By using the definition of a polynomial in product form is described by y = - 0.8 · (x - 1)² · (x + 2)
How to determine a least degree polynomial
According to algebra, polynomials are products of binomials of the form x - r, where r is a root of the polynomial. The product form of polynomials is described by the following formula:
p(x) = a · Π (x - r), for i = {1, 2, 3, n}, where n is the grade of the polynomial and a is the lead coefficient.
If we know that y(0) = - 1.6, r₁ = r₂ = 1 and r₃ = - 2, then the equation of the polynomial is:
- 1.6 = a · (0 - 1)² · (0 + 2)
- 1.6 = a · (- 1)² · 2
- 1.6 = 2 · a
a = - 0.8
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triangle DEF and triangle CBD are similar right triangles which statement is slopes is DF and CDs true
We can calculate the slope of a line segment by using the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are two points of the line.
In this case the side DF goes from the point D(-2,-2) to the point F(1,7), then its slope is:
[tex]m=\frac{7-(-2)}{1-(-2)}=\frac{7+2}{1+2}=\frac{9}{3}=3[/tex]For the side, CD, it goes from D(-2,-2) to C(0,4), then its slope is:
[tex]undefined[/tex]why is 25 a compiste number
Answer: 25 is divisible by 5, so it is composite
Step-by-step explanation:
Looking to receive help on the following problem, thank you!
olution
or this case we have the following vectors:
u= -3i +2j, w= 4j, v= 6i -4j
And we can do the following:
art a
u*v= -3*6 + 2*-4= -18 -8= -26
Part b
w*v= 0*6 + 4*-4 =-16
What is the value of −5 + (−18) + 32? −45 −19 9 55
Answer:
9
Step-by-step explanation:
[tex]-5+(-18)+32 \\ \\ =-5-18+32 \\ \\ =-23+32 \\ \\ =9[/tex]
A herd of 52 horses has 12 appaloosas and the rest are mustang and its most simplified form. What is the ratio of appaloosa to mustang horses?
The ratio of appaloosa to mustang horses is 12:40
The total number of horses is given as 52.
Number of white horses =12
Let the number of black horses be x
This means that ratio of white: black horses is 12 : x
Using the ratio above, we can find the number of black horses as follows:
[tex]\frac{x}{12+x} of 52 = x[/tex]
[tex]\frac{52x}{12+x} = x[/tex]
52x = x(12 + x)
[tex](12x + x^{2} ) = 52x[/tex]
[tex]x^{2}[/tex] + 12x - 52x = 0
[tex]x^{2}[/tex] - 40x = 0
Taking out the common factor x from equation we have:
x(x - 40) = 0
This gives us with two solution:
x = 0 and x = 40
Since the question said there are some black horses, the x=0 value can be ignored. So we have x = 40
Hence, The ratio of appaloosa to mustang horses is 12:40
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please hurry due today I will give you brainlest
Which numbers are solutions of 4p+6 < 3p? Choose exactly two answers that are correct.
6 and -6
please give brainliest
4(5x - 2) = 2(9x + 3)
Answer: x = 7
Explanation - 4(5x-2)=2(9x+3)
20x-8=18x+6
20x-18x=6+8
2x=14
x=14÷2
x=7
Hello there!
Here we need to solve for x.
The first thing that we're going to do is this:
Expand both sides by using the distributive property.[tex]\implies\boldsymbol{4(5x-2)=2(9x+3)}[/tex]
[tex]\implies\boldsymbol{20x-8=18x+6}[/tex]
Next, add 8 to both sides.[tex]\implies\boldsymbol{20x=18x+14}[/tex]
Then, subtract 18 from both sides.[tex]\implies\boldsymbol{20x-18x=14}[/tex]
[tex]\implies\boldsymbol{2x=14}[/tex]
Lastly, divide both sides by 2.[tex]\implies\boldsymbol{x=7}[/tex]
Therefore x=7. I hope this helps you, feel free to comment if you have any queries :)
PLEASE HELP DUE SOON WILL GIVE 20 POINTS!!
Answer:
$5.19
Step-by-step explanation:
10.33 × $2.51 = $25.93
$25.93÷5=$5.19
Write the equation of a Circle with the given information.Center: (-4,7) Point on the Circle: (8,-4)
Given:
Center of circle: (-4, 7)
Endpoint on the circle: (8, -4)
Let's write the equation of the circle with the given information.
Apply the equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
Center of circle: (h, k) ==> (-4, 7)
Radius = r
Substitute the values of (h, k) in the equation:
[tex]\begin{gathered} (x-(-4))^2+(y-7)^2=r^2 \\ \\ (x+4)^2+(y-7)^2=r^2 \end{gathered}[/tex]To find the radius, let's find the distance between the points (-4, 7) and (8, -4).
Apply the distance formula:
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]Given:
(x1, y1) ==> (-4, 7)
(x2, y2) ==> (8, -4)
Thus, we have:
[tex]\begin{gathered} d=\sqrt[]{(-4-7)^2+(8-(-4))^2} \\ \\ d=\sqrt[]{(-4-7)^2+(8+4)^2} \\ \\ d=\sqrt[]{(11)^2+(12)^2} \\ \\ d=\sqrt[]{121+144} \\ \\ d=\sqrt[]{265} \\ \\ d=16.3 \end{gathered}[/tex]Therefore, the radius is 16.3
Therefore, we have the equation of the circle as:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]ANSWER:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]Answer both questions if possible or just the main questions if that's all you can do,
ASAP
Step-by-step explanation:
domain = width
range = height
closed point (filled in) means the number is included and we use ()'s.
set builder nation format: (x,y)
domain: (-5, -1)
range: (3,3)
f(1) means what does y equal when x equals 1:
locate on the graph where y is when x = 1:
f(1) = 2
Let A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)} what type of function is this? Give reason
It is observed that f is a subset of A×B
What is subset ?A subset is a subset (another set or the same set). It is expressed as A⊆ B in the set notation to indicate that set A is a subset of set B.Set 1 is a subset of Set 2 if all of its components are included in Set 2. A set, as far as we are aware, is a clearly defined grouping of letters, objects, numbers, or anything else. Set 1 is a subset of Set 2 if Set 1 = A, B, C, and Set 2 = A, B, C, D, E, and F. This is because all the items in Set 1 are also present in Set 2.
Given that :A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)}
A={1,2,3}
B={7,8,9,10}
A×B ={(1,7)(1,8)(1,9)(1,10)(2,7)(2,8)(2,9)(2,10)(3,7)(3,8)(3,9)(3,10)}
f={(1,7),(2,9),(3,8)}
A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×B
It is observed that f is a subset of A×B
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The answer to one and two
Solution
(a) There are 9 students entering the school district science project:
medals for 1st, 2nd and 3rd
k1 = 1O ways to choose first person to be chosen from the group of 10.
99
k2 = 8 ways for the second person to be chosen from the remaining people(9–1).
k3 = 7 ways for the second person to be chosen from the remaining people(8–1).
then all you need to do is multiply these k1 * k2 * k3.
[tex]\begin{gathered} 1st\text{ 2nd 3rd} \\ 1st=9\text{ option} \\ 2nd=8\text{ }options \\ 3rd=7\text{ options} \end{gathered}[/tex][tex]\begin{gathered} 9\times8\times7 \\ =504 \end{gathered}[/tex](b) There are 7 unique names in a bowl. In how many orders can 2 names be chosen:
This is a permutation problem in order
There are 7 names, and the 2 name have to be in same order
[tex]\begin{gathered} 7P_2 \\ \frac{7!}{(7-2)!} \\ =\frac{7!}{5!} \\ =\frac{7\times6\times5!}{5!} \\ =42 \end{gathered}[/tex]Factor each of the following completely:
y² + 7y +6
I
y² - 7y + 6
Answer: 31y2 + 6
Step-by-step explanation:
61 y2 + 1 y2 = 62 y2
7y + -7y = 0
6+6 =12
62y2 + 12 then divide by 2 and it's 31y2 + 6
A square swimming pool is surrounded by a cement walkway with a uniform width. The swimming poa
has a side length of (x - 5) feet. The side length of the entire square area including the pool and the
walkway is (x+4) feet.
Enter an expression for the area of the walkway. Then find the area of the cement walkway when
x = 8 feet.
The area of the walkway is
ft².
When x = 8 feet, the area of the cement walkway
The expression of the square walkway is (x + 4)² - (x - 5)² and the area of the square cement walkway is 135ft².
Area of square:
The area of a square is refers the place covered by the square.
The formula to calculate the area of square is,
Area = s²,
where, 's' refers the side of the square.
Given,
A square swimming pool is covered by a cement walkway with a uniform width.
Length of swimming pool = (x-5) feet.
Length of square walkway including the swimming pool = (x+4) feet
Here we need to find the area of the cement walkway and when the value of x is 8 then the value of the cement walkway.
1) Here we have to write an expression for the area of the entire square minus area of the pool.
Remember the equation for the area of a square is , where
A = area of square and
s = side value of the square.
We are given that the side of the entire square including walkway and pool is s = (x+4)ft.
Apply the value of the side into the formula for the area of the square, then we get,
A = s²
A = (x + 4)² --------------(1)
We are also given that the side length of the swimming pool is s = (x-5)ft. Apply that into the equation for the area of a square to get the expression for the area of the pool:
A = s²
A = (x - 5)² --------------(2)
Now subtract the area of the pool (x - 5)² from the area of the entire square (x + 4)² to get your expression for the area of the walkway.
Expression for the area of the walkway:
=> (x + 4)² - (x - 5)²
2) Since you know that x = 8ft, you can solve your expression for the area of the walkway. Plug x into your expression:
=> (8 + 4)² - (8 - 5)²
=> (12)² - (3)²
=> 144 - 9
=> 135
The area of your walkway is 135ft².
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Multiply 4(Q+2) what's the answer
Given the expression:
[tex]4(Q+2)[/tex]Let's multiply the expression.
To multiply apply the distributive property of multiplication.
Distribute 4 to the values in the parentheses:
[tex]\begin{gathered} 4(Q)+4(2) \\ \\ =4Q+8 \end{gathered}[/tex]ANSWER:
[tex]4Q+8[/tex]the formula for finding the area of a rectangle is A=LWSolve this formula for LL=______if the length of a rectangle is 18 feet qnd the width is 9 inches. what is the area of the rectangle in units of square feet? _______ ft^2
1) Dividing the given formula by W we get:
[tex]\begin{gathered} \frac{A}{W}=\frac{LW}{W}, \\ \frac{A}{W}=L. \end{gathered}[/tex]2) We know that:
[tex]1in=\frac{1}{12}ft.[/tex]Therefore:
[tex]9in=9*\frac{1}{12}ft=\frac{3}{4}ft.[/tex]Then:
[tex]W=\frac{3}{4}ft.[/tex]Substituting W=3/4ft and L=18ft in the given formula we get:
[tex]A=(18ft)(\frac{3}{4}ft)=13.5ft^2[/tex]Answer:
1)
[tex]L=\frac{A}{W}.[/tex]2)
[tex]13.5ft^2.[/tex]Find all solutions of the equation x^2+2x+6=0 and give your answer as a list of complex numbers, such as 3-4i, 5+i.
Given equation [tex]x^{2} +2x+6=0[/tex]
we use in Quadratic formula
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
So a=1, b=2, c=6
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {2^{2}-4*1*6}}}{2*1}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {4-24}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {20}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm 2i{\sqrt {5}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x= {-1\pm i{\sqrt {5}}}[/tex]
What is the Quadratic formula?
A second-degree equation is a quadratic equation. It implies that at least one term in which the variable is squared will be present. This equation's conventional form is:
ax²+ bx + c = 0
where a, b, and c are variables or coefficients.
X is also an unknowable variable.
The fact that the coefficient "a" cannot be 0 is one unbreakable law.
Two potential choices for its variable X will fulfill the equation because of the degree of 2. Quadratic equations may reflect a wide range of real-world scenarios, as is clear to observe. We'll now look at several solutions.
Quadratic is derived from the term "quad," which means square. Here, we'll create the formula for quadratic equations so that they may be solved.
The factorization approach fails to reduce a large number of equations. Such equations are solved using a more potent approach. Every quadratic problem may be solved using this technique. This is the formula for a quadratic equation in general.
This is how it is explained:
If ax2 + bx + c = 0, then
is a quadratic equation, then the following formula provides the value of x.
Simply enter the numbers for a, b, and c, and the computations will be performed.
The values of a, b, and c are extracted from the equation and entered into the quadratic equation formula.
A, B, and C in this case only numbers. These are the quadratic equation's numerical coefficients, which you must solve.
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
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pls help i dont get it
Name the line of reflection used to map the preimage to its image.
Option E, the x-axis is the line of reflection used to map the preimage to its image.
The graph represents that if the graph is folded by an x-axis,
Point Y will cross-point Y', which is two coordinates away from the x-axis.
Point X will cross point X', which is five coordinates away from the x-axis.
Points W will cross-point W', which is eight coordinates away from the x-axis.
Points V will cross-point V', which is five coordinates away from the x-axis.
A mirror image is symmetric about the x or y-axis. Reflection is called "inverse geometry". A mirror reflector is a type of reflector. When the line reflects the image, the reflection line appears. A shape is said to reflect a different shape if a point on a shape is equidistant from a point on another shape.
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The first four terms of a sequence are given below.
11, 9, 7, 5, ...
What is the seventh term of the sequence?
A. 5
B. -3
C. 1
D. -1
Answer: D:-1
Step-by-step explanation: 11,9,7,5,3,-1,-3,... => dãy số trên có quy luật là số lẻ
Jared lost a total of $56.00 on his investment over 7 months. He lost an equal amount of money each month. Jared used this equation to figure out how much money he lost each money. -56.00/7=-8.00 what does -56.00/7=-8.00 tell us?
Answer:
I'm not so very sure but I really need points
Maggie has space in her yard for a garden. A scale drawing of the garden is shown below. The scale of the drawing is 1 cm - 2.5 ft.6 cm!616 cmWhat is the area of Maggie's actual garden?
Units change translation from cm to feets
1 cm is equivalent to 2.5 feets
triangle is a rectangular triangle suported with the bigger side
this means the height of triangle is 6cm
the base is 16 cm
the area is (base x height)/2
so then area= 16x 6/2= 48cm ^2
BUT because 1cm is equivalent to 2.5 feets then
multiply 48 x 2.5 x 2.5 = 48 x 6.25 = 300 ft^2
The following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.
Test positive Test negative Total
Have diabetes 36.1% 1.9% 38%
Do not have diabetes 5.2% 56.8% 62%
What percent of those who do not have diabetes test negative for the disease?
A 10.9%
B 56.8%
C 91.6%
D 96.8%
If the following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease. The percent of those who do not have diabetes test negative for the disease is: B. 56.8%.
ProbabilityProbability can be defined as the tendency or likelihood that something will happen.
Hence,
Percentage of people do not have diabetes and test positive is 5.2%
Percentage of people do not have diabetes and test negative is 56.8%
Total percentage of people who tested positive and negative is 62%
Based on the above analysis for people who does not have a diabetes we can see that the Percentage of people do not have diabetes and test negative is 56.8%.
Therefore the correct option is B.
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(-4, 2) and (5, 6) slope
In order to find the slope between those two points, we can use the following formula for the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m is the slope between the points (x1, y1) and (x2, y2).
So using the points (-4, 2) and (5, 6), we have:
[tex]m=\frac{6-2}{5-(-4)}=\frac{4}{9}[/tex]So the slope is 4/9
Answer asap what’s the correct answer answer now for brainlis5?
Answer: Smooth muscle contractions
Use a linear approximation to estimate 3√28 write your exact answer with fractions
The estimated value of 3√28 using linear approximation is 82/27 which is answered in form of fraction.
What is linear approximation?A general function can be approximated using a linear function in mathematics using the term "linear approximation" (more precisely, an affine function). They are frequently utilised in the finite difference method to create first order approaches for resolving or approximating solutions to equations.
We need to find the approximate value of ∛28 using linear approximation
Let f(a) = ∛a
then F(27) = ∛27 = 3
We compute the derivative of f(a) as being
[tex]f(a)=a^{\frac{1}{3}}[/tex] ⇒ [tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex]
Hence,
[tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex] = [tex]\frac{1}{3}(3)^{-2}=\frac{1}{3}(\frac{1}{9})=\frac{1}{27}[/tex]
Recall the equation of a line is given by
⇒ y - b = m(x - a)
⇒ [tex]y-3=\frac{1}{27}(x-27)[/tex]
⇒ [tex]y=\frac{1}{27}x-1+3[/tex]
⇒ [tex]y=\frac{1}{27}x+2[/tex]
So the approximation at x= 27.5 would be
⇒ [tex]y=\frac{1}{27}(28)+2[/tex]
⇒ y = 82/27
⇒ y = 3.037
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where we can use Adding and Subtracting Polynomials in real life??
Polynomials are utilized in management, business, farming, computer science, and math-related fields.Expressions defining known and unknown numbers are created using variables and constants in all professions that need proficiency with polynomials.
where we can use Adding and Subtracting Polynomials in real life?
Finance Loan computations and firm valuation utilize an assessment of present value.In order to determine an equal liquid value (present, cash, or in-hand), it uses polynomials that back interest accumulation out of hypothetical future liquid transactions.Fortunately, if the payment schedule is regular, many payments can be rewritten in a straightforward manner.Economic and tax calculations can frequently be expressed as polynomials as well.Electronics
Polynomials are widely used in electronics.The polynomial V=IR, which defines resistance, connects the resistance of a resistor to the current flowing through it and the potential drop across it.While many conductors (but not all) abide by Ohm's law, this is comparable to that law but not the same.It claims that on a graph, the relationship between voltage drop and current flowing through a resistor is linear.In the equation V=IR, resistance is therefore constant.Electronics also uses other polynomials, such as P=IV=IR2, which describes the relationship between voltage drop and power loss.Kirchhoff's loop rule and the Kirchhoff's junction rule, which both describe voltage drop around closed circuits and the current at junctions, respectively, are polynomials.Curve Fitting
In both regression and interpolation, polynomials are fitted to data points.Regression is the process of fitting a large set of data points with a function, typically a line: y=mx+b.Numerous linear regression is used when there are multiple dependent variables (or "x"s) in the equation.Chemistry
In chemistry, polynomials are frequently used.The ideal gas law, PV=nRT (where n is the mole count and R is a proportionality constant), is an example of a gas equation linking diagnostic parameters that can typically be represented as a polynomial.Molecule concentration equations at equilibrium can alternatively be expressed as polynomials.For instance, the equilibrium concentration equation can be stated in terms of the related equilibrium constant K: KC=AB if A, B, and C are the concentrations of OH-, H3O+, and H2O in solution, respectively.Engineering and physics
Proportionality is a key study in both physics and engineering.How much does the beam deflect when a stress is raised?How far will a trajectory land if it is shot at a specific angle?F=ma (from Newton's laws of motion), E=mc2, and F—-r2=Gm1—-m2 (from Newton's law of gravitation, though typically the r2 is put in the denominator) are well-known examples from physics.To learn more about polynomials refer
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When 3x² + 7x - 6 + 2x³ is written in
standard form, the leading coefficient is
(1) 7
(2) 2
(3) 3
(4) -6
Answer:
Your leading coefficient is 2
please show all work
Domain and Range of Functions
Given a function y = f(x), the domain of f is
The range of f is the
We are given the function:
[tex]f(x)=\frac{1}{2x}-3[/tex]It's required to find the domain and range of the inverse function.
We must recall that, if the inverse function exists, its domain is the range of f, and its range is the domain of f.
Since f(x) is a rational function, it may not exist for the values of x where the denominator is 0.
Concretely, for x=0, the denominator is 0 and the function does not exist, thus the domain of f consists of every real number except x=0.
This can be written as (-∞,0) U (0,∞). This is also the range of the inverse function.
Now let's find the inverse function. We must solve for x the equation:
[tex]y=\frac{1}{2x}-3[/tex]Adding 3:
[tex]y+3=\frac{1}{2x}[/tex]Multiplying by x and dividing by y+3:
[tex]x=\frac{1}{2(y+3)}[/tex]Swapping letters:
[tex]y=\frac{1}{2(x+3)}[/tex]This is the inverse function of f.
Thus the domain of the inverse is:
-3-3
And the range:
Answer: Choice d
I will give brainliest, like and rating if u solve this right
which of the following is not true?
As per the given matrix [tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex], Option (C) is not true.
Matrix:
The matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Given,
[tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex]
Here we need to find which of the option is not true.
To find the incorrect options first we have to calculate the |A| and A⁻¹.
And we have also check whether is matrix has inverse or skew symmetric matrix.
First, we have to calculate the value of |A|,
|A| = (2 x 1) - (-1 x 2)
|A| = 2 - (-2)
|A| = 2 + 2 = 4
Therefore, option (A) is true.
Now we have to check this matrix has inverse,
It can be calculated using the formula,
[tex]A^{-1} =\frac{1}{|A|} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]
So, the inverse of the matrix is,
[tex]A^{-1} =\frac{1}{4} \left[\begin{array}{ccc}1&-2\\-(-1)&2\end{array}\right][/tex]
Which is equal to,
[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-2/4\\1/4&2/4\end{array}\right][/tex]
When we simplify it then we get,
[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-1/2\\1/4&1/2\end{array}\right][/tex]
Through this we have conclude that Option (B) and (D) are true.
We know that,
In the skew-symmetric matrix, a matrix whose transpose is equal to its negative.
So, the transpose of the given matrix is,
[tex]A^{T}=\left[\begin{array}{ccc}2&-1\\2&1\end{array}\right][/tex]
So, the given matrix is not a skew-symmetric matrix.
Therefore, the incorrect option is (c).
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