[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +2}{2}~~~ ,~~~ \cfrac{ -1 +4}{2} \right) \implies \left(\cfrac{ 7 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies \left(3\frac{1}{2}~~,~~1\frac{1}{2} \right)[/tex]
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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I need help.. but we are only doing question 34 please answer quickly
Answer: 33. r=13.6 34. m=12
Step-by-step explanation:
33.
-0.8+r=12.8
-0.8+r+0.8=12.8+0.8
r=13.6
34.
[tex]\displaystyle\\-\frac{m}{3}=-4\\\\\frac{m}{-3}=-4[/tex]
Multiply both parts of the equation by -3:
[tex]\displaystyle\\\frac{m}{-3}(-3)=(-4)(-3)\\\\ \frac{m(-3)}{-3} =12\\\\m=12[/tex]
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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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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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
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
A box of chocolates has 3 milk chocolates for every 2 white chocolate. There are 60 chocolates in a box. How many white chocolates are in the box?
Answer: so the answer will be 90 white chocolates that are in the box
Step-by-step explanation:
so first you have a box of chocolates has 3 milk chocolates for every 2 white chocolate. so first you need to divide 3 divided by 2 which is 1.5
and after you need to multiply 1.5 x 60= 90
Simplify -3r(-12r + 4r - 16) please!!
Answer:FIRST ONE
Step-by-step explanation:
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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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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Triangle G is a scaled copy of triangle F
What scale factor takes triangle F to Trangle G?
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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If 21 and 22 are vertical angles, <2 and <3 are complementary angles
and m/3 = 56°, find m/1.
Answer:
........................................
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.
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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F=GmM/r^2 solve for G
Solution of the equation for G is given as G = Fr²/Mm
According to the question we have been given the formula for evaluating the value of F which is given as :
F = GmM/r²
Now we need to solve the equation for evaluating G. Which is given step by step as :
F = GmM/r²
Multiplying both the sides by r² we get
Fr² = GmM*r²/r²
Fr² = GmM
dividing both the sides by Mm we get
Fr²/Mm = GmM/Mm
Fr²/Mm = G
or, G = Fr²/Mm
Hence the solution for G is given as G = Fr²/Mm
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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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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
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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timmy is downloading movies from the internet. He can download 6 movies every 15 minutes. jonathan, who is also downloading movies, can download at a rate of 12 movies every 20 minutes
The unit rate of downloading per movie for each person is for Timmy it will take 2.5 minutes and for Jonathan it will take 1.66 minutes.
In question it is not given that what to do, so we will find the rate of downloading per movie for each person.
With the help of following steps as given below :
Timmy takes 15 minutes to download 6 movie.
6 Movies = 15 Minutes
1 Movie = 15/6
1 Movie = 2.5 Minutes
Jonathan takes 20 minutes to download 12 movies.
12 Movies = 20 Minutes
1 Movie = 20/12
1 Movie = 1.66 Minutes
Therefore, Timmy and Jonathan will take 2.5 and 1.66 minutes, respectively, to download one movie.
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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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I WILL MARK BRAINLY ASAP! Please Help its A Math Question (geometry) .
thank you alot!
Answer:
25 degrees
Step-by-step explanation:
A logging company is funding a study to determine the best practice for reforesting a cut section of forest. the previous best practice has been to plant the same type of tree with equally spaced intervals. the proposed method of reforestry is to plant a variety of trees at differing intervals. in the study, some tracts of land are reforested using the previous best practice. what are these tracts of land in the study?
The tracts of land in the study is the Control group.
The tracts of land in the study are reforested using the previous best practice whose results are already known. Now, it is not known, how the proposed method of reforestrey to plant a variety of trees at different intervals would grow. So, the tracts of land of previous plant can serve as a standard to which comparisons can made as to whether the newly proposed method is performing better than the previous or not.
This study was conducted at the Agua Salud Project site located in the Panama Canal Watershed (9° 13 N′, 79° 47′ W, 33 m amsl) with an average rainfall of 2700 mm annually, 80% of which falls between May and mid-December. Mean daily maximum and minimum temperatures are 32 °C and 23 °C . The topography is characterized by short and steep slopes. Soils are silt clay to clay with pH values of 4.4 to 5.8 and have very low levels of both plant available and total phosphorus. The data were collected from the Agua Salud native species and T. grandis plantation, both established in 2008 and planted in the same 3 m by 3 m spacing configuration.
Despite this information, changing landowners’ perceptions and transitioning from one species to a lesser known one, is a risk for the landowner and may require financial incentives.
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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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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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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
What are the factor pairs of 63
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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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: