Answer:
sector area = [central angle / 360] * PI * radius²
central angle = sector area * 360 / [PI * radius²]
central angle = 9 cm² * 360 / [3.14159 * 6²]
central angle = 28.6479139544 degrees
Source: http://www.1728.org/radians.htm
Step-by-step explanation:
7(3n + 2) - 3n - 5 i need to factor it tysvm!!
The answer to the Linear expression 7(3n + 2) - 3n - 5 is 18n + 11
What is a linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
From the expression 7(3n + 2) - 3n - 5
By expanding the bracket, we have
21n + 14 - 3n - 5
By collecting like terms, we have
21n - 3n + 14 - 3
18n + 11
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Find the equation of the line. Write the answer in standard form.
Answer:
1.Given points are:-
(1,2)=(x1/,y1)
(3,4)=(x2,y2)
Now,from two point formula,
y-y1=(y2-y1)/(X2-X1)×(X-X1)
or,y-2=(4-2)/(3-1)×(X-1)
or,y-2=2/2×(X-1)
or,y-2=1(X-1)
or,y-2=X-1
or, X -1-y+2=0
or,X-y+1=0 is the req. eqn in standard form
2.Given points are:-
(2,5)=(x1, y1)
(3,7)=(x2,y2)
Now, from two point formula,
y-5=(7-5)/(3-2)×(X-2)
or,y-5=2/1×(X-2)
or,y-5=2(X-2)
or,y-5=2X-4
or,2X-y-4+5=0
or,2x-y+1=0 is the req. eqn in standard form.
c.do similarly
and*mark me brainliest
Answer:
see explanation
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equations in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
(1)
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (3, 4 )
m = [tex]\frac{4-2}{3-1}[/tex] = [tex]\frac{2}{2}[/tex] = 1 , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 4 ) , then
4 = 3 + c ⇒ c = 4 - 3 = 1
y = x + 1 ( subtract y from both sides )
0 = x - y + 1 ( subtract 1 from both sides
- 1 = x - y , that is
x - y = - 1 ← in standard form
Use the same procedure for the next 2 questions
(2)
(x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (3, 7 )
m = [tex]\frac{7-5}{3-2}[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then
y = 2x + c ← is the partial equation
using the point (2, 5 ) to find c
5 = 2(2) + c = 4 + c ( subtract 4 from both sides )
1 = c
y = 2x + 1 ( subtract y from both sides )
0 = 2x - y + 1 ( subtract 1 from both sides )
- 1 = 2x - y , that is
2x - y = - 1 ← in standard form
(3)
(x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (3, 12 )
m = [tex]\frac{12-2}{3-5}[/tex] = [tex]\frac{10}{-2}[/tex] = - 5 , then
y = - 5x + c
using the point (5, 2 ) to find c
2 = - 5(5) + c = - 25 + c ( add 25 to both sides )
27 = c
y = - 5x + 27 ( add 5x to both sides )
5x + y = 27 ← in standard form
After 2+3/2-x+1/3x have been combined using the least common denominator of 6x, what is the numerator?
On solving the provided question, we can say that In light of this, the lowest common denominator of the equation is (x - 4)(x + 1)(x - 2) (x - 2)
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
equation is given as:
x2 — 3x — 4 = x2 — Ox + 8
x2 — 4x + x — 4 =
x(x — 4) + I(x — 4)
Factor out x - 4
(x + I)(x — 4) = x-2(x-4)
The common factor between the two sides of the equation is x – 4.
In light of this, the lowest common denominator is (x - 4)
(x + 1)(x - 2) (x - 2)
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Let u = PQ be the directed line segment from P(0,0) to Q(9,12), and let c be a scalar such that c < 0. Which statement best describes cu?
A) the terminal point of vector cu lies in quadrant II
B) the terminal point of vector cu lies in quadrant III
C) the terminal point of vector cu lies in quadrant I
D) the terminal point of vector cu lies in quadrant IV
The terminal point of vector cu lies in quadrant III.
Option B is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
p = (0, 0) and Q = (9, 12)
u = PQ = (9 - 0, 12 - 0) = (9 , 12)
Now,
cu = (9c, 12c)
where c < 0
If c = -1
cu = (-9, -12)
The coordinates (-x, -y) lie in quadrant III.
(-9, -12) is in quadrant III.
Thus,
Vector cu lies in quadrant III.
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Cheese pizza was preferred by 40 students pepperoni pizza was preferred by 28 based on the results how many of the 340 students can be expected to prefer cheese pizza?
The number of students expected to prefer cheese pizza from the 340 students is 200 stduents.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Cheese pizza = 40 students
Pepperoni pizza = 28
The ratio of cheese and Pepperoni pizzas.
= 40:28
= 10:7
Now,
Cheese pizza = 10x
Pepperoni pizza = 7x
The number of expected students who prefer cheese pizza.
= (10x)/(17x) x 340
= 10/17 x 340
= 10 x 20
= 200
Thus,
The number of expected students preferring cheese pizza is 200.
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You bought the meat for Saturday’s cookout a package of hotdogs cost 160 and a package of hamburgers cost five dollars you brought a total of eight packages of me and you spent $23. How many packages of hamburger meat did you buy?
The total number of hamburger meat he bought is 3.
Find the number of hamburger meat bought?Package of hot dogs cost $1.60 and package of hamburgers cost $5.
You bought total of 8 packages of a meat and you spent $23.
Therefore we have,
let
x = total number of package of hot dogs.
y = total number of package of hamburger.
Hence,
x + y = 8
1.60x + 5y = 23
multiply equation(i) by 5
5x + 5y = 40
1.60x + 5y = 23
Subtract equation(ii) from equation(i) we get
3.4x = 17
x = 17 / 3.4
x = 5
y = 8 - 5
y = 3
Therefore, total number of hamburger meat he bought is 3.
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After my salary was increased by $16\%,$ it was $\$52{,}200$. What was my salary before the increase
%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.
What is percentage?A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.
Considering the query
It was $52,200 after a 16% raise in my pay.
In light of the conditions stated, come up with
[tex]$=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$[/tex]
= $45000
Before the raise, I was making $45,000.
Therefore, the answer is $45,000.
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If f(x)=3x, g(x)=x+4, and h(x)=x2-1, find the value of h[f(5)]
Answer:
29
Step-by-step explanation:
Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)
The union of the intervals is (-∞,∞)
The intersection of the intervals is [0,2)
Hope this helped!
(i) Six donkeys are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
pls I really need the answer
Hello there!
Answer:
33 days
Step-by-step explanation:
Every day you give 5 ml of medicine to 6 donkeys. So you spent 5 ml * 6 = 30 ml per day
1 L = 1000 ml
To find the answer you should volume of bottle divide by 30 ml per day:
1000 ml / 30 = 33.333...
It means that if will be possible to use the bottle 33 days but then it will be left
I need help with this question. :Probability and Statistics thanks
The number of possible combinations of 4 digit codes would be 72.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, I am creating a 4 digit code with the numbers 1 to 10.
Now, From 1 to 10 there are (10 - 1 + 1 ) = 10 and we are taking 4 numbers at a time.
Therefore the number of combinations of 4 digit codes would be,
[tex]^9C_4\times2![/tex]. As the number consists of two digits.
= [9!/(9 -2)!×2!]×2!.
= 9!/7!.
= 72 possible ways.
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What is the solution to the system of linear equations 3x 2y equals 14 5x y equals 32?
The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).
3x + 2y = 14
5x + y = 32
Subtracting 3x from both sides of the first equation:
2y = 14 - 3x
Substituting this into the second equation:
5x + (14 - 3x) = 32
Simplifying:
8x = 18
x = 18/8
x = 2.25
This x value is substituted into the first equation.:
2y = 14 - 3(2.25)
2y = 14 - 6.75y
= 7.25
The solution is (x, y) = (2.25, 7.25)
The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).
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Molly and Liza are exercising. Molly does
10 push-ups at the same time
as Liza
does 15 push-ups. When Molly does
40 push-ups, how many push-ups does
Liza do?
Answer:
25
Step-by-step explanation:
so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.
Analyze the function graph.
Select the best option to describe the function graph.
Linear Increasing
Linear Decreasing
Linear Constant
Nonlinear Increasing
Nonlinear Decreasing
The function graph is Linear Constant. Option C
What is the graph?We know that when we plot a graph, there would be the vertical and the horizontal axis. We can be able to deduce the nature of the graph when we look at how the graph is going.
In this case, we can see that the graph is flat. The flatness of the graph would show us that there is neither an increase nor a decrease in the function that we have in view. The increase or the decrease can be seen from the direction of the line that is drawn across the graph.
Hence, the fact that the line is flat on the graph shows that it is linear constant.
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f(n) = 2n-1 find the arithmetic sequence ?
An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where "a" is the first term of the sequence, and "d" is the common difference between successive terms.
Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.
Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.
Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.
If you have any other question feel free to ask.
I don't understand help
Volume of the triangle is 1420m³ given in the question.
What is Volume?There are various volumes for various geometric shapes. Cubes, cuboids, spheres, cylinders, cones, etc. are examples of common 3D shapes that we encounter on a daily basis.
Finding the volume is simple when dealing with shapes with a flat surface, like a cube or a cuboid. Cones, cylinders, and spheres are examples of curved shapes, and it is necessary to take into account both their curved surfaces' dimensions and their overall curvature. Possibly their diameters or radii
The term "irregular solids" refers to solids that lack precise measurements or shapes. A fixed formula that can be used to calculate the volumes of such solids is typically absent. It is possible to obtain these volumes in a variety of ways, one of which is the liquid displacement method, which is based on the Archimedes Principle.
Now volume triangle = area × height
⇒ 1/2 × 20 × 14.2 × 10
= 1420m³
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The sixth-grade class is holding a week long fund-raiser. The class set a goal of raising $700. 0. So far they have raised $176. 95. Write an equation that can be used to solve for x, the amount of money the class still must raise to meet their goal
An equation that can be used to find the value of,x=$700.0 - $176.95.
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.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
x= $700.0 - $176.95
523.05
Hence, An equation that can be used to find the value of,x=$700.0 - $176.95.
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5 whole 1/7- 2 whole 5/21
The value of 5 1/7 minus 2 5/21 will be 2 19 / 21.
How to solve the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Based on the information, the value of 5 1/7 minus 2 5/21 will be:
= 5 1/7 - 2 5 / 21
= 5 3/21 - 2 5 / 21
= 2 19 / 21
The value is 2 19/21.
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Question 1 : (2.3 × 10^4) × (1.5 × 10^-2)
Question 2: (3.6 × 10^-5) ÷ (1.8 × 10²)
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expressions are given below.
(2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
Simplify the expression (2.3 × 10⁴) × (1.5 × 10⁻²), then the value of the expression will be given as,
⇒ (2.3 × 10⁴) × (1.5 × 10⁻²)
⇒ 345
Simplify the expression (3.6 × 10⁻⁵) ÷ (1.8 × 10²), then the value of the expression will be given as,
⇒ (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
⇒ 2 × 10⁻⁷
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
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What is the answer to 2/3x=-36
the answer to your question is 36
In right triangle ABC,b is the right angle and m2C -30°, If AC - 10, what is AB?
The value of AB after solving the triangle is 10√3.
Since angle C is the right angle in triangle ABC, we know that angle A = 90 - m2C = 90 - 30 = 60. And since triangle ABC is a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse, AB.
The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So in this case,
AB^2 = AC^2 + BC^2 = 10^2 + BC^2 = 100 + BC^2.We know that angle A is 60, so we can use the trigonometric function sine to find the value of BC/AB. We know that
sin(A) = BC/AB. So BC/AB = sin(60) = √3/2.We can then square both sides of this equation to get
(BC/AB)^2 = (√3/2)^2 = 3/4.Since we know that BC/AB = 3/4, we can substitute this value into the equation
AB^2 = 100 + BC^2 to get
AB^2 = 100 + (BC^2) = 100 + (3/4)AB^2.
Solving this equation for AB, we get AB = 10√3
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When a space shuttle returns from a mission, the last part of its descent to the ground
must be between 17 degrees and 19 degrees with the horizontal (ZZ). If the pilot of
space shuttle Pioneer plans to descend from 11,700 feet (UH) at an angle of 18
degrees (ZZ) from the runway, determine the horizontal distance from the landing site
(ZU) at which the pilot must begin the descent.
Use the diagram to determine the measure of the sought side.
Answer:
please see the followings,
11700 ÷ tan 18 = ZU
Sport
Soccer
Jogging
Walking
Skiing
Football
Total
Hrs
5
20
10
5
10
50
Calculate the
portion for jogging
in degrees
[?]
20 hrs.
Total Sport Hours
The portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours is 72 degrees.
Therefore the answer is 72°.
To calculate the portion of walking in degrees, we first need to find the total amount of time spent walking. In this case, it is 10 hours.
Next, we need to find the total amount of time spent on all sports, which is 50 hours.
Now we can calculate the portion of walking by taking the amount of time spent walking (10 hours) and dividing it by the total amount of time spent on sports (50 hours).
This gives us the fraction of time spent walking which is
10/50
= 1/5
Finally, we can convert this fraction to degrees by multiplying it by 360 (the number of degrees in a full circle).
So the portion of walking in degrees is
(1/5) × 360
= 72 degrees
--The question is incomplete, complete question is given below--
"Calculate the portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours."
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I just need help with number 9 in this picture if anyone could pls help!
the survey is a research method in which: group of answer choices individuals are carefully observed in their natural environments. a representative, random sample of individuals are questioned regarding their attitudes or behaviors. an individual is studied in great depth. an investigator determines the extent to which two variables influence each other.
The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.
B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.
C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.
D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.
Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
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having trouble with this, can anyone help?
(equation needs to be put in y=mx+b form)
Check the picture below.
In δfgh, g = 64 cm, ∠f=131° and ∠g=47°. find the length of f, to the nearest centimeter.
The length of f = 66 centimeters
What is the sine rule for triangle?It is a law that express a relationship between side length of triangle and their opposite angles.
If ABC is triangle, then sine rule can be expressed as
BC/ sin A = AB /sin C = AC /sin B
How can we determine the length of f of the above triangle?Given, a triangle fgh where angle ∠ f = 131° and ∠g = 47°
also, side length, g = 64 cm
the remaining angle ∠ h = 180° - (131°+47°)
∠h = 2°
this is because angle sum of three angle for a triangle is 180 degrees.
what is the length of f?
we know that Δf g h has three side f g, g h and f h.
we denote the side f g = h, side g h = f and side f h = g
according to the sine rule for a triangle
h/ sin h = f /sin f = g /sin g
f/ sin f = g/ sin g
f / sin 131° = 64 / sin 47°
f = (64 × sin 131°) / sin 47°
f = 66 cm
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30 PTS: Please help me
You can earn money by shoveling your neighbors' driveways in the winter and get paid $10 per hour. What is a function that would define this situation? Define the domain and range of this function and describe reasonable values for each.
The function that will define the situation is y = 10x
The domain: {0, ∞)
The range: {0, ∞)
How to write the functionThe function that will define the situation is a linear function of the form
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = there is no condition defined here hence = 0
m = cost of per hour = $2.50
x = time in hours
y = amount paid in hours
y = 10x
The domain in this case is time from 0 to infinity {0, ∞)
The range is also {0, ∞)
there are no limitations to hep set the range and domain
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How many real solutions of 2x 3y 5 are possible?
The equation 2x + 3y = 5 has one real solution.
To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.
For example, you can solve for y to get y = (5 - 2x)/3, and then substitute this into the equation to get 2x + 3((5 - 2x)/3) = 5, which you can then solve for x. Doing this will give you x = 5/4, which means that the solution is (5/4, 5/3).
Linear equations are equations that involve two variables and can be expressed in the form ax + by = c, where a and b are constants and x and y are the variables. These equations have one real solution, which can be found by solving for one of the variables and then substituting the result into the equation to find the other variable. Once both variables are known, the solution to the equation is the point (x,y) that satisfies both equations.
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I really need help on this one too
The solution is Option C and Option D.
The exponential function is given by f ( x ) = 2 ( 3 )ˣ
The exponential function is given by f ( x ) = 800 / 4ˣ
What are the laws of exponents?
When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 7 , 19 , 31 , 43 }
The equation of line is y = 12x + 7
This is a linear equation
b)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 5 , 10 , 15 , 30 }
The equation is a quadratic equation
c)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 2 , 6 , 18 , 54 }
The equation is y = 2 ( 3 )ˣ
This is an exponential function
d)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 800 , 200 , 50 , 12.5 }
The equation is f ( x ) = ( 800 / 4ˣ )
This is an exponential function
Hence , the exponential equations are solved
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