal part ;
So , the total number of parts in the pizza is = 4 parts ,
one part of the pizza will be written in fraction form as : 1/4 ;
We can say that each pizza slice is 1/4 of whole pizza and 1/4 is read out as "one fourth".
The given question is incomplete , the complete question is
What fraction names the 4 equal parts of the whole pizza ?
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What is the value of the expression below when y=3 y=3?
3 y^2 - 4 y + 8 3 y 2 − 4 y + 8
Answer:
When y = 3, we can substitute 3 for y in the expression 3 y^2 - 4 y + 8
3(3^2) - 4(3) + 8
= 3(9) - 12 + 8
= 27 - 12 + 8
= 15
Therefore, the value of the expression 3 y^2 - 4 y + 8 when y = 3 is 15.
Answer:
Basically since y = 3 we just have to remove the 'y' from the equation and replace it with the number 3. (Also pretty sure you wrote the equation twice)
Original Equation:
3 y^2 - 4 y + 8
Modified Equation:
→ 3 (3²) - 4(3) + 8
→ 3 (9) - 12 + 8
→ 27 - 12 + 8
→ 15 (answer)
Equation with 'y' included:
→ y (y²) - 4 (y) + 8
→ y (9) - 12 + 8
→ 27 - 12 + 8
→ 15 (answer)
At the movies, John was sent to the lobby to buy refreshments for his friends. Some wanted popcorn which sold for 50 cents a bag and others wanted caramel corn which was 75 cents a bag. If John bought 9 bags and spent $5.00, how many of each kind of bag did he buy?
If John bought 9 bags and spent $5.00, using simultaneous equations, the number of each kind of bag he bought is 7 bags of popcorn and 2 bags of caramel corn.
What are simultaneous equations?Simultaneous equations are two or more equations solved simultaneously or concurrently.
When two or more equations are solved at the same time, they are described as simultaneous equations or a system of equations.
The cost of popcorn per bag = $0.50
The cost of caramel corn per bag = $0.75
The total number of bags bought = 9
The total cost of the 9 bags = $5
Let the number of bags of popcorn = p and the number of caramel corn = c
Equations:0.5p + 0.75c = 5 ... Equation 1
p + c = 9 ... Equation 2
Multiply Equation 2 by 0.5:
0.5p + 0.5c = 4.5 ... Equation 3
Subtract Equation 3 from Equation 1:
0.5p + 0.75c = 5
-
0.5p + 0.5c = 4.5
0.25c = 0.5
c = 2
p = 9 - 2
= 7
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Suppose Nigel has a bag of colored wristbands,
and he chooses one without looking. The bag
contains a total of
25 wristbands and 6 of
the wristbands are blue.
What is the probability that he will choose a blue wristband
The probability that he will choose a blue wristband is 6/25.
Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.
Total number of wristbands = 25
Number of blue colour wristbands = 6
As we know, the formula of experimental probability is
Probability of an Event P(E) = Total Number of times an event occurs/Total number of trials.
Number of blue colour wristbands = 6
Total number of wristbands = 25
∴ Probability of an Event P(Blue) = 6/25
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Helpppp
could somebody help me with the following question?
Answer: y = -4x -2
Step-by-step explanation:
For a linear equation, we can use this formula:
y - y_1 = m(x - x_1)
We have the slope and the coordinates, so we can just plug everything in:
y - 14 = -4( x + 4)
y - 14 = -4x -16
y = -4x -2
If the domain of f(x) is -3 ≤ x ≤ 9 and the range of f(x) is 2 ≤ y ≤ 15, then which of the following
statements is correct about the domain and range of 9 (x) = f(x-2) - 8?
"The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.
What is the Domain and Range of the function?
The domain of a function is the set of all input values (x-values) for which the function is defined. It is the set of all values of x for which the function is defined.
The range of a function is the set of all output values (y-values) that the function can produce. It is the set of all possible values that the function can take on.
The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.
When we shift a function horizontally, the domain remains unchanged, but the range will change. In the case of a shift of -2, the domain of f(x) is still -3≤x≤9
For 9(x) = f(x-2) - 8, it means that we are taking the output of f(x-2) and subtracting 8 from it. So, the range of 9(x) will be (2-8) ≤ y ≤ (15-8) = -6 ≤ y ≤ 7.
In summary,
The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9
The range of 9(x) = f(x-2) - 8 is -6 ≤ y ≤ 7
Hence, statement "The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.
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The most Ellsworth can afford to pay per year in mortgage payments is
$14,000, and his credit score is currently 498. According to the following table
for a $150,000 mortgage, by how many points would he need to improve his
credit score in order to take a mortgage for $150,000?
FICO
Interest
Score
Rate
720-850
700-719
675-699
620-674
560-619
500-559
5.59%
5.71%
6.25%
7.40%
8.53%
9.29%
A. 2 points
OB. 177 points
O C. 122 points
OD. 62 points
Monthly
Payment
$860
$872
$924
$1039
$1157
$1238
62 points, he would need to improve his credit score in order to take a mortgage for $150,000.
What is a mortgage?
It is an agreement between you and a lender that allows you to borrow money to purchase or refinance a home and gives the lender the right to take your property if you fail to repay the money you've borrowed. A mortgage is a type of loan that's used to finance the property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.
To calculate the monthly payment, we can use the formula:
M = P [i(1 + i)^n] / [(1 + i)^n – 1]
Where M is the monthly payment, P is the loan amount, i is the interest rate, and n is the number of payments (in this case, the number of months in 30 years)
Plugging in the values,
M = 150000 * (0.0929 / 12) / [ (1 + (0.0929 / 12))^(12 * 30) - 1]
This gives a monthly payment of $1238.
To find out how many points he needs to improve his credit score, we can compare this monthly payment to the maximum monthly payment he can afford, which is $14,000.
If $1238 is more than $14,000, he would need to improve his credit score to a point where the monthly payment would be less than $14,000. By looking at the table, we can see that the interest rate for credit score of 620-674 is 7.40%.
Hence, (D) option is the correct answer.
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Adya makes 9/38 liters of soup for a party. The guests eat 3/57 liters. Use estimation to complete the statements below about Adya's soup.
the remaining soup at Adya's place is 24/114 liters As per the given ratio.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Adya makes 9/38 liters of soup for a party. The guests eat 3/57 liters.
Since the total soup was 9/38 liters
Thus,
Remaining soup at Adya = 9/38 -3/57
LCM of 38 and 57 are 114
Remaining soup at Adya = 27/114 - 6/114
Remaining soup at Adya = 27/114 liters
Therefore, the remaining soup at Adya's place is 24/114 liters.
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are 1/2x + 3/4 - 5/8x - 7/8 and 1/8(x + 1) equivalent expressions? show your work help plss
Answer: No they are not.
Step-by-step explanation:
1/2x and -5/8x are like terms, if subtracted you get 1 1/8x. But then you are left with an unlike term, 3/4 so your first equation would equal out to 1 1/8x + 3/4
Now for equation 2, you use your distributive property and get 1/8(x)=1/8x
Then you must distribute 1/8(1)=1/8
1/8x + 1/8
So, 1 1/8x + 3/4 ≠ 1/8x + 1/8
What is the equation of the line that passes through the point (-3,4) and has a slope of 2/3?
Answer:
y = 2/3x + 6
Step-by-step explanation:
for this problem, we need to find the value of b (the y-intercept). to do so, all we have to do is plug in the x and y values of the given ordered pair into the x and y values of the function. this will give us:
[tex]4=\frac{2}{3}(-3)+b[/tex]
solve for b and we get 6.
so, our slope-intercept equation is [tex]y=\frac{2}{3}x +6[/tex] .
hope this helped, good luck!
number of ice cream bars needed to sell 100 each weekend for a year
I year of weekends= 105days therefore 105, therefore you need 105 ice cream bars? hoped this helped
Mr. Rankin took his family out to dinner last night and their subtotal was $88.24. The sales tax was 5% and he left a 20% tip after the tax was added.
If Mr. Rankin put $120 on the table, how much change did he receive?
If Mr. Rankin put $120 on the table, the change he would receive $8.82
What is Percentage ?
Percentage can be defined as the product ratio of given value, total value and hundred.
Mr. Rankin took his family out to dinner last night and their subtotal was $88.24. The sales tax was 5% and he left a 20% tip after the tax was added.
If Mr. Rankin put $120 on the table, the change he would receive
tax = 5/100 * 88.24
tax = 4.412
tip = 20/100 * 88.24
tip = 17.648
Total amount = 88.24 +4.412+17.648
= 111.18
So, If Mr. Rankin put $120 on the table, the change he would receive
= 120 -111.18 = 8.82
Therefore, If Mr. Rankin put $120 on the table, the change he would receive $8.82
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GIVING 50 POINTS!
The right triangle below has legs of length a=7 and b=10. The hypotenuse has length c.
(look at the image)
Part 1: compute the total combined area of the four triangles.
Part 2: Compute the area of the large (outer) square.
Part 3: Using your answers from parts 1 and 2, find the area of the small inner square.
Part 4: We are given the side lengths a=7 and b=10. Compute a²+b².
Part 5: use <, >, or = to complete the statement below.
Part 1
The area of one triangle is [tex](1/2)(7)(10)=35[/tex]. Multiplying this by 4 yields [tex]\boxed{140}[/tex].
Part 2
[tex](10+7)^2=\boxed{289}[/tex]
Part 3
[tex]289-140=\boxed{149}[/tex]
Part 4
[tex]10^2+7^2=\boxed{149}[/tex]
Part 5
The statement is missing.
1) The total combined area of the four triangles is: 140; 2) The area of the outer square is c² = c * c; 3) The area of the small inner square is: c² - 70; 4) The sum of the squares of the two legs of a right triangle is: 149.
How to solve the area problem?Part 1:
The area of each triangle is (a * b) / 2, so the total combined area of the four triangles is 4 * (a * b) / 2 = 2 * 7 * 10 / 2 = 70.
Part 2:
The side length of the outer square is c, the hypotenuse, so the area of the outer square is c² = c * c.
Part 3:
The area of the small inner square is the area of the outer square minus the total combined area of the four triangles, so it is c² - 2 * 7 * 10 / 2 = c² - 70.
Part 4:
The formula for the sum of the squares of the two legs of a right triangle is a² + b² = c², so a² + b² = 7² + 10² = 49 + 100 = 149.
Part 5:
c > a and c > b, so c > 7 and c > 10. Therefore, c must be the largest of the three values: a, b, and c.
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If you help you get a cookie :)
What operation is happening between this coefficient and variable?
4y
Responses
A DivisionDivision
B AdditionAddition
C MultiplicationMultiplication
D Subtraction
Answer: the answer is A SO WERE IS MY COOKIE :(
Step-by-step explanation:
Use the screen shot- that has the question on it :)
Answer:
C
Step-by-step explanation:
This looks like a case of multiplying the number of X's by the respective number below it.
For example: the 1/2 has 3 X's, so we multiple (1/2)(3), making it (3/2) or 1.5
Next is the 1 having 2 X's, so (2)(1) is 2
Continuing that trend we get the following
1.5, 4, 2.5, and 3.
So all of our totals are 1.5, 2, 1.5, 4, 2.5, and 3.
Our last step will be adding all these answers together.
1.5 + 2 = 3.5
+ 1.5 = 6
+ 4 = 10
+ 2.5 = 12.5
and finally +3 = a grand total of 15.5 or 15 1/2
A fast ferry takes 4 hours to cross a lake an average speed of
108 km/h. On a particular day, it traveled at an average speed
of 94 km/h for 4 hours. What was the remaining distance?
____km
Answer:
The remaining distance will be "56 km".
Step-by-step explanation:
Speed and Time:
The speed (s) of an object seems to be the rate at which it travels from one location to some other. It's also calculated by dividing the distance (d) traveled by the timeframe (t) or duration.
According to the question,
Average speed when cross a late, 108 km/h
On particular day, average speed 94 km/h
Time taken, 4 hours
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^^^^^^
not my work
where I found the answer
Translate each verbal description into an algebraic expression. Simplify the expression when you can. 120% of 5x
120% can be expressed as a decimal by dividing it by 100: 120 / 100 = 1.2 So, 120% of 5x can be expressed as: 1.2 * 5x = 6x The expression simplifies to 6x.
What is algebraic expression?Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient. An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression.
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a track star runs two races on a certain day. the probability that she wins the first race is 0.7, the probability that she wins the second race is 0.6, and the probability that she wins both races is 0.5. what is the probability that: note: define your events, and write the probability statement before you calculate an answer. you can show your work using equations or venn diagrams.
The probability that the track star wins at least one race is 0.8, the probability that she wins the first race but not the second is 0.2, and the probability that she wins the second race but not the first is 0.1
Let A be the event that the track star wins the first race, B be the event that the track star wins the second race.
The probability that the track star wins at least one race is: P(A U B) = P(A) + P(B) - P(A ∩ B)
The probability that the track star wins the first race but not the second race: P(A ∩ B') = P(A) - P(A ∩ B)
The probability that the track star wins the second race but not the first race: P(A' ∩ B) = P(B) - P(A ∩ B)
Given:
P(A) = 0.7
P(B) = 0.6
P(A ∩ B) = 0.5
P(A U B) = 0.7 + 0.6 - 0.5 = 0.8
P(A ∩ B') = 0.7 - 0.5 = 0.2
P(A' ∩ B) = 0.6 - 0.5 = 0.1
So the probability that the track star wins at least one race is 0.8, the probability that she wins the first race but not the second is 0.2, and the probability that she wins the second race but not the first is 0.1.
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Pyrotechnicians can use polynomials to plan complex fireworks displays. A firework is launched from a platform 6 feet above the ground at a speed of 200 feet per second. The firework has a 5-second fuse. The height of the firework in feet is given by the polynomial -16t² + 200t + 6, where t is the time in seconds. How high will the firework be when it explodes?
the fireworks will be 612 feet high when it explodes.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, Pyrotechnicians can use polynomials to plan complex fireworks displays. A firework is launched from a platform 6 feet above the ground at a speed of 200 feet per second.
Expression that represents the height of firework = -16t² + 200t + 6
Since The firework has a 5-second fuse.
Thus, the firework will explode at t = 5
So, height at t= 5:
height of firework = -16 * 5² + 200*5 +6
height of firework = -16 * 25 + 1000 +6
height of firework = - 400 + 1000 + 6
Height of firework = 606
Since it started at 6 feet height
Thus total height at firework starts = 606 +6
total height at firework starts = 612
Therefore, the firework will explode at 612 feet in height.
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write an algebraic expression for each verbal expression, then simplify indicating the properties used:
1. the product of 9 and t squared, increased by the sum of 2 and the square of t
2. 3 times the quantity of d squared plus r, minus 2 times the quantity of d squared plus r
An algebraic expression for each verbal expression, and simplified indication of the properties are
1. 10t² + 2
2. d² + 2r
What is meant by algebraic expression?Arithmetic operations including subtraction, addition, division, multiplication, and exponentiation are used to build any algebraic expression from a combination of variables and integers. The word can be either a variable, a number, or the result of multiplying a variable by a number and adding an exponent.
Mathematical formulas like 3x + 4 are examples of algebraic expressions. They are distinct from algebraic equations because they lack the equals sign (=). The mathematics curriculum and mathematics in general place a lot of emphasis on algebraic expressions.
1. 9t² + 2 + t²
= 10t² + 2
2. 3d² + r - 2d² + r
= 3d²- 2d² + r + r
= d² + 2r
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The line inside this circle is its
A)
radius
B)
center
C)
diameter
D)
circumference
The line inside the circle depicted in the figure is radius.
A circle is defined as the round shape lacking corners and line. However, it does comprise of all the points in a plane. The center of the circle is the middle point which is equidistant from the outer surface of the circle. The outer surface or boundary of circle is called circumference.
A line joining the centre of the circle with circumference is called radius and the same is exhibited in the adjoining figure. A line that passes through the centre of the circle and touches the circumference at two ends is called diameter. Diameter is double in size to the radius.
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The complete question is attached in the figure.
An angle is two collinear rays with a common endpoint. Find an example that contradicts this definition. How would you change the definition to make it more accurate? (5 points)
Part B: Give an example of an undefined term and how it pertains to angles
As per the collinear point, the common endpoint is called the vertex of the angle, and the rays are called the sides of the angle.
The term collinear point in math is defined as a set of three or more points that exist on the same straight line
Here we have given that an angle is two collinear rays with a common endpoint.
And we need to find an example that contradicts this definition.
Here we also know that an angle is the union of two noncollinear rays with a common endpoint.
Then the common endpoint is called the vertex of the angle and the rays are called the sides of the angle.
And it is measure of an angle is a number representing the spread of the two arms of the angle.
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rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} \sqrt{3} \sqrt{7}}$, and write your answer in the form\[ \frac{a\sqrt{2} b\sqrt{3} c\sqrt{7} d\sqrt{e}}{f}, \]where everything is in simplest radical form and the fraction is in lowest terms, and $f$ is positive. what is $a b c d e f$?
The sum of a+b+c+d+e+f=57.
Apparently, you want to simplify: [tex]\frac{1}{\sqrt{2} +\sqrt{3} +\sqrt{7} }[/tex]
so the denominator is rational. It looks like the form you want is:
[tex]\frac{A\sqrt{2}+B\sqrt{3} +C\sqrt{7} +D\sqrt{E} }{F}[/tex]
And you want to know the sum A+B+C+D+E+F.
We can start by multiplying the numerator and denominator by a conjugate of the denominator. Then we can multiply the numerator and denominator by a conjugate of the resulting denominator.
[tex]\frac{1}{\sqrt{2} +\sqrt{3} +\sqrt{7}} .\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{\sqrt{2} +\sqrt{3} -\sqrt{7}} =\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{2\sqrt{6-2} } \\\\\\=\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{2\sqrt{6} -2} .\frac{\sqrt{6}+1 }{\sqrt{6} +1} =\frac{(1+\sqrt{6} )(\sqrt{2} +\sqrt{3} -\sqrt{7})}{10} \\\\\\=\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}+2\sqrt{3}+3\sqrt{2} -\sqrt{42} }{10} =\frac{4\sqrt{2} +3\sqrt{3} -\sqrt{7} -\sqrt{42} }{10}[/tex]
Comparing this to the desired form we have:
A = 4, B = 3, C = -1, D = -1, E = 42, F = 10
Then the sum is : A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57
The sum of interest is 57.
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A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $25. The total cost to rent 5 chairs and 6 tables is $65. What is the cost to rent each chair and each table?
The cost to rent each chair and table, based on the total cost to the party rental company, is:
Cost to rent chair = $ 2.50Cost to rent table = $ 8.75How to find the cost to rent the chairs and tables ?Let x be the cost of renting one chair and y be the cost of renting one table.
From the first piece of information given, we can write the equation:
3x + 2y = 25
From the second piece of information given, we can write the equation:
5x + 6y = 65
Solving these equations using elimination gives:
3x + 2y = 25
5x + 6y = 65
15x + 10y = 125
15x + 18y = 195
Subtracting gives:
0x + 8y = 70
y = $ 8.75
The cost to rent a chair is:
3x + 2 (8.75) = 25
3x + 17.5 = 25
3x = 7.5
x = $ 2.5
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What percent of the men surveyed shop online? Round your answer to the nearest whole number percent.