a. Let t represent the time in hours when it started raining. We can use function notation to represent the amount of rain r at any time t with r(t) = 37 millimeters. This is because after 6 hours, the amount of rain was 37 millimeters. Therefore, we can use the equation r(t) = 37 millimeters to represent this statement.
b. We can use function notation to represent the amount of rain at any time t with r(t) = r(t-1.5). This is because the amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining. Therefore, we can use the equation r(t) = r(t-1.5) to represent this statement.
This type of function notation is useful for representing relationships between different values related to the same property or phenomenon. It allows us to quickly and easily analyse and compare data, as well as make predictions about future values. It is also useful for describing how certain parameters are changing over time.
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Use the diagram to answer the question.
Which of the following statements are true based on the diagram?
Points B, C, and D lie in Plane N.
Points B, C, and D are on line n
Points B and D are on line n, but Point C is not.
Answer:
Points B, C, and D are on line n
Step-by-step explanation:
Answer:
лттьло. ьнеь е екбюедку к е. еккд
What is a degree 3 polynomial called?.
A polynomial of degree 3 is called a cubic polynomial.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Which of the following shows that polynomials are closed under addition when two polynomials 4x2 − 8x − 7 and −5x + 16 are added?
A. 4x^2 − 13x + 9; may or may not be a polynomial
B. 4x^2 + 13x − 23; may or may not be a polynomial
C. 4x^2 − 13x + 9; will be a polynomial
D. 4x^2 + 13x − 23; will be a polynomial
According to the information, the correct option is C. . 4x^2 − 13x + 9, since the expression is a polynomial.
How to add the two expressions?To add the expressions we must add each of its components (those that are similar) to form a single expression. Below is the procedure:
4x^2-8 -5 = -13- 7 + 16 = 9Now we must reassemble the expression that would look like this.
4x^2 - 13 + 9. Additionally, we know that it is a polynomial because none of the terms related to x are affected by a square or fractional root.
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When X 3x² 1 is divided by x 1 then remainder will be?.
After solving, the remainder when [tex]-x+3x^2-1[/tex] is divided by x + 1 is 3.
In the given question, we have to find the remainder when [tex]-x+3x^2-1[/tex] is divided by x + 1.
The given polynomial is [tex]-x+3x^2-1[/tex].
We have to find the remainder of the polynomial when we divide this polynomial x + 1.
To find the polynomial we equate x+1 equal to zero to find the value of x.
x + 1 = 0
x = -1
Now putting x = -1 in the given equation [tex]-x+3x^2-1[/tex].
P(x) = [tex]-(-1)+3(-1)^2-1[/tex]
P(x) = 1 + 3×1 - 1
P(x) = 1 + 3 - 1
P(x) = 3
Hence, the remainder when [tex]-x+3x^2-1[/tex] is divided by x + 1 is 3.
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The complete question is:
When [tex]-x+3x^2-1[/tex] is divided by x + 1 then remainder will be?
what is the solution for x^2 - 18x < -77
Answer:
7 < x < 11
Step-by-step explanation:
Please help me<3 Each pair of polygons is similar. Find each missing side measure
Answer:
it's 8
Step-by-step explanation:
I find it because 96÷8=12
and 64÷8=8
Does the following equation has the sum of its roots as 3 3x² 3x 3 0?.
The equation -x² + 3x - 3 = 0 has the sum of the roots as 3. Given that a quadratic equation's roots add up to three.
A quadratic polynomial in terms of the zeroes (α,β) is given by
x2 - (sum of the zeroes) x + (product of the zeroes)
f(x) = x2 -(α +β) x +αβ
From the options,
A) 2x² - 3x + 6 = 0
Dividing by 2,
x² - 3/2x + 3 = 0 ------------------ (2)
Comparing (1) and (2),
α + β = 3/2
Therefore, the sum of the roots of the equation is 3/2.
B) -x² + 3x - 3 = 0
The equation can be written as x² - 3x + 3 = 0 ------------- (3)
By comparing (1) and (3),
α + β = 3
Therefore, the sum of the roots of the equation is 3.
C) √2x² - 3/√2x + 1 = 0
Dividing by √2,
x² - 3/2x + 1/√2 = 0 ------------ (4)
By comparing (1) and (4),
α + β = 3/2
Therefore, the sum of the roots of the equation is 3/2.
D) 3x² - 3x + 3 = 0
Dividing by 3,
x² - x + 1 = 0 -------------------------- (5)
By comparing (1) and (5),
α + β = 1
The equation's roots are added together, and the result is 1.
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f(x)=-x^2-4x+5
find the vertex, zeros, and y-int.
The vertex, zeros, and y-intercept for the given quadratic equation f(x)= -x² - 4x+5 are respectively,
Vertex- (2, 1)
Zeros- (2 + i)
Y-intercept- 5
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
f(x) = y = -x² - 4x+5
y = -x² - 4x+5
For making it perfect square, we can add and subtract square value of half of coefficient of x
So, adding and subtracting +4 and -4 in the given equation
y = -x² - 4x+5+4-4
= -x² - 4x+4+5-4
= (-x +2)² +1
y-1 = (-x +2)²
So, for vertex
-x +2 = 0
x = 2
y-1 = 0
y = 1
For Zeros, y = 0
y-1 = (-x +2)²
(-x +2)² = -1
x = 2 + i, -2-i
the zeros are imaginary
For y intercept, x = 0
y-1 = (-x +2)²
y = 1 + (2)²
y = 5
Hence, vertex, zeros, and y-int. are respectively (2, 1), (2 + i), 5
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Why does the operations subtraction and division Cannot be applied by commutative property and associative property?.
The commutative property and associative property do not hold for subtraction and division, as the end results are completely different after changing the order of numbers.
The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.
For example, 4 + 5 gives 9, and 5 + 4 also gives 9. The order of two numbers being added does not affect the sum. The same concept applies to multiplication too.
Thus, The commutative property and associative property do not hold for subtraction and division, as the end results are completely different after changing the order of numbers.
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Mrs. Kurz has five counters that each have a red side and a yellow side. If she dumps all of the counters out of the bag, what is the Probility that they all land yellow side up
Answer:
1/32
Step-by-step explanation:
5 counters, 1/2 chance of it being yellow, therefore...
[tex](\frac{1}{2})(\frac{1}{2})(\frac{1}{2})(\frac{1}{2})(\frac{1}{2}) = (\frac{1}{32})[/tex]
help pls i need to pass
Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation:
NOOOOOO FIGURE IT OUT YOUR SELF THATS WHY THEY TEACH YOU DUHHHHHHHHHHHHH
Graph the function y=−x+4 , represented by the given function table
The graph of the linear equation:
y = -x + 4
can be seen on the image at the end.
How to graph the inear function?Here we want to graph the following linear function:
y = -x + 4
To graph it, we need to find two points that lie on that line, and to get that we need to evaluate the line.
When x = 0.
y = -0 + 4
y = 4
So we have the point (0, 4)
When x = 2
y = -2 + 4
y = 2
So we have the point (2, 2)
Now we just need to graph these two poins and connect them with a line, we will get:
Sarah went shopping at a store and bought some hats that cost $6 each and 2 necklaces that cost $12 each. The cost of Sarah’s total purchases was $66. How many hats did Sarah buy?
The number of hats Sara bought is 7.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Sarah went shopping at a store and bought some hats that cost $6 each and 2 necklaces that cost $12 each.
The number of hats will be calculated as,
12N + 2H = 66
12 x 2 + 2 H = 66
2H = 66 - 24
2H = 42
H = 42 / 2
H = 21
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Please help and show work only do the left side
Writing linear equations given two points can be a useful skill when graphing linear equations.
Write a linear equation that passes through the given two points?To write a linear equation given two points, you need to first find the slope of the line. You can do this by finding the change in the y-value and dividing it by the change in the x-value. From there, you can use the slope to solve for the y-intercept and write the equation.For example, if the two points are (3, 4) and (0,5), you would find the slope by calculating the change in the y-value (5-4 = 1) and dividing it by the change in the x-value (0-3 = -3).The slope would then be 1/-3, which can be simplified to -1/3. To solve for the y-intercept, you can plug in one of the points and solve for b. In this case, you would plug in (3, 4) and solve for b, giving you b = 5. Now that you have the slope and y-intercept, you can write the equation as y = -1/3x + 5.y = -1/2xy = 5/3x + 5/3y = 3/5x + 1y = -1/2x - 2y = 6/5x + 5y = -4/4x - 8y = -3/5x - 7/5y = -2x - 4y = 5/6x + 7y = -1/2x + 4To learn more about linear equation refer to:
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To support a triangular kite, Hana
attaches thin strips of wood from each vertex
perpendicular to the opposite edge. She
then attaches the kite's string at the point
of concurrency. To calculate the point of
concurrency, she determines the coordinates
of each vertex on a coordinate plane. What
are the coordinates where the wood strips
cross? Round your answer to the nearest
hundredth.
The circumcenter of the triangle is at the point (22, 36). This is the point where the three thin strips of wood cross and where Mike attached the kite's string.
How to calculate the circumcenter of the triangle ?The point of concurrency of the lines perpendicular to the sides of a triangle is known as the circumcenter of the triangle. To find the circumcenter of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), you can use the following formula:
x = (x1 + x2 + x3) / 3
y = (y1 + y2 + y3) / 3
Plugging in the coordinates of the three vertices, we get:
x = (0 + 44 + 0) / 3 = 22
y = (58 + 36 + 0) / 3 = 36
So the circumcenter of the triangle is at the point (22, 36).
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How many linear solutions are there?.
There are a lot of linear solutions to problems. In fact, there are an infinite number of them.
Linear solutions are the most common type of solution. They're also the easiest to solve. These solutions are used in algebra and geometry. There are six different types of equations in which a linear solution exists. These are:
1) One variable equals zero
2) Two variables are equal
3) Three variables are equal
4) Any equation with one constant and one other variable
5) Two variables have an equal ratio to another variable
6) Two variables are equal to a certain number One solution that's linear is a quadratic equation with two variables. It has the form x2 + bx + c = 0 To solve this equation, you can use basic algebraic skills like factorization, substitution, and addition.
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how much water do you add to make this concentration? 25% sugar syrup using 15 g sugar
The amount of water to add is 45 grams
How to determine the amount of water to addFrom the question, we have the following parameters that can be used in our computation:
Sugar = 15 grams
Proportion of syrup = 25%
So organizing the information given in the statement we have that:
25% sugar syrup means it has 25% sugar and 75% waterAmount of sugar = 15g = 25%In this way, we can calculate the missing value for this percentage as:
25% of x = 15 grams
Express as decimal
So, we have
0.25 * x = 15
Divide both sides by 0.25
x = 60
This means that the total amount is 60 grams
If the syrup contains 25% of sugar, then 75% would be water (assume no other item is present)
So, we have
Water = 75% * 60g
Water = 45g
Hence, the amount is 45 grams
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Answer: 45 g of water
Step-by-step explanation:
How do you use the zero product property to solve a quadratic equation in factored form?.
Quadratic equations in factored form can be solved by using the Zero Product Property, which states that if the product of two numbers equals zero, then at least one of the values must also equal zero.
The Zero Product Property can be used to resolve any factored quadratic equation, such as (a + b)(a b) = 0. In accordance with the zero product property, if a+b=0, then either an or b must also be equal to zero. This essential characteristic allows us to solve equations like (x+2)(x-5)=0.
The zero product property states that if two quantities are added together and the result is zero, then one or both of the individual quantities must also be zero. You can solve this problem by rewriting it as (x + 3) (2 x 1) = 0.
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which best shows an identity property?
Answer:
I believe the first one
Step-by-step explanation:
What is the formula for F G )( X?.
Answer:
I'm sorry, but the formula you provided "F G )( X" is not a valid mathematical notation, it doesn't make sense in mathematical or scientific context. Please provide more information or context about the formula or correct the formula if it has any typo.
APEX QUIZ ANSWER
What else would need to be congruent to show that ABC=AXYZ by ASA?
B
A. ZB=LY
B. AC = XZ
C. BC = √2
OD. LC= LZ
Correct
This is the correct answer.
Z
Givenc
ZA ZX
2C=22
Please like this to help others
We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.
What is ASA congruence of triangle?
The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.
We are given the following:
1. ∠A ≅ ∠X
2. ∠C ≅ ∠Z
Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.
The sides in between both the angles are AC and XZ.
Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.
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What is the range of the function FX =- 2 6x )+ 3?.
The range of the function FX = -2(6x) + 3 is [-3, +∞).
First, let's simplify the equation.
FX = -2(6x) + 3
FX = -12x + 3
To determine the range of the function, start by graphing the equation.
The graph will be a line with a slope of -12 and a y-intercept of 3.
To find the range, we need to determine the y-values of the graph as x-values increase. Since the slope is negative, the y-values will decrease as x-values increase.
The range of the function is all real numbers less than or equal to 3.
Therefore, the range of the function FX=-12x+3 is all real numbers less than or equal to 3.
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Suppose Mike surveyed 300 students. How many students would you expect to choose reptiles as their favorite pet?
Answer:150
Step-by-step explanation:
suppose he asks 300 and only 1/2 say yes,
How do you do thissss♀️..?
Answer:
the answer is A because you can know
Please need ASAP!!!!
40 points
Answer: A or C i would go with C but ur instict
Step-by-step explanation:
Answer:
A or C
Step-by-step explanation:
Good Luck!
X - 3.5 > 6.9
Pls what is the solution to the inequality
Answer:
x > 10.4
Step-by-step explanation:
Isolate X by adding 3.5 to each side of the inequality
That leaves you with x > 6.9 + 3.5
Why is equivalence important in maths?.
Equivalence relations are important in maths because of the following parts,
The fundamental theorem of equivalence relations is basic theorem.In integration theoryIn case of equivalent fractionA relation R on a set A is called an equivalence relation if and only if the relation R is recursive, symmetric, and transitive. An equivalence relation is a relation on sets, and is generally represented by the symbol “~”. For example: "Equal to (=)" is the equivalence relation on any set of numbers A for all elements a, b, c ∈ A,
Reflexive: a = a ,
Symmetric: a = b ⇒ b = a and
Transitive: a = b, b = c ⇒ a = c.
This means that (=) is recursive, symmetric, and transitive. Equivalence relations are used in several areas of mathematics.
In integration theory, functions are considered "equal" if they differ only in a small set. in some respects. If the function is not identified in this way, some commonly used standards conditiondoes not satisfy || f || = 0 <=> f=0.
Two fractions are equivalent if they have the same decimal number. That is, if ad = b, a/b is equivalent to c/d. (One example is based on equivalence relations).To learn more about equivalence relation , refer:
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Complete question:
Why is equivalence relation important in maths?.
A bicycle wheel is centimeters from top to bottom. When the wheel goes all the way around one time, the bicycle travels 198 centimeters. How can this information be used to estimate the value of π?
The height of the wheel is 63 centimeters that is the diameter of the circular wheel.
How do you explain distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.The International System of Units defines a metre as the distance unit. It's interesting to note that many other derived units or quantities, such as volume, area, acceleration, and speed, may be constructed using this as the basic unit and a few formulae.Given data :
A bicycle wheel is 63 centimeters from top to bottom.When the wheel goes all the way around one time, the bicycle travels 198 centimeters.a) The height of the wheel is 63 centimeters that is the diameter of the circular wheel.
b) The distance traveled by the wheel when it goes all the way around one time is 198 centimeters that is the perimeter of the circular wheel.
c) The distance traveled by the wheel when it goes all the way around one time is the perimeter of the circle. To estimate the value of t, divide the distance traveled by the wheel when it goes all the way around by its height.
Completed question :
A bicycle wheel is 63 centimeters from top to bottom. When the wheel goes all the way
around one time, the bicycle travels 198 centimeters. How can this information be used to
estimate the value of ?
63 cm
Click the arrows to choose an answer from each menu.
Because the wheel is circular, the height of the wheel is the Choose...
of
the circle. The distance traveled by the wheel when it goes all the way around one time is the
Choose...
of the circle. To estimate the value of t, Choose... the distance
traveled by the wheel when it goes all the way around by Choose...
y
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Two cards are selected, without replacing the first card, from a standard deck. Find the probability that both cards are sevens.
The probability that both cards are sevens is 0.0044
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
There are 52 cards, 4 are sevens.
So the probability of picking the first 7 is 4/52.
If you don't replace the card, then there are only 51 cards left, 3 of which are sevens.
So the probability of picking a seven on the second draw is 3/51.
The probability of picking sevens on both draws is:
P(picking two sevens) = (4/52)·(3/51) =0.076*0.058=0.0044
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18. Find the equation of the circle with center (5, -3) and radius of 3. Show work.
Answer:
(x - 5)² + (y + 3)² = 9
Step-by-step explanation:
The standard equation of a circle with center (a, b) and radius r is given by
(x - a)² + (y-b)² = r²
Here the center is (5, -3) and r = 3
Substituting values for a = 5, b = -3 and r = 3
(x - 5)² + (y-(-3))² = 3²
(x - 5)² + (y + 3)² = 9
It is OK to leave it in this form without expanding
