find an equation of the form f(x)=ax^2+bx+c. must solve algebraically and check using a calculator (state, the steps used to perform the check).
f(1)=4, f(2)=13, f(4)=46
Answers
By using algebra resolution methods for systems of linear equations, we find that the equation of the form f(x) = a · x² + b · x + c that passes through the three points is equal to f(x) = (5 / 2) · x² + (3 / 2) · x.
How to determine the quadratic equation that passes through three points
In this problem we must determine the coefficients of a quadratic equation that passes through the points (x₁, y₁) = (1, 4), (x₂, y₂) = (2, 13) and (x₃, y₃) = (4, 46). First, we need to create a system of linear equations by substituting on y and x thrice:
(x₁, y₁) = (1, 4)
a · 1² + b · 1 + c = 4
a + b + c = 4
(x₂, y₂) = (2, 13)
a · 2² + b · 2 + c = 13
4 · a + 2 · b + c = 13
(x₃, y₃) = (4, 46)
a · 4² + b · 4 + c = 46
16 · a + 4 · b + c = 46
Then, we find a system of three linear equations with three variables that offers an unique solution:
a + b + c = 4 (1)
4 · a + 2 · b + c = 13 (2)
16 · a + 4 · b + c = 46 (3)
There are different methods to find the solution to this system, we proceed to use algebraic substitution:
By (1):
c = 4 - a - b
(1) in (2) and (3):
4 · a + 2 · b + (4 - a - b) = 13
3 · a + b = 9 (2b)
16 · a + 4 · b + (4 - a - b) = 46
15 · a + 3 · b = 42 (3b)
By (2b):
b = 9 - 3 · a
(2b) in (3b):
15 · a + 3 · (9 - 3 · a) = 42
15 · a + 27 - 9 · a = 42
6 · a = 15
a = 15 / 6
a = 5 / 2
By (2b):
b = 9 - 3 · (5 / 2)
b = 9 - 15 / 2
b = 18 / 2 - 15 / 2
b = 3 / 2
By (1):
c = 4 - 5 / 2 - 3 / 2
c = 4 - 8 / 2
c = 4 - 4
c = 0
The coefficients of the quadratic equation are (a, b, c) = (5 / 2, 3 / 2, 0).
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Related Questions
If Gabriella has 3 more nickels than dimes and they have a combined value of 90 cents, how many of each coin does she have?
Correct dimes
nickels
Answers
If Gabriella has 3 more nickels than dimes and they have a combined value of 90 cents, The number of coin she have is; 4 nickels and 7 dimes.
Nickels and dimesx = number of nickels that Gabriella has
x +3 =number of dimes that Gabriella
Hence,
0.05x + 0.10 ( x + 3 ) = 0.9
Solving for x
Multiply both sides of the equation by 100 so as to eliminate two decimal places
5x + 10x + 30 = 90
Collect like terms
15x = 60
Divide both side by 15x
x = 60/15
x = 4 nickels
So,
x + 3 where x = 4
4 + 3 =7 dimes
Therefore she has 4 nickels and 7 dimes.
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Rewrite 23 + 42 = 65 using the Commutative Law of Addition.
Answers
Answer: 23+42=42+23
how the heak is this a colledge question*_* i learned this in 2nd grade lol
We have rewritten 23 + 42 = 65 as 23 + 42 = 65 using the Commutative Law of Addition.
What is Number system?A number system is defined as a system of writing to express numbers.
The Commutative Law of Addition states that changing the order of the addends does not change the sum.
a+b=b+a
Therefore, we can rewrite 23 + 42 as 42 + 23, and the equation becomes:
42 + 23 = 65
or 42+23=23+42
So, we have rewritten 23 + 42 = 65 using the Commutative Law of Addition.
Hence, we have rewritten 23 + 42 = 65 as 23 + 42 = 65 using the Commutative Law of Addition.
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Please answer I give Brainliest
Answers
2 cm * 3/2
6/2
3 cm
X = 3 cm
Answer:
The value of x is 3 cm
Step-by-step explanation:
x is 3 cm because we can take 3/2 and make it easier for us and turn it into 1 and 1/2. As you can see 6, is 1 and 1/2 of 4, so all we have to do is find out what x equals by finding out what is 1 and 1/2 of 2. 2 is already 1, so we take half of 2 and add it and we get our answer 3 cm.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
B) The blue square on the right contains the yellow square + the green square on the left
Step-by-step explanation:
hope this helps ;)
The price of sweaters starts at Pa= $120 each and a quantity supplied of Qa= 40 sweaters. If the price falls to Pb= $12 each, what is the new quantity supplied (Qb) if the slope of the supply curve is m=3 Round your answer to nearest whole number of sweaters.
Answers
The quantity of the new sweaters at a price of $12 is gotten using the slope of 3 to be 36 sweaters
How to find the new quantity if the price falls to $12given data
Pa = $120
Qa = 40
Pb = $12
slope of the supply curve is m=3
The slope represents the relationship between the the input variable and the output variable.
The input variable is the price while the output variable is the quantity supplied.
The slope is the factor that multiplies the input to get the output, we therefore solves as follows
= Pb * slope
= $12 * 3
= 36
Therefore at the price of$15 the quantity supplied is 36 sweaters
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Answer:
4 sweaters
Step-by-step explanation:
Pa-Pb /Qa-Qb
What is the value of the estimated standard error for the following set of D-scores?
Scores: 4, 8, 4, 4
-2
-4
-12
-1
Answers
The value of the estimated standard error for the following set of D scores 4, 8, 4, 4 is 1.
The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.
Consider the following set of D scores,
4, 8, 4, 4
We will calculate ∑D and ∑D² to find the SS for the D scores.
Therefore,
∑D = 4 + 8 + 4 + 4
∑D = 20
∑D² = 4² + 8² + 4² + 4²
∑D² = 16 + 64 + 16 + 16
∑D² = 112
Now, the formula for the standard score is given as:
[tex]SS=\sum D^2- \frac{(\sum)^2}{n}[/tex]
SS = 112 - [ (20)² /4 ]
SS = 112 - 100
SS = 12
Now,
[tex]S_{D}=\sqrt{\frac{SS}{n-1} }[/tex]
[tex]S_{D}=\sqrt{\frac{12}{4-1} }[/tex]
[tex]S_{D}=\sqrt{4}\\ S_{D}=2[/tex]
[tex]S_{\overline D}=\frac{S_{D}}{\sqrt{n} }[/tex]
[tex]S_{\overline D}=\frac{2}{\sqrt{4} }[/tex]
[tex]S_{\overline D}=\frac{2}{2}=1[/tex]
Hence, the standard error of the set of D scores is 1.
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1.
find a
a =
21°
explain why using one of these
words: adjacent,
complementary, supplementary,
vertical
explanation goes here
add a pic of your work
(or just type it here)
to show HOW you got your
answer
pic (or typing) goes Hereford
Answers
∠a=90° as the rays of the angles meet at the right angle that is 90°.One of the angle is 21, The remaining would be 90-21=69°.
What is an angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
What is ray?A ray is a vector that extends from one point to another. A ray is typically defined in geometry as a half-infinite line (also known as a half-line) with one of the two points and taken to be at infinity.
What is right angle?The right angle is formed when two straight lines intersect at 90 degrees or are perpendicular to each other at the intersection. The symbol is used to represent a right angle.∠
Here, The total sum of angles is 90°.
one the value is 21°. The value of adjacent angle would be,
remaining angle=90-21
=69°
So the remaining value of adjacent angle is 69°.
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Which of the binomials below is a factor of this trinomial?
8x²+2x-3
OA. 2x-3
B. 4x-3
O C. 2x+3
OD. 4x+3
Answers
Factor of trinomial 8x+2x-3 is 4x-3(binomial).
What is factorizing?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. Complete factoring is a three-step process: If at all possible, factor a GCF from the expression. Try to factor a trinomial if you can. Factor as many times as you can using a Difference Between Two Squares. Factorizing is the practice of expressing a number or other mathematical object as the sum of a number of other, typically smaller or more basic items of the same kind.
Given Data
8x² + 2x -3
Factorizing,
8x² + 2x -3 =0
8x² - 6x + 4x - 3 = 0
2x(4x -3) +1(4x - 3) =0
(2x + 1) (4x-3) = 0
Binomials are (2x+1) and (4x-3)
Binomial is 4x-3.
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Multiply using the associative property.
Enter your answer by filling in the boxes.
(7×5) x2=
(7×5) x2=7x
(7 × 5) x 2 =
X
x 2)
Answer this problem
Answers
The answer of (7 ×5) ×2 using associative property is 70.
What is associative property?
(a ×b) ×c = a ×(b ×c) and (a+b)+c = a+(b+c)
Addition and multiplication are supported by the associative property but not division and subtraction.
Using associative property ,
(7 ×5) ×2 = 7×(5 ×2)
(7 ×5) ×2 = 7×10
(7 ×5) ×2 = 70
Therefore, the answer of (7 ×5) ×2 using associative property is 70.
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13. An increase of speed of 4 km/h on a journey of 32 km reduces
the time taken by 4 hours. Find the original speed.
Answers
Answer:
What is the role of ethnocentrism in defining the concept of “progress”
Step-by-step explanation:
Translate the phrase into an Algebraic expression The sum of 6 and b
Answers
The translation of the phrase into an algebraic expression which is the sum of 6 and b is 6+b.
What is an algebraic expression?It should be noted that an algebraic expression is used in Mathematics to show the relationship between the terms that are given. The concept of utilizing letters or alphabets to convey numbers without defining their exact values is known as algebraic expressions.
We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
In this case, we want to translate the phrase into an algebraic expression. The phrase is the sum of 6 and b. This will simply be:
= 6 + b
Therefore, the expression is 6+b.
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Solve by completing the square.
x² + 10x = -81
O {6+i√42, 6-i√/42}
O {12+√133, 12-√133}
O {11, 1}
O {-5+2i√/14, -5-2i√/14}
Answers
Answer:
Option 4
Step-by-step explanation:
[tex]x^2+10x=-81 \\ \\ x^2+10x+25=-56 \\ \\ (x+5)^2=-56 \\ \\ x+5= \pm \sqrt{-56}=\pm 2i \sqrt{14} \\ \\ x=-5 \pm 2i \sqrt{14}[/tex]
1. A car starting from rest has a constant acceleration of 4 meters per second per second. How fast will it be going in 5 seconds?
Answers
Answer: 20m/s
Step-by-step explanation:
Velocity final= Velocity initial+acceleration*time
Vf=0+4*5= 20m/s
How many ones are in 23.47? How
many whole ones?
Answers
Answer: The answer is 234.7
Step-by-step explanation:
Find the slope of the line that passes through the pair of points.
(-3, 5), (3, 6)
Answers
The slope of the line passing through the given pair of points would be [tex]m=\frac{1}{6}[/tex].
Hope this helps!
What is 2 2/5 as a percentage? How would I plot on a number line?
Answers
Answer:
240%
Step-by-step explanation:
Times the two whole number by five, add the result to top number, divide by denominator.
Miguel reads that the average low temperature today is −8.5°F and that the average high temperature is 10.2º F.
Miguel plots the points on the number line to determine the temperature change between these two readings.
What is the temperature change?
Answers
The change in temperature between the two readings as measured by Miguel is 18.7°F .
In the question ,
the temperature readings on the Miguel is
Average low temperature = -8.5°F
Average high temperature = 10.2°F
the change in the temperature , is given by the difference between the two reading .
which means
Change in temperature = Average high temperature - Average low temperature .
Substituting the values of average high and average low reading of the temperature from above ,
we get ,
Change in temperature = 10.2 -(-8.5)
= 10.2 + 8.5
= 18.7
the temperature change is 18.7°F .
Therefore , the temperature change is 18.7°F .
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Pls answer
Indicate which property is illustrated in Step 2.
Answers
Which property is illustrated in Step 2 ? Option B. Commutative property
How is this explained?
Given:
Step 1 = 10+ 8x - 10 - 4x +4 = 0
Step 2 = 10 + (-10+ 8x) -4x + 4
Here , 8x - 10 = -10 + 8x
This is of the form , A+B = B+A
Commutative property of addition = A+B = B+A
What is the commutative property?
The addition and multiplication arithmetic operations are covered by the commutative property. This implies that the outcome of adding or multiplying two numbers remains unchanged if the order or position of the numbers are changed. According to the commutative property formula, the result is unaffected by the sequence in which two numbers are added or multiplied. However, the order of the integers matters for subtracting and dividing any two real numbers, so it cannot be changed.Commutative property of addition = A+B = B+A Commutative property of multiplication = A B = B ATo learn more about commutative property, refer:
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Convert 67/9 into a mixed number.
Answers
The answer for this is 7 4/9
There are approximately 3.1 x 108 people in the United States. If each person has 4.1 x 10¹ coins how many coins are there all together?
Answers
Using simple multiplication, we concluded that Total coins equals 127 × 10 ⁷
What is a multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.
People in the United States = 3.1 x 10⁸
each person has 4.1 x 10¹ coins
Total coins = ( 4.1 x 10¹ ) × ( 3.1 x 10⁸ )
Total coins = 12710000000
= 127 × 10 ⁷
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HELP ! THIS IS DUE IN A FEW HOURS!
Answers
The maximum height reached by the ball is 22 feet
The ball stayed in the air for 1 second
What is a function?A function can be defined as a rule, law or expression that shows the relationship between two identifiable variables:
The independent variableThe dependent variableGiven the function:
h(t) = -16t² + 32t + 6
Where;
h is the maximum height measured in feett is the time in secondsTo determine the maximum height in feet that the ball reached, we would be required to substitute the value of t as 1
We have:
h(1) = -16(1)² + 32(1) + 6
expand the bracket
h(1) = -16 + 32 + 6
Add the values
h(t) = 22 feet
To determine the time, we have;
-16t² + 32t + 6 = 22
-16t² +32t + 6 - 22 = 0
Add like terms
-16t² +32t - 16 = 0
Factorize further
-16t² + 16t + 16t - 16 = 0
Factorize in pairs
16t( t - 1) + 16 ( t - 1) = 0
Then,
t - 1 = 0
t = 1 second
Thus, the maximum height is 22 feet
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find the quotient 1 3/5÷3 1/5
Answers
1 3/5 ÷ 3 1/5
Change the mixed fraction to improper fraction
8/5 ÷ 16/5
Change the division to multiplication, thereby inverting 16/5
8/5 x 5/16
= 8/16
= 1/2
Answer:
0.5
Step-by-step explanation:
Find the slope of the line passing through the points (7, -2) and (4, -5).
Answers
I believe the slope of the the line passing through the given points would be m = 1.
Hope this helps!
(-5) - (-2) = -3
4 - 7 = -3
The slope of the line passing through these points is 1, which can be represented in a slope equation as “x.”
I need the answer for these 2
Answers
after solving each compound given in the picture
there was a existing solution that is as follows -
a ) ( - ∞ , 1] U [12 , ∞ )
b) ( - ∞ , 8] U [4 , ∞)
What is inequality ?inequality, When two integers or algebraic expressions are stated to be greater than, greater than or equal to, less than, or less than or equal to each other in order.
A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa. Literal inequalities occur when the relationship between two algebraic expressions is shown using the inequality symbol. An inequality in algebra is a mathematical statement that demonstrates the relationship between two expressions. In other words, the expression on the left should be greater or smaller than the expression on the right.
Calculationa ) ( - ∞ , 1] U [12 , ∞ )
b) ( - ∞ , 8] U [4 , ∞)
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What is the slope of the line on the graph?
need answer asap pls help
Answers
Answer:
-2/6
Step-by-step explanation:
go down the y axis 2 times (-2) and over 6
y=-2/6x+4
write 7298 to nearest thousand?
Answers
Answer:
Rounds down to 7000.
Step-by-step explanation:
 line m || line n m<4 = 72°
what is the measure of angle 1?
Answers
Answer:
angle 1 = 108°
Step-by-step explanation:
You want the measure of angle 1, given the measure of angle 4 is 72° in the diagram.
Linear pairAngles 1 and 4 are a linear pair, so are supplementary:
angle 1 + angle 4 = 180°
angle 1 + 72° = 180°
angle 1 = 108° . . . . . . . subtract 72°
Every quart is 2 pints. This can be expressed using the equation y × 2 = Z, where y is equal to the number of quarts and Z is equal to the total number of pints. Using this equation find the total pints in 10 quarts._____ pints
Answers
Given data:
The expression for the total nummber of pints is Z=yx2.
The given value of y is,
y=10 quarts.
Substitute the given values in the aabove expression.
Z=10x2
=20 pints.
Thus, the total pints is 20
Find all points on the x-axis that are 12 units from the point (3,-6)
Answers
The points on the x-axis that are 12 units away from the point (3,-6) is found to be 3 ± [tex]6\sqrt{3}[/tex].
What is the circle equation?r² = (x - h)² + (y - k)²is the standard equation for a circle, where (h,k) are the coordinates of the circle's center and r is the radius.
We must locate all points on the x-axis that are 12 units away from the starting point (3,-6).
Let these points be (x,0)
All points 12 units away from the point (3,-6) form a circle with a radius of 12 and a center at (3,-6). The formula would be as follows:
r² = (x - h)² + (y - k)²
12² = (x-3)² + (0+6)²
144 = (x-3)² + 36
(x-3)² = 108
x-3 = ± [tex]\sqrt{108}[/tex]
x = ± [tex]\sqrt{108}+3[/tex]
x = 3 ± [tex]6\sqrt{3}[/tex]
Therefore, the points on the x-axis 12 units away from point (3,-6) is calculated as 3 ± [tex]6\sqrt{3}[/tex].
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Simplify Number 539
Answers
Okay, here we have this:
Considering the provided expression, we are going to simplify it, so we obtain the following:
539.A:
Then by properties of exponents we get the following:
[tex]\begin{gathered} 216^{\frac{1}{3}} \\ =(6^3)^{\frac{1}{3}} \\ =6^{\frac{3}{3}} \\ =6^1 \\ =6 \end{gathered}[/tex]Finally we obtain that the given expression is equal to 6.