The quadratic equation in standard form is y = 3 · x² + 2 · x - 1. (Correct choice: C)
How to derive the quadratic equation associated with a set of three points
In accordance with the fundamental theorem of algebra, a quadratic function can be found by knowing three distinct points. Quadratic functions are polynomials of the form, known as standard form:
y = a · x² + b · x + c
Where a, b, c are real coefficients.
If we know that (x₁, y₁) = (- 3, 20), (x₂, y₂) = (0, - 1) and (x₃, y₃) = (2, 15), then the coefficients of the polynomial are found by numerical methods:
9 · a - 3 · b + c = 20
c = - 1
4 · a + 2 · b + c = 15
The solution to the system of linear equations is (a, b, c) = (3, 2, - 1). The equation is y = 3 · x² + 2 · x - 1.
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Find the angle B and the value of z if ABC=DEF
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
The question provides that ΔABC and ΔDEF are similar. By the definition of similar triangles, we have that:
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Since congruent angles are equal, we have:
[tex]\begin{gathered} m\angle A=m\angle D \\ m\angle B=m\angle E \\ m\angle C=m\angle F \end{gathered}[/tex]From the provided diagram, we have the measures of the following angles:
[tex]\begin{gathered} m\angle A=105\degree \\ m\angle E=(10z-5)\degree \\ m\angle F=30\degree \end{gathered}[/tex]Comparing the congruent angles, we have that:
[tex]m\angle D=105\degree[/tex]The sum of angles in a triangle is 180°. If we add up the angles of ΔDEF, we can get the value of z:
[tex]\begin{gathered} 105+10z-5+30=180 \\ 10z=180+5-105-30 \\ 10z=50 \\ z=5 \end{gathered}[/tex]Given the value of z, we can get the measure of [tex]\begin{gathered} m\angle E=10z-5 \\ m\angle E=10(5)-5=50-5=45\degree \end{gathered}[/tex]By comparing the congruent angles, we have that:
[tex]m\angle B=m\angle E=45\degree[/tex]ANSWER:
Angle B = 45 degrees.
The value of z is 5.
A lake in East Texas was stocked with 3,000 trout in the year 2000. The number of fish in the lake is modeled by f(x) = 3000 + 100x, where x represents the number of years after 2000. Which of the following is the most reasonable domain and range for the function if domain is time, and range is number of fish?
Domain:
Range:
The Domain and the range of the function are given as
x ≥ 0, y ≥ 3000
What is the domain of a function?This is the complete set of values that is used to represent the independent variable in the function. The independent variable that we have here is represented by x and it is 0.
What is the range of a function?This is the set of the possible values that the dependent variable in the function is to have. The dependent variable is given by y.
The range of x would have to start from 0 for the range of all values of x. Hence x ≥ 0, while y is seen to be in the form of y ≥ 3000 because this is the value of trout that was stocked.
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y is inversely proportional to the square root of x.
When x = 16, y = 10.
What does x equal when y = 8?
Answer:
x = 25 when y = 8
Step-by-step explanation:
If y is inversely proportional to square root of x we write it as
[tex]y \propto \dfrac{1}{\sqrt{x}}[/tex]
This is also equivalent to
[tex]y = k \dfrac{1}{\sqrt{x}} \;\;\;\;\ \text{ [1]}[/tex]
where k is a constant known as the constant of proportionality
Given y = 10 when x = 16 we can find k by substituting for y and x in [1]
[tex]\rightarrow 10 = k\dfrac{1}{\sqrt{16}}\\\\\rightarrow 10 = k \dfrac{1}{4}\\\\\drightarrow 40 = k \:\:\:\: \text{by multiplying both sides by 4}\\\\\text{which can be written as }\\\\k = 40\\[/tex]
So constant of proportionality k = 40
To find x when y = 8, substitute y and k in [1] to get
[tex]y = k \dfrac{1}{\sqrt{x}}\\\text{Multiply both sides by \sqrt{x} and divide by y at the same time to get}\\\\\sqrt{x} = \dfrac{k}{y}[/tex]
Dividing both sides by y and multiplying by √x gives us
[tex]\sqrt{x} = \dfrac{k}{y}\\\\\text{Substituting k = 40, y = 8}:\\\\\sqrt{x} = \dfrac{40}{8}\\\\\sqrt{x}= 5\\\\\text{Squaring both sides: }\\\\(\sqrt{x})^2 = 5^2\\\\x = 25 \;\;\;\text{since $(\sqrt{x})^2$ = x}[/tex]
The answer is
x = 20
Formulate y=k/x based on the following criteria.
Replace: 10= k/16
Change the sides so that k/16 = 10.
Subtract the coefficient of the variable from both sides of the equation: k = 10×16
Determine the quotient or product: k = 160
Replace with y = 160/x.
Replace with: 8 = 160/x
The denominator cannot be zero if the fraction is defined: as x ≠ 0
As the domain, append the inequality: 8= 160/x, x≠0
Divide the common denominator by both sides of the equation: 8x = 160x/x, x≠0
8x=160x/x, where x ≠ 0. Reduce the fraction.
By the variable's coefficient, multiply both sides of the equation (x=160÷8, x ≠ 0).
Calculate the quotients or product: x = 20,x ≠ 0
Find the junction at x=20.
Answer : x = 20
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A triangle has an angle that measures 111°. The other two angles are in a ratio of 6:17. What are the measures of those two angles?
Answer:
18 and 51
Step-by-step explanation:
the sum of the two other angles would be 69 degrees because there has to be 180 degrees in a triangle
given that we can create the equation 6x + 17x = 69 and solve for x
x = 3
so now we can plug in each part of that equation and find out the two angles
A 2 cm pink block has been placed below the blue blocks. How many blue blocks would be needed in order make a stack of blocks that is 50 cm high?
a=2cm. b=50cm. x=?
x=b:a. x=50:2. x=25
Can someone please answer (picture)
The expansion of ( 2x - y⁵)² using algebraic identity, as a polynomial is 4x² - 4xy⁵+ y¹⁰
What are algebraic identities?Algebraic identities are the identities which aids in solving products or powers of algebraic expressions. Most common identities are :
(a+ b)² = a² + 2ab + b²
(a- b)² = a² - 2ab + b²
a² -b² = (a+ b) (a- b), where a and b can be variable or constants or algebraic expressions.
For expanding (2x - y⁵)²
Use identity (a-b)² = a²-2ab+b², let a = 2x and b = y⁵
Then, ( 2x - y⁵)² = (2x)² - 2(2x)( y⁵) + (y⁵)²
⇒ ( 2x - y⁵)² = 4x² - 4xy⁵+ y¹⁰
Therefore, the standard form of ( 2x - y⁵)² as a polynomial is 4x² - 4xy⁵+ y¹⁰
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Guenther drove 260 miles in 5 hours. He has 494 more miles to drive on his trip. If he continues at this same average speed, what will his driving time in hours be for the remainder of his trip?
The driving time in hours for the remaining of Guenther's trip would be = 9.5 hours.
What is speed?The Speed of a moving object is defined as the change in distance divided by change in time.
The first distance covered by Guenther = 260 miles.
The time it took to cover the first distance= 5 hours.
The remaining distance = 494 miles
The time it will take to cover the remaining distance = X hours
But if , 260 miles = 5 hours
494 miles = X hours
Make X the subject of formula;
X hours= 494 × 5 / 260
X hours = 2,470 / 260
X hours = 9.5 hours.
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John has $400 June has 1/10 of that. June has 0.1 of Maria’s money how much money does Maria and June have.
I really need help please figure this out I need it by Monday October 17 2021 please help me thank you
The amount of money that June has is $40 and Maria has $400. The total amount is $440.
What is the total amount?From the information, John has $400 June has 1/10 of that and June has 0.1 of Maria’s money.
Therefore the amount that June has will be:
= 0.1 × John's money
= 0.1 × 400
= 40
June has 0.1 of Maria’s money. Let Maria's money be x. Therefore, 0.1 × x = 40
0.1x = 40
Divide
x = 40 / 0.1
x = 400
Maria's money = 400
Therefore, the total amount that they have will be:
= Amount that John has + Maria's amount
= 400 + 40.
= $440
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write an equation in slope-intercept form of the line that passes through the points (2,15) and (5,21)
Answer:
y=2x+11
Step-by-step explanation:
suppose 48 out of every 120 people like baseball/softball. of the people who like baseball/softball, 3 out of 5 play the game. if you ask 500 people, how many would you expect play baseball/softball?
out of 500 people 200 like baseball and 120 people like to play game baseball/softball
suppose 48 out of every 120 people like baseball/softball.
of the people who like baseball/softball, 3 out of 5 play the game.
if you ask 500 people,
how many would you expect play baseball/softball
it means 40% like baseball and 60% like to play game
if there are 500 people
then 500 *(40/100)=200
thus 200 people like baseball
and 200*(60/100)=120
Hence 120 people to play game
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If g(x) = x² + 2, find g(3).
Answer:
11
Step-by-step explanation:
[tex]3^{2}[/tex] + 2
9 + 2
11
Question 2 of 10
Which of the following is most likely to be a relative maximum for this graph?
8-
(-1.0) (20)
-8 -84
6
Answer:it’s (-1,8)
Step-by-step explanation:
Él ___ mi primo. (To express relationships)
Answer: es
Step-by-step explanation: I know Spanish
find the difference.
A.41-275
B-15-47
C-72-(-151)
D.612-(-144)
A. -234
B. -62
C. [tex]-72+151=79[/tex]
D. [tex]612+144=756[/tex]
The pages of Jack's book are numbered from 1.
ann
The page numbers have a total of 555 digits.
How many pages has the book?
How many of the digits are a 5?
Answer:
he has 556 pages in his book
PLEASE HELP ME HURRY
The number has been assigned to be number line and attached as a picture
What is a number line?A number line refers to a picture representing array of numbers arranged to suit the calculation intended to represent.
How to arrange the numbers in the number lineThe picture shows a number line from -6 to 6
The division in the number line is showing two lines representing 1/3 and 2/3 before the next number.
This means that the point before point 6 counting from point 5 is 5 1/3, 5 2/3 then point 6
For the negative direction we have
-5, -5 1/3, -5 2/3, -6
The required answer to the questions attached
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Graph each equation using slope-intercept form
8. y = x + 6
Help Me please it do today hurry
Answer:
look at the step by step
Step-by-step explanation:
I think -12 x-12 and something with the other number I think you have to mulitply it all
A woman has twice as many dimes as quarters in her purse. if the dimes were quarters and the quarters were dimes, she would have $1.20 more than she has now. how many of each type of coin does the woman have?
The number of Quarter coins that she has is 8 and the number of Dimes is 16.
It is given in the question that the woman has twice as many Dimes as the quarters in her purse.
We know that the value of Dimes is 0.10$ and the value of Quarters is
0.25 $
Let the number of Quarter coins is y and the number of Dimes coin be u.
According to the question above,
u = 2y equation (i)
The total value z = 0.25y + 0.10u
Putting here the value of u from equation (i) we have,
z = 0.25y + 0.10(2y)
⇒ z = 0.25y + 0.20y
⇒ z = 0.45y equation (ii)
Now it has been mentioned that if the Dimes were Quarters and the Quarters were the Dimes, she would have $ 1.20 greater than she has now.
So we have,
z + 1.2 = 0.25u + 0.10y
Putting the value of u from above eqation (i),
z + 1.2 = 0.25(2y) + 0.10y
⇒ z + 1.2 = 0.50y + 0.10 y
⇒ z + 1.2 = 0.60y
Putting the value of z from equation (ii)
⇒ 0.45y + 1.2 = 0.60y
⇒ 0.45y - 0.60y = - 1.2
⇒ -0.15y = - 1.2
⇒ y = [tex]\frac{-1.2}{-0.15}[/tex]
⇒ y = 8
Therefore u = 2y
⇒ u = 2 x 8 = 16
Hence the number of Quarter coins is 8 and the number of Dimes is 16
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16 dimes, 8 quarters
I checked RSM it's correct
Find a point-slope form for the line with slope 1/2
and passing through the point (-3,-8).
The point slope form for the line with slope 1/2 and passing through the point (-3,-8) is y + 8 = m(x + 3)
How to find point slope equation?A linear equation can be represented in point slope form as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesTherefore, the point slope form is represented as follows;
m = 1 / 2
It passes through the points (-3,-8).
Hence,
y + 8 = m(x + 3)
Therefore, the point slope form of the line is y + 8 = m(x + 3)
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Which graph best represents the solution set to this system of inequalities?
x+y <1
x-y ≤2
The graph of the inequality (x + y >1), will be:
{(x^2+(y-1)^2-0.05)((x-1)^2+y^2-0.05)(x+y-1)=0 [-10, 10, -5, 5]} and we can shade right-side of the line.
As per the question statement, we are supposed to graph the inequality
x + y >1. So, first we solve for two points as an equation instead of an inequality to find the boundary line for the inequality.
For x = 0, y = 1 or (0,1)
For y = 0, x = 1 or (1,0)
So now we can graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.
The boundary line would be solid because the inequality contains "or equal to" clause.
Graph: {(x^2+(y-1)^2-0.05)((x-1)^2+y^2-0.05)(x+y-1)=0 [-10, 10, -5, 5]}
We can shade right-side of the line.
Because the inequality operator lacks a "or equal to" phrase, the boundary line will be altered to a dashed line.
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On his fruit stand, Mr.Roberts has 13 papayas, 23-star fruits, 35 mangos, and 19 strawberries. What is the ratio of the number of mangos to the number of strawberries?
Answer:
The answer is 35:19
Step-by-step explanation:
First what is a ratio?
A relationship between two quantities, normally expressed as the quotient of one divided by the other. For example, if a box contains six red marbles and four blue marbles, the ratio of red marbles to blue marbles is 6 to 4, also written 6:4. A ratio can also be expressed as a decimal or percentage.
So as a result
= There are 35 mangoes and 19 strawberries
And since we are comparing mangoes to strawberries
The answer would be
= 35:19
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What is the value of x
x = 41/6 is value of x in transversal lines.
What are transversal lines?
A line that crosses two lines in the same plane at two different geometric locations is referred to as a transversal. Different sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.A line that crosses other lines is known as a transversal. When transversals intersect parallel lines, such as the two railroad tracks, we often operate with them.( 12x + 1)° = 2
2 = 83°
( 12x + 1)° = 83°
12x° + 1° = 83°
12x = 83 - 1
12x = 82
x = 82/12
x = 41/6
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WORTHHHHHHH.......30 POINTS
PLEASE HELP ASAP YOU GOT 20 MINUTES
Parin digs a hole at a rate of 5/6 feet every 15 minutes. After digging for 45 minutes, Parin places a bush in the hole that fills exactly 3/4 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
!!!!!!I REPEAT ENTER YOUR ANSWER AS A SIMPLIFIED MIXED NUMBER!!!!!!!
Answer: 3 1/4 Is the correct answer.
Question 9 (1 point)
Identify each slope as POSITIVE, NEGATIVE, ZERO, OR UNDEFINED.
Answer:
positive
Step-by-step explanation:
this is because it is going up if it is going down it’ll be negative and if it was zero it would be flat
i need help pls and thank you...
Answer:
AB = 32
Step-by-step explanation:
Since line l bisects AB at point M, we have AM = MB.
[tex]4x = 5x - 4[/tex]
[tex]4x + 4 = 5x[/tex]
[tex]x = 4[/tex]
AM = 4(4) = 16, MB = 5(4) - 4 = 16.
So AB = AM + MB = 16 + 16 = 32.
I just need to know if the answer is B or D
Firslty, we need to find the function, whcih we can do by substituting one into the other:
[tex]f(g(x))=2(g(x))^2-1=2(\sqrt[]{x-2})^2-1=2(x-2)-1=2x-4-1=2x-5[/tex]Now, for the domain we have more complicated approach.
We first have to find the domain for both f(x) and g(x).
The domain of f(x) is all real number, because it is a quadratic polynomial.
The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:
[tex]\begin{gathered} x-2\ge0 \\ x\ge2 \end{gathered}[/tex]Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).
Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).
The domain of g(x), as we saw, is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]So, the correct alternative is:
[tex]\begin{gathered} f(g(x))=2x-5 \\ D\colon\mleft\lbrace x\mright|x\ge2\} \end{gathered}[/tex]Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) ?
Responses
The graph of g(x) is the graph off(x) translated 7 units down.
The graph of , g begin argument x end argument, is the graph of , , , f open argument x close argument, , , translated 7 units down.
The graph of g(x) is the graph off(x) translated 7 units up.
The graph of , g begin argument x end argument, is the graph of , , , f open argument x close argument, , , translated 7 units up.
The graph of g(x) is the graph off(x) translated 7 units right.
The graph of , g begin argument x end argument, is the graph of , , , f open argument x close argument, , , translated 7 units right.
The graph of g(x) is the graph off(x) translated 7 units left.
The graph of g(x) is the graph of f(x) translated 7 units right
According to the question; g(x)=f(x−7).
Given f(x) then f(x + a) represents a horizontal translation of f(x).
If a > 0 then shift a units leftIf a < 0 then shift a units rightThus, f(x - 7) represents a shift right of 7 units.
What is Graph ?
Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.
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Answer: The graph of g(x) is the graph of f(x) translated 7 units right.
Step-by-step explanation:
Seven times the sum of a number and four is the same as 8 decreased by three times the number 
Answer: The equation is written as: " 7x + 28 = 8 − 3x " .
The value for x , when the equation is solved, is: " -2 ."
Step-by-step explanation:
Let the "unknown number" be represented by the variable, x ;
7 (times) the [sum of: (x + 4)] ; (is the same as): 8 [decreased by]:
3(times)x ;
Rewrite: " 7(x + 4) = 8 − 3x ". This is the written expression.
____
Now, if we wish to "solve for x" ;
Let's examine the 'left-hand side' of the equation:
7(x + 4) ;
Note the 'distributive property' of multiplication:
a(b + c) = ab + ac ;
____
So: 7(x + 4) = 7*x + 7*4 = 7x + 28 ;
Now, let's write the entire equation:
7x + 28 = 8 − 3x ;
Let's add 3x , and subtract 8 ; from Each Side of the equation:
7x + 28 + 3x − 8 = 8 + 3x − 8 ;
→ 7x + 3x + 28 − 8 = 8 − 3x + 3x;
to get:
10x + 20 = 0 ;
Now: Subtract 20 from Each Side of the equation:
10x + 20 − 20 = 0 − 20 ;
to get:
10x = -20 ; Now, divide both sides of the equation by 10 ;
to isolate x on one side of the equation; & to solve for x :
10x/10 = -20/10 ;
to get: " x = - 2 " .
____
Alternate method:
10x + 20 = 0 ;
Divide the Entire Equation by 10 ;
(10x + 20) / 10 = 0____ ;
to get: (10x/10) + (20/10) = 0 ;
→ x + 2 = 0 ;
Now subtract 2 from each side of the equation;
to isolate x on one side of the equation; & to solve for x :
x + 2 − 2 = 0 − 2 ;
to get: " x = -2 " .
____
Answer:
The equation is written as:
" 7x + 28 = 8 − 3x " .
The value for x, when the equation is solved, is "-2".
____
Hope this is helpful to you! Best wishes!
____
132 = -w + 236 solve for w