Answers
To begin with, let us look at a few definitions that will help
A relation is a function if each x-value is paired with exactly one y-value. A vertical line test on a graph can be used to determine whether a relation is a function.
If we use a graph to check, we will have
We can see that there is no overlapping of coordinates. The table satisfies the vertical line test.
Hence, it is a function
The domain and range of function is the set of all possible inputs and outputs of a function respectively. The domain and range of a function y = f(x) is given as domain= {x ,x∈R }, range= {f(x), x∈Domain}.
The domain of the function, D is given by
[tex]D=\mleft\lbrace-1,0,1,2,3\mright\rbrace[/tex]The range, R is given by
[tex]R=\mleft\lbrace-6,-1,2,5,8\mright\rbrace[/tex]
Related Questions
the polynomial p(x)=2x^3+17x^2+41x+30 has a known factor of (x+5) rewrite p(x) as a product of linear functionp(x)=
Answers
Answer:
Rewriting p(x) as a product of linear functions, we have;
[tex]p(x)=(2x+3)(x+5)(x+2)[/tex]Explanation:
We want to write the given polynomial p(x) as a product of linear functions.
[tex]p(x)=2x^3+17x^2+41x+30[/tex]To write it as a product of linear functions we have to find the other factors;
let us divide the given polynomial by the given factor;
[tex]\begin{gathered} \text{ }2x^2+7x+6 \\ (x+5)\sqrt[]{2x^3+17x^2+41x+30} \\ \text{ - (}2x^3+10x^2) \\ \text{ }7x^2+41x+30 \\ \text{ }-(7x^2+35x) \\ \text{ }6x+30 \\ \text{ - (}6x+30) \\ \text{ 0} \end{gathered}[/tex]So, the division gives;
[tex]p(x)=2x^3+17x^2+41x+30=(x+5)(2x^2+7x+6)[/tex]next, we need to find the factors of the quadratic function;
[tex]\begin{gathered} 2x^2+7x+6 \\ 2x^2+4x+3x+6 \\ 2x(x+2)+3(x+2) \\ (2x+3)(x+2)_{} \end{gathered}[/tex]Substituting the factors of the quadratic function, we have;
[tex]\begin{gathered} p(x)=2x^3+17x^2+41x+30=(x+5)(2x^2+7x+6) \\ p(x)=(x+5)(2x+3)(x+2)_{} \\ p(x)=(2x+3)(x+5)(x+2) \end{gathered}[/tex]Therefore, rewriting p(x) as a product of linear functions, we have;
[tex]p(x)=(2x+3)(x+5)(x+2)[/tex]Question 11 of 25 Which of the following functions is graphed below? A. y = x +51 + 4 B. V = x + 51-4 C. y = x-5|+4 D. y = x-51-4
Answers
The simple way to answer this is to take a few points from the graph and compare it with each option.
Let's take points at x = 0, 1, 2
From graph,
When x = 0, y = 1, hence the point is (0, 1)
When x = 1, y = 0, hence the point is (1, 0)
When x = 2, y = -1, hence the point is (2, -1)
Now, put the same x values in the given options to evaluate the output.
For x = 0, the pair should be (0, 1),
1) |x + 5| + 4 = |0 + 5| + 4 = |5| + 4 = 9 => (0, 9) Not true
2) |x + 5| - 4 = |0 + 5| - 4 = |5| - 4 = 1 => (0, 1) True
3) |x - 5| + 4 = |0 - 5| + 4 = |-5| + 4 = 5 + 4 = 9 => (0, 9) Not True
4) |x - 5| - 4 = |0 - 5| - 4 = |-5| - 4 = 5 - 4 = 1 => (0, 1) True
Hence, 2nd and 4th options can be true. Now, evaluate these two options with some other point.
For x = 1, the pair should be (1, 0),
2) |x + 5| - 4 = |1 + 5| - 4 = |6| - 4 = 2 => (0, 2) Not True
4) |x - 5| - 4 = |1 - 5| - 4 = |-4| - 4 = 4 - 4 = 1 => (0, 0) True
Hence, the 4th option is true.
solve the system x+3y=62x+4y=12
Answers
x+3y=6 ----------------------------(1)
2x+4y=12---------------------------(2)
Using elimination method to solve;
we will eliminate x variable
To do that, we must make sure the coefficient of x in the two equation are the same.
This can be achieved by multiplying equation (1) by 2 and equation (2) by 1
That is;
2x + 6y = 12 ----------------------(3)
2x + 4y = 12 -----------------------(4)
subtract equation (4) from equation (3)
2y = 0
Divide both-side of the equation by 2
y=0
substitute y = 0 into equation (1)
x + 3(0) = 6
x = 6
Find a formula for the nth termof the arithmetic sequence.First term 9Common difference -2an = [? ]n + []
Answers
Given:
First term 9
Common difference -2
Required:
Find a formula for the nth term of the arithmetic sequence.
Explanation:
The general formula for the nth term of the an arithmetic sequence is given by the formula:
[tex]a_n=a+(n-1)d[/tex]Where a = first term
d = common difference
Put a = 9 and d = -2 in the formula.
[tex]\begin{gathered} a_n=9+(n-1)(-2) \\ a_n=9-2(n-1) \\ a_n=9-2n+2 \\ a_n=-2n+11 \end{gathered}[/tex]Final Answer:
The nth term of the arithmetic sequence is
[tex]a_n=-2n+11[/tex]Brian likes to go bird watching along the Harvest Park Trail in a nearby forestpreserve. He wants to calculate the area enclosed by the trail which is shownbelow. Based on the diagram, what is the closest approximation of the area insquare yards of the land enclosed by the trail?
Answers
Answer:
(B)138,000 square yards.
Explanation:
To determine the area of the land enclosed by the trail, we divide the diagram into two as shown below:
Therefore, the area will be:
[tex]\begin{gathered} \text{Area}=(800\times900)+(400\times1300) \\ =720,000+520,000 \\ =1,240,000\text{ square feet} \end{gathered}[/tex]We then convert it to square yards.
[tex]\begin{gathered} \text{9 square feet=}1\text{ square yard} \\ \text{Therefore:} \\ 1,240,000\text{ square feet}=\frac{1,240,000}{9}\text{ square yard} \\ \approx137777\text{ square yards} \end{gathered}[/tex]Therefore, the closest approximation of the area in square yards is 138,000 square yards.
help me with this simple math18. look for this simple math riddle1+4=52+5=123+6=218+11=?I'm stuck here when 8+11
Answers
Given,
The mathematical expressions are
1+4=5
2+5=12
3+6=21
8+11=?
The pattern of the expression is,
[tex]\begin{gathered} 1+1\times4=5 \\ 2+2\times5=12 \\ 3+3\times6=21 \end{gathered}[/tex]Similarly,
[tex]8+8\times11=96[/tex]Hence, the value is 96.
Calculate the area of each shape. Remember that the area of a triangle is: A= 1/2bh, and thearea of a rectangle is: A=bh1)2)E.dLaWG3)4)
Answers
The area of the (1)triangle is 1 square units and the area of the rectangle(5) is 24 square units,
Given area of a triangle is = 1/2 × b × h (b = base , h = height)
1) now from the figure we can see that the base of the triangle is 1 units and the height is 2 units,
∴area = 1/2 ×1 × 2 = 1 square units
2) now from the figure we can see that the base of the triangle is 2 units and the height is 4 units,
∴area = 1/2 ×2 × 4 = 4 square units
3) now from the figure we can see that the base of the triangle is 2 units and the height is 3 units,
∴area = 1/2 ×2 × 3 = 3 square units
4) now from the figure we can see that the base of the triangle is 3 units and the height is 2 units,
∴area = 1/2 ×3 × 2 = 3 square units
5) now from the figure we can see that the base of the rectangle is 6 units and the height is 4 units,
∴area of rectangle = b × h = 6 × 4 = 24 square units
6) now from the figure we can see that the base of the rectangle is 3 units and the height is 9 units,
∴area of rectangle = b × h = 3 × 9 = 27 square units
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O.
O
45
39
IS
15
6 2
If Alm and mz6= 4x - 15 and m₂7 = x + 30, then mz6=
35
3
8
7
m
Answers
In the given figure, the measure of angle ∠6 is (B) 45°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.
The vertex of an angle is the location where two points come together.
The Latin word "angulus," which means "corner," is where the term "angle" originates.
So, the measure of angle 6:
We know that
∠6 = 4x - 15
∠7 = x + 30
We can easily tell while looking at the figure that ∠7 and ∠6 are alternate angles which means they are equal.
So, we can write this is:
4x - 15 = x + 30
3x = 45
x = 15
Now, substitute x = 15 in 4x - 15:
4x - 15
60 - 15
45
Therefore, in the given figure, the measure of angle ∠6 is (B) 45°.
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Suppose a jar contains 6 red marbles and 27 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answers
SOLUTION
Now the jar contains 6 red marbles and 27 blue marbles
Total number of marbles is
[tex]6+27=33\text{ marbles }[/tex]Now taking two red marbles at random means the first marble is red and the second marble is red.
Probability that the first marble is red is
[tex]\begin{gathered} =\frac{\text{ number of red marbles }}{\text{ total number of marbles}} \\ =\frac{6}{33} \end{gathered}[/tex]After taking the first red marble, we will have 5 red marbles remaining and a total of 32 marbles remaining
So probability of picking the second marble is
[tex]\begin{gathered} =\frac{\text{ number of red marbles remaining }}{\text{total number of marbles remaining }} \\ =\frac{5}{32} \end{gathered}[/tex]So probability both marbles are red means the first is red and the second is red.
And here means we have to multiply, this becomes
[tex]\begin{gathered} \frac{6}{33}\times\frac{5}{32} \\ =\frac{5}{176} \end{gathered}[/tex]Hence the answer is
[tex]\frac{5}{176}[/tex]The volume of a cube is 27000 cubic inches. What is the length of one side?
Answers
Given:
Volume of a cube = 27,000 in^3
(Note: A cube has equal sides)
The volume of a cube = a^3
So,
[tex]\begin{gathered} 27000=a^3 \\ \sqrt[3]{27000}\text{ = a} \\ a\text{ = 30 in.} \end{gathered}[/tex]Therefore, the lenght of one side is 30 inches.
I keep get 35 and it wrong? Can you please help me ?
Answers
Given: 7 different jellybeans
To Determine: How many ways the 7 different jellybeans can be lined up in a row of 3
Solution
We are considering an arrangement, so we would be using the permutation formula
The permuation formula is as shown below
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]Applying the formula above to the given as shown below
[tex]\begin{gathered} _7P_3=\frac{7!}{(7-3)!} \\ _7P_3=\frac{7\times6\times5\times4!}{4!} \\ _7P_3=7\times6\times5=210 \end{gathered}[/tex]Hence, the different ways 7 different jellybeans be lined up in a row of 3 is 210ways
Factor this question Q3+125
Answers
write 125 as a power in base 5
[tex]q^3+5^3[/tex]then, apply the rule for the addition of cubes
[tex]\begin{gathered} a^3+b^3=(a+b)\cdot(a^2-a\cdot b+b^2) \\ \text{then, } \\ q^3+5^3=(q+5)\cdot(q^2-5x+5^2) \\ q^3+5^3=(q+5)\cdot(q^2-5x+25) \end{gathered}[/tex]Addison Stinson
Axis of Symmetry and Vertex (with Formula)
Nov 15, 8:00:24 PM
Find the equation of the axis of symmetry of the following parabola algebraically.
y = -2x² + 8x + 6
Answer:
?
Submit Answer
attempt 1 out of 2
Answers
Focus: (2, 111/8)
Axis of Symmetry: x=2
Directrix: y= 113/8
X= 0 1 2 3 4
Y= 6 12 14 12 6
I hoped this worked
2. Kiran is spending $12 on games and rides at another carnival, where a game costs $0.25 and a ride costs $1. Which graph represents therelationship between the quantities in this situation? Explain how you know.
Answers
Explanation: The graph represents the relation between how many dollars were spent on rides and games at the same time once Kiran has just $12 to spend.
First: Once Kiran has just $12 to spend we know the maximum must be 12 rides once 1 ride costs $1.
Second: Let's imagine Kiran spends all the $12 dollars in rides, it means there is nothing left for the games which means she spends $0 on games (number of games = 0).
Third: Now let's imagine Kiran spent just $10 on rides ($10 on rides = 10 rides), so she has still $2 to spend on games. Once each game costs $0.25 it means Kiran is able to pay for 8 games (2/0.25=8) this time.
Fourth: Now let's imagine Kiran spent just $8 on rides ($8 on rides = 8 rides), so she has still $4 to spend on games. Once each game costs $0.25 it means Kiran is able to pay for 16 games (4/0.25=16) this time.
Final answer: As we can see the only graph that represents the pattern represented above is the letter C.
Jessica is the secretary of the Hillside Players.They are going to put on a show at the village hall.Jessica needs to arrange 4dates in October for rehearsals
Answers
ANSWER :
EXPLANATION :
a
x + 3 = y, make x the subject of the formula 1. x = y + 3 2. x = 3y3. x = y-3 4. x=y/3PLEASE HELP ME
Answers
Make x the subject of the formula
x + 3 = y
This means you re-write the equation such that x woukd be on one side of the equation alone (usually the left side) and all other terms would be on the other side of the "equal to" sign.
[tex]\begin{gathered} x+3=y \\ \text{Subtract 3 from both sides} \\ x+3-3=y-3 \\ x+0=y-3 \\ x=y-3 \end{gathered}[/tex]The answer is x = y - 3
=Find the variance for the set of data: 26, 34, 17, 24, 24.The variance is0.
Answers
The variance is:
[tex]\sigma^2=\frac{\Sigma(x-\mu)^2}{N}[/tex]So we have 5 values, which means that N=5 and the mean is:
[tex]\mu=\frac{26+34+17+24+24}{5}=25[/tex]So the variance is 29.6.
What is the value of(-* - ) =( 4 )?-1516-516
Answers
Answer
Option B is correct.
[tex]-1\frac{5}{16}[/tex]Explanation
To answer this, we will first deal with the value in the first bracket by taking LCM
[tex]\begin{gathered} (-\frac{1}{4}-\frac{1}{2}) \\ =\frac{-1-2}{4} \\ =\frac{-3}{4} \end{gathered}[/tex]Then to solve the part with division, we know that the division involving fractions are solved by changing the division sign into multiplication sign and the fraction after the sign changes to its reciprocal or its inverse.
[tex]\begin{gathered} (-\frac{3}{4})\div\frac{4}{7} \\ =-\frac{3}{4}\times\frac{7}{4} \\ =-\frac{21}{16} \\ =-1\frac{5}{16} \end{gathered}[/tex]Hope this Helps!!!
Determine if the situation below are biased or unbiased and explain why. Two people from each 8th period class are asked what they think the theme of the next dance should be.
Answers
Given,
Two people from each 8th period class are asked what they think the theme of the next dance should be.
Required
The situation is biased and unbiased.
Here 2 students from each 8th class period is asking for dance theme.
The students are not getting equal chances.
So, the situation is unbiased.
Hence, the situation is unbiased.
I have this question and I can’t figure it out
Answers
SOLUTION:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Therefore from the question, the integers are:
[tex]-2,-1,0,2[/tex]The number line is shown below
i need help with this HW problem it is ,the length of a rectangle is 2 more thn 3 times the width.If the perimeter is 46 ,si what would the length and width be?
Answers
If w is the width of the rectangle, then, you have for the length l of the rectangle:
l = 3w + 2
take into account that the perimeter of the rectangle is 46, and the expresionf for the perimeter P is:
P = 2l + 2w
in order to determine the value of the length l, replace the expression
l = 3w + 2 into the expression for the perimeter P, then, solve for w:
P = 2(3w + 2) + 2w
P = 6w + 4 + 2w
P = 8w + 4
replace P = 46:
46 = 8w + 4
46 - 4 = 8w
42 = 8w
42/8 = w
21/4 = w
5.25 = w
replace the previous value of w into the expression l = 3w + 2
l = 3(5.25) + 2
l = 17.75
Hence, the length of the rectangle is 17.75
If beginning finished good rupees 45000 and cost of goods manufactured rupees 25,000 and ending finished goods to go to rupees 50,000 then what is the value of cost of goods sold:Answer 20000
Answers
Answer:
20000
Step-by-step explanation:
Answer:
Hello, just a slight bit confused by your phrasing?
I would love to help, I just can't seem to understand how.
Step-by-step explanation:
Just let me know, here to help!
Multiply and simplify completely: (4p + 2)(6p - 3) Show all work
Answers
(4p + 2)(6p - 3) = 4p(6p - 3) + 2(6p -3) = 24p^2 - 12p + 12p -6 = 24p^2 - 6 = 6(4p^2 -1)
[tex](4p\text{ + 2)(6p-3) = 4p(6p-3) + 2(6p-3) = }24p^2-12p+12p-6=24p^2-6=6(4p^2-1)[/tex]Answer:
[tex]6(4p^2-1)[/tex]how do u find weather the system has one solution,no solutiin,solution,infinitely many solutions
Answers
1st case: the system has one solution
For example:
Given this system:
[tex]\begin{gathered} x+y=5 \\ 2x-y=4 \\ \text{Let:} \\ x+y=5\text{ (1)} \\ 2x-y=4\text{ (2)} \\ \text{ Using elimination method:} \\ (1)+(2)\colon \\ x+2x+y-y=9 \\ 3x=9 \\ x=\frac{9}{3} \\ x=3 \\ y=5-x \\ y=5-3 \\ y=2 \end{gathered}[/tex]graphically, a system has a solution if the two lines intersect, the point of intersection is the solution.
--------------------------------------------
2nd case: the system has no solution
A system has no solution, when the lines are parallel and have different intercepts, for example:
[tex]\begin{gathered} y=2x+1 \\ y=2x-3 \end{gathered}[/tex]as you can see the lines never cross each other.
3rd case: the system has infinitely many solutions
occurs when one line is a scalar multiple of the other, in other words it is the same line. for example:
[tex]\begin{gathered} x+y=5 \\ 2x+2y=10 \end{gathered}[/tex]Solve the equation 3=4-5^3sqrtx^8
Answers
The solution of the equation is x =3.33.
What is a solution?A solution is a value assignment to an unknown variable that makes the equality of the equation true. In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown. In mathematics, solving an equation means finding its solution, which is a value (number, function, set, etc.) that satisfies the conditions specified by the equation, usually two equations separated by an equal sign. Connected. When looking for a solution, one or more variables are called unknowns. A solution is a value assignment to an unknown variable that makes the equality of the equation true.In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown.Solutions of equations are often called roots of equations and are not specifically limited to polynomial equations. The set of all solutions of an equation is the solution set.3 = 4 - 5³ × √x⁸
3 = 4 - 125 × x⁴
124 = x⁴
x = 3.33
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The solution of the equation is x =3.33.
What is a solution?A solution is a value assigned to an unknown variable that makes the equality of the equation true.In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown.In mathematics, solving an equation means finding its solution, which is a value (number, function, set, etc.) that satisfies the conditions specified by the equation, usually two equations separated by an equal sign.A solution is a value assigned to an unknown variable that makes the equality of the equation true.Solutions of equations are often called roots of equations and are not specifically limited to polynomial equations.The set of all solutions of an equation is the solution set:
3 = 4 - 5³ × √x⁸3 = 4 - 125 × x⁴124 = x⁴x = 3.33Therefore, the solution of the equation is x =3.33.
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If one zero of 5² + 13 + is the reciprocal of the other, find the value of k?
Answers
Answer:
k = 5
Explanation:
The given polynomial is
5² + 13 +
Let one of the zeros be z. Given that one of the zero is the reciprocal of the other, the reciprocal of z is 1/z. The roots are z and 1/z
The standard form of a quadratic polynomial is
ax^2 + bx + c
By comparing the polynomial expressions,
a = 5, b = 13, c = k
The product of the roots of a quadratic polynomial is c/a = k/5
Thus,
1/z * z = k/5
1 = k/5
By cross multiplying,
k = 5
5. If the area of a parallelogram is 456 cm2 and the base is 24 cm. Find the height. Height = 1.
Answers
The area of a parallelogram is computed as follows:
A = base*height
Substituting with A = 456, and base = 24,
456 = 24*height
456/24 = height
19 cm = height
4. A field mouse hops along a parabolic path given by y=-0.2x^2+1.3x where x is the mouse's horizontal position (in feet) and y is the corresponding height (in feet).
Answers
Given that A field mouse hops along a parabolic path given by
[tex]y=-0.2x^2+1.3x[/tex]To find how far does the mouse jump, substitute with y = 0 and solve for x
so,
[tex]\begin{gathered} y=0 \\ -0.2x^2+1.3x=0 \\ x(-0.2x+1.3)=0 \\ x=0 \\ -0.2x+1.3=0\rightarrow x=\frac{1.3}{0.2}=6.5 \end{gathered}[/tex]So, the midpoint of the parabola will be:
[tex]x_m=\frac{6.5}{2}=3.25[/tex]so, substitute with the last value to find the highest point:
[tex]y=-0.2\cdot3.25^2+1.3\cdot3.25=2.1125[/tex]so, the answer will be y = 2.1125
This means the mouse can jump to 2.1125 feet
Also, the highest value of the bath will be 6.5 feet
Part B:
Can the mouse jump over 3 feet?
As the highest point is 2.1125 feet, the mouse can not jump over 3 feet.
Solve the system using substitution. You can eliminate the decimals if you like, but you don’t have to. The solution will be the same in either case. {0.45x + 0.10y = 4.30 y = 22-x (x,y)= (_, _)
Answers
SOLUTION:
Case: System of equations
Method:
[tex]\begin{gathered} 0.45x+0.10y=4.30....(1) \\ y=22-x....(2) \\ Substitute\text{ }y=22-x\text{ }into\text{ }eqn(1) \\ 0.45x+0.10y=4.30 \\ 0.45x+0.10(22-x)=4.30. \\ 0.45x+2.2-0.1x=4.30 \\ 0.45x-0.1x=4.3-2.2 \\ 0.35x=2.1 \\ x=\frac{2.1}{0.35} \\ x=\frac{210}{35} \\ x=6 \end{gathered}[/tex]Put x = 6 in y= 22 -x
[tex]\begin{gathered} y=22-x \\ y=22-6 \\ y=16 \end{gathered}[/tex]Final answer:
(x,y) = (6, 16)
how do you write 7,500,000,000,000,000,000 in scientific notation
Answers
7,500,000,000,000,000,000
In scientific notation, the 10 raised to a power having put the number to standard form
7,500,000,000,000,000,000
= 7.5 * 10^18