The most appropriate choice for matrices will be given by-
Required Equation
[tex]y = 2x^2 - 3x + 1[/tex]
What are matrices?
If the numbers are arranged in the form of rows and columns, then the arrangement is called matrix.
Here,
The equation is [tex]y =Ax^2 + Bx + C[/tex]
The function contains the points (0, 1), (-2, 15), (3,10).
On putting these coordinates in the equation,
C = 1
[tex]15 = A(-2)^2 + B(-2) + 1\\4A - 2B = 15-1\\2(2A - B ) =14\\2A - B = \frac{14}{2}\\2A -B = 7[/tex]................ (1)
[tex]10 = A(3)^2 + B(3) + 1\\9A + 3B = 10-1\\3(3A + B ) =9\\3A + B =\frac{9}{3}\\3A + B = 3[/tex].................... (2)
Here matrix method will be used
Let
[tex]P = \begin{bmatrix} 2 & -1\\ 3 & 1 \end{bmatrix}[/tex], [tex]Q = \begin{bmatrix} x \\ y\end{bmatrix}[/tex], [tex]R = \begin{bmatrix} 7\\3 \end{bmatrix}[/tex]
PQ = R
[tex]Q = P^{-1}R[/tex]
Adjoint P =
[tex]\begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}^T\\\\\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}[/tex]
Det P = [tex]\begin{vmatrix} 2 & -1\\3&1\end{vmatrix}[/tex]
= [tex]2\times 1 - 3 \times (-1)\\5[/tex]
[tex]P^{-1} = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}[/tex]
[tex]Q = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\begin{bmatrix}7\\3\end{bmatrix}[/tex]
[tex]Q = \frac{1}{5}\begin{bmatrix} 10\\-15\end{bmatrix}\\Q= \begin{bmatrix} 2\\-3\end{bmatrix}[/tex]
A = 2, B = -3
Required Equation
[tex]y = 2x^2 - 3x + 1[/tex]
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Complete Question
Use matrices to write the equation of the function in the form [tex]y = Ax^2 + Bx + C[/tex]that contains the points (0, 1), (-2, 15), (3,10).
Find the average rate of change of his annual salary between 2017 and 2020
We were told that the salary, t years after 2015 is given by the function,
S(t) = 3100t + 56000
When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2
We would substitute t = 2 into the function and find S(2)
Thus,
S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200
When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5
We would substitute t = 2 into the function and find S(2)
Thus,
S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500
Thus, we can say that
when
x1 = 2, y1 = 62200
when x2 = 5, y2 = 71500
Recall,
slope or average rate of change = (y2 - y1)/(x2 - x1)
average rate of change = (71500 - 62200)/(5 - 2) = 9300/3
average rate of change = 3100
The last option is correct
I need help ASAP
write an equitation of the line shown
The equations of the lines are:
7. y = 3/2x - 3/2
8. y = -1/3x - 8/3
What is the Equation of a Line?The equation that represents a line, in slope-intercept form is, y = mx + b.
Slope of the line = m = rise/run or change in y / change in x.Y-intercept of the line = b = the point where the line intercepts the y-axis.7. Find the slope (m) between (5, 6) and (1, 0):
Slope (m) = (6 - 0)/(5 - 1) = 6/4
Slope (m) = 3/2
Find the y-intercept of the line, b, by substituting m = 3/2 and (x, y) = (1, 0) into y = mx + b:
0 = 3/2(1) + b
-3/2 = b
b = -3/2
To write the equation, substitute m = 3/2 and b = -3/2 into y = mx + b:
y = 3/2x - 3/2
8. Find the slope (m) between (-5, -1) and (1, -3):
Slope (m) = (-1 -(-3))/(-5 - 1) = 2/-6
Slope (m) = -1/3
Find the y-intercept of the line, b, by substituting m = -1/3 and (x, y) = (1, -3) into y = mx + b:
-3 = -1/3(1) + b
-3 = -1/3 + b
-3 + 1/3 = b
-8/3 = b
b = -8/3
To write the equation, substitute m = -1/3 and b = -8/3 into y = mx + b:
y = -1/3x - 8/3
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Find the velocity of the car at the end of a drag race. Round to the nearest whole number.
Answer:
183 miles per hour.
Explanation:
The estimated velocity(v) at the end of a drag race is modeled using the formula below:
[tex]v=234\sqrt[3]{\frac{p}{w}}[/tex]Given:
• The horsepower, p = 1311
,• The weight (in pounds), w = 2744 pounds.
Substitute into the formula above:
[tex]\begin{gathered} v=234\sqrt[3]{\frac{1311}{2744}}=182.9 \\ v\approx183\text{ miles per hour} \end{gathered}[/tex]The velocity is approximately 183 miles per hour.
please help to find the value of x and explain how to get it in simple terms.
SOLUTION
From the image above
[tex]\begin{gathered} z^2=6^2+3^2\ldots\text{ by pythagora's rule } \\ z^2=36+9 \\ z^2=45 \\ z=\sqrt[]{45} \end{gathered}[/tex]Considering the bigger right angle triangle,
[tex](3+x)^2=y^2+45[/tex]We can obtain the expression of y from the smaller right angle triangle,
Using pythagora's rule, we have
[tex]y^2=6^2+x^2[/tex]Then, recall
[tex](3+x)^2=y^2+45[/tex]Substite the expression for y², we have
[tex](3+x)^2=6^2+x^2+45[/tex]Expand the paranthesis, we have
[tex]\begin{gathered} 9+6x+x^2=x^2+36+45 \\ \text{Subtract x}^2from\text{ both sides } \\ 9+6x=36+45 \\ \end{gathered}[/tex]subtract 9 from both sides, we have
[tex]\begin{gathered} 6x+9-9=81-9 \\ 6x=72 \end{gathered}[/tex]Divide both sides by 6, we obtain
[tex]\begin{gathered} \frac{6x}{6}=\frac{72}{6} \\ \text{Then} \\ x=12 \end{gathered}[/tex]Therefore
Answer: x= 12
please help please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please
part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:
[tex]a^2=a\times a[/tex]Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:
[tex]\begin{gathered} 1^2=1\times1=1 \\ 2^2=2\times2=4 \\ 3^2=3\times3=9 \end{gathered}[/tex]In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:
[tex]\sqrt[]{a}=b[/tex]it means:
[tex]b^2=b\times b=a[/tex]For example:
[tex]\begin{gathered} \sqrt[]{1}=1 \\ \sqrt[]{4}=2 \\ \sqrt[]{9}=3 \end{gathered}[/tex]The third part of the questions asks us to solve for "x" the following equation:
[tex]x^2=9[/tex]To do that we take square root on both sides:
[tex]\sqrt[]{x^2}=\sqrt[]{9}[/tex]Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:
[tex]x=3[/tex]Evaluate the inverse when y=4. Show all of your work.
The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.
What is termed as the inverse of the function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function "f" takes x to y, then its inverse will take y to x. The inverse function is signified by f-1 or F-1 if the function is signified by 'f' or 'F'. Here, (-1) should not be confused with exponent or reciprocal.For the given question;
The function is given as;
y=4ˣ
Interchange the variables of the function.
x = 4∧y
Taking log both side.
㏑ x = ㏑(4∧y)
Using the power rule of log function.
㏑ x = y㏑(4)
y = ㏑ x/㏑(4)
Now, replace y with f⁻¹(x).
f⁻¹(x) = ㏑ x/㏑(4)
Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.
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The correct question is-
Evaluate the inverse when y=4ˣ. Show all of your work.
A line passes through the points (–3, –4) and (6, 2).
A coordinate plane.
What is the x-intercept of this line?
Answer:
x intercept is -3
Step-by-step explanation:
We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1) = (2- -4)/(6- -3) = (2+4)/(6+3) =6/9 = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3
a total of tickets were sold for the school play. they were either adult tickets or student tickets. there were 53 more student tickets sold than adult tickets. how many adult tickets were sold?
Total 250 adult tickets are sold.
Let a = number of adult tickets sold
Let s = number of student tickets sold
a + s = 553
s = a + 53
From above equations;
a + a + 53 = 553
2a = 553 - 53
2a = 500
a = 250
Total 250 adult tickets are sold.
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Find the measure of
Answer: 93°
Step-by-step explanation:
[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]
3.2+2(-1.5)-3.4
(pls solve by doing the order of operations)
(step by step pls)
AS per the order of operations, the value of the expression 3.2+2(-1.5)-3.4 is -3.2
Order of operations:
Order of operations states the rule that tells the correct sequence of steps for evaluating a math expression.
The order using PEMDAS:
Parentheses,
Exponents,
Multiplication and Division (from left to right),
Addition and Subtraction (from left to right).
Given,
Here we have the expression. 3.2+2(-1.5)-3.4
Now, we have to use the order of operations concept in order to solve it.
The highest priority for the order of operation is brackets and the next priority is for division and multiplication,
So, here we have to solve those things first, then we get,
=> 3.2 + (-3) - 3.4
We know that (+) x (-) = -, so, the expression is rewritten as,
=> 3.2 - 3 - 3.4
The next priority is for addition and subtraction,
So, the result is,
=> 3.2 - 6.4
=> -3.2
Therefore, the resulting number is -3.2
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1/2 x - 2 = x - 4
answersss??
Elizabeth Oliver sells luxury cars. She earns a 4 percent straight commission. Lastmonth her sales totaled $128,000. What was her commission?
$128,000 represents 100%
To find how much is 4% we can use the next proportion:
[tex]\frac{128,000\text{ \$}}{x\text{ \$}}=\frac{100\text{ \%}}{4\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 128,000\cdot4=100\cdot x \\ \frac{512,000}{100}=x \\ 5,120=x \end{gathered}[/tex]Her commission is $5,120
Which ordered pair is a solution to the system of linear equations?
2x + 3y= 6
–3x + 5y = 10
(0,2)
(2,0)
(3,2)
(2,3)
The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).
Linear equation:
Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.
Given,
Here we have the following system of linear equations.
2x + 3y = 6
-3x + 5y = 10
Now, we need to find the solution for the equations.
Here we have to use the substitution method to solve this one,
To do the substitution method we have to follow the following steps:
Step 1) Solve anyone of the equations either for the variable x or y
Step 2) Now, substitute the value obtained from step 1 to the other equation
Step 3) Finally, solve the equation to find the value of the remaining variable.
Here we have to take the equation (2), and we have to solve it for the value of y,
For that we have to rewrite the equation as,
5y = 10 + 3x
y = (10 + 3x)/5
Apply the value of y on the equation (1), in order to get the value of x,
So,
2x + 3(10 +3x)/5 = 6
2x + (30 + 9x)/5 = 6
(10x + 9x + 30)/5 = 6
19x + 30 = 30
19x = 0
x = 0
Now, apply the value of x on the equation in order to get the value of y,
y = (10 + 3(0))/5
y = 10/5
y = 2.
Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).
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Write an expression for the calculation triple 4 and then add 6 times 6
Answer:
4x3+6x6=48
Step-by-step explanation:
PEMDAS
4x3=12
6x6=36
12+36=48
therefore, the answer is 48
You start at (2, -5). You move up 5 units and right 3 units. Where do you end?
the answer would be (0,5)
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 14 fl oz per hour. How fast was the pipe leaking in gallons per day?
Answer:
6.5625 gal per hour
Step-by-step explanation:
Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.
A virtual environment created by game engine renders non-character objects
more efficiently than it renders characters. If the assumption is that 72
percent of objects must be devoted to non-character objects and this reset
cache is set at 67 non-character objects, how many objects can be
characters before the cache resets?
Answer:18
Step-by-step explanation:
Elisa gets a tax free allowance of $6000 and pays tax at 25% on the next $20 000. She pays tax at a rate of 30% on the rest. If she earns $72000 per year, how much tax must she pay?
Find y please help me !
Answer:
y = 5
Step-by-step explanation:
since the triangles are congruent then corresponding sides are congruent, so
AB = CD , that is
7y = 3y + 20 ( subtract 3y from both sides )
4y = 20 ( divide both sides by 4 )
y = 5
Question
Evaluate the expression when k = 3 and j = 10.
(5k−j)2+2k
Responses
80
80
45
45
31
31
20
Answer:
31Step-by-step explanation:
Given Expression (5k − j)² + 2kEvaluateWhen k = 3, j = 10SolutionSubstitute and calculate:
(5k − j)² + 2k = (5*3 - 10)² + 2*3 = (15 - 10)² + 6 = 5² + 6 = 25 + 6 = 31Amira is younger than Marques. Their ages are consecutive integers. Find Amira's age if the sum of Amira's age and 2 times Marques's age is 38.
Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.
According to the question,
We have the following information:
Amira is younger than Marques.
Their ages are consecutive integers.
The sum of Amira's age and 2 times Marques's age is 38.
Now, let's take Amira's age to be x years.
Then, Marques's age will be (x+1) years.
So, we have:
x + 2(x+1) = 38
x + 2x + 2 = 38
3x+2 = 38
3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)
3x = 36
x = 36/3
x = 12 years
Hence, Amira's age is 12 years.
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3 What is the range of the function shown
in the graph?
Answer:
D y < 8
Step-by-step explanation:
the range is the interval or set of all valid y (functional result) values.
we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.
8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").
and therefore we cannot say y <= 8.
we have to use y < 8.
A garden store sells two types of potted palm trees. The Mediterranean palms sell for $150 each, and the palmetto palms sell for $125 each, including tax. The store wants to sell a total of at least 15 of the plants each day and have total sales of at least $2,000. Which of these systems of inequalities can be used to determine x, the number of Mediterranean palms, and y, the number of palmetto palms, that must be sold?
The system of inequalities that can be used to determine the number of each type of plant to be sold are :
x + y ≥ 15
$150x + $125y ≥ $2000
What are the system of inequalities?The first step is to determine the inequality signs that would be used in the system of inequalities:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is the greater than or equal to sign, ≥.
Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:
number of Mediterranean palms sold + number of palmetto sold ≥ least number of plants
(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold ≥ least number of sales
x + y ≥ 15
$150x + $125y ≥ $2000
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In Central city, there are 29,791 registered voters and 93 voting centers. Each voting centers serves about _____ of the city's population, what's the answer?
If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.
Total number of registered voters in Central city = 29791 voters
Total number of voting centers = 93 voting centers
The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers
Substitute the values in the equation
The number of population serves by each center = 29791/93
= 320.33
≈ 320
Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.
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Which equation does not represent a linear function?
a. y = 8x
by = ½x+2
c. y=0.5x - 1
d. y = 2x³
Answer:
d. y= 2x³
Step-by-step explanation:
All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.
Solve for x: -3x-6= -7x+34
Answer:
x = 10
Step-by-step explanation:
-3x - 6 = -7x + 34
+7x
4x - 6 = 34
+6
4x = 40
/4
x = 10
Answer:
x = 10
Step-by-step explanation:
-3x - 6 = -7x + 34 Add 7x to both sides
4x - 6 = 34 Add 6 to both sides
4x = 40 Divide both sides by 4
x = 10
( f - 12) + Pf decreased by the sum of 12 and p is it correct?
The sum of 12 and P can be written as 12 + P
Then, f decreased by the sum of 12 and P can be written as:
f - (12 + P)
Answer: it isn't correct, the correct answer is f - (12 + P)
The length of a piece of paper is 11 inches. What is the length of the paper in
centimeters?
(1 inch = 2.5 centimeters).
Answer:
Length in inches → 11
1 inch = 2.5 centimeters
Length in Centimetres → 11 × 2.5 → 27.5 cm
Find the mean of the data in the dot plot below.
Answer:
There is no dot plot below
Step-by-step explanation:
60 pointsssssssss
algebra 1
Answer:
-16
Step-by-step explanation:
fog(18)=f(g(18))
g(18)=[tex]\sqrt{18-9} =\sqrt{9} =3[/tex]
f(3)=-8(3)+8
=-16