Patty is 12 years old, and Terry is 4 years old. After setting up an equation based on their ages now and in 10 years, we determine that Terry is 4, and since Patty is three times as old, she is 12.
The problem presented is a typical age-related algebraic question. To solve it, we can set up equations based on the information given. Let's define Patty's current age as 3T, where T represents Terry's current age. In 10 years, Patty will be 3T + 10 and Terry will be T + 10. According to the problem, the sum of their ages in 10 years will be 36. So, we can write the following equation:
3T + 10 + T + 10 = 36
Solving this equation:
Combine like terms: 4T + 20 = 36Subtract 20 from both sides of the equation: 4T = 16Divide both sides by 4 to find Terry's age: T = 4With Terry's age being 4, Patty's current age is 3 times Terry's age, which means Patty is 3 × 4 = 12 years old. So, Patty is 12 and Terry is 4 years old right now.
Inga lives 3 miles more than twice as far from school as Brent does. If Brent lives b miles from school then Inga lives ____ miles from school
Inga lives 2b + 3 miles from school, where b is the distance Brent lives from school in miles.
Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.
Explanation:The problem states that Inga lives 3 miles more than twice the distance that Brent lives from school. If the distance Brent lives from school is b miles, this can be expressed algebraically as 2*b (twice the distance of Brent) + 3 (the extra 3 miles that Inga lives). Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.
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the function a(b) relates The area of a trapezoid with a given height of 12 and one base length of 9 with the length of its other base
The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.
What is the area of a trapezoid?If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as
= [(a + b)h]/2
Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.
Therefore, 'b' is the parallel side of the base.
The given function that represents the area of the trapezoid is:
A(b) = [12(b + 9)]/2
Let, A(b) = a.
Therefore, a = [12(b + 9)]/2
⇒ 2a = 12(b + 9)
⇒ a = 6(b + 9)
⇒ a = 6b + 54
⇒ 6b = a - 54
⇒ b = (a - 54)/6
⇒ b = a/6 - 9
If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:
B(a) = a/6 - 9
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What's a fraction for 77/200
What’s 2ax2b simplified?
Michael owns a lawn care service. He charges each customer 30 + 12h dollars, where h represents the number of hours spent working on a lawn. What does each part of the expression represent? Drag the answer into the box to match each part of the expression.
The linear expression 30 + 12h represents Michael's lawn care service charges, where '30' is the fixed fee and '12h' is the variable fee depending on the hours worked.
Explanation:Michael's lawn care service uses an equation to calculate the charges for his customers: 30 + 12h dollars, where h represents the number of hours spent working on a lawn. In this expression, the number 30 represents a fixed fee, likely covering base expenses such as equipment, transportation, or administrative costs. The term 12h represents the variable fee, where 12 is the hourly rate in dollars Michael charges for his labor, and h is the number of hours he works on the lawn.
Thus, to determine the total cost to a customer, one would multiply the number of hours Michael works (h) by his hourly rate (12) and then add the fixed fee (30). For instance, if Michael works 5 hours on a lawn, the total cost would be calculated as follows: 30 + 12(5) = 30 + 60 = 90 dollars.
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Determine whether the inequality is always, sometimes, or never true. 4x - 8 > 1 + 4(x+3)
Answer:
Never true
Step-by-step explanation:
Given inequality,
[tex]4x - 8 > 1 + 4(x+3)[/tex]
[tex]4x-8 > 1 + 4x + 12[/tex]
[tex]4x-8 > 4x + 13[/tex]
[tex]-8 > 13[/tex] ( false )
Since, when after solving an equation or inequality we get a true statement then the equation or inequality has infinitely many solution or true for all numbers while if we get a false statement then the equation of inequality has no solution or not true.
Hence, the given inequality is never true.
Which set of data contains one outlier? 15, 19, 26, 51, 18, 21 22, 33, 31, 20, 28, 19 18, 20, 16, 22, 28, 26 27, 21, 31, 18, 21, 29
Answer:
The correct answer is A) 15, 19, 26, 51, 18, 21
Step-by-step explanation:
So let me start by explaining what an outlier is: An outlier is any data that falls outside of the given points, The reason the answer is A) is because 51 is included in the points, While most of the points in A) Are anywhere from 15-26 51 is an outlier because its outside of that standard range. The other ones don't have an outlier.
The data set that contains one outlier is,
{15, 19, 26, 51, 18, 21}.
The correct option is A.
What is set?Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Given:
We have data set:
15, 19, 26, 51, 18, 21
22, 33, 31, 20, 28, 19
18, 20, 16, 22, 28, 26
27, 21, 31, 18, 21, 29
From the given choices,
the first data set has an outlier 51.
Because it is nowhere from the range of the data set.
Therefore, the set is {15, 19, 26, 51, 18, 21}.
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Which exponential function is represented by the table? f(x) = 2(2x) f(x) = 0.8(0.8x) f(x) = 2(0.8x) f(x) = 0.8(2x)
table
-2 0.2
-1 0.4
0 0.8
1 1.6
2 3.2
What methods could you use to calculate the x-coordinate of the midpoint of a horizontal segment with the endpoints of (-12, 0) and (12, 0)?
** choose all that apply **
A. calculate the average of the x-coordinates
B. divide 0 by 12
C. divide 12 by 2
D. take the average of the endpoint
E. divide 2 by 12
A. calculate the average of the x-coordinates
C. divide 12 by 2
D. take the average of the endpoint
can u guys show me how 58 is the right answer? i need to see where i went wrong so please include the whole process.
NMO = LMO = x+34
LMO = 1/2 of LMN
so 2(x+34) = 6x-28
2x+68 = 6x-28
2x +96 = 6x
96 = 4x
x =96/4 = 24
x = 24
LMO = x+34 = 24+34 = 58
since NMO = LMO, NMO = 58
Which of the following examplebles are substantiantiated fact?
All dogs kill sheep.
Poorly bred dogs kill sheep.
Two Neighbors and saw Eliot's dog kill a sheep.
A recent survey of sheep farmers revealed that 100,000 sheep were killed by dogs last year.
The response explains which statements are substantiated facts and why. It clarifies the concept by using examples from the question.
Explanation:Substantiated facts are statements supported by evidence or proof. In the given examples:
All dogs kill sheep - Not substantiated as it is a generalization.Poorly bred dogs kill sheep - Not substantiated as it lacks evidence.Two Neighbors saw Eliot's dog kill a sheep - Substantiated as it provides specific eyewitness evidence.A recent survey of sheep farmers revealed that 100,000 sheep were killed by dogs last year - Substantiated with data from a survey.Writing explain how you know when a linear system in three variables has infinitely many solutions.
A linear system in three variables has infinitely many solutions when the equations are dependent on each other and represent the same line or plane. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.
Explanation:When a linear system in three variables has infinitely many solutions, it means that the three equations are dependent on each other and represent the same line or plane. This happens when the coefficients of the variables in the equations are proportional to each other. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.
Let's take the system of equations given in the question:
7y = 6x + 84y = 8y + 7 = 3xWe can start by solving equations (1) and (2) for y:
7y = 6x + 8 (equation 1)4y = 8 (equation 2)Simplifying equation (2), we get:
y = 2
Substituting y = 2 into equation (1), we have:
7(2) = 6x + 8
14 = 6x + 8
6x = 14 - 8
6x = 6
x = 1
Now, let's substitute the values of x and y into equation (3):
y + 7 = 3x
2 + 7 = 3(1)
9 = 3
This equation is not true. Therefore, the system of equations is inconsistent and does not have infinitely many solutions. The system does not represent the same line or plane.
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please help! I am totally lost!
Joel borrowed $18,000 for 6 years at simple interest to purchase a vehicle. If Joel repaid a total of $20,953.80, at what rate did he borrow the money?
Joel borrowed money at an interest rate of approximately 2.73%. This was determined by using the simple interest formula to calculate the interest paid over 6 years and then re-formulating to find the interest rate using the known principal amount and time period.
Explanation:The subject of this question is simple interest which is a concept in Mathematics. The question is asking for the interest rate at which Joel borrowed money to purchase a vehicle. By knowing that Joel borrowed $18,000, repaid a total of $20,953.80 after 6 years, and by applying the simple interest formula I = PRT (where I is interest, P is principal amount, R is interest rate and T is time in years), we can find out the interest rate.
The first step is to calculate the simple interest itself, which can be found by subtracting the original principal amount from the total amount repaid. So, $20,953.80 - $18,000 = $2,953.80 is the interest paid over 6 years.
Then we rearrange the simple interest formula to solve for the rate: R = I / (PT). Substituting the known values, our equation is: R = $2,953.80 / ($18,000 * 6), which gives R = 0.027325, or approximately 2.73% when expressed as a percentage.
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You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324π324π cubic inches. What is the least possible height of the container?
Suppose a and b give the population of two states where a>b . Compare the expressions and tell which of the given pair is greater or if the expression are equal.
b/a+b and 0.5
What is the measurement of JKM
Factoring pattern for x squared plus bx plus c
Final answer:
To factor a quadratic expression in the form of x² + bx + c, find two numbers whose sum is equal to b and whose product is equal to c.
Explanation:
To factor a quadratic expression in the form of x² + bx + c, we look for two numbers whose sum is equal to b and whose product is equal to c. Let's illustrate with an example:
For the expression x² + 5x + 6, we need to find two numbers whose sum is 5 and whose product is 6. In this case, the numbers are 2 and 3.
Therefore, we can factor the expression as (x + 2)(x + 3).
∠C and ∠D are vertical angles with m∠C=−2x+90 and m∠D=x−30 . What is m∠D ?
The measure of m∠D is 10 degrees
In line geometry, vertical angles are always equal.
Given the following vertical angles
m∠C=−2x+90 and m∠D=x−30
Since m∠C= m∠, hence;
-2x + 90 = x - 30
-2x - x = -30 - 90
-3x = -120
x = 40
Get the measure of m∠D
m∠D = x - 30
m∠D = 40 - 30
m∠D = 10degree
Hence the measure of m∠D is 10 degrees
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Please help asap! Ignore the answer selected
While solving an equation, Lenny wrote the following steps on the board.
(2x + 1) + 5 = 9
2x + (1+5) = 9
What property of real numbers guarantees that the second equation is equivalent to the first?
A. Associative property of addition
B. Additive inverse property
C. Commutative property of addition
D. Distributive property
Lenny used the Associative property of addition to show that rearranging the grouping of numbers being added does not change the outcome of the equation.
While solving an equation, Lenny used the Associative property of addition which guarantees that the second equation (2x + (1+5) = 9) is equivalent to the first ((2x + 1) + 5 = 9). This property states that the grouping of numbers being added does not change the sum, as shown:
(A + B) + C = A + (B + C).
In the context of the provided equations, Lenny grouped the 1 and 5 together without changing the sum, illustrating that it doesn't matter how the numbers are grouped in addition.
-38d-57 greater than or equal to -19d+76
Final answer:
To solve the inequality -38d-57 ≥ -19d+76, we isolate d, resulting in d ≤ -7, meaning d is any number less than or equal to -7.
Explanation:
The question asks us to solve an inequality: -38d - 57 ≥ -19d + 76. This requires us to isolate the variable d on one side of the inequality.
Add 19d to both sides: -38d + 19d - 57 ≥ 76.
Simplify: -19d - 57 ≥ 76.
Add 57 to both sides: -19d - 57 + 57 ≥ 76 + 57.
Simplify: -19d ≥ 133.
Divide both sides by -19, and remember to reverse the inequality sign when dividing by a negative number: d ≤ -7.
The solution to the inequality is d ≤ -7. This means that d can be any number less than or equal to -7.
Henry Is 4 Years Older Than Half Linda's Age . If Linda is 10 Years Old, How Old Is Henry
Bob roller blades 9 miles each morning. today, he averaged 10 miles per hour for the first 6 miles but then slowed to 5 miles per hour for the rest of the trip. how long did the entire trip take?
Where the graphs of supply and demand functions intersect the market is in equilibrium
Find the value of y for a given value of x, if y varies directly with x.
If y = -252 when x = 84, what is y when x = 74?
Please explain with steps, thank you!
From the question given above, we were told that y varies directly with x. This can be expressed mathematically as:
y ∝ x
Replacing the proportionality sign (∝), we have
y = Kx
K => constant of proportionality
Next, we shall determine the value of K. This can be obtained as follow:
y = –252
x = 84
K =?y = Kx
–252 = K * 84
Divide both side by 84
[tex]K = \frac{-252 }{84}[/tex]
K = –3Finally, we shall determine the value of y when x = 74. This can be obtained as follow:
x = 74
K = –3
y =?y = Kx
[tex]y = - 3 * 74[/tex]
y = –222Therefore, the value of y when x = 74 is –222
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A 90-inch board is cut into two pieces. one piece is two times the length of the other. find the lengths of the two pieces
Final answer:
To find the lengths of the two pieces, set up an equation using the given information. Solve for x and find the lengths of the two pieces.
Explanation:
To solve this problem, let's assume the length of one piece is x inches. Since the other piece is two times the length of the first piece, its length is 2x inches. According to the given information, the total length of the board is 90 inches. Therefore, setting up the equation x + 2x = 90, we can solve for x and find the lengths of the two pieces.
Combining like terms, we have 3x = 90. Dividing both sides of the equation by 3, we get x = 30. Therefore, the length of one piece is 30 inches, and the length of the other piece is 2(30) = 60 inches.
you are building a fence 13ft long. on monday you build 4 1/3 feet of the fence, on tuesday 5 3/4 feet. how much do you still need to build
Given G (1,2) and K(8,12) Part A what does it mean to find the point ponline gk such that 3(GP)=2(PK)?
Answer:
To find point [tex]\( P \)[/tex] on line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're seeking a point dividing [tex]\( GK \)[/tex] into segments at a \( 3:2 \) ratio.
Explanation:
To find the point [tex]\( P \)[/tex] on the line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're essentially looking for a point [tex]\( P \)[/tex] that divides the line segment [tex]\( GK \)[/tex] into two segments, where the ratio of the length of the segment from [tex]\( G \) to \( P \)[/tex] to the length of the segment from [tex]\( P \) to \( K \) is \( 3:2 \).[/tex]
Here's how to approach it:
1. Calculate the distances [tex]\( GP \) and \( PK \)[/tex] using the distance formula (or Pythagorean theorem if it's a 2D coordinate plane).
2. Let [tex]\( x \)[/tex] be the distance from [tex]\( G \) to \( P \)[/tex] and [tex]\( y \)[/tex] be the distance from [tex]\( P \)[/tex] to [tex]\( K \).[/tex]
3. Set up the equation [tex]\( 3x = 2y \),[/tex] representing the ratio of the lengths.
4. Solve for [tex]\( x \) and \( y \)[/tex] to find the coordinates of point [tex]\( P \).[/tex]
This process ensures that the point [tex]\( P \)[/tex] divides the line segment [tex]\( GK \)[/tex] into two segments according to the given ratio.
What is the standard form of the number in the calculator’s display?
The calculator shows five point seven e plus eleven
A.
0.00000000057
B.
0.000000000057
C.
570,000,000,000
D.
5,700,000,000,000