Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is B.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and non-negative exponentiation of variables involved.
Example:
x² + 3x + 5
In order to find the values at which the given polynomial will have zeros of the function, we need to find the values at which f(x) changes from positive to negative or vice versa. Since this is the range at which the function must have crossed the x-axis on the graph.
As per the given table, the value of f(x) is changing from negative to positive and positive to negative are between 2.5 and 3.0 and between 4.0 and 4.5.
Hence, the correct option is B.
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6x+2y=20 2x-3y=3 solve by substitution
The solution of the system of linear equation by substitution method is (3,1).
What is the method of substitution?The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.
Given here the linear equations are
Equation 1: 6x+2y=20
Equation 2: 2x-3y=3
in equation 1 the value of y will be
6x+2y=20
⇒2y=20-6x
⇒y=(20-6x)/2
⇒y=10-3x
substituting the value of y in the equation 2, we will get
2x-3y=3
⇒2x-3(10-3x)=3
⇒2x-30+9x=3
⇒11x-30=3
⇒11x=30+3
⇒11x=33
⇒x=33/11
⇒x=3
putting the value of x in value of y in equation 1
y=10-3x
⇒y=10-3(3)
⇒y=10-9
⇒y=1
The solution of the system of linear equation by substitution method is (3,1).
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How do I simplify the following expression by writing it as a term with only one trigonometric function?
(4-2sec^2(x))/(sec^2(x))
Answer:
2 cos (2x)
Step-by-step explanation:
[tex]\frac{4 -2 sec^2x}{sec^2x} \\=\frac{4-\frac{2}{cos^2x} }{\frac{1}{cos^2 x} } \\=\frac{\frac{4 cos^2x-2}{cos^2 x} }{\frac{1}{cos^2x} } \\=\frac{2(2 cos^2x-1)}{cos^2x} \times \frac{cos^2x}{1} \\=2(2cos^2x-1)\\=2cos(2x)[/tex]
Look at the attachment! This is algebra. 10 points!
If x∆y = 3x - y², then
5∆1 = 3×5 - 1² = 15 - 1 = 14
and
14∆6 = 3×14 - 6² = 42 - 36 = 6
So (5∆1)∆6 = 6.
What was the initial quantity of vanadium-49, which has a half-life of 330 days, if after 540 days there is a 1,750 g sample remaining?a.)5,440.42g b.)3,500g C.) 8,700g d.)2,863.63g e.)98g
Answer:
(a) 5440.42 g
Step-by-step explanation:
The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...
Q = Q₀(1/2)^(t/330) . . . . . where t is in days
__
The amount after 540 days is ...
1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀
Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g
The initial quantity was about 5440.42 grams.
Q6. This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.
The following is the actual question: Find the highest and lowest value of the equation in the given picture within the unshadowed region.
The graph of all the inequalities are given below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.
y ≥ x, the region is left to the line.
y < -(3/7)x – 7, the region is left to the line.
y ≤ (5/3)x – 8, the region is right to the line.
y ≥ 14 – (11/12)x, the region is right to the line.
y = -(3/2)x + 5, this is the equation of line.
All the graphs are shown below.
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Help needed! Thank you!
Part 1
[tex](f\circ g)(x)=f(g(x))=\frac{\frac{1}{x}}{\frac{1}{x}-3}[/tex]
Multiplying the numerator and denominator by x,
[tex](f\circ g)(x)=\boxed{\frac{1}{1-3x}}[/tex]
Part 2
The domain for this function is all values of x except for when the denominator equals 0 (because then, it would be undefined).
The denominator is equal to 0 when x=1/3, so the domain is [tex]\boxed{x \neq \frac{1}{3}}[/tex]
Please help asap! 30 points
Given that f(x)=11, g(x)=x^2-6x+3, and h(x)= -x+4, find the function (g •h)(x).
Answer:
[tex](g \cdot h)(x)=x^2-2x+23[/tex]
Step-by-step explanation:
For composite functions, it's important to understand what the functions mean:
[tex](g\cdot h)(x)[/tex] which is read as "g of h, of x" means [tex]g ( \text{ }h(x) \text{ })[/tex] which is read as "g of, h of x" (with slight pauses at the comma). This means that x goes into the h function, and the output of the h function goes into the g function.
Putting "x" into the h function
[tex]h(x)=-x+4[/tex]
Since it is just "x" going into the h function, the function as written is the output when x is the input.
Putting the h function output, into the g function
[tex]g(x)=x^2-6x+3[/tex]
[tex]g(h(x))=(h(x))^2-6(h(x))+3[/tex]
Substitute
[tex]g(h(x))=(-x+4)^2+-6(-x+4)+3[/tex]
Squaring means the something multiplied by itself
[tex]g(h(x))=(-x+4)*(-x+4)+-6(-x+4)+3[/tex]
Use distributive property; (some people know binomial distribution as "FOIL" -- First, Outer, Inner, Last):
[tex]g(h(x))=[(-x)(-x)+4(-x)+4(-x)+4*4)]+[6x+4]+3[/tex]
Simplify the binomial terms:
[tex]g(h(x))=[x^2-8x+16]+[6x+4]+3[/tex]
Group like terms:
[tex]g(h(x))=x^2-2x+23[/tex]
Remember that [tex](g\cdot h)(x)[/tex] means [tex]g ( \text{ }h(x) \text{ })[/tex]
[tex](g \cdot h)(x)=x^2-2x+23[/tex]
So, [tex](g \cdot h)(x)=x^2-2x+23[/tex]
which matrix can be used to solve the system
Answer:
6x + 7y = 14
7x + 8y = 27
6 7. x = 14
7 8. y = 27
option B
Use Modus Ponens to deduce the conclusion from each of the following pairs of premises:
a = b ∧ b = c
(a = b ∧ b = c) ⇒ a = c
The conclusion is a=c statement
A modus ponens argument has the same structure as a syllogism, with two premises and a conclusion:
If P, then Q.
P occurs.
Consequently, Q occurs.
The Modus Ponens rule of inference or rule of logic requires a single premise and its logical consequences. A conditional statement states that if event 1 occurs, event 2 will also occur and that event 2 will be inferred as the outcome if event 1 occurs. For instance, if A implies B and A is assumed to be true, then it follows that B must also be true according to the Modus Ponens rule.
Hence, By modus Ponens
a=b∧b=c ⇒ a=c
So, given a=b∧b=c Then
⇒a=c.
Hence the conclusion is a=c statement .
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The functions f(x) = x^2 – 2 and g(x) = –x^2 + 5 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x^2 – 2
y ≥ –x^2 + 5
The set of inequalities do not have a solution.
What is inequality?The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal. But to compare the values, whether it is less than or greater than, different inequalities are used.
Given:
f(x)= x²-2
g(x) = -x²+5
To derive, y ≤ x² + 5 simply change the equality sign in the function g(x).
To derive y > x² - 2 , following transformation on the function f(x)
Shift the function f(x) down by 2 unitsReflect across the x-axisShift the function g(x) up by 5 unitsChange the equality sign in the function g(x) to greater than.The inequalities of the graphs become
y < x² - 2 and y ≤ x² - 5
From the graph of the above inequalities it can be seen that curves of the inequalities do not intersect.
Hence, the set of inequalities do not have a solution
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Order these numbers from least to greatest.
3.3661, 3.5, 3.36, 3.036
Answer:
3.036, 3.36, 3.3661 , 3.5
Step-by-step explanation:
Look at the first 2 numbers
3.3661, 3.5, 3.36, 3.036
We can order them as 3.0 , 3.3 , 3.3 . 3.5
So 3.036 is first one
Now we have 2 of the 3.3's
One is 3.3661 and the other one is 3.3600
Because if you add a number to the end it will always be a zero and it wont change the answer
So 3.36 is second and 3.3661 is third one
3.5 is bigger than 3.3
So 3.5 is last
Which of the following is a root of the polynomial function below?
In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)
How to determine the roots of a cubic equation
In this case we have a cubic equation, that is, a third order polynomial. There are two strategies to determine the roots of cubic equations: (i) Cardano's formula, (ii) Numerical methods.
The quickest though most effective way consists in determining the roots by numerical methods (i.e. Newton-Raphson method). By using numerical methods we conclude that the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7
x₁ = - 1, x₂ = (- 5 + i √3)/2, x₃ = (- 5 - i √3)/2
In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)
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Which pair of statements describes the end behavior of the graph of the function f(x) = x3 + 2x2 − 5x − 6?
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?
A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.
B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.
C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.
D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.
If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.
Hence, the correct option is D.
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The graph shows that is translated horizontally and vertically to create the function .
On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.5) and crosses the y-axis at (0, 1). g (x) approaches y = 2 in quadrant 2 and increases into quadrant 1. It goes through (0, 2) and (2, 3).
What is the value of h?
−2
−1
1
2
According to the function transformations, the value of h is -2
How to determine the value of h?The complete question is in the attachment
The functions are given as:
[tex]f(x) = (2.5)^x[/tex]
[tex]g(x) = (2.5)^{x-h[/tex]
From the question, we understand that the function f(x) is translated to the left to get g(x)
From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).
This transformation is represented by:
(x, y) => (x + 2, y)
So, we have:
x - h = x + 2
Evaluate the like terms
h = -2
Hence, the value of h is -2
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Answer:H=-2
Step-by-step explanation:
Solve for x : 7x + 8 < 1/6 (42x+48)
X = all real number
X has no solution
X = 0
Answer:
[tex]\fbox {all real numbers}[/tex]
Step-by-step explanation:
7x + 8 = 1/6 (42x + 48)
7x + 8 = 7x + 8
x = all real numbers
-2/9u=12
Solve for u
u=-54
you have -54 because
-54(-2)=108/9=12
Answer:
u =-54
Step-by-step explanation:
-2/9u=12
To solve for u multiply each side by -9/2 to isolate u
-9/2 * -2/9 u= 12 * -9/2
u =-54
Question 10 of 33
Which of the following is a characteristic of a regular tessellation?
O A. It uses only one type of regular polygon.
OB. It uses more than one type of regular polygon.
O C. It allows for overlaps and spaces between shapes.
OD. It does not cover a surface completely.
SUBMIT
A tessellation that uses only one type of regular polygon.
What is Polygon?
The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.
When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.
A regular tessellation is tessellation made up by using only one type of regular polygon. These are made up of entirely congruent regular polygons all that joining vertex to vertex.
Hence, A is the correct option.
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Steps are very much required they should be clear and neat please i need to understand this I'm taking a practice test for my future sats
ill report in inappropriate answers
Answer:
2nd option
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
= [tex]\frac{4x+5+7x-6-8x+2}{3}[/tex]
= [tex]\frac{3x+1}{3}[/tex]
= [tex]\frac{3x}{3}[/tex] + [tex]\frac{1}{3}[/tex]
= x + [tex]\frac{1}{3}[/tex]
The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?
Answer:
212520 different committees
Step-by-step explanation:
Candidates
For a President: 23
For a Vice President: 22
For a Secretary: 21
For a Treasurer: 20
Number of ways: (23)(22)(21)(20) = 212520
Hope this helps
Answer:
To whom it may concern the answer to this problem would be 212,520.
Step-by-step explanation:
Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...
[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]
Remember that the 19! cancel each other out. Hope this helps!
Solve the right triangle, AABC, for the missing sides and angle to
the nearest tenth given angle B = 27° and side c = 15.
Answer:
please see photo for detailed analysis.
The measure of B is (3x-4)° and the measure of D is (2x-6)°. What are the measures of angles B and D?
Answer:
5x - 10
Step-by-step explanation:
→ Find the sum of the expression
3x - 4 + 2x - 6
→ Collect all the x terms
3x + 2x - 4 - 6
→ Simplify
5x - 10
A pool a possible candidate for a student council consists of 14 freshmen and 8 softwares how many different councils consisting of 5 freshmen and 7 sophomores are possible
The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.
We have given that,
A pool of possible candidates for a student council consists of 14 freshmen and 8 software.
We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible
What is the combination?[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]
The total number of the council is
[tex]_{10} C_5\times _9 C_7[/tex]
=252(36)
=9216
The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.
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Make a tree diagram to show all possible arrangements of the letters in the word MAT. If each of the letters is ordered randomly, what is the fractional probability of M being the last letter?
If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We have to make a tree diagram to show all possible arrangements of the letters in the word MAT.
M ⇒ A ⇒ T
⇒ T ⇒ A
A ⇒ M ⇒ T
⇒ T ⇒ A
T ⇒ M ⇒ A
⇒ A ⇒ M
If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.
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For the data set 7, 5, 10, 11, 12, the mean, X, is 9. What is the standard
deviation?
Answer:
The standard deviation is about 2.915
Step-by-step explanation:
Answer:
= 2.9154759474227
Step-by-step explanation:
A club organises a lottery, selling tickets at 25 cents each. The club will be giving a prize of
€58
to the winner but also plans to make a profit of
€150
from the whole event. What is the least number of tickets that the club needs to sell?
Using proportions, it is found that the club needs to sell at least 832 tickets to make their desired profit.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The prize is of €58, with the event making a profit of €150, hence the amount of money they have to earn from tickets is given by:
A = 150 + 58 = €208.
The tickets are sold at €0.25, hence the number of tickets they have to sell is:
n = 208/0.25 = 208 x 4 = 832.
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Simplify:
(x-1)+(12–7.5x)
Answer:
[tex]-6.5x+11[/tex]
Step-by-step explanation:
Expand The Brackets:
[tex]x-1+12-7.5x[/tex]
[tex]=x+(-1)+12+(-7.5x)[/tex]
Combine Like Terms:
[tex]=x+(-1)+12+(-7.5x)[/tex]
[tex]=(x+-7.5x)+(-1+12)[/tex]
Answer:
[tex]-6.5x+11[/tex]
I Hope This Helps
Luis created the graph below to show the temperature from 8:00 a.m. (8 hours after midnight) until 8:00 p.m.
On this graph, 4:00 p.m. occurs at 16 hours after midnight, and 6:00 p.m. occurs at 18 hours after midnight. Which statements are true about the temperatures Luis recorded on the graph? Select THREE answers.
The temperature increased until 4:00 p.m.
The temperature was not recorded between 4:00 p.m. and 6:00 p.m.
The temperature decreased after 6:00 p.m.
The temperature increased and then decreased before holding constant.
The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.
A slope also known as the gradient of a line is a number. The correct option is A, C, and D.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
For the given question,
The temperature increased until 4:00 p.m.This can be observed in the graph, as the slope of the graph before 4 pm is positive, it can be concluded that the temperature is increased until 4 pm.
The temperature decreased after 6:00 p.m.This can be observed in the graph, as the slope of the graph after 4 pm is negative, it can be concluded that the temperature is decreasing after 4 pm.
The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.This can be probed by calculating the slope of the line between the two points. Therefore, the slope between 8 am to 12 pm will be 1, while the slope from 12 pm to 4 pm will be equal to 4/3.
Hence, the correct option is A, C, and D.
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Answer:
ACD
Step-by-step explanation:
Solve x2 − 3x = −8. (2 points)
x equals quantity of 3 plus or minus I square root of 29 all over 2
x equals quantity of 3 plus or minus I square root of 23 all over 2
x equals quantity of negative 3 plus or minus I square root of 29 all over 2
x equals quantity of negative 3 plus or minus I square root of 23 all over 2
x equals negative 2 plus or minus 4 I square root of 2
x equals negative 2 plus or minus 2 I square root of 2
x equals negative 1 plus or minus 4 I square root of 2
x equals negative 1 plus or minus 2 I square root of 2
The value of x equals quantity of (3 ± √23)/2.
What is Quadratic Equations?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Here, given equation;
x² - 3x = -8
x² - 3x + 8 = 0
x² - 2 X 3/2 x + 8 = 0
x² - 2.3/2 x + (3/2)² - (3/2)² + 8 = 0
(x - 3/2)² - 9/4 + 8 = 0
(x - 3/2)² + 23/4 = 0
(x - 1.5)² = -5.75
x - 1.5 = ±√(-5.75)
x = 1.5 ± i√(5.75)
x = (3 ± i√21)/2
Thus, x equals quantity of 3 plus or minus I square root of 23 all over 2.
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The radius of a circle is 3ft. What is the circumference of the circle? Use 3.14 for pie.
How to find the a in the equation y=ax^3 + d given the two points (0,10), (2,20)
Answer:
[tex]y=\dfrac{5}{4}x^3+10[/tex]
Step-by-step explanation:
Given information:
[tex]y=ax^3+d[/tex](0, 10)(2, 20)Create two equations by substituting the given points into the given equation:
Equation 1: point (0, 10)
[tex]\implies a(0)^3+d=10[/tex]
[tex]\implies 0+d=10[/tex]
[tex]\implies d=10[/tex]
Equation 2: point (2, 20)
[tex]\implies a(2)^3+d=20[/tex]
[tex]\implies 8a+d=20[/tex]
Substitute Equation 1 into Equation 2 and solve for a:
[tex]\implies 8a+d=20[/tex]
[tex]\implies 8a+10=20[/tex]
[tex]\implies 8a+10-10=20-10[/tex]
[tex]\implies 8a=10[/tex]
[tex]\implies \dfrac{8a}{8}=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{5}{4}[/tex]
Finally, substitute the found values of a and d into the original formula:
[tex]\implies y=\dfrac{5}{4}x^3+10[/tex]
Check by substituting the x-values of the two given points into the found equation:
[tex]x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}[/tex]
[tex]x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}[/tex]
Put(0,10)
10=a(0)³+dd=10Now
Put again (2,20) this time
20=2³a+1010=8aa=10/8a=5/4