[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=2\\ k=3 \end{cases}\implies y=a(x-2)^2 +3\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ 2=a(0-2)^2 + 3\implies -1=a(-2)^2\implies -1=4a\implies \cfrac{-1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x-2)^2 + 3 \end{array}} ~\hfill[/tex]
Evaluate the expression when y=6. y^2+5y+9
Answer:
75
Step-by-step explanation:
y² + 5y + 9
since y = 6 we will just substitute for y
= (6)² + 5(6) + 9
= 36 + 30 + 9
= 66 + 9
= 75
i hope this helps
if n is an integer, what is the sum of the next three consecutive even integer great than 2n
The required sum is given as 6n + 12.
What are integers?Integers can be defined as the set of counting numbers and their negative values along with zero. An integer can be written in the form of a fraction by writing the denominator as 1.
The given problem can be solved as follows,
The consecutive three even integers greater than 2n can be written as,
2n + 2, 2n + 4 and 2n + 6
Now, the sum of these integers are given as follows,
2n + 2 + 2n + 4 + 2n + 6
= 6n + 12
Hence, the sum of the next three consecutive even integer greater than 2n is given as 6n + 12.
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help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
this is the same principle in every posted question.
I hope you understand this now.
if not please let me know what is still a "riddle" to you, so that I can explain it better.
remember, the inverse function of y = e^x is x = ln(y).
and the inverse function of y = ln(x) is x = e^y.
we want to find the value of x, where f(x) = 28.
28 = 0.48ln(x + 2) + 27
1 = 0.48ln(x + 2)
1/0.48 = ln(x + 2)
e^(1/0.48) = x + 2
x = e^(1/0.48) + 2 = 10.03119499... miles ≈ 10 miles
the pressure of 28 inches of mercury occurs about 10 miles from the eye of the hurricane.
Select the equivalent fraction for the fraction represented on the given number line.
1/2
2/6
2/3
3/6
2/6 is the equivalent fraction for the fraction represented on the given number line. So, B is the correct option
What is an equivalent fraction ?
According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.
For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.
The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
as 2/6 can further reduced to 1/3 which is represented on to the number line as 1/3 which is equal to 2/6
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6 -4 3
2 4 -2
Photo provided
The equations of the system would be 6x - 4y = 3 and 2x + 4y = -2.
What is the system of linear equations in matrices?
A system of linear equations in matrices is a set of linear equations that can be expressed in matrix form. In this form, the equations are written as a matrix equation of the form Ax = b, where A is an m × n matrix of coefficients, x is an n × 1 matrix of variables, and b is an m × 1 matrix of constants. The solution to the system of equations can be found by solving for the matrix x using the matrix equation Ax = b. This can be done using various techniques, such as Gaussian elimination or matrix inversion. Matrix equations can be used to solve systems of linear equations for which the traditional algebraic methods are difficult or impossible.
We can prepare the equations as:
Equation 1: 6x - 4y = 3
Equation 2: 2x + 4y = -2
Hence, the equations of the system would be 6x - 4y = 3 and 2x + 4y = -2.
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j(m) = 2^m-1
What is j (4)?
Enter your answer in the box.
j(m) = 2ᵐ ⁻ ¹
for functions you will replace the number in the brackets with the letter! so:
j(4) = 2⁴ ⁻ ¹
= 2³
= 8
URGENt please help me all I need is the answer of b
write the equation of a line of standard form that has a slope of 4 and has same x-intercept as a line 3x+y=18
PLEASEE I WILL GIVE BRANILEST PLSS THIS IS URGENT
Answer: The slope is 3
Step-by-step explanation:
Explanation:
The slope of a line in the form
y
=
m
x
+
b
is
m
.
3
x
−
y
=
4
−
y
=
−
3
x
+
4
subtract
3
x
from both sides
y
=
3
x
−
4
multiply both sides by
−
1
When a local office supply store sells
5 packs of paper, it also sells 8 packs
of envelopes. How many packs of
envelopes would the store sell if it sold
15 packs of paper?
Answer:
If the local office supply store sells 5 packs of paper, it also sells 8 packs of envelopes. This means that the store sells 8 packs of envelopes for every 5 packs of paper.
If the store sells 15 packs of paper, it will sell 15 packs of paper * (8 packs of envelopes / 5 packs of paper) = <<15*(8/5)=24>>24 packs of envelopes.
Therefore, if the local office supply store sells 15 packs of paper, it will sell 24 packs of envelopes.
Choose ALL answers that describe the polygon QRST if QR =11, RS =20, ST =11, TQ=20, QR || ST, and RS || TQ
The given polygon could be parallelogram , quadrilateral , rectangle.
What is a polygon?
In geometry, a polygonal shape could be a two-dimensional figure that's delineate by a finite range of line segments connected to make a closed two-dimensional figure chain. The delimited plane region, the bounding circuit, or the 2 along, is also referred to as a polygonal shape.
Main body:
As opposite sides of polygon QRST are parallel , it a parallelogram .
A quadrilateral is a polygon with for sides , so it also satisfies the condition.
The opposite sides of rectangle are equal and parallel , which is also satisfied.
Hence ,the given polygon could be parallelogram , quadrilateral , rectangle.
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CAN SOMEONE PLEASE HELP ME WITH THIS GEOMETRY?
Answer:
x = -18
Step-by-step explanation:
Please tell me If I am wrong..
5 x 2 = 10 = numerator.
-9 x 2 = ? = denominator
? = -18
-9 x 2 = -18…
Follow me please. The answer is -18
what is (13.4 - 0.896 , 8.4 + 4.095) =
The difference of given decimal numbers is (12.504, 12.495).
Given that, (13.4-0.896, 8.4+4.095).
What is the difference of two decimal numbers?Subtracting decimals:
1. Write down the two numbers, one under the other, with the decimal points lined up.
2. Add zeros so the numbers have the same length.
3. Then subtract normally, remembering to put the decimal point in the answer.
Here,
13.4-0.896 =12.504
8.4+4.095 =12.495
So, (13.4-0.896, 8.4+4.095) =(12.504, 12.495)
Hence, the difference of given decimal numbers is (12.504, 12.495).
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How many people Mark and Heather can invite to the party?
Stefan sells Jin a bicycle for $163 and a helmet for $.17 The total cost for Jin is %150
of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
The cycle originally cost $120, and he made a $60 profit by selling it for $163 with a $17 helmet.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
Here,
The cost of bicycle=$163
Cost of helmet=$17
Total cost,
=163+17
=$180
Let the original cost be c,
180=150%*c
180=1.5c
c=$120
He made a profit,
=180-120
=$60
The original cost of cycle was $120 that he sold in $163 with the helmet of $17 making a profit of $60.
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Which of the following interpretations of the mean is correct?
A. The observed number of hits per game ail be less than the mean number of hills per game for most games.
B. The observed number of hits per garret will bees equal to the mean number of hiss per game for most sties.
X C. In any number 0f game, one will expect the man number of hits per game to be its mean of the random variable
D. Chess the course of many games, one would expect the mean number of its per game to be the mean of the random variable.
Over the course of many games, one would expect the mean number of hits per game to be the mean of the random variable.
What is Mean?
A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilises the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.
There are two different types of means that can be calculated: the arithmetic mean and the geometric mean.
The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of numbers in the set.
Mean is the ratio of sum of observations to the total number of observation.
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What is the equation of the line through the points(0,0) and (9,-4)
Answer:
y = -4/9x
Step-by-step explanation:
You want the equation of the line through (0, 0) and (9, -4).
ProportionA line through the point (0, 0) represents a proportion. The slope of the line is the constant of proportionality, the ratio of y to x.
k = y/x = -4/9
The equation of the line is ...
y = kx
y = -4/9x
PLEASE PLEASE HELP ME
make a list of at least 15 different phrases and expressions you can write using the variable y and the integer 2. Include all operations
I need this ASAP!!!
Answer:
y/2
y*2
y-2
y+2
y%2
y^2
Operations on Algebraic Expressions: The three major components of an algebraic expression are variables, constants, and coefficients. Addition, subtraction, multiplication, and division are the four fundamental operations. We solve both difficult and straightforward equations using operations on algebraic expressions.There are three categories of algebraic expressions: monomial, binomial, and polynomial or multi-term expressions.These are the algebraic terms: Alphabetic letters alone or in combination with numbers or fractions are the variables.The numbers that are connected to the variables in a single term are called coefficients.Constants: Single integers or numbers that are typically connected to other terms through elementary operations.Examples include 8xyz, 25x+12y+9, 2yz23zy, and 3a+2b+5c.Algebraic Expression Types
There are three different categories for algebraic expressions. As follows:
Expressions with a monomial or single word. For instance, 4xy2, 3ab, 7p, 5xyz, etc., where 3,4,5,7 are the coefficients and x, y, z, a, b, p are the variables.Expressions with two terms or a binomial. For instance, 2xyx, pq5p2, etc.Multi-term or polynomial expressions. as in 2x+5y4, 2xy2+3y+1, etc.To learn more about Operations on Algebraic Expressions refer to:
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"y/2," "y*2," "y-2," "y+2," "y%2," and "y". Constants, coefficients, and variables make up the three main parts of an algebraic expression.
Procedures for Algebraic Expressions:Constants, coefficients, and variables make up the three main parts of an algebraic expression. These four operations—addition, subtraction, multiplication, and division—are known as the fundamental operations.By performing operations on algebraic expressions, we are able to solve both complex and simple equations.Polynomial or multi-term expressions, binomial expressions, and monomial expressions are the three types of algebraic expressions.The variables are either alphabetic letters alone or in combination with numbers or fractions.The term "coefficients" refers to the numbers that link the variables in a single term.Single integers or numbers known as constants are those that are often connected to other terms through simple mathematical procedures. There are more examples, such as 8xyz, 25x+12y+9, 2yz23zy, and 3a+2b+5c.Monomial expressions or single-word phrases. For instance, 4xy2, 3ab, 7p, 5xyz, etc., where 3,4,5,7 are the coefficients and x, y, z, a, b, p are the variables. two-term or binomial expressions pq5p2, for instance, or 2xyx. such as 2x+5y4, 2xy2+3y+1, etc., are examples of multi-term or polynomial expressions.To learn more about Algebraic expressions refer to:
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What is the 6th term in the Fibonacci sequence?
The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.. .
What is Fibonacci sequence?
One of the most well-known mathematical formulae is the Fibonacci sequence. Each number in the Fibonacci sequence is calculated by adding the two numbers that came before it. Typically, the Fibonacci series' first two terms are 0 and 1. Hundreds of years before Leonardo Pisano Bigollo was even aware of it, the Fibonacci sequence was well-known in India. Because the date November 23 contains the numbers "1, 1, 2, 3," which are a part of the sequence, it is recognized as Fibonacci Day.
The Fibonacci sequence is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946,….
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8. Which is a solution of the equation y = 2x + 5? (1 point)
5,20
6,12
3,11
4,14.
I need this really quickly. Thanks to anyone willing to help.
Answer:
3,11
Step-by-step explanation:
Since y = 2x + 5, if you chose (x,y) (3,11):
11 = 2*3 + 5
11 = 6 + 5
11 = 11
Answer:
(3, 11 ) is a solution
Step-by-step explanation:
substitute the x- coordinate of the points into the equation and if the value of y obtained equals the y- coordinate then the point is a solution.
(5, 20 )
y = 2(5) + 5 = 10 + 5 = 15 ≠ 20 ← not a solution
(6, 12 )
y = 2(6) + 5 = 12 + 5 = 17 ≠ 12 ← not a solution
(3, 11 )
y = 2(3) + 5 = 6 + 5 = 11 ← solution
(4, 14 )
y = 2(4) + 5 = 8 + 5 = 13 ≠ 14 ← not a solution
10. If m and n are positive integers and
2x(5x+3y) = mx² + nxy, what is the value
of m-n?
(A) -4
(B) -1
(C) 1
(D) 4
Answer:
D.)
Step-by-step explanation:
1.) Expand the expression with distributive property. If we expand, we get 10x^2+6xy.
2.) Figure out m and n based on the expression. Since m is in front of the x^2, that means that m=10, and since n is in front of the xy, that means that n=6.
3.) Compute based on m and n. Since m is 10 and n is 6, m - n = 10 - 6 = 4. Therefore, D.) is the answer.
Which function represents the graph?
A. y = –cos (x)
B. y = -sin (x)
C. y = cos (x)
D. y = sin (x)
In using quarterly time series data, which quarter can serve as the base period for interpretation of dummy variables?
A. Any of the above.
B. Quarter two
C. Quarter one
D. Quarter four
E. Quarter three
In using quarterly time series data, Quarter two can serve as the base period for interpretation of dummy variables.
What do you mean by interpretation?
The process of interpreting anything involves elaborating, rephrasing, or otherwise demonstrating your own understanding of it.
Because they are explaining what someone is saying to someone who doesn't understand, a person who translates one language into another is known as an interpreter.
What are examples and variables?
A trait that is measurable and capable of taking on several values is known as a variable. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling.
The two primary categories of variables are categorical and numeric.
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Divide 2x^-13x+x^2+6 by x-4
The Quadratic Equation [tex]3x^{2}-13x+6[/tex] divided by [tex]x-4[/tex] for all the values of the x(except x=4).
Let us consider [tex]3x^{2}-13x+6[/tex] as equation→(1) of a Quadratic Equation assume some values for x which is satisfies the equation and doesn't satisfy equation by "hit and trail method".
x=1 substitute in the equation (1) we get ⇒ [tex]\frac{4}{3}[/tex]
x=2 we get [tex]3(2)^{2}-13(2)+6[/tex] [tex]=4[/tex]
x=4 we get[tex]3(4)^{2}-13(4)+6[/tex] ⇒ [tex]\frac{2}{0}[/tex] which is not defined.
x=6 we get [tex]3(6)^{2}-13(6)+6[/tex] [tex]= 12[/tex]
x= -2 we get [tex]3(-2)^{2}-13(-2)+6[/tex] ⇒[tex]\frac{22}{-3}[/tex]
And so on for the remaining values of x the equation will satisfy. Except for the value x= 4 the equation doesn't satisfy because if we substitute x=4 in x-4 we get 4-4 =0 anything divided by zero is not defined.
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Divide [tex]3x^{2}-13x+6 by x-4[/tex]
Put the following equation of a line into slope intercept form, simplifying all fractions
20y - 4x = -160 what would be the answer
Answer:
do it yourslef
dont be silly
lol
11111111
Question 3 4 pts Solve the equation for the variable. Show your work and be sure to not forget to show all of your steps. -3(3 + 6b) = 36 - 3b
Answer:
[tex]\huge\boxed{\sf b = -3}[/tex]
Step-by-step explanation:
Given equation:-3(3 + 6b) = 36 - 3b
Distribute
-9 - 18b = 36 - 3b
Add 3b to both sides
-18b + 3b - 9 = 36
-15b - 9 = 36
Add 9 to both sides
-15b = 36 + 9
-15b = 45
Divide -15 to both sides
b = 45/(-15)
b = -3[tex]\rule[225]{225}{2}[/tex]
Answer:
The value of b is -3.
Step-by-step explanation:
The equation is,
→ -3(3 + 6b) = 36 - 3b
Now the value of b will be,
→ -3(3 + 6b) = 36 - 3b
→ -3(3) - 3(6b) = 36 - 3b
→ -9 - 18b = 36 - 3b
→ -18b + 3b = 36 + 9
→ -15b = 45
→ b = -(45/15)
→ [ b = -3 ]
Hence, the value of b is -3.
Help with this plsss !!!
Answer:
Just about 50%, depending on if the data set is a odd or even number
Step-by-step explanation:
At 45, is the median value. The median of a box plot is not necessarily 50% of the data. The median is the middle value in a dataset, or the value that divides the data into two equal halves. If the dataset has an odd number of values, the median will be one of the values in the dataset. If the dataset has an even number of values, the median will be the average of the two middle values.
Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?
AAS
SSS
SAS
HL
Answer:
AAS
Step-by-step explanation:
BECAUSE OF THE QUESTION
ITS GIVEN IN QUESTION
it's congruent
32-39 Fill in >,< or = for each prob
3
15
4
-6
-8
-15
Fill in the inequality for each problem as follows 32 > -39, 3 < 15, 4 > -6 and -8 > -15
How to fill in the correct sign for each problem?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
We have different inequality signs as follows:
Greater than (>)
Less than(<)
Less than or equal to (≤)
Greater than or equal to (≥)
Given:
32__-39
3__15
4__-6
-8__-15
For 32__-39:
Since 32 is greater than -39. we can write:
32 > -39
For 3__15:
Since 3 is less than 15. we can write:
3 < 15
For 4__-6:
Since 4 is greater than -6. we can write:
4 > -6
For -8__-15:
Since -8 is greater than -15. we can write:
-8 > -15
Thus, fill in for each problem accordingly
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Complete Question
Fill in >,< or = for each prob
32__-39
3__15
4__-6
-8__-15
The perimeter of a rectangle is 20 ft. The length is 6 ft. Which equation can be
solved to find the width of the rectangle?
Answer: 20ft - 6ft
Step-by-step explanation:
the manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5100 tickets were sold and the receipts totaled $29,484. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there
By solving equations, we know that there were 2187 adult partons.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A function is an equation with a single solution for y for each value of x.
Each input of a particular type receives exactly one output when using a function.
Instead of y, a function is frequently named f(x) or g(x).
When x equals 2, we should determine our function's value because f(2) says to do so.
So, the number of adult patrons was:
Let, a be an adult and c be children.
Total tickets:
a + c = 5200
c = (5200-a)
Total amount:
7.50a + 4.50c = 29961
Replace c in the first equation with (5200-a).
7.5a + 4.5(5200-a) = 29961
7.5a + 23400 - 4.5a = 29961
7.5a - 4.5a = 29961 - 23400
3a = 6561
a = 6561/3
a = 2187
Therefore, by solving equations, we know that there were 2187 adult partons.
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