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Which equation could represent each graphed polynomial function?
y = 14 - 5x² + 4
y = x³ + 27
y = x(x + 3)(x - 2)
y = (x + 1)(x − 3)(x² + 1)
Answers
y = x⁴- 5x² + 4 represents the first graph.
y = x(x + 3)(x - 2) represents the second graph.
How to Interpret the graph of a Polynomial?
1) The first polynomial is;
y = x⁴- 5x² + 4
Simplifying this gives us;
y = x⁴- 4x² - x² + 4
y = x²(x² - 4) - 1(x²- 4)
y = (x² - 1)(x² - 4)
y = (x - 1)(x + 1)(x - 2)(x + 2)
Thus, the zeros of this polynomial are; x = -2, -1, 1, 2
From the given graphs attached, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.
So graph (1) represents the polynomial y = x⁴- 5x² + 4
2). The second graph shows the x-intercepts at x = -3, 0, 2
Since, y = x(x + 3)(x - 2) is the polynomial with x-intercepts at x = -3, 0, 2
Therefore, y = x(x + 3)(x - 2) represents the second graph.
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Related Questions
X^2 + y^2 = 169 and y = -5 as a graph and where are the coordinates of intersection
Answers
Step-by-step explanation:
please mark me as brainlest
A gas mixture has a total pressure of 0.56 atm and consists of He and Ne. If the partial pressure of the He in the mixture os 0.27 atm. What is the partial pressure of the Ne in the mixture?
Answers
The partial pressure of the Ne in the mixture is 0.29 atm if the as mixture has a total pressure of 0.56 atm and consists of He and Ne.
What is Dalton's law?Dalton's law states that the total partial pressures of all the gases in a mixture of non-reacting gases at a constant temperature equal the pressure the mixture exerts.
We have:
A gas mixture has a total pressure of 0.56 atm and consists of He and Ne. If the partial pressure of the He in the mixture os 0.27 atm.
According to Dalton's law
Total pressure = partial pressure of He + Partial pressure of Ne
0.56 = 0.27 + P(Ne)
P(Ne) = 0.29 atm
Thus, the partial pressure of the Ne in the mixture is 0.29 atm if the as mixture has a total pressure of 0.56 atm and consists of He and Ne.
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The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the
smaller number?
O 24
O 15
O 30
O 33
Answers
Answer:
15 (second option listed)
y = 15
x = 30
Step-by-step explanation:
setting up this statement algebraically:
[where x = one of our numbers, y = other number]
x + y = 48
x = (2y + 3)
x = 2y + 3
plug x [now in terms of y] into the original equation
(2y + 3) + y = 48
3y + 3 = 48
- 3 - 3
3 y = 45
÷3 ÷3
y = 15
from this value, we can plug it back into the y-value of the original equation to find our x-value
x + y = 48
x + 15 = 48
- 15 - 15
x = 33
{to check: 33 is 2y + 3}
we know that y = 15 (smaller number) and that x = 33 (larger number)
so, the solution to the question of which is the smaller number is 15
Hope this helps
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answers
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.
What is inequality?inequality the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
We can start by dividing the inequality by 3 to get ...
8 -4x < 2(x -5)
And we can divide by 2 to simplify further to ...
4 -2x < x -5
Now, we can add 2x+5, which gives ...
9 < 3x
and then divide by 3 again:
3 < x
Therefore number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.
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Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answers
Answer:
I'm pretty sure it is d... .......
HELP ITS ABOUT ANGLES :((((
Answers
Answer:
its D. 2 and 3
Step-by-step explanation: supplementary angles are angles that add up to 180 (or that make a straight line) the angle pairs that make a straight line are 1 and 2, 2 and 3, 3 and 4, and 4 and 1.
So D would be correct
what is the area of the trapezium?
Answers
Answer:
156 cm²
Explanation:
This figure is a trapezium.
Formula of Area of Trapezium = 1/2 × (a + b) × height
Here given:
a = 9 cmb = 30 cmh = 8 cm==============
Area of trapezium: 1/2 × (9 + 30) × 8 = 156 cm²
Answer:
area of the trapezium is 156
Step-by-step explanation:
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to the following linear inequality in the coordinate plane.
5x - y > -3
27
Drawing Tools
Select
Line
Dashed Line
Shaded Region
Click on a tool to begin drawing.
10
8
6
Answers
The solution to the inequality 5x - y > -3 is shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An inequality shows the non equal comparison of two or more variables and numbers.
The solution to the inequality 5x - y > -3 is shown in the graph.
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Line q and m are cut by transversal lines j and k. The line and the measures of some of the angles created by the intersections of the lines are shown in the diagram below. What is the measure, in degrees, of angle 1?
Answers
Answer:
70
Step-by-step explanation:
180 minus 110 is 70
straight lines are 180 degrees
I dive to 17 metres for 23 minutes. after a 30 minute surface interval, i plan to dive to 16 metres. what is the maximum allowable time for the second dive
Answers
Answer:
i don't know
Step-by-step explanation:
i don' know
Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
Answers
Answer:
-2x - 1 = 3^(-x); 2^(-x) + 2 = -5^x + 3
Step-by-step explanation:
for this question you are choosing the lines that do not touch
the graphs for the second third and fourth ones all touch
but
the first and last one do not
therefore those are the ones with no solution
Answer:
Graph 1 and Graph 5
Step-by-step explanation:
As the first and final graphs do not intersect at any points on their graphs, they have no solution.
What are “like terms”? Why can we only add like terms?
13.)What is the closure property? What does it have to do with adding, subtracting, and multiplying polynomials?
Answers
Answer:
Like terms are mathematical terms that contain the same variables. We combine like terms, because it simplifies algebraic expressions.
Closure property is the term for when you add or multiply two whole numbers together, and the result is always just a whole number. It is related to adding, subtracting, and multiplying polynomials, because when something is closed, the output will result in being the same type of object as the inputs.
Step-by-step explanation:
Like terms: When combining like terms, we add their coefficients. For instance, if we have 3y and 4y, we get 7y. That is because we added (3+4) to get 7, and plugged in the variable "y".
Closure property: Adding, subtracting, or multiplying two polynomials will output a polynomial.
What is closure property? That’s a good question. Closure property is a method and idea used in math that often emphasizes the explanation that the sum of two whole numbers will always result in a whole number (that is what it has to do with addition). In subtraction, closure property states that the difference between two rational numbers (pi excluded) will always result in a rational number. When multiplying polynomials, the rule is that, like subtraction, the multiplication of two rational numbers always will end in a rational number.
Can someone look at this image ?
Answers
Answer:
3x-2y=13
Step-by-step explanation:
7litres of petrol cos t £3.50. Find the cost of 23 litresof petrol of the same grade.
Answers
Answer:
£11.50
Step-by-step explanation:
7litres of petrol cos t £3.50. The cost of 1 liter will be:
= £3.50/7
= £0.50
The cost of 23 litres of petrol of the same grade will be:
= £0.50 × 23
= £11.50
Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x+4y=-28
Answers
Answer:
y=-x-7
Step-by-step explanation:
Slope-intercept form is y=mx+b
We have the equation 4x+4y=-28 and must put it into the form above. To do this first subtract 4x from both sides.
4x-4x+4y=-28-4x
This equals 4y=-4x-28. Now, divide 4 from both sides.
4y/4=-4x/4-28/4
y=-x-7
Hope this helps!
If not, I am sorry.
What is the area of ruth's mural?
Answers
Answer:
Step-by-step explanation:
Comment
The shape consists of a rectangle on the bottom and a trapezoid on the top.
Rectangle
A rectangle has a very simple Area formula. It is Area = L*W. In this case the L = 14 m and is horizontal. The width is at right angles to the length and is marked as 3.
Area = L * w
L = 14
w = 3
Area = 14 * 3 = 42 m^2
Trapezoid
The trapezoid is a bit more complicated and some things have to be found. First of all b1 is the first base of the trapezoid. It is parallel to and equal to the Length of the rectangle. b2 is marked 10 meters. The height is just a bit more complicated. The total height of the figure is 8 m. You can't count the 3 m of the rectangle as part of the height because b1 comes only to the top of the rectangle. The height is 8 - 3 = 5
Area = 1/2(b1 + b2)*h/2
b1 = 14
b2 = 10
h = 8 - 3 = 5
Area = 1/2 ( 14 + 10) * 5 / 2
Area = 1/2 (24)*5
Area = 12 * 5
Area = 60 m^2
Total Area 102 m^2
Which table represents a linear function?
Answers
Answer:
The table on the far left is a linear function.
Step-by-step explanation:
The table on the far left is the function
[tex]y = \frac{1}{2} x[/tex]
A/n ____ is a part of a circle that represents an angle.
Answers
Answer:
An Arc is a part of a circle that represents an angle.
DNA molecules include the base units adenine, thymine, cytosine, and guanine
(A, T, C, and G). The sequence of base units along a strand of DNA encodes
genetic information. In how many different sequences can A, T, C, and G be
arranged along a short strand of DNA that has only 5 base units?
Answers
The number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120
What is permutation?
Permutation is the number of ways of arrangement for a given set.
The formula for a permutation is given as P(n, r) = n! / (n-r)!
Where n = items chosen from = 5
r is the number of items = 4
Substitute values into the formula
P(5, 4) = [tex]\frac{5!}{5-4!}[/tex]
P(5,4) = [tex]\frac{5 * 4* 3*2*1}{1}[/tex]
P(5,4) = [tex]\frac{120}{1}[/tex]
P(5,4) = 120
Therefore, the number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120
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Answer:
The answer is actually 120.
Step-by-step explanation:
I have the keysheet to the questions.
Lucy is knitting a blanket and needs to buy some more yarn. at her local craft store, 2 skeins of yarn cost $7 and 8 skeins of yarn cost $28. what is the constant of proportionality in this direct variation?
Answers
Answer:
4
Step-by-step explanation:
Proportionality between skein values
8:2=4:1
Proportionality between cost values
28:7=4:1
The variation(both the skein values and cost values) has the constant of 4 ie the 1st skein value × 4= the last skein value & the 1st cost value × 4=the last cost value
One polygon has a side of length 2 feet. A similar polygon has a corresponding side of length 4 feet. The
ratio of the perimeter of the smaller polygon to the larger is
021
01/2
014
Answers
Answer:
the largest is 014 because I did it and the teacher said it is correct
Step-by-step explanation:
teacher checked work
A pair of equations is shown below.
Answers
Answer: (2,5)
Step-by-step explanation: Step 1: Identify key concepts for Part A
y=7x-9
Slope: 7
y int. : -9
y=3x-1
Slope: 3
y int. : -1
Since you know this information, you can plot the points and graph it.
Part B
To solve a system of equations, you need to identify the point whereby the two graphs intersect, and since you're solving it graphically, just find the point of intersection. You should get an answer of: (2,5)
(x=2) and (y=5)
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. persons taking a 70-hour review course average a score of 780. based on these two data points, create a linear equation for the function that describes how score varies as a function of time. use this function to predict an average score for persons taking a 43-hour review course. round your answer to the tenths place.
Answers
Answer:
Answer for linear equation: y=4x+500 and Avg score for persons taking 43-hour review course is 672
What is the probabily of the 90th percentile given mean of 262 and a standard deviation of 45
Answers
The probability of the 90th percentile given a mean of 262 and a standard deviation of 45 is 319.672
Here,
The formula for the percentile probability is
[tex]P=\mu+z\sigma[/tex]
P=262 + 1.2816(45)
P = 319.672
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If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.
( x/6, y/4 )
( x - 4, y - 6)
(-6 x, -4 y)
( x - 6, y - 4)
Answers
T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)
A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.
Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)
and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)
So, the matrix of the transformation is
[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]
The inverse of the matrix is
[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]
So, the Inverse Transformation is given by
[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]
So, no option is correct. And the answer is
[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]
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Classify the following polynomials. Combine any like terms first.
2x-x²+4x+x²
x^3-5x^2 + 3-2
x^3-x^3+x²-x²+3
7x-x^2+x³+4x²
-6x-x^3 +6x-4x
Answers
Answer:
A resposta certa é:
[tex]6x \\x^3 - 5x^2 + 1 \\3 \\x^3 + 3x^2 + 7x \\-x^3 - 4x[/tex]
Step-by-step explanation:
1° equação:
Como há um x² positivo e um negativo, ambos irão se anular, sobrando apenas as incógnitas de potência 1 (ou, 6x)
2° equação:
Esta resulta em uma equação de 3° grau incompleta, já que há uma incógnita de potência 3, uma de potência 2, não há uma incógnita de potência 1 mas há as constantes, que as unindo forma a constante 1.
3° equação:
As incógnitas presentes há uma negativa e uma positiva de mesma potência, anulando-as e sobrando apenas a constante 3.
4° equação:
Considerando que há um 4x² e um -x² na equação, unindo-os forma o 3x², após isso é só repetir a equação.
5° equação:
Há -10x (-6x -4x = -10x) e 6x, resultando em um -4x, e então é só repetir a equação
Nota: I'm Brazilian, so I found it more practical to write the entire explanation in Portuguese, so if you can't understand, I ask you to use the translator, thanks for understanding :)
Give the equation of a line that goes through the point ( 4 , 9 ) and is parallel to the line − 3 x + 7 y = 21 .
Answers
Answer:
[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
Step-by-step explanation:
Given equation: -3x + 7y = 21
Slope-Intercept Form: y = mx + b -
where:
m is the slopeb is the y-intercept (when x = 0)Note: parallel lines have the same slope.
1. Rewrite the given equation in slope-intercept form:
[tex]\sf -3x + 7y = 21\ \textsf{[add 3x to both sides]}\\\\-3x + 3x + 7y = 21 + 3x\\\\7y = 3x + 21\ \textsf{[divide both sides by 7]}\\\\\dfrac{7y}{7}=\dfrac{3x+21}{7}\\\\\implies y=\dfrac{3}{7}x+3[/tex]
Here, this equation has a slope of ³⁄₇ and a y-intercept of 3.
2. Find the equation of the parallel line:
substitute the point (4, 9) into the equation to find the value of b
[tex]\sf y=\dfrac{3}{7}x+b\\\\9=\dfrac{3}{7}(4)+b\\\\9=\dfrac{12}{7}+b\\\\\dfrac{63}{7}-\dfrac{12}{7}=\dfrac{12}{7}-\dfrac{12}{7}+b\\\\\dfrac{51}{7}=b[/tex]
[tex]\sf \textsf{Equation:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
3. Check your work:
[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}\\\\9=\dfrac{3}{7}(4)+\dfrac{51}{7}\\\\9=\dfrac{12}{7}+\dfrac{51}{7}\\\\9=\dfrac{63}{7}\\\\9=9\ \checkmark[/tex]
[tex]\sf \textsf{Therefore, the equation of the parallel line is:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
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Answer:
[tex]\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]
Step-by-step explanation:
First, write the given equation in slope-intercept form. That is, you can make y the subject in the given equation.
Slope intercept form
y = mx + c
Here,
m = slope
c = y-intercept
Let us write the given equation in slope-intercept form.
− 3x + 7y = 21
Add 3x to both sides.
7y = 3x + 21
Divide both sides by 7.
[tex]\sf y=\dfrac{3}{7}x +\dfrac{21}{7} \\\\y=\dfrac{3}{7}x +3[/tex]
We know that the slopes of parallel lines are equal. Therefore, the slope(m) of the new line is 3/7.
The new line is going through ( 4, 9 ). Using that, let us find the value of c (y-intercept), by substituting the values of m, y, and x.
( 4, 9 ) → ( x , y )
m → 3/7
Let us find the value of c
[tex]\sf y = mx+c\\\\9 =\dfrac{3}{7}*4+c\\\\ 9=\dfrac{12}{7}+c\\\\ 9-\dfrac{12}{7}=c\\\\\dfrac{63-12}{7} =c\\\\\dfrac{51}{7} =c[/tex]
And now let us write the equation of the new line.
[tex]\sf y =mx+c\\\\\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]
. An elevator in a building starts with five passengers and stops at seven floors. Say every passenger is equally likely to get off at each floor and all the passengers leave independently of each other. a. How many ways are there for the passengers to be assigned a floor? b. How many ways are there for the passengers to be assigned a floor but no two passengers are on the same floor?
Answers
There are 16807 number of ways the passengers to be assigned a floor and there are 2520 number of ways the passengers to be assigned a floor but no two passengers are on the same floor.
Given that an elevator starts with five passengers and stops at the seven floors of a building.
From the given information, the total number of floors n=7.
The number of passengers r = 5.
(a) Compute the number of ways that 5 passengers can be assigned to seven floors.
Here, repetition is allowed.
From the known information, if r numbers are selected from n number of observations then the total number of observations that can be drawn from n number of observations is [tex]n^r[/tex].
If 5 passengers can be assigned to seven floors is 7⁵ = 16807.
(b) Compute the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor.
Here, repetition is not allowed.
If 5 passengers can be assigned to seven floors but no two passengers are on the same floor is 7x6x5x4x3 = 2520.
Hence, the number of ways that 5 passengers can be assigned to seven floors is 16807, and the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor is 2520.
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What is the factored form of the following expressions?
x2 – x – 42
Answers
Answer:
(x-7)(x+6)
Step-by-step explanation:
So you find what is common between the two then fix it
only a genius can solve it !!
[tex] \frac{ \cos(A) }{1 - \sin(A) } + \frac{ \sin(A) }{1 - \cos(A) } + 1 = \frac{ \sin(A) \cos(A) }{(1 - \sin(A)(1 - \cos(A)} [/tex]
Answers
[tex]\text{L.H.S}\\\\=\dfrac{\cos A}{1-\sin A} + \dfrac{\sin A}{1-\cos A} +1\\\\\\=\dfrac{\cos A(1-\cos A) + \sin A(1-\sin A) + (1-\sin A)(1 - \cos A)}{(1-\sin A)(1 -\cos A)}\\\\\\=\dfrac{\cos A - \cos^2 A + \sin A - \sin^2 A + 1 - \cos A - \sin A + \sin A \cos A}{(1 -\sin A)(1 - \cos A)}\\\\\\=\dfrac{-(\sin^2 A + \cos^2A) +1 + \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\dfrac{-1 + 1 + \sin A \cos A }{(1 - \sin A)((1 - \cos A)}\\\\\\=\dfrac{0+ \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\[/tex]
[tex]=\dfrac{\sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
