Answer: The length of First piece = 6
The length of second piece = 18
The length of third piece = 30
Step-by-step explanation:
Given data,
A 54-inch board is to be cut into three pieces.
so that the second piece is 3 times as long as the first piece and the third piece is 5 times as long as the first piece.
So, we can write,
Let us assume, first piece is represented by = x
Then,
second piece is 3 times as long as the first piece
So, we can write,
second piece is represented by = 3 ( first piece )
second piece is represented by = 3x
Then,
third piece is 5 times as long as the first piece
So, we can write,
third piece is represented by = 5 ( first piece )
third piece is represented by = 5x
So, we can find the all 3 pieces length,
we can solve it :
combine all three pieces = x + 3x + 5x
length of all three pieces = x + 8x
= 9x
Total board is to be cut into three pieces = 54
Hence,
9 x = 54
x = 54/9
x = 6
Now we know that the base length, x, is equal to 6.
From there, we can find the length of the all three pieces is :
The length of First piece = x = 6
The length of second piece = 3x
= 3(6)
= 18
The length of third piece = 5x
= 5(6)
= 30
Therefore,
The length of First piece = 6
The length of second piece = 18
The length of third piece = 30
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If m∠ADB=( 3a + 10)° and m∠BDC= 13a°, find a, m∠ADB, and m∠BDC.
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
What is the numerical value of a, ∠ADB and ∠BDC?When two angles have measures adding to up to 90 degrees, they are called complementary .
Given that;
m∠ADB = ( 3a + 10 )m∠BDC = 13aNumerical value of a = ?For complimentary angles;
m∠ADB + m∠BDC = 90°
Plug in the given values and solve for a.
( 3a + 10 ) + 13a = 90
3a + 10 + 13a = 90
10 + 16a = 90
16a = 90 - 10
16a = 80
a = 80/16
a = 5
Now, find the measure of ∠ADB and ∠BDC.
m∠ADB = ( 3a + 10 ) = 3(5) + 10 = 15 + 10 = 25°
m∠BDC = 13a = 13( 5 ) = 65°
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
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Solve each equation. Round to the nearest ten-thousandth. Check your answers.
8+10x=1008
8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.
What is exponentiation?Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as [tex]b^n[/tex].Its pronunciation is "b (raised) to the (power of) n."Given: 8 + [tex]10^x[/tex] = 1008
=> [tex]10^x[/tex] = 1000
=> [tex]10^x[/tex] = 10³
=> x = 3
Hence, 8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.
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what does UIF stand for ?
UIF stands for Unemployment Insurance Fund.
When workers become unemployed or are unable to work due to maternity, adoption, or parental leave, or illness, the Unemployment Insurance Fund (UIF) provides them with short-term assistance. It also helps the dependents of a deceased contributor.South Africa's unemployment insurance system is governed by the following legislation: 2001 Unemployment Insurance Act (the UI Act). 2002 Unemployment Insurance Contributions Act (the UIC Act)These Acts, which went into effect on April 1, 2002, provide for the benefits to which contributors are entitled, as well as the imposition and collection of contributions to the UIF.Contributions to the UIF are due from all employees and their employers. However, an employee is not eligible to contribute to the UIF if he or she: is employed by the employer for less than 24 hours per month; is employed as an officer or employee in the national or provincial spheres of government; or is employed as an officer or employee in the national or provincial spheres of government. Is a traditional leader, a member of the province House of Traditional Leaders, and a member of the Council of Traditional Leaders.Thus this is the full form of UIF.
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Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. How many cans of paint did Tim buy?
If Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. The number of cans of paint that Tim buy is: 6 cans.
Number of can of paints boughtLet x represent the number of can
Quantity of addictive mixed in each liter=3/8
Total addictive mixed=3/4
Hence,
x(3/8)=3/4
Cross multiply
x=8(3/4)
x=6 cans of paint
Therefore If Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. The number of cans of paint that Tim buy is: 6 cans.
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alicia bought 2 1/2 dozen donuts for $8.10 . what was the cost per dount
Answer: $3.70
Step-by-step explanation:
30 divided by 8.10 equals 3.70
Simplify -3r(-12r + 4r - 16) please!!
Answer:FIRST ONE
Step-by-step explanation:
A triangle has sides with lengths of 57 yards, 74 yards, and 95 yards. Is it a right triangle?
The triangle with side lengths of 57 yards, 74 yards, and 95 yards is not a right triangle because it does not obey Pythagoras theorem.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Pythagoras theorem shows the relationship between sides of a right triangle. It states that for a right angled triangle:
Hypotenuse² = Leg1² + Leg2²
To prove that a triangle with side lengths of 57 yards, 74 yards, and 95 yards is a right triangle:
95² = 74² + 57²
9025 = 5476 + 3249
9025 ≠ 8725
The triangle with side lengths of 57 yards, 74 yards, and 95 yards is not a right triangle because it does not obey Pythagoras theorem.
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Ivan bought a new television. He was able to pay $120 at the time he received the television,
He will pay $44 each month on the balance. The original cost of the television was $736. Ilow
many months will it take Ivan to pay off the television?
Find the area of this circle.
Use 3.14 to approximate .
A = πr²
14 ft
A = [?] ft²
The area of the circle, using 3.14 to approx. The area of this circle is 615.44[tex]ft^{2}[/tex].
How to find the area of circle?The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = [tex]\pi r^{2}[/tex], where r is the circle's radius, is the formula for calculating a circle's surface area.
The square unit—for instance, [tex]m^{2}, cm^{2}, in^{2}[/tex] etc.—is the unit of area. In square units, the area of a circle is equal to [tex]\pi r^{2}[/tex]or [tex]\frac{\pi d^{2} }{4}[/tex]where (Pi) = [tex]\frac{22}{7}[/tex] or 3.14. The ratio of a circle's circumference to its diameter is known as pi (π). This unique mathematical constant exists.
Area = [tex]\pi r^{2}[/tex]
3.14×14×14 = 615.44[tex]ft^{2}[/tex].
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savannah is working two summer jobs, making $10 per hour washing cars and making $22 per hour tutoring. In a given week she can work at most 8 total hours and must earn no less that $110. Of x represents the number of hours washing cars and y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities are 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively.
What is inequality?In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Total amount by washing cars = 10x
Total amount by tutoring = 22y
Total hours should be no less than 8
So,
x + y ≥ 8
And,
Total amount ≥ 10
10x + 22y ≥ 10
By substitution,
10(8 - y) + 22y ≥ 10
y ≥ 2.5
And x ≥ 5.5
Hence "The system of inequalities is 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively".
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If 21 and 22 are vertical angles, <2 and <3 are complementary angles
and m/3 = 56°, find m/1.
Answer:
........................................
On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .
b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?
The height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² = 2 m
What is gravitational acceleration ?Gravitational acceleration can be defined as the acceleration of any object when the object is in free fall. or we can say that the gravitational acceleration is the quantity which describes the acceleration of free falling object within vacuum. It is denoted by g .
What is Potential Energy ?Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy.
Formula of potential energy :
U = mgh
where, U = gravitational energy
m = mass of object
g = gravitational acceleration
h = vertical height of object
In the question given,
g= -9.8m/s² , U = -39.2 kg m² /s²
as, U = mgh
h = U / mg
put the values in this equation
h = -39.2 / 2 (-9.8 )
h = 2
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The complete question is :
On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .
a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?
b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?
2. In a triangle, the measure of the first angle is six times a number. The measure of the second angle is nine less than the first angle. The measure of the third angle is three times the number more than the measure of the first angle. Determine the measure of each angle in degrees.
The measure of the angle 1, 2, and 3 will be 54°, 45°, and 81°, respectively.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The initial angle of a triangle is measured by multiplying a value by six. The second angle's measurement is nine less than the first angle's. The third angle's measure is three times greater than the first angle's measurement. Let x be the number. Then the measure of the angle 1, 2, and 3 will be
∠1 = 6x
∠2 = 6x - 9
∠3 = 3x + 6x
The sum of all angles will be 180°, then the equation will be
∠1 + ∠2 + ∠3 = 180°
6x + 6x - 9 + 3x + 6x = 180°
21x = 189°
x = 9°
Then the measure of the angles will be
∠1 = 6x = 6 × 9 = 54°
∠2 = 6x - 9 = 6 × 9 - 9 = 45°
∠3 = 3x + 6x = 9x = 9 × 9 = 81°
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John is driving to his office to attend a meeting. In the first 10 minutes, he covers a distance of 1 mile every minute. Then he stops at a local restaurant for 15 minutes to have breakfast. After that, he covers a distance of 0.5 miles every minute in the next 10 minutes to reach his office.
Which graph models the piecewise function for the given situation?
Answer:
Letter D is the correct answer.
Step-by-step explanation:
In the graph, the first line is an increasing diagonal and it stops in 10, meaning that John travelled 10 miles in 10 minutes.
After that, there is a horizontal line that indicates how much time he spent at the restaurant.
Finally, the last diagonal shows the distance travelled (5 miles) and the time it took (10 minutes.)
had the same question a couple minutes ago
hope it helps you;)
24 -7.2(-4x + 3) ≤-26.4
Answer:
x [tex]\leq[/tex]-1
Step-by-step explanation:
first distribute
24+28.8x-21.6[tex]\leq[/tex]-26.4
add like numbers
2.4+28.8x[tex]\leq[/tex]-26.4
move the constant to the right
28.8x[tex]\leq[/tex]-26.4-2.4
calculate
28.8x[tex]\leq[/tex]-28.8
divide both sides by 28.8
x[tex]\leq[/tex]-1
What number has the prime decomposition of 5 (power of 2) x 61?
The prime decomposition is [tex]5^{2}[/tex]×61.
Prime factor decomposition of a number means writing it as a product of prime factors. To factorize a number, divide it by the first possible prime number. Take a resulting quotient below the number.
Therefore the prime decomposition is
[tex]5^{2}[/tex] × 61
Here 5 and 61 is a prime number .
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Q 100+ 10+ 20 ÷4-5 x 2 + 8
Answer:
113 explanation I just took the test
Answer: 113
Step-by-step explanation:
100 + 10 +5 -10 +8 = 113
A gardener can care for the greens property in 5 hours. if his helper assists him, they will be done in 4 hours. how many hours does it take for the helper to do it alone
If a gardener can care for the greens property in 5 hours and if his helper assists him, they will be done in 4 hours, then the number of hours it takes for the helper to do it alone is equal to 20.
The number of hours it takes for the helper to do it alone can be found as follows;
Time taken by both the gardener and the helper to complete the job=4
Work done by both the gardener and the helper in one hour = 1/4
Similarly,
Time taken by the gardener to complete the job = 5
Work done by the gardener in one hour = 1/5
The number of hours it takes for the helper alone can be calculated by subtraction. Subtracting the fraction done by the gardener in 1 hour from the fraction done by both the gardener and the helper in 1 hour;
1/4 - 1/5
As the common denominator is 20, we multiply 1/4 by 5 and 1/5 by 4.
5/20 - 4/20 = 1/20
The number of hours it takes for the helper to do it alone can be found by finding the reciprocal of 1/20 which is equal to 20/1
20/1 = 20
Hence, the helper takes 20 hours to do it alone.
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What are the factor pairs of 63
29) Explain the difference of the two expressions in the question.
What is the difference between (f g)(x) and (fog)(x)?
The function fg(x) seems to be the product of f and g, whereas the function fog(x) is the composition of f and g.
Definition of a composite function:A function whose values are discovered by applying another function to an independent variable and then applying that second function to the result, and whose domain consists of those possible values for which the result yielded by the first function lies inside the domain of both the second.
What kind of math are composite functions?A composite function is one that is dependent on another. When one function is swapped for another, a composite function is formed. For example, f(g(x)) is the composite function created when g(x) is replaced for x in f. (x). f(g(x)) can be translated as "f of g of x."
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Sam flipped a coin 20 times. He got heads 12 times. What was the experimental probability of getting heads in Sam's coin toss experiment?
Answer: 60%
Step-by-step explanation:
12/20=.6
.6 is 60%
Answer:
21
Step-by-step explanation:
In the given right-angled triangle ABC, ∠B = 90°. Find the value of x.
Given - Sides of a triangle
Find - Value of x
Solution - The value of x is 3.
The sides of the right angled triangle are calculated by the Pythagoras theorem. As per the theorem,
Hypotenuse² = Base² + Perpendicular²
In the given triangle, Hypotenuse is (x+2), Perpendicular is 5 and Base is (x-3).
(x+2)² = 5² + (x-3)²
x² + 4x + 4 = 25 + x² - 6x + 9
On solving, the equation will be -
6x + 4x = 25 + 9 - 4
Performing addition and subtraction to find the value of x
10x = 30
x = 30/10
Performing division to find the value of x
x = 3
So, the value of x is 3.
A full bag of dog food weighs 51/2 pounds
How much dog food do you have if there are 334
bags in the cupboard
Step-by-step explanation:
I guess the question really is how much weight of dog food do you have.
1 bag = 51/2 pounds
334 bags = 334 × 1 bag = 334×51/2 = 167×51 =
= 8,517 pounds
Which expression is equivalent to log₅32 ?
(A) log 5+ log 32 (B) log 5- log 32 (C) (log 5)(log 32) (D) log 32/log 5
The given expression log₅32 is equivalent to the expression (D) log32/log5.
What do we mean by an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent rules. To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.To find which expression is equivalent to log₅32:
Law of logarithms:
The law of logarithms states that: log(a) b = log(10)b/log(10)aGiven the log function, which is written as log₅32
a = 5b = 32Substitute as: log₅32 = log32/log5
Therefore, the given expression log₅32 is equivalent to the expression (D) log32/log5.
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Find the value of f(5) for each function
1. f(x) = -2(x+1)
2. f(a) = 3(a +2)-1
3. f(h) =- h/10
4. f(m) = 1 - 4 (m/2)
5. f(m) = 2(m-3)
Answer:
1. -12
2. 20
3.-1/2
4. -9
5. 4
Step-by-step explanation:
1. -2(5+1) = -12
2. 3(5+2)-1 = 21-1 = 20
3. -5/10 = -1/2
4. 1-4(5/2) = 1-20/2 = 1-10 = 9
5. 2(5-3) = 4
The minimum distance from Earth to the Sun is 91.4 million miles. The maximum distance is 94.5 million miles. represent these 2 distances on a number line.
The required number line representation is attached
To solve this question we need to know the concept of number line :
Number lines are a horizontal straight lines in which the integers are placed in equal intervals all this numbers in a sequence can be represented in a number line . this line extends infinitely in both sides.
the numbers on the number line increases as one move right and decreases on moving from right to left . A number line can be used to depict both positive and negative integers. Writing numbers on a number line facilitates number comparison. The numbers on the left of the number line are smaller than the numbers on the right.
A number line can also be used to carry out addition , subtraction , multiplication and division . We move right to add move left to subtract and skip count to multiply .
The required number line is attached in the picture below :
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Assume that 632 people purchased pies that day. Explain how you could determine exactly how many people bought each type of pie.
In order to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.
How to illustrate the information?It should be noted that this is a pie chart and the information shows the percentage for each group.
In this case, to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.
For example, berry will be:
= 15.4% × 632
= 97
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Brian goes to the arcade with $20. The arcade charges $2.00 a game and a $1.50 entrance fee.
Write and solve an equation to find the number of games Brian can play. SHOW ALL WORK!
Brian can play only 9 games
How to calculate the number of games played ?Brian goes to the arcade with $20
The arcade charges $2 per game and $1.50 entrance fee
The equation can be represented as follows
20-1.50= 2x
18.5 = 2x
divide by the coefficient of x which is 2
x= 18.5/2
x= 9.25
Hence Brian will be able to plat only 9 games
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The figure shown is composed of a triangle within
a trapezoid. Determine the area of the
shaded region.
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
What is the Area of a Trapezoid?Area of ay trapezoid is determined using the formula:
Area = 1/2 × (a + b) × h, where a and b are the lengths of the bases of the trapezoid that are parallel, and h is the height or distance between the bases of the trapezoid.
What is the Area of a Triangle?
To find the area of a triangle, use:
Area = 1/2 × base × height of the triangle.
The area of the shaded region = area of the trapezoid - area of the triangle
Area of the trapezoid:
a = 5 m
b = 9 m
h = 6m
Substitute
Area of the trapezoid = 1/2 × (5 + 9) × 6
Area of the trapezoid = 1/2 × (14) × 6
Area of the trapezoid = 7 × 6
Area of the trapezoid = 42 m²
Area of the triangle:
Base = 7 m
Height = 6 - 4 1/2 = 1.5 m
Substitute
Area of triangle = 1/2 × 7 × 1.5
Area of triangle = 5.25 m².
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
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You are helping your friend with his math homework. He made an order of operations mistake. Which part did he do in the wrong order