The percent of nonconforming items in the sample is 5.3%.
1. Calculate the total number of items in the sample (300).
2. Calculate the number of nonconforming items in the sample (16).
3. Calculate the total number of conforming items in the sample (284).
4. Divide the number of nonconforming items by the total number of items in the sample to get the percentage of nonconforming items (16/300 = 0.053).
5. Divide the number of conforming items by the total number of items in the sample to get the percentage of conforming items (284/300 = 0.947).
6. Multiply the result by 100 to get the percent of nonconforming items in the sample (0.053 x 100 = 5.3%).
7. Multiply the result by 100 to get the percent of conforming items in the sample (0.947 x 100 = 94.7%).
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Find the Perimeter of the triangles.
GEOMETRY HONORS I
the perimeter of the given triangles will be 119 inches and 73.5 inches.
What is Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given a triangle that has two angles equal,
Since the isosceles triangle has both two equal sides and two equal angles.
Thus, the given triangle is an isosceles triangle
So,
7x - 13 = x + 29
6x = 42
x = 8
From the general formula of the perimeter:
The perimeter of a triangle = sum of all sides
In our case,
perimeter = 7x - 13 + x + 29+ 3x + 5
perimeter = 11x +31
Substitute the value of x
Perimeter = 11 * 8 + 31
The perimeter of the triangle = 119 in.
The same process will be followed in question number 11
and the perimeter of the triangle in question 11 will be 73.5 inches
Therefore, the perimeter of the given triangles will be 119 inches and 73.5 inches.
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Write a polynomial function of least degree that has the following zeros. 3,6 square root of 6
there are four factors, giving it a fourth degree. This is the polynomial function of least degree that has the zeros 3, 6, and √6.
f(x) = (x - 3)(x - 6)(x - √6)(x + √6)
We start by listing out the zeros
3, 6, √6
Now, we can write the polynomial function of least degree that has these zeros
f(x) = (x - 3)(x - 6)(x - √6)(x + √6)
Note that this is a fourth degree polynomial because it has four factors.
We can write a polynomial function of least degree that has the following zeros: 3, 6, and √6. This polynomial function is a fourth degree polynomial, which means it has four factors. We can write it as f(x) = (x - 3)(x - 6)(x - √6)(x + √6). This polynomial function has the zeros 3, 6, and √6, and any other x-value that makes the equation equal to 0. The degree of the polynomial depends on how many factors are in the equation, and in this case, there are four factors, giving it a fourth degree. This is the polynomial function of least degree that has the zeros 3, 6, and √6.
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finally, you meet a group of six natives, u, v, w, x, y, and z, who speak to you as follows. u says: none of us is a knight. v says: at least three of us are knights. w says: at most three of us are knights. x says: exactly five of us are knights. y says: exactly two of us are knights. z says: exactly one of us is a knight. which are knights? (select all that apply.) u v w x y z incorrect: your answer is incorrect. which are knaves? (select all that apply.)
None of U, V, W, X, Y, and Z are knights, but some of them are knaves. V, W, X, and Y are knaves because their statements are false, and Z is a knight because their statement is true.
The group of six natives, U, V, W, X, Y, and Z, all make statements about how many of them are knights. U says that none of them are knights, which is false. V says that at least three of them are knights, which is also false. W says that at most three of them are knights, which is false. X says that exactly five of them are knights, which is also false. Y says that exactly two of them are knights, and this is false. Finally, Z says that exactly one of them is a knight, and this is true. Therefore, none of U, V, W, X, Y, and Z are knights, but some of them are knaves. V, W, X, and Y are knaves because their statements are false, and Z is a knight because their statement is true.
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Is the given set, taken with the usual addition and scalar multiplication, a vector space? Give reason. If your answer is yes, find the dimension and basis. A. All skew-symmetric 3 times 3 matrices. B. All functions y(x) = a cos(2x) + b sin(2x) with arbitrary real constants a and b.
A. No, B. Yes, dimension is 2 and basis is y(x) = cos(2x), y(x) = sin(2x).
A. No, this set is not a vector space. The set of all skew-symmetric 3x3 matrices does not contain the zero matrix, which is a requirement for a vector space.
B. Yes, this set is a vector space. The dimension is 2, and the basis is the functions y(x) = cos(2x) and y(x) = sin(2x). To verify this is a vector space, we need to check that the set is closed under addition and scalar multiplication. For arbitrary real constants a and b, the function y(x) = a cos(2x) + b sin(2x) is a linear combination of the basis vectors. This means that it is closed under addition and scalar multiplication, so the set is a vector space
A. No, B. Yes, dimension is 2 and basis is y(x) = cos(2x), y(x) = sin(2x).
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Solving equations: 12x + 5 = 4x + 37
Answer:
x = 4
Step-by-step explanation:
12x + 5 = 4x + 37
subtract 5 from both sides:
12x + 5 - 5 = 4x + 37 - 5
12x = 4x + 32
subtract 4x from both sides:
12x - 4x = 4x + 32 - 4x
8x = 32
divide both sides by 8:
8x/8 = 32/8
x = 4
y = 3x + 2
y = 4x-5
Please help i need to show my work
Answer: To solve for x, we need to find the value of x that makes both equations equal to each other. We can do this by setting the two equations equal to each other and solving for x:
3x + 2 = 4x - 5
Subtracting 4x from both sides:
-x - 2 = -5
Adding 2 to both sides:
-x = -3
Finally, dividing both sides by -1:
x = 3
So x = 3 is the solution that makes both y = 3x + 2 and y = 4x - 5 equal to each other.
You can substitute x = 3 into either equation to find the corresponding y value:
y = 3x + 2, when x = 3, y = 3(3) + 2 = 9 + 2 = 11
y = 4x - 5, when x = 3, y = 4(3) - 5 = 12 - 5 = 7
So the solution is (x, y) = (3, 11) or (3, 7).
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue graph?
A. G(x) = (x - 1)^2 - 3
B. G(x) = (x - 1)^2 + 3
C. G(x) = (x + 1)^2 - 3
D. G(x) = (x + 1)^2 + 3
14y+37/5 - 8 (2y - 1)
Step-by-step explanation:
[tex]14y + \frac{37}{5} - 8(2y - 1)[/tex]
BODMAS:
We deal with the brackets first
[tex]8(2y - 1) [/tex]
we multiply everything in the brackets with 8
[tex] - 8 \times 2y = - 16y[/tex]
[tex] - 8 \times - 1 = 8[/tex]
[tex]14y + \frac{37}{5} - 16y + 8[/tex]
Let's bring the like-terms together by rearranging the question
[tex]14y - 16y + 8 + \frac{37}{5} [/tex]
[tex]14y - 16y = - 2y[/tex]
[tex]8 + \frac{37}{5} = 15.4[/tex]
Answer[tex] - 2y + 15.4[/tex]
Solving inequalities #2
3. For a different shipment, cars are loaded first, and then trucks are loaded afterwards. a. Write an equation you could enter into a calculator or a spreadsheet tool to find the number of trucks that can be shipped if the number of cars is known. SEMI
b. Use vour equation and a calculator or a computer to find the number of trucks that can be shipped if the cargo already has 1,000 cars. What if the cargo already has 4,250 cars?
a) The solution to the equation is y = ( 21,600 - 3.6x ) / 7.5 , where y is the number of trucks and x is the number of cars
b) when x = 1,000 cars , y = 2,400 trucks and
when x = 4,250 cars , y = 840 trucks
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of cars be x
Let the number of trucks be y
The total cargo the ship can hold = 21,600 tons
The weight of one car = 3.6 ton
The weight of one truck = 7.5 tons
Now , the equation will be
3.6x + 7.5y = 21,600
On simplifying the equation , we get
Subtracting 3.6x on both sides of the equation , we get
7.5y = ( 21600 - 3.6x )
Divide by 7.5 on both sides of the equation , we get
y = ( 21,600 - 3.6x ) / 7.5
The number of trucks y = ( 21,600 - 3.6x ) / 7.5
b)
Now , when x = 1000 cars
Substitute the value of x in the equation , we get
y = ( 21,600 - 3.6 ( 1000 ) ) / 7.5
y = 2,400 trucks
And , when x = 4250 cars
Substitute the value of x in the equation , we get
y = ( 21,600 - 3.6 ( 4250 ) ) / 7.5
y = 840 trucks
Hence , the equation is y = ( 21,600 - 3.6x ) / 7.5
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The graph of y = |x| is reflected across the x-axis and then scaled vertically by a factor of
1/4
What is the equation of the new graph?
A.y= -4|x|
B.y= |x| -4
C.y= -1/4 |x|
D.y= |x-4|
The most appropriate choice for dilation and vertical dilation will be given by:
Equation of new graph => C.y= -1/4 |x|
What is dilation and vertical dilation?Dilation is the process of changing the dimension of an object by some scale factor.
Suppose the scale factor is K. Let the equation be y=f(x) . Then vertical dilation of is y= K.f(x)
Here, we have,
y = |x| ,
is reflected across the x-axis
Equation after reflection from x - axis = - |x|
Now, y = - |x|, is scaled vertically by a factor of 1/4
Equation of new graph => y= -1/4 |x|
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A total of 444 tickets were sold for a school play. They were either adult tickets or student tickets. There were 56 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
250 adult tickets
Step-by-step explanation:
s = number of student tickets
a = number of adult tickets
s = a - 56 ==> 56 fewer student tickets sold than adult tickets
s + a = 444 ==> 444 total tickets were sold
(a - 56) + a = 444 ==> plug in a - 56 for s to solve for one variable
a - 56 + a = 444
a + a - 56 = 444 ==> combine like terms
2a - 56 = 444
2a = 500 ==> add 56 on both sides
a = 250 adult tickets
s:
s + a = 444
s + 250 = 444 ==> plug in 250 for a
s = 194 student tickets sold
a - s = 56
250 - 194 = 56 √
Hence, the difference between the number of student and adult tickets is 56.
Blitzstein, 1.43) Let A and B be events. The symmetric difference AAB is defined to be the in A or B but not both. In logic and engineering, this event is also set of all elements that are called the XOR (exclusive or) of A and B. We will show P(AAB) P(A)+ P(B) 2P(An B) in two ways: words and a picture and (a) via an explanation of why this makes using your own sense (b) by using the definition and properties of probability.
The XOR (exclusive or) of two events A and B can be defined as the set of all elements that are in either A or B but not both.
The probability of this event, P(AAB), can be calculated by summing the probabilities of A and B and subtracting twice the probability of the intersection of A and B, as follows:
P(AAB) = P(A) + P(B) - 2P(AnB)
This can be illustrated with a Venn diagram, where A and B are represented by two overlapping circles. The intersection of A and B, AnB, is represented by the overlapping region, and the symmetric difference, AAB, is represented by the non-overlapping regions of A and B.
The probability of AAB can then be calculated by adding the area of the two non-overlapping regions and subtracting twice the area of the overlapping region.
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if we increase the compounding interval (from annual to daily) what will be the impact on 1) future value of an investment 2) present value of an investment.
Increasing the compounding interval from annual to daily has a positive impact on the future value of an investment and a negative impact on the present value of an investment.
The compounding interval refers to the frequency at which interest is calculated and added to the balance of an investment. Increasing the compounding interval from annual to daily will impact the future value and present value of an investment.
Future value of an investment: The future value of an investment increases with a higher compounding interval. With daily compounding, interest is calculated and added to the balance more frequently, leading to a higher future value of the investment. This is because each new interest calculation builds on the previous interest, which compounds over time to increase the overall value of the investment.Present value of an investment: The present value of an investment decreases with a higher compounding interval. This is because with a higher compounding interval, the expected future value of the investment is higher, making the present value lower. The present value represents the value of an investment today, and a higher future value means that the investment is worth more in the future, making the present value lower.Learn more about interest :
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the graph pf a linear function passes through the points (4,21) and (12,35). write an equation for the function. Write your answers in the blank
Answer:
y = 7x - 7
Step-by-step explanation:
The equation for the function can be found using the slope-point form of a linear equation: y = mx + b, where m is the slope of the line and (x, y) is a point on the line.
To find the slope, we can use the two points:
m = (35 - 21) / (12 - 4) = 7
To find the y-intercept, we can substitute one of the points and the slope into the equation:
21 = 7 * 4 + b
Solving for b, we get:
b = 21 - 28 = -7
So, the equation of the line is:
y = 7x - 7
A box has 36 straws in it Thare are O blue travs, 12 pink stran the screws ts orange . straws, and 3 white straws. here are 6 blue stricent, what part of the straws is oranger
The orange straws make up 41.7 percent of the total straws in the box.
How to find the percentage of the orange part?First, let's find the total number of blue straws:
Number of blue straws = Number of blue stricent + Number of blue straws = 6 + 0 = 6
Next, let's find the total number of pink straws:
Number of pink straws = 12
And finally, let's find the number of orange straws:
Number of orange straws = Total number of straws - (Number of blue straws + Number of pink straws + Number of white straws)
Number of orange straws = 36 - (6 + 12 + 3)
Number of orange straws = 36 - 21
Number of orange straws = 15
So, the orange straws make up 15 out of 36 total straws, or 15/36 of the total. To express this as a decimal, we can divide 15 by 36:
15/36 = 0.417
And to express this as a percentage, we can multiply the decimal by 100:
0.417 * 100 = 41.7%
So, the orange straws make up 41.7% of the total straws in the box.
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Suppose that the perimeter of a rectangle is 34 feet, and the length is 7 feet more than the width. Find the width of the rectangle, in feet.
Answer:
5 feet
Step-by-step explanation:
Let's call the width of the rectangle "w". Then, the length would be "w + 7".
The perimeter of the rectangle is given as 34 feet, so we can set up an equation using the two sides of the rectangle:
2w + 2(w + 7) = 34
Expanding the second term and simplifying the equation, we get:
2w + 2w + 14 = 34
4w + 14 = 34
4w = 20
w = 5
Therefore, the width of the rectangle is 5 feet.
Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10. One piggy bank has $7.31 in it. Select the choices that make the inequality and statement about the possible amount of money in the other piggy bank correct.
Answer:
Step-by-step explanation:
c
A primary credit cardholder's card has an APR of 22.99%. The current monthly balance, before interest, is $4,528.34. Determine how much more the cardholder will pay, making monthly payments of $200, until the balance is paid off, instead of paying off the current balance in full.
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$1,771.34
$1,275.17
$1,486.76
$1,465.96
The amount more that the cardholder will pay, given the amount owed and the monthly payment, is D. $ 1, 465. 96.
How to find the amount ?You can use a credit card repayment calculator to find the payment period when you have a credit card balance of $ 4, 528. 34, an interest rate of 22. 99 % and monthly payments of $ 200.
This repayment period would be 29. 97 or 30 months approx. which means that the total paid would be:
= 29. 97 x 200 per month
= $ 5, 994. 30
The amount that the credit card holder would pay over paying the current balance is:
= 5, 994. 30 - 4, 528. 34
= $1,465.96
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Answer: D- $1,465.96
Step-by-step explanation: I got it right on the test :)
You have a beginning balance of $200.00. You purchase groceries at Albertson’s on November 13th, 2004 for $42.63. Next you receive a check on November 14th, 2004 for $20.45 and deposit into your account. Finally, you write another check to Ms. Talisman on November 15th, 2004 for a textbook that costs $35.10.
The ending balance on your account on November 15, 2004, was $142.72.
What is the ending balance?The ending balance is the arithmetic difference between the beginning balance, deposits, and withdrawals, including interest and finance charges.
To determine the ending balance, add all deposits to the beginning balance and deduct all charges against the account
Beginning balance $200.00
Nov. 13, 2004 Groceries Purchase $42.63 $157.37
Nov. 14 Deposit $20.45 $177.85
Nov. 15, 2004 Check for textbook $35.10 $142.72
Thus, based on your beginning balance, deposits, purchases, and checks, the ending balance has been determined as $142.72.
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Question Completion:Indicate your remaining balance.
Is the question below
(one solution)
(infinite number of solutions) or
(no solution)
The graph of the equation shown above has infinite number of solutions.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solution (infinite number of solutions) when the left hand side and right hand side of the equation are the same or equal.
Since the line representing this equation extends infinitely, we can reasonably infer and logically deduce that it has infinitely many solution (infinite number of solutions). Therefore, every point located on this line would satisfy the equation.
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In a triangle ABC with an orthocenter O, prove that angle BOC plus angle BAC equal to 180°.
Prove: <BOC + <BAC = 180°
This can be proved by considering triangle BOC and triangle BAC as right triangles. The sum of the angles in a triangle is 180°, and in a right triangle, one of the angles is 90°. So, in each of triangles BOC and BAC, the sum of the other two angles must be 90°.
What is a triangle?A triangle is a geometric shape that consists of three points, called vertices, connected by three line segments, called sides. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified based on their sides (equilateral, isosceles, scalene) and their angles (acute, right, obtuse).
Hence, the sum of angle BOC and angle BAC must be 180°
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the last digit in a measured value, whose exact value we cannot know for sure, is referred to as the . multiple choice question. rate-limiting digit certain digit uncertain digit determinant digit
The "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.
Explain about the uncertain digit?The total number of certain digits in a measurement plus one estimated or uncertain digit make up the significant figures.
Specific graduations or markings on the tool that is used to record the measurement are the basis for some of the digits. A measurement with the more significant figures will be produced by a tool with much more graduations. A guess or estimate of the object's location between the closest graduations is a "uncertain digit." As a result, in a measurement that is accurately reported, the last digit is important but uncertain.Thus, the "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.
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Write the "to prove" statement for the following theorem.
If one angle of a triangle is 90°, then the other two add to 90°.
To prove: If one angle of a triangle is 90°, then the sum of the other two angles is equal to 90°. is sum of angles on a triangle is 180 degrees
What is sum of angles on a triangle?In a triangle, the sum of the interior angles in the triangle is 180 degrees
For right triangle, that is angle that has one side as 90 degrees, the sum of the other two sides will be 90 degrees
Assuming the other angles are x and y, then a side is 90 degrees
x + y + 90 = 180 (sum of interior angles on a triangle)
x + y = 180 - 90
x + y = 90 degrees
hence the sum of the interior angles is 90 degrees
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y=-7x+14x-5 in vertex form
The vertex form of an equation is,
⇒ y = - 7 (x - 1)² + 2
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ y = - 7x² + 14x - 5
Now, We can solve the equation for the vertex form as;
⇒ y = - 7x² + 14x - 5
⇒ y = - 7 (x² - 2x + 1) + 7 - 5
⇒ y = - 7 (x - 1)² + 2
Thus, The vertex form of an equation is,
⇒ y = - 7 (x - 1)² + 2
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Pierre is 3 years older than his brother, Claude. 1. Write an equation that represents how old Pierre is (p) when Claude is c years old.
The equation which is used to represent the ages of Pierre and Claude is given by p = c + 3.
The question can be formulated in the form of Linear equation in two variables.Linear equation in two variables can be written in the form of ax + by = c where a, b and c are constant terms and x, y are independent and dependent variables respectively. Here in this question the age of Pierre is represented as p and the age of Claude is represented as c. Since, Pierre is 3 years older than Claude then the equation representing their age can be formulated as:
p = c + 3 where p is Pierre's age and c is Claude's age and this represents that Pierre's age will be given when we will add 3 years more in the age of Claude.
Thus, the equation representing the age of Pierre is p = c + 3.
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Answer:
p=c+3
20 years old
Step-by-step explanation:
Jori ordered packets of beads. Three packets contained a total of 36 beads. Four packets had a total of 48 beads, 5 packets had a total of 60, and 6 packets had a total of 72.
This a proportional relationship.
Let p represent the number of packets and b represent the number of beads.
Given that the relationship between packets and beads is proportional, which equation models this relationship?
Answer:
Step-by-step explanation:
We can use the concept of unit rate to find the constant of proportionality between the number of packets and the number of beads.
For the first case, with 3 packets and 36 beads, the unit rate is 36/3 = 12 beads per packet.
For the second case, with 4 packets and 48 beads, the unit rate is 48/4 = 12 beads per packet.
We can see that the unit rate is the same for both cases, so we can conclude that the relationship between the number of packets and the number of beads is proportional, and the constant of proportionality is 12 beads per packet.
Therefore, the equation that models this relationship is:
b = 12p,
where b is the number of beads and p is the number of packets.
lesson 15 hinduism assingment
Vaishyas were merchants and farmers, Shudras were manual laborers, and Dalits, also known as Untouchables, were considered outside the caste system and faced significant social and economic discrimination.
How to explain the social casteThese are the traditional castes or social classes in Hinduism. The Brahmins were highly respected as they were members of this highest caste. Priest, scholars, and teachers were some of the jobs in this cast so I chose praying hands and a book to represent them.
The praying hands shows they were religious leaders who passed down oral and written traditions. The book represents the teachers in this caste, they would share knowledge and Information about their way of life.
Kshatriyas were warriors and rulers,
However, the caste system has been officially abolished in India, and discrimination based on caste is now illegal.
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Luis tiene bolitas azules y rojas.
Cada día gana 2 bolitas azules y pierde
3 rojas.
Al cabo de 5 días tiene igual cantidad de azules que de rojas.
Al cabo de 9 días tiene el doble de azules que de rojas.
¿Cuántas bolitas rojas tenía al principio?
Answer:
47
Step-by-step explanation:
a = número original de bolitas azules
r = número original de bolitas rojas
Al cabo de 5 días:
a + 5 × 2 = r - 5 × 3
Al cabo de 9 días:
a + 9 × 2 = 2(r - 9 × 3)
a + 10 = r - 15
a + 18 = 2r - 54
a = r - 25
a + 18 = 2r - 54
a = r - 25
r - 25 + 18 = 2r - 54
a = r - 25
-r = -47
r = 47
Answer: 47
One side of a triangle is 9 cm shorter than the base, x. The other side is 17 longer than the base.
What lengths of the base will allow the perimeter of the triangle to be at least 32 cm? Write your
answer as an interval.
Answer:
(26, ∞)
Step-by-step explanation:
(I am assuming the question has been copied and pasted properly because the answer is not as simple as computing inequalities. It also involves using triangle properties)
Let the sides of the triangle be
x, y and z where x is the base
Let y be the side which is 9cm shorter than x:
y = x - 9
Let z be the side which is17cm longer than x:
z = x + 17
Perimeter = x + y + z
= x + (x-9) + (x + 17)
= x + x + x -9 + 17
= 3x + 8
We are told that the perimeter should be at least 32 cm
So 3x + 8 ≥ 32
Subtract 8 from both sides of the inequality:
==> 3x + 8 - 8 ≥ 32 - 8
==> 3x ≥ 24
Divide by 3 both sides:
==> 3x/3 ≥ 24/3
==> x ≥ 8
If these were inequalities in x, then this would be the solution and the interval will be [8, ∞ ]
However, we can see that some of the values for x are impossible within this inequality
For example, for x = 8, y = -1
for x = 9 y = 0 and both these are not possible in a triangle
Since these are the sides of a triangle. In any triangle, the sum of any two sides must be greater than the third side
In this particular triangle, the shortest side is y= x - 9 and the longest side is z = x + 17
So the shortest side + x > longest side
x + y > z
==> x + x -9 > x +17
2x - 9 > x + 17
Moving x to the left side and -9 to the right side
2x - x > 17 + 9
x > 26
So x must be greater than 26 and it can go all the way to infinity. Remember x need not be an integer
The interval is (26, ∞)