The polar equation for the curve is x = √3cosФ and y = √3 sinФ.
Here we have to find the polar equation of the curve.
Data given:
The equation is:
x² + y² = 3
This is an equation of a circle.
Its radius is √3 and its √center is (0,0)
To find the polar equation of a circle we use the following formula:
x = h + rcosФ
y = k + r sinФ
where (h,k) is the center of the circle which in this case is (0,0) and by substituting we get:
x = √3 cosФ
y = √3 sinФ
Therefore the polar equation is x =√3cosФ and y = √3sinФ.
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an urn is filled with marbles of various colors. if the probability of pulling a red marble at random is 1/10, the odds of pulling a red marble are:
The value of the odds of pulling a red marble is equivalent to 1/9 from an urn filled with marbles of various colors.
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
By definition, the theoretical probability is equal to the ratio of the favorable event to the total number of events.
Given that:
The probability of pulling a red marble at random is 1/10
Probability of not pulling red marble is = 1-(1/10)= 9/10
The odds of pulling red marble is (1/10)/(9/10)
The probability of odds of pulling red marble is 1/9.
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Ira enters a competition to guess how many buttons are in a jar.
Ira’s guess is 200 buttons.
The actual number of buttons is 250.
What is the percent error of Ira’s guess?
The percent error of Ira’s guess for the number of buttons is 25%
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Ira’s guess is 200 buttons but the actual number of buttons is 250.
The net amount error is (250 - 50) = 50 buttons.
Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,
= (50/200)×100%.
= 25%
So, the percentage error is 25%.
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Label each pair of angles as corresponding angles, alternate interior angles, alternate exterior angles, or consecutive interior angles.
Angle 1 and Angle 5
Angle 1 and Angle 8
Angle 2 and Angle 8
Angle 3 and Angle 5
The solution is
Angle 1 and Angle 5 = Corresponding Angles
Angle 1 and Angle 8 = Co-Interior Angles
Angle 2 and Angle 8 = Alternate Interior Angles
Angle 3 and Angle 5 = Alternate Exterior Angles
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
From the figure , we can see that
The angles 5 , 6 , 7 and 8 are all on the straight line t
The angles 1 , 2 , 3 and 4 are all on the straight line n
The line m is the transversal line
Now ,
From the theorem of angles on a parallel lines , we get
Alternate angles are equal
So , 2 = 8 and 3 = 5
Now ,
Angle 2 and Angle 8 = Alternate Interior Angles
Angle 3 and Angle 5 = Alternate Exterior Angles
Corresponding angles are equal
So , 1 = 5 and 2 = 6
Now ,
Angle 1 and Angle 5 = Corresponding Angles
Co-Interior angles are supplementary
So , 1 + 8 = 180°
Now , Angle 1 and Angle 8 = Co-Interior Angles
Hence ,
Angle 1 and Angle 5 = Corresponding Angles
Angle 1 and Angle 8 = Co-Interior Angles
Angle 2 and Angle 8 = Alternate Interior Angles
Angle 3 and Angle 5 = Alternate Exterior Angles
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  Is it true that 7w + 4 = 5w + 12.
A. Write three more equations that you know are true based on this information.
B. Find the value of 2w.
C. Find the value of w.
Answer:
A. Here are three more equations that are true based on the information you provided:
1. 3w + 2 = 2w + 6
2. 5w - 6 = 4w - 8
3. 7w - 5 = 6w - 7
B. To find the value of 2w, we need to first solve for w in the original equation 7w + 4 = 5w + 12. We can do this by subtracting 5w from both sides of the equation, which gives us 2w + 4 = 12. Then we can subtract 4 from both sides to get 2w = 8. Therefore, the value of 2w is 8.
C. To find the value of w, we can divide both sides of the equation 2w = 8 by 2, which gives us w = 4. Therefore, the value of w is 4.
a woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, how tall is the tree?
A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet tall is the tree.
Let the tree height = x
From the question, we have
5/8 = x/120
x = (5*120)/8
x = 75 feet
Tree height = 75 feet
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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a little boy is placing 20 of his marbles in a row. if 12 are red and 8 are blue and he decides not to place 2 blue marbles next to each other, how many arrangements of the marbles are possible?
There are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.
What is a combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Here, we
Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:
x BR x BR x BR x BR x BR x BR x BR x B x
Note that this is the same even if our arrangement is
x B x RB x RB x RB x RB x RB x RB x RB x
There is a total of 13 places to arrange 8 blue marbles among 12 red marbles.
8 marbles can be placed in ¹³C₈ ways
Total possible arrangements = ¹³C₈ = 1287
Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.
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if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength. what is this an example of?
The given statement is an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) ".
What is Principle of specificity ?
According to the specificity of training principle, each physical activity has a very unique physiological response. For instance, someone who jogs can anticipate that both their running performance and their level of aerobic fitness will be favorable.
if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength.
This an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) "
Tenet according to which the body will adjust to the unique demands imposed upon it.
Higher degrees of endurance can be attained by regularly lifting lesser weights for a large number of repetitions.
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y=-6x+3 y=6x+3 solve with subsititution
Answer:
the answer is
-3/2
I hope that helps
please help, answers only!!
The rate of change of the graphs are as follows:
rate of change = 4 / 5rate of change = 3 / 4How to find rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.
Therefore,
rate of change = change in y / change in x
Hence,
rate of change = y₂ - y₁ / x₂ - x₁
let's find the rate of change of the graphs.
a.
using (-5, -1) and (5, 7)
rate of change = 7 + 1 / 5 + 5
rate of change = 8 / 10
rate of change = 4 / 5
b.
using (0, 3)(-4, 0)
rate of change = 0 - 3 / -4 - 0
rate of change = - 3 / - 4
rate of change = 3 / 4
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How many possible dish combinations are there with 5 kinds of pasta, 2 cheeses, and 3 sauces.
Answer: 30 combinations
Step-by-step explanation:
Multiply 3x2x5 to get 30.
-1 For the following image, find the measure of
Answer:
48°
Step-by-step explanation:
this is because no if you take any two points in along line AB and CB it will always be 48°.
in a database, a _____________ is a unit of information about one individual or item.
Answer: Record
Step-by-step explanation:
Need help with this problem
By using some exponent properties, we will see that the equivalent expression to √(x⁵*y⁶) is:
x²*y³*√x
So the correct option is the first one.
How to simplify the given expression?
Here we need to remember 3 properties about exponents that we will need to use.
These are:
√x = x¹´²
Also remember that:
(xⁿ)ᵃ = xⁿ*ᵃ
And that:
√(a*b) = √a*√b
Well, our expression is:
√(x⁵*y⁶)
We can rewrite this as:
√x⁵*√y⁶
And using the first and second properties we can rewrite.
√x⁵ = x⁵´² = x⁴´²*x¹´² = x²*√x
√y⁶ = y⁶´² = y³
Replacing all that we get:
√(x⁵*y⁶) = x²*y³*√x
Thus, the correct option is the first one.
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here are the number of hours that 9 students spend on the computer on a typical day:2 5 5 7 11 11 11 14 15what is the mode number of hours spent on the computer?
By using the concept of mode, it can be calculated that-
Mode number of hours spent on the computer is 11 hours.
What is mode?
Mode of a data set is that value which occurs most number of times in the data set. In other words, the value whose frequency is the largest is the mode of the data set.
The number of hours that 9 students spend on the computer on a typical day: 2 5 5 7 11 11 11 14 15
Here 11 occurs most number of times (3 times)
Mode number of hours spent on the computer is 11 hours.
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I need this as soon as possible pleaseee
A bag contains 6 red marbles and 4 blue marbles.
How many red marbles must be added to the bag to make the probability of drawing a red marble 5/7????????
Answer: 4
Step-by-step explanation:
10/14 = 5/7
Tyler used 1 1/4 gallons of paint to paint 5/8 of a fence. How many gallons will it take to paint the whole fence?
Answer:
2 gallons
Step-by-step explanation:
1 1/4 = 1 + 1/4 = 4/4 + 1/4 = 5/4
Then:
5/4 gallons ⇒ 5/8 fence
x gallons ⇒ 8/8 fence
x = (5/4)(8/8) / (5/8)
x = ((5*8)/(4*8)) / (5/8)
x = (5/4) / (5/8)
x = (5*8)/(4*5)
x = 40/20
x = 2
a and b are playing a game where a has n 1 coins, b has n coins, and they each flip all of their coins. what is the probability that a will have more heads than b?
The probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.
Given, a and b are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.
we have to find the probability that a will have more heads than b.
Now, p1 = "probability that A obtains more heads than B.".
p2 = "probability that B obtains more heads than A.".
p3 = "probability that A obtains as many heads as B.".
Such that p1 + p2 + p3 = 1.
Since, both flips n coins, A wins with the same probability as B.
p1 = p2
Now, A flips and extra coin.
½ of the time it gives tails and doesn't contribute, but ½ of the time is gives heads meaning that A now wins if they before had equal number of heads.
p1+1/2(1 − p1 − p2)=1/2.
Hence, the probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.
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a person with height 1.8 metres is walking away from a 5 metre tall lamppost at a speed of 1.2 metres per second. find the rate at which their shadow is lengthening.
The length of the shadow of man is 0.8 m/s.
How to solve word problems?
Here are some actions to take:
1. Recognize the issue.
Recognize every term used to describe the issue, Recognize what you need to look for, Recognize the issue's context.
2. Convert the issue into an equation. Give the unknown a variable (or variables) to symbolise, Indicate exactly what the variable stands for.
3. Put the strategy into action and find a solution.
dx/dt =1.2 m/s
4.5 / x+ y = 1.8 / y
1.8x + 1.8y = 4.5y
1.8x = 2.7y
2x = 3y
3 dy/dt = 2dx/ dt = dy/dt = 2/3
=0.8
Hence, The length of the shadow of man is 0.8 m/s
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Graph the following function by moving the points to match two ordered pairs, including the x-intercept:
f(x) = log 1/8(x)
The graph of function f(x) = log 1/8(x) is shown in figure with x - intercept
(8, 0).
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The function is,
⇒ f (x) = log 1/8 (x)
Now,
Since, The function is,
⇒ f (x) = log 1/8 (x)
Hence, The x - intercept = (8, 0)
And, The graph is show in figure.
Thus, The figure is shown in figure.
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WILL GIVE BRAINLY
Henry has $150.00 to spend on a rental car for 2 days. It costs $39.90
per day plus $0.20 per mile to rent the car. Which inequality represents
how many miles, m, Henry can drive the car?
A. m ≤ 351
B. m ≥ 351
C. m ≤ 550.5
D. m ≥ 550.5
Answer:
The inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality can be derived by first calculating the total cost of renting the car for 2 days at $39.90 per day and $0.20 per mile. This gives us a total cost of $79.80 for the rental plus $0.20 per mile for the number of miles Henry drives. Since Henry has $150.00 to spend, we can set up the following inequality to represent the maximum number of miles he can drive:
150.00 >= 79.80 + 0.20m
We can then solve for m by subtracting 79.80 from both sides of the inequality and dividing both sides by 0.20, which gives us:
m <= 550.5
Therefore, the inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality states that Henry can drive the car for a maximum of 550.5 miles.
Step-by-step explanation:
Find the result graphically. Click and drag the arrows to represent each term. Type in the result. 7-5
7 is initially represented by 7 units to the right, Now, if we remove 5 from 7, we must move 5 units to the left, arriving at unit 2.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
On the number line, 7 is represented 7 units right from the origin.
Now subtracting 5 from 7 implies we have to go 5 units to the left so we end up in unit 2.
The graphical representation is illustrated in the attached image.
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What values are excluded from the domain of the function
2
-3
3
-2
0
f(x) =
2x²-3x-2
g2–52+6?
The values that would be excluded from the domain of the function are those that create vertical asymptotes in the graph.
Vertical asymptotes can be found by setting the expression in the denominator equal to 0 (zero) and solving for x. The resulting values of x are the values that are excluded from the domain of the function.
Expression in the denominator = x^2 - 5x + 6
x^2 - 5x + 6 = 0
(Factor to solve)
(x - 3)(x - 2) = 0
x - 3 = 0 || x = 3
x - 2 = 0 || x = 2
The values that are excluded from the domain of the function are 3 and 2.
Hope this helps!
How many solutions can a system of 2 linear equations in 2 variables have?
The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.
In the question ,
it is given that ,
the system of 2 linear equations in 2 variables .
we know that the linear equations represent a line .
(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .
(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .
(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .
Therefore , the number of solutions of linear equation is explained above .
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What expression shows 0.5 ( x +3) written as a sum
The expression 0.5 (x + 3) written as a sum is 0.5x + 1.5
How to determine the expression written as a sum?From the question, we have the following parameters that can be used in our computation:
0.5 ( x +3)
Write the expression properly
So, we have the following representation
0.5 (x + 3)
Express the brackets as products
So, we have the following representation
0.5 (x + 3) = 0.5 * (x + 3)
Open the brackets using products i.e. distributive property
So, we have the following representation
0.5 (x + 3) = 0.5 * x + 0.5 * 3
Evaluate the products
So, we have the following representation
0.5 (x + 3) = 0.5x + 1.5
Hence, the expression as a sum is 0.5x + 1.5
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Answer:
1. 0.5x + 1.5
2. are not
The costs of a company are represented by the function c(x)=0. 38x+700. Its revenues are represented by the function r(x)=2. 9x.
The function that represent the company's profit is (2.52x - 700).
As per the known formula, Profit = Revenue - Cost
Now keeping the functions of revenue and cost to find the function of profit.
Profit = 2.9x - (0.38x + 700)
Performing subtraction on Right Hand Side of the equation to find the profit of company
Profit = 2.9x - 0.38x - 700
Performing subtraction on Right Hand Side of the equation to find the profit of company
Profit = 2.52x - 700
Thus, the the profit of company will be represented by the function 2.52x - 700.
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The complete question is -
The costs of a company are represented by the function c(x)=0. 38x+700. Its revenues are represented by the function r(x)=2. 9x. Find the function that represent the company's profit.
An amusement park sold 15 child tickets. The other 35 tickets it sold were
adult tickets. What is the ratio of the number of adult tickets to the number of
child tickets?
Answer:
3 : 7
Step-by-step explanation:
RatioRatios are Proportinalised Numbers that we can use to compare number of units relative to the other value.
Eg. 3 : 15 = 1 : 5
SolutionGiven Information from the Question:
15 Child Tickets : 35 Adult Tickets
Now we reduce them to simplest form.
(15 ÷ 5) : (35 ÷ 5) = 3 : 7.
Therefore the ratio of Child Tickets to Adult Tickets is 3 : 7.
Relation 3
{(4, 4), (1, -7), (-6, 4), (-7,4)}
Function
Not a function
Answer:
It is a function
Step-by-step explanation:
for a relation to be a function, every X must have one and only one y. That is true for the given values
What is the product when x- 5 is multiplied by
2x + 3?
1.) 2x² - 7x - 15
2.) 2x² - 13x - 15
3.) 2x² +13x + 15
4.) 2x² +7x - 15
Answer:
2x² + 7x - 15.
Step-by-step explanation:
The product when x- 5 is multiplied by 2x + 3 is 2x² +7x - 15. To find the product, we need to use the distributive property. This states that for any two expressions, a and b, and a constant, c, we have the following:
c * (a + b) = c * a + c * b
We can use this property to expand the expression (x - 5)(2x + 3) as follows:
(x - 5)(2x + 3) = (x * 2x) + (x * 3) + (-5 * 2x) + (-5 * 3)
= 2x^2 + 3x + (-10x) + (-15)
= 2x^2 + 7x - 15
Therefore, the product of the expression (x - 5)(2x + 3) is 2x^2 + 7x - 15, which matches the answer choice 2x² + 7x - 15.
there is a light on the top of the building. if a person is standing 50m from the building and looks up at an angle of 60°, how far from the ground is the light?
Answer:
Step-by-step explanation: Here's your answer 50√3 m.
sara gets paid 1,500.00 per month plus 5.5% commission on all her sales. how much will sara get apid for the month of November if she sold $35,000 worth of merchandies
Answer: $1925 is the commission she gets from the merchandise, which means if you add 1,500 + 1925 = $3425. $3425 is what she got for that month.
Step-by-step explanation: if its wrong tell me