Answer:
[tex]\large\boxed{(x+y)^2:(x-y)^2=49}[/tex]
Step-by-step explanation:
[tex]3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=\dfrac{y}{3}\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=\dfrac{7y}{3}\qquad(**)\\------------------[/tex]
[tex](x+y)^2:(x-y)^2=\dfrac{(x+y)^2}{(x-y)^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x+y}{x-y}\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(\dfrac{\frac{7y}{3}}{\frac{y}{3}}\right)^2=\left(\dfrac{7y}{3}\cdot\dfrac{3}{y}\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49[/tex]
Which of the following rational functions is graphed below?
Answer:
c)
[tex]f(x)=\frac{1}{x(x+4)}[/tex]
Step-by-step explanation:
Hi there!
This is a Rational Function. The process of graphing it takes a lot more hard work than graphing other functions like linear, quadratic, modulus, and so on.
Here a list on how to proceed
First
1) Find the point of intersections by calculating the zeros of the function on the Numerator. In this case, we just have a 1 on top, so our graph won't intercept x-axis.
2) Calculate the vertical asymptotes by calculating the zeros of the function in the denominator, x²+4x=0 S=(0,-4) on green on the graph below.
3) Construct the table of values for x, and y
4) Trace the graph
By analyzing the asymptotes on the graph, we conclude that the correct option is C.
How to determine the rational function graphed?
To do it, we need to see at which x-values we have asymptotes. These are the values of x where the denominator becomes equal to zero.
Here we can see that we have asymptotes at:
x = 0 and x = -4
Then the denominator must be a polynomial with roots at x = 0 and x = -4, this is written as:
(x - 0)*(x - (-4)) = x*(x + 4)
So the rational function is something like:
[tex]f(x) = \frac{1}{x*(x + 4)}[/tex]
So the correct option is C.
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Study the triangle. What can you conclude about the angle measures? The angle measures are 30°, 60°, and 90°. The angle measures are 45°, 45°, and 90°. The triangle has a 90° angle, but the other angle measures cannot be determined.
Answer:
A. The angle measures are 30°, 60°, and 90°.
on edge
Step-by-step explanation:
If the question provides the angles of a triangle as 30°, 60°, and 90°, or 45°, 45°, and 90°, we are dealing with a right triangle. Depending on the measures of the angles, the triangle can be classified as either a 30-60-90 triangle or a 45-45-90 isosceles right triangle. Without sufficient information, the exact measures of the angles cannot be determined.
Explanation:When considering a triangle with angle measures provided as options, we recall the fundamental property that the sum of internal angles in any triangle is 180 degrees. The question presents three possible sets of angle measures:
30°, 60°, and 90°45°, 45°, and 90°A 90° angle, with unspecified other anglesBoth of the first two options include a 90° angle, indicating that we are dealing with a right triangle. Right triangles have specific properties and can be classified as either 30-60-90 or 45-45-90 triangles, depending on the measures of the other two angles. A 30-60-90 triangle has angles in the ratio of 1:2:√3, and a 45-45-90 triangle, also called an isosceles right triangle, has two angles of 45° each. The third option implies insufficient information to determine the exact measures of all angles.
The vertices of a polygon ABCD is A (1, 2), B (1,4), C(2,6), and D (5, 4). The polygon is dilated by a scale factor 3. Find the
coordinates of the dilated polygon...
If polygon ABCD with vertices A (1, 2), B (1,4), C(2,6), and D (5, 4) is dilated by a factor 3, the coordinates of the dilated polygon are A' (3, 6), B' (3, 12), C' (6, 18), and D' (15, 12).
Explanation:When a polygon is dilated by a scale factor, all the coordinates of its vertices are multiplied by that scale factor. In this case, the scale factor is 3. Thus, we should multiply the x and y coordinates of each vertex by 3.
Let's calculate:
Vertex A (1, 2) dilated by scale factor 3 becomes A' (1*3, 2*3) => A' (3, 6)Vertex B (1,4) becomes B' (1*3, 4*3) => B' (3, 12)Vertex C (2,6) becomes C' (2*3, 6*3) => C' (6, 18)Vertex D (5, 4) becomes D' (5*3, 4*3) => D' (15, 12)So, the coordinates of the dilated polygon ABCD are A' (3, 6), B' (3, 12), C' (6, 18), and D' (15, 12).
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subtract
4x^2-5x + 1
(2x^2+9x-6)
Answer:
[tex]\large\boxed{2x^2-14x+7}[/tex]
Step-by-step explanation:
[tex](4x^2-5x + 1)-(2x^2+9x-6)\\\\=4x^2-5x+1-2x^2-9x-(-6)\\\\=4x^2-5x+1-2x^2-9x+6\qquad\text{combine like terms}\\\\=(4x^2-2x^2)+(-5x-9x)+(1+6)\\\\=2x^2-14x+7[/tex]
Answer:
The answer is option B. which is 2x^2 - 14 + 7.
Remember to reverse the signs.
Solve for x: −7 < x − 1 < 8
Answer:
−6 < x < 9
Step-by-step explanation:
−7 < x − 1 < 8
Add 1 to all sides
−7+1 < x − 1+1 < 8+1
−6 < x < 9
Answer: [tex]-6<x<9[/tex]
Step-by-step explanation:
You have the following expression provided in the exercise:
[tex]-7 < x - 1 < 8[/tex]
Then, in this case, in order to solve the expression, it is necessary to add 1 to both sides.
Therefore, applying the procedure mentioned before, you get that the solution is the following:
[tex]-7 < x - 1 < 8\\\\-7 +(1)< x < 8+(1)\\\\-6<x<9[/tex]
Which of the following is a polynomial function in standard form with zeros at –6, 2, and 5?
f(x) = (x + 6)(x – 2)(x – 5)
f(x) = x3 + x2 – 32x – 60
f(x) = x3 – x2 – 32x + 60
f(x) = (x – 6)(x + 2)(x + 5)
Answer:
Option C is correct.
Step-by-step explanation:
We need to find the polynomial function in standard form with zeros at –6, 2, and 5
If a is a zero of polynomial then x-a is the factor of polynomial
So, (x+6)(x-2)(x-5) are factors of polynomial.
Multiplying these factors to find the standard polynomial function
(x+6)(x-2)(x-5)
We need to solve this:
(x+6)(x^2-5x-2x+10)
(x+6)(x^2-7x+10)
x^3-7x^2+10x+6x^2-42x+60
x^3-7x^2+6x^2+10x-42x+60
x^3-x^2-32x+60
So, Option C f(x) = x3 – x2 – 32x + 60 is correct.
Answer:
option A is correct
Step-by-step explanation:
gradpoint
1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the account be worth in 20 years? What if the deposit were compounded monthly with simple interest? Could you see the situation in a graph? From what point one is better than the other?
Answer:
Part A) [tex]\$42,888.48[/tex]
Part B) [tex]A=\$22,304[/tex]
Part C) The graph in the attached figure
Step-by-step explanation:
Part A) What will the account be worth in 20 years?
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12[/tex]
substitute in the formula above
[tex]A=8,500(1+\frac{0.0812}{12})^{12*20}[/tex]
[tex]A=8,500(1.0068)^{240}[/tex]
[tex]A=\$42,888.48[/tex]
Part B) What if the deposit were compounded monthly with simple interest?
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=20\ years\\ P=\$8,500\\r=0.0812[/tex]
substitute in the formula above
[tex]A=8,500(1+0.0812*20)[/tex]
[tex]A=\$22,304[/tex]
Part C) Could you see the situation in a graph? From what point one is better than the other?
Convert the equations in function notation
[tex]A(t)=8,500(1.0068)^{12t}[/tex] ------> equation A
[tex]A(t)=8,500(1+0.0812t)[/tex] -----> equation B
using a graphing tool
see the attached figure
Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.
The retirement account will be worth $27,627.24 after 20 years with compound interest and $23,180 with simple interest. Compound interest grows at a faster rate and becomes better than simple interest when the compounding periods are more frequent.
Explanation:To calculate the value of the retirement account after 20 years with compound interest, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal deposit, r is the interest rate, n is the number of times compounded per year, and t is the number of years. In this case, P = $8,500, r = 8.12%, n = 12 (monthly compounding), and t = 20. Plugging in these values, we get A = $8,500(1 + 0.0812/12)^(12*20) = $27,627.24.
If the deposit were compounded monthly with simple interest, we can use the formula A = P + (P*r*t), where A is the final amount, P is the principal deposit, r is the interest rate, and t is the number of years. In this case, P = $8,500, r = 8.12%, and t = 20. Plugging in these values, we get A = $8,500 + ($8,500 * 0.0812 * 20) = $23,180.
To compare the two situations on a graph, we can plot the value of the retirement account over time for both compound and simple interest. We would see that the compound interest account grows at a faster rate and reaches a higher value compared to the simple interest account. Compound interest becomes better than simple interest when the compounding periods are more frequent, as it allows the interest to be reinvested more often and generate additional earnings.
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if u=1+3 i and v=-2-i what is u+v
The answer is:
[tex]u+v=-1+2i[/tex]
Why?To solve the problem, we just need to consider that the variable "u" and "v" represents different expressions, and then, perform the operation and add the like terms.
We must remember that the like terms are the terms that share the same variable and the same exponent.
We have that:
[tex]u=1+3i\\v=-2-i[/tex]
So, calculating we have:
[tex]u+v=(1+3i)+(-2-i)=(1-2)+(3i-i)=-1+2i[/tex]
Hence, we have that:
[tex]u+v=-1+2i[/tex]
Have a nice day!
a = 310 rounded to the nearest 10
b = 66.1 rounded to 1 DP
Find the minimum (to 2 DP) of a÷b
To find the minimum of a divided by b, round a and b and then divide.
Explanation:To find the minimum of a divided by b, we need to divide the rounded values of a and b. First, round a to the nearest 10, which is 310. Next, round b to 1 decimal place, which is 66.1. Now divide 310 by 66.1 to get the minimum value. The result, rounded to 2 decimal places, is 4.69.
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Select the polynomial that is a perfect square trinomial.
36x2 − 4x + 16
16x2 − 8x + 36
25x2 + 9x + 4
4x2 + 20x + 25
Answer:
Option D. It's a perfect square trinomial.
Step-by-step explanation:
(a) 36x² - 4x + 16
= (6x)² - 2(2x) + (4)²
It's not a perfect square trinomial
(b) 16x² - 8x + 36
= (4x)² - 2x(4x) + (6)²
It's not a perfect square trinomial
(c) 25x² + 9x + 4
= (5x)² + 2[tex](\frac{9}{2}x)[/tex] + (2)²
It's not a perfect square trinomial
(d) 4x² + 20x + 25
= (2x)² + 2(10x) + (5)²
= (2x+5)²
It's a perfect square trinomial.
Answer:
the answer is d indeed pls like it up and give 5 stars
Step-by-step explanation:
Given the frequency table, what percentage of the students in grades 9–10 like country music? Round to the nearest whole percent.
Band Preference for School Dance
Rap Rock Country Row totals
Grades 9–10 40 30 55 125
Grades 11–12 60 25 35 120
Column totals 100 55 90 245
a. 22%
b.44%
c.55%
d.61%
Answer:
b: 44%
Step-by-step explanation:
From grades 9-10 there are 55 students who like country music.
While there are 125 grades 9-10 students in total.
This gives us a percentage of (55/125) *100% = 44%
Answer:
b.44%
Step-by-step explanation:
44% of the students in grades 9–10 like country music.
Round to the nearest whole percent.
(55/125)
100% = 44%
This kind of transformation can change the _________.
A. The lengths of some or all of the sides
B. The area of the shape
C. Both A and B
Answer:
The correct answer option is C. Both A and B.
Step-by-step explanation:
We are given a figure of a rectangle which when transformed changes it length of two sides AB and DC to AB' and DC'.
By looking at the figure, we can conclude that the transformation has changed the lengths of some sides of the given figure as well as changed the area of the figure.
Therefore, the correct answer option is C.
9m=4.5? 3v=-105? 17m=85? please help me:)
please show work:
please show work:
please show work:
thank you
9m = 4.5
divide by 9 for 9m and 4.5
9m/9= 4.5/9
m= 0.5
3v= -105
divide by 3 for 3v and -105
3v/3=- 105/3
v= -35
17m = 85
divide by 17 for 17m and 85
17m/17= 85/17
m= 5
Answers: 0.5,-35 and 5
if 8a + 7b + c = 9, what is -6c - 48a - 42b
Answer:
-54
Step-by-step explanation:
8a + 7b + c = 9
We want -6c, but we have c in the equation so multiply by -6
-6(8a + 7b + c) = 9*-6
-48a -42b -6c = -54
Rearranging the equation
-6c - 48a - 42b = -54
RS is the diameter of circle T. Point R is located at (11, 10) and point S is located at (5, 4). What are the coordinates of the center of this circle?
ANSWER
[tex]( 8 ,7 )[/tex]
EXPLANATION
Use the midpoint formula to find the center of this circle.
The midpoint formula is
[tex]( \frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
The reason is that, the midpoint of the diameter RS gives the center of the circle.
Point R is located at (11, 10) and point S is located at (5, 4).
We plug in the values to get:
[tex]( \frac{11+5}{2} ,\frac{4+10}{2} )[/tex]
[tex]( \frac{16}{2} ,\frac{14}{2} )[/tex]
[tex]( 8 ,7 )[/tex]
Answer:
(8,7)
Step-by-step explanation:
I got it correct on founders edtell
II. Using Radians to Measure Arcs and Angles
A. Convert each radian measure to degrees
2."
4. 18
B. Convert each degree measure to radians
1. 100°
3. 30°
5. 10
C. Determine each arc length
Carnegie Learning, Inc.
1. The radius of a circle is 1 centimeter. What is
the length of an arc intercepted by an angle
of radians?
2. The radius of a circle is 4 inches. What is
the length of an arc intercepted by an angle
of radians?
4 in.
1 cm
Two fair dice are rolled 4 times and the sum of the numbers that come up are recorded. Find the probability of these events. A) the sun is 5 on each of the four rolls. B) the sun is 5 exactly three times in the four rolls.
Answer:
See below in bold.
Step-by-step explanation:
A. On one roll the possible ways to get a sum of 5 is (2,3, ) and (4, 1).
There are 36 possible outcomes from the one roll of the 2 dice.
So the probability of getting a sum of 5 on one roll = 2/36 = 1/18.
So the probability of 5 on 4 rolls = (1/18)^4
= 1/104976.
B.
The probability of the first 3 rolls being a 5 and the last one being not 5
= (1/18)^3 * (17/18)
= 17/104976
There are 4 ways to pick 3 out of 4 so the required probability
= 4 * 17/104976
= 68/104976.
Final answer:
The detailed answer explains the probability of rolling specific sums with two fair dice in four rolls, covering events A and B.
Explanation:
The Probability of Rolling Sums with Two Fair Dice
For event A, the probability of getting a sum of 5 on each of the four rolls is (4/36)⁴.
For event B, the probability of getting a sum of 5 exactly three times in the four rolls is 4*(4/36)³*(32/36).
Use parallelogram ABCD What are the values of X and
y?
Based on parallelogram ABCD shown below, the values of x and y include;
x = 17 units.
y = 10 units.
In Euclidean Geometry, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that has two equal and parallel opposite sides.
Generally speaking, a parallelogram has both pairs of opposite sides parallel to each other and the opposite angles (vertical angles) are congruent:
AB ║ CD
AB = CD
3x - 9 = 42
3x = 42 + 9
3x = 51
x = 51/3
x = 17 units.
Next, we would determine the value of y as follows;
4y - 3 = 37
4y = 37 + 3
4y = 40
y = 40/4
y = 10 units.
Complete Question:
Use parallelogram ABCD. What are the values of x and y?
On Tuesday you use your debit card for 3 separate transactions, $5 each, and pay 2 ills for $20 each from your checking account. If you had a starting balance of $50, what is the ending balance in your checking account?
Answer: -5
Step-by-step explanation:
You start with 50.
Then subtract the 3 transactions: 50-(3×5)=50-15=35
Then you subtract the 2 ills: 35-(2×20)=35-40=-5
And that's how get the answer!
If f(x) = 3* + 10 and g(x) = 2x - 4, find (f - g)(x).
Answer:
(f - g)(x) = 3ˣ - 2x + 14Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
We have f(x) = 3ˣ + 10 and g(x) = 2x - 4. Substitute:
(f - g)(x) = (3ˣ + 10) - (2x - 4) = 3ˣ + 10 - 2x - (-4) = 3ˣ + 10 - 2x + 4
(f - g)(x) = 3ˣ - 2x + 14
Determine the input that would give an output value of 2/3
Answer:
x = 19
Step-by-step explanation:
Question: find x such that f(x) = 2/3
Given f(x) = (-1/3) x + 7
equate the value of f(x) to be 2/3
hence,
(2/3) = (-1/3)x + 7 (multiply both sides by 3)
(3) (2/3) = (3) (-1/3)x + (3) 7
2 = -x + 21
x = 21 - 2
x = 19
So to get the output value 2/3 we will input x = 19
What is a function?A mathematical relationship from a set of inputs to a set of outputs is called a function.
What are equations?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
How to find the input that would give an output value of 2/3 ?The function used here is f(x) = [tex]-\frac{x}{3} + 7[/tex]Clearly, all the values of x and f(x) are satisfying it.
Now, the output is given as 2/3.
So, we can write,
[tex]\frac{2}{3} = -\frac{x}{3} + 7[/tex]
⇒ [tex]\frac{2}{3}-7 = -\frac{x}{3}[/tex] ( changing the side of 7)
⇒ [tex]-\frac{19}{3} = - \frac{x}{3}[/tex]
⇒ x = 19
So to get the output value 2/3 we will input x = 19
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What is the length of the hypotenuse of the triangle below?
Answer:
C
Step-by-step explanation:
Since the triangle is right with hypotenuse h
Use Pythagoras' identity to solve for h
The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
h² = ( 5[tex]\sqrt{2}[/tex] )² + ( 5[tex]\sqrt{2}[/tex] )²
= 50 + 5 0 = 100
Take the square root of both sides
h = [tex]\sqrt{100}[/tex] = 10 → C
In △ABC, m∠A=16°, m∠B=49°, and a=4. Find c to the nearest tenth.
Answer:
c=13.2 units
Step-by-step explanation:
step 1
Find the measure of angle C
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
A+B+C=180°
substitute the given values
16°+49°+C=180°
65°+C=180°
C=180°-65°=115°
step 2
Find the measure of c
Applying the law of sines
c/sin(C)=a/sin(A)
substitute the given values and solve for c
c/sin(115°)=4/sin(16°)
c=4(sin(115°))/sin(16°)
c=13.2 units
What is the center of the circle shown below?
Answer:
B is the center of the circle.
Step-by-step explanation:
Given is a circle in the picture.
A is the point on the circle.
Y is another point on the circle
AY is hence the chord
B is equidistant from the circumference
B is the center of the circle.
Point B is established as the center of the circle because it is equidistant from the circumference. This property defines B as the central point from which all points on the circle are equally distant, confirming its role as the circle's center.
In the given scenario, the information provided indicates that point B is equidistant from the circumference of the circle. This property characterizes point B as the center of the circle.
To articulate this differently, since B is equidistant from any point on the circle, it serves as the central point from which all points on the circle are equally distant.
Therefore, B is unequivocally identified as the center of the circle. This conclusion is drawn from the fact that the center of a circle possesses the unique property of being equidistant from all points on its circumference.
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Nick is researching a possible link between cosmetic surgery and depression.
Which of the following would likely be a credible source for him to use?
O
A. A blog written by a popular actress
O
B. An online photo gallery of before and after pictures
O
c. A medical journal published in 1982
O
D. A news interview with a psychologist
Answer:
Step-by-step explanation:So to me I would trust the medical journal published in 1982. Back then they were more people that studied those kind of things. And back then there was like people finding out different types of plants and medical resources. (hope this helps you)..:)
Answer:
The correct answer will be option- C
Step-by-step explanation:
A research journal is considered as the reliable or credible source of the research as the research articles published in the journal are always verified by the peer-group which includes the scientists.
The peer-group verifies the credibility of the research paper by checking and correcting the steps of the scientific method and checking the eligibility of the collected data and the conclusions drawn from it.
Therefore, Nick should use a medical journal published in 1982 as the credible source for him and thus option- C is the correct answer.
Cecilia simplified an expression. Her work is shown below.
Where did Cecilia make her first mistake?
Answer:
Option B.
Step-by-step explanation:
The given expression is ([tex]6\frac{1}{2}+2\frac{3}{4}-1.5\times (\frac{4.5}{0.5})[/tex]
Since [tex]6\frac{1}{2}+2\frac{3}{4}=8+\frac{1}{2}+\frac{3}{4}[/tex]
= 8 + 1 + [tex]\frac{1}{4}[/tex]
= [tex]9\frac{1}{4}[/tex]
Step 1 [tex]9\frac{1}{4}[/tex] - 1.5(4.5÷0.5)
Step 2 9.25 - 1.5(9)
Step 3 9.25 - 13.5
Step 4 (- 4.25)
Cecilia did her first mistake in step 2.
Option B is the answer.
Answer:
Step 2 is the answer.
Match the following items.
1. Commutative property of adfition
2. Multiplicative inverse
3. Associative property of addition
4. Distributive property
5. Additive identity
Answer:
1-------------- Commutative property of addition
You can commute the terms in a addition, so doesn't matter wat therm goes left or right,
2 ------------ is multiplicative inverse
Each number X has another number Y so X*Y=1
3-------------- Associative property of addition
When you have parentheses in this type of addition, the order in what you do te equation doesn't matter
4 ------------- distributive property
You can distribute the multiplication here, so x(a +b) = x*a + x*b
5 ------------ Additive identity
There exist one number a so for every number x, x+a = x, and the number a is te zero.
A baseball player has 546 plate appearances in his first year, 627 plate appearances in his second year, and 712 plate appearances in his third year. How many plate appearances has the player had in three years?
Answer:
1885 plate appearances
Step-by-step explanation:
546 plate appearances + 627 plate appearances + 712 plate appearances = 1885 plate appearances
Answer:
1885
Step-by-step explanation:
546+627+712=1885
Given the two sets:
A = {1, 2, 3}
B = {3, 2, 1}
Which of the following is a true statement?
4 ∈ B
A ⊆ B
A is an infinite set
∅ ∉ B
Answer:
Step-by-step explanation:
B and c
The correct statement is that set A is a subset of set B, as they contain exactly the same elements. The statements about set B containing the number 4 and set A being infinite are false, while the empty set is a subset of every set, including B.
The correct statement regarding the sets A = {1, 2, 3} and B = {3, 2, 1} is A ⊆ B. This is because every element in set A is also in set B, regardless of the order the elements are listed. Sets are collections of distinct objects and their definition does not depend on the order of the elements. Therefore, A and B have exactly the same members, making them equal sets, and conversely, every set is a subset of itself. This can also be seen as both sets having the same cardinality, which is the number of members in a set, and for both A and B, this is 3.
As for the other statements, the number 4 is not an element of set B (4 ∈ B), the set A is not infinite since it has a finite cardinality of 3 (A is not an infinite set), and the empty set is actually a subset of every set, including B ⊂ \⊆cannot be true.
40 POINTS!!!!
graph the function g(x) = x3 − x2 − 4x + 4. (an actual graph that you can attach)
Answer:
see below
Step-by-step explanation:
g(x) = x^3 − x^2 − 4x + 4
We know the graph will have up to 3 zero's because it is a cubic
g(x) = x^3 − x^2 − 4^x + 4
I will factor by grouping, taking an x^2 from the first 2 terms and -4 from the last 2 terms
g(x)= x^2(x-1) -4(x-1)
Now factor out x-1
g(x)= (x-1)(x^2 -4)
We can factor the (x^2-4) as a difference of squares
g(x) = (x-1) (x-2)(x+2)
Using the zero product property
0= (x-1) (x-2)(x+2)
x-1 =0 x-2 =0 x+2=0
We have zeros at x=1 x=2 and x=-2
Then we can plot points to determine where the function is between the points We will pick negative infinity 0 1.5 and infinity
at g(-inf) = -inf because x^3 dominates and that goes to -infinity
at g(0) = 0+000+4 =4
at g(1.5) =-.875
at g(inf)=because x^3 dominates and that goes to infinity