the graph below represents y=x. If the slope of the above equation is changed from 1 to 4 which graph best represents the new equation
Answers
Answer:
The graph of the new equation is shown in figure 2.
Step-by-step explanation:
Consider the provided function.
[tex]y=x[/tex]
The graph of the above function is shown in figure 1.
The slope intercept form is:
[tex]y=mx+c[/tex]
Where m is the slope and c is the y intercept.
Now, compare the slope intercept form with the provided function.
By the comparison it can be conclude that the slope of the provided function is 1 and y intercept is 0. As the coefficient of x is 1.
We need to change the slope from 1 to 4.
So change the coefficient of x from 1 to 4.
Thus, the required function is [tex]y=4x[/tex]
The graph of the new equation is shown in figure 2.
Related Questions
A culture of 2.4×1011 bacteria is in petri dish A. A culture of 8×109 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
Answers
2.4/8=0.3
10^11-9=10^2
0.3•10^2
(This is not in scientific notation 1 or 1 to 9)
Move the decimal right once and subtract one from the exponent.
3•10^1
Standard notation is 30.
Hoped I helped!
The number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
What is bacteria?Bacteria are small single-celled organisms. Bacteria are found almost everywhere on Earth and are vital to the planet's ecosystems.
Given is a culture of 2.4 × 10¹¹ bacteria is in petri dish 'A' and a culture of
8 × 10⁹ bacteria is in petri dish B.
Number of bacteria's in petri dish A = n[A] = 2.4 × 10¹¹ bacteria
Number of bacteria's in petri dish B = n[B] = 8 × 10⁹ bacteria
For comparison, lets assume that -
k = n[A]/n[B]
k = 2.4 × 10¹¹ / 8 × 10⁹
k = 240 / 8
k = 30
n[A] = 30 n[B]
Therefore, the number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
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How do you write an equation in slope intercept form when the slope is undefined?
Answers
When the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.
When the slope of a line is undefined, it means that the line is vertical. In the slope-intercept form of a linear equation, y = mx + b, m represents the slope of the line. However, when the slope is undefined (infinite), you cannot express it as a finite value m.
For a vertical line passing through a point (a, b), the equation can be written as: x = a.
In this case, there is no slope term, because the line is vertical and does not have a slope in the traditional sense. Instead, the equation simply states that for all points on the line, the x coordinate remains constant at a.
Thus, when the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.
H E L P PLEASE COME ON WHY WONT ANYONE HELP
Corey deposited $1,500 in a savings account that earns simple interest at 5.75%. What is the balance in his account at the beginning of the third quarter?
A. $1,556.78
B. $1,528.13
C. $1,543.13
D. $1,612.50
Please explain your answer CLEARLY so i can use the principles for future reference. Thanks!
Answers
At the beginning of the third quarter means at the end of two quarters which is 6 months
So the formula is
A=p (1+rt)
A future value?
P present value 1500
R interest rate 0.0575
T time 6 months/12
A=1,500×(1+0.0575×(6÷12))
A=1,543.13
The answer is c
Hope it helps!
What is the product of −2 1/4 and 2 1/2?
Answers
product means multiply
-2 1/4 times 2 1/2:
-2 1/4 = -9/4
2 1/2 = 5/2
-9/4 x 5/2 = -45/8 = -5 5/8
~thanks for letting me answer your questions! x lots of love, lilly <3
Which of the following is a solution of x2 − 6x = –22?
A. -6-i√52
B. -6+i√13
C. 3-i√13
D. -3+i√52
Answers
For this problem, I'll be completing the square.
x² - 6x = -22
Since the constant has been moved to the right side already, we can move on to the next step which is adding (b/2)² to both sides of the equation.
x² - 6x + (-6/2)² = -22 + (-6/2)²
x² - 6x + 9 = -22 + 9
Factor the left side of the equation into a perfect square and simplify the right side.
(x - 3)(x - 3) = -13
Take the square of both sides.
x - 3 = ± √-13
Take out the negative from the square root as the letter "i"
x - 3 = ± i√13
Add 3 to both sides of the equation to let x be by itself.
x = 3 ± i√13
So your two roots will be:
x = 3 + i√13 and x = 3 - i√13
Solution: C. 3 - i√13
2. The coordinates of the vertices of are P(-2,5), Q(-1,1) and R(7,3) . Determine whether PQR is a right triangle. Show your work.
Answers
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 5}})\quad % (c,d) &({{ -1}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-5}{-1-(-2)}\implies \cfrac{1-5}{-1+2} \\\\\\ \cfrac{-4}{1}\impliedby\stackrel{slope~of}{PQ}[/tex]
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 1}})\quad % (c,d) &({{ 7}}\quad ,&{{ 3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{3-1}{7-(-1)}\implies \cfrac{3-1}{7+1} \\\\\\ \cfrac{2}{8}\implies \cfrac{1}{4}\impliedby \stackrel{slope~of}{QR}[/tex]
now, two lines who meet at a perpendicular angle, have a negative reciprocal slope of each other, to make it short, if you multiply their slopes, you should get -1 as the product, if they're indeed perpendicular.
[tex]\bf \stackrel{PQ}{-\cfrac{4}{1}}\cdot \stackrel{QR}{\cfrac{1}{4}}\implies -1[/tex]
low and behold, they're indeed perpendicular, thus that angle is indeed a right-angle.
What is the maximum product of two numbers whose sum is 13? what numbers yield this product?
Answers
Which of these triangle pairs can be mapped to each other using a single translation?
pls help need it fast
Answers
Answer:- D shows the triangle pairs which can be mapped to each other using a single translation.
Explanation:-
Translation is a rigid transformation which creates a congruent image as that of the original figure such that the distance between the each point of the original figure and the image is fixed and same.
The translation mapping is given by (x,y)→(x+h,y+k) ,where h is the distance of the x coordinate of the each point of the original figure to the image and k is the distance of the y coordinate of the each point of the original figure to the image.
In figure D we can see that the distance between each point of ΔCED is equal to the distance between each point of ΔMPN. Thus it shows the triangle pairs which can be mapped to each other using a single translation.
The Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.
Further explanation:
Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.
Explanation:
The angle MNP is equal to the angle CDE.
The side PN is equal to the side ED.
The side MN is equal to the side CD.
The translation mapping of a single translation can be expressed as follows,
[tex]\left( {x,y}\right) \Rightarrow \left({x + h,y + k} \right)[/tex]
Here, h represents the distance of translation in x-axis and k represents the distance of translation in y-axis.
In Figure 1 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 2 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 3 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 4 the triangle MNP and CDE can be mapped to each other using a translation.
Hence, the Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides.
The perimeter of an isosceles triangle is 15.6m. Find the lengths of its sides, if: The base is 3m smaller than a leg ____m, ___m, _____m
Answers
we know that
An isosceles triangle is a triangle with two equal sides and two equal angles
Let
x-------> the length of the equal sides
y-----> the length of the base
[tex]y=x-3[/tex] -----> equation A
The perimeter of an isosceles triangle is equal to
[tex]P=2x+y[/tex]
[tex]P=15.6\ m[/tex]
so
[tex]15.6=2x+y[/tex] ------> equation B
substitute equation A in equation B
[tex]15.6=2x+[x-3][/tex]
[tex]15.6=3x-3[/tex]
[tex]3x=18.6[/tex]
[tex]x=6.2\ m[/tex]
Find the value of y
[tex]y=x-3[/tex]
[tex]y=6.2-3=3.2\ m[/tex]
therefore
the answer is
The dimensions of the triangle are
[tex]leg1=6.2\ m[/tex]
[tex]leg2=6.2\ m[/tex]
[tex]base=3.2\ m[/tex]
I need help... please...
A scale drawing of a kitchen is shown below. The scale is 1 : 20.
Show your work to determine the area of the room in square feet.
Answers
so the 4X5 room is actual 4(20)X5(20)
80X100
Area = 80X100
Area = 8000 square inches.
It wants square feet though.
For that you simply divide by 144 (since there are 12 inches in a foot for length and 12 inches in a foot for width).
8000/144= 55.55 Square Feet
You could also covert inches to feet before calculating area
Remember it was 80inchesX100inches
80/12=6.66feet
100/12=8.33feet
6.66X8.33= 55.55 square feet
Works both ways.
scale of 1:20 means for every 1 inch on the drawing it is 20 inches in real life
5 inches * 20 = 100 inches = 8.33 feet
4 inches *20 = 80 inches = 6.67 feet
8.33 * 6.67 = 55.56 square feet
Susan divides the fraction 5/8 by 1/16 . Her friend Robyn divides 5/8 by 1/32 predict which person will get the greater quotient . Explain and check your prediction
Answers
So 5/8 times 16/1. 80/8. Simply to 10.
Now do the same with 5/8 and 1/32
5/8 times 32/1. 160/8. Simplify to 20.
So I good prediction would be 1/32 since you have to flip the divisor and multiply.
Answer:
Robyn will get the greater quotient
Step-by-step explanation:
Prediction: Since 1/16 >1/32
So, it will prove the smaller quotient
Susan divides the fraction 5/8 by 1/16 .
Calculation : [tex]\frac{5}{8} \div \frac{1}{16}[/tex]
[tex]\frac{\frac{5}{8}}{\frac{1}{16}}[/tex]
[tex]\frac{5}{8} \times 16[/tex]
[tex]10[/tex]
Robyn divides 5/8 by 1/32
Calculation : [tex]\frac{5}{8} \div \frac{1}{32}[/tex]
[tex]\frac{\frac{5}{8}}{\frac{1}{32}}[/tex]
[tex]\frac{5}{8} \times 32[/tex]
[tex]20[/tex]
So, The prediction is true.
Robyn will get the greater quotient
Erica has found a pair of running sneakers that she likes, costing $150. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford the sneakers?
B) 18
C) 22
D) 14
Answers
Suppose △DEF≅△MNO. Which congruency statement is true?
EF¯¯¯¯¯≅MN¯¯¯¯¯¯¯DE¯¯¯¯¯≅MN¯¯¯¯¯¯¯DF¯¯¯¯¯≅NO¯¯¯¯¯¯EF¯¯¯¯¯≅MO¯¯¯¯¯¯
Answers
△DEF≅△MNO
answer
DE≅MN
Answer:
DE≅MN
Step-by-step explanation:
We know that corresponding parts of congruent triangles are congruent (CPCTC). Using the congruence statement we can match up the corresponding sides.
From the statement, ∠D matches ∠M, ∠E matches ∠N, and ∠F matches ∠O.
We also see that DE matches MN, EF matches NO, and DF matches MO.
Thus we have that DE≅MN.
The given line segment has a midpoint at (3, 1).
What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?
y = x
y = x – 2
y = 3x
y = 3x − 8
Answers
We need to find the slope of the blue given line to determine the slope of the perpendicular bisector of this blue line.
From the graph, we see that if x increases from 2 to 4, y decreases from 4 to -2. Thus, the slope of the blue line is [-2-4] divided by 4-2, or m = -6/2, or m = -3.
The slope of the perpend. bisector of the blue line is the negative reciprocal of -3, or m= 1/3.
Let's find the slope-intercept form of this bisector. We need to determine b in y=mx+b. Referring to the midpoint of the blue line, x= 3; y= 1; and m=1/3. Then
y=mx+b becomes 1=(1/3)(3) + b. Solving for b: 1=1+b. Then b=0.
Thus, the equation of the perpendicular bisector of the blue line through (3,1) is y=mx + b, or y=(1/3)x + 0, or y=x/3.
The equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.
What is the Slope-intercept Form of an Equation?The slope-intercept form is given as, y = mx + b.
b is y-intercept, and m is the slope.
Slope = change in y/change in x.
The slopes of two lines that are perpendicular to each other are negative reciprocal of each other.
Thus, let's find the slope of the blue line:
Slope = (-2 - 4)/(4 - 2) = -3
Therefore, the slope of the line perpendicular to it would be, 1/3.
Equation of the perpendicular bisector that passes through (3, 1):
Since slope (m) is 1/3, find b by substituting m = 1/3 and (x, y) = (3, 1) into y = mx + b.
Thus:
1 = 1/3(3) + b
1 = 1 + b
1 - 1 = b
b = 0.
Substitute b = 0, and m = 1/3 into y = mx + b:
y = 1/3x + 0
y = 1/3x
Therefore, the equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.
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The bedroom of a house is 1,200 cubic meters. We know that there are 3.4 x 109 particles of dust per cubic meter. How many particles of dust are present in the bedroom of the house
Answers
To find the number of dust particles in a 1200 cubic meter bedroom with 3.4 x 10⁹ particles per cubic meter, multiply the volume by the number of particles per volume, resulting in approximately 4.08 trillion dust particles.
To calculate the number of dust particles in the bedroom, we need to multiply the volume of the bedroom by the number of dust particles per cubic meter. Given that the bedroom is 1200 cubic meters and that there are 3.4 x 10⁹ particles of dust per cubic meter, we can use the following calculation:
Number of particles = Volume of the bedroom x Number of particles per cubic meter
Number of particles = 1200 m³ x 3.4 x 10⁹ particles/m3
Number of particles = 4.08 x 10¹² particles
Therefore, there are approximately 4.08 trillion dust particles in the bedroom of the house.
to find the weight of the golden 22 karat gold object
Answers
i hope this helped and have a wonderful day filled with joy!
If ABC XYZ, mA = 50°, and mY = 70°, find mC
Answers
Final answer:
Using the properties of congruent triangles and the fact that the sum of the angles in a triangle is 180°, the measure of angle C (mC) is found to be 60°.
Explanation:
Given that triangle ABC is congruent to triangle XYZ, we know that corresponding angles of congruent triangles are equal. Since the measure of angle A (mA) is given as 50°, and in triangle XYZ, the measure of angle Y (mY) is 70°, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C (mC).
The sum of the angles in triangle ABC would be:
mA + mB + mC = 180°
50° + mB + mC = 180°
Since triangle ABC is congruent to triangle XYZ, mB will be equal to mX, which is the same as mY, that is 70°:
50° + 70° + mC = 180°
Now, we just need to subtract the sum of mA and mB from 180° to find mC:
mC = 180° - (50° + 70°)
mC = 180° - 120°
mC = 60°
In a 10 x 10 grid that represents 800, one square represents
Answers
If it is 10×10 then there is 100 squares
800÷100=8
what is the solution of sqrt(2x+4)-sqrt(x)=2 A. x = 0 B. x = 0 and x = 16 C. x = 0 and x = –16 D. x = 16 and x = –16
Answers
√(2x+4) - √(x) = 2
Write equation as
√(2x+4) = √x + 2
Square each side.
2x + 4 = x + 4√x + 4
x = 4√x
x - 4√x = 0
√x (√x - 4) = 0
Either
√x = 0 => x = 0
or
√x = 4 => x = 16
Test for extraneous solutions.
When x = 0:
√(2x+4) - √x = 2 (Correct)
When x = 16:
√(2x+4) - √x = √(36) - √(16) = 6 - 4 = 2 (Correct)
A plot of f(x) = √(2x+4) - √x - 2 = 0 confirms hat the solutions are correct.
Answer: B. x = 0 and x = 16.
what is the union of the two sets R= {10, 11, 13, 15, 17} T= {5, 7}?
Answers
union is { 5,7,10,11,13,15,17 }...and if they repeat, u would only have to write them once...although that doesn't apply in this situation...I am just letting u know
HELP NEEDED
Which system of linear inequalities is graphed? See screenshot!
Answers
u have another line that has a y int of 2....it has a slope of -1/2....it has a solid line...so there is an equal sign in the problem...it is shaded below the line...so it is less then....
y < = -1/2x + 2
1/2x + y < = 2...multiply by 2
x + 2y < = 4
so ur answer is : y > = 3x - 2 and x + 2y < = 4...the 2nd one
6+ 4/a + b/3 a=4 b=3
Answers
6+1+1=
The answer is 8.
I hope this helped! :))
If x + b > c and x > 0 have the same solutions, what is the relationship between b and c
Answers
Mr. Gonzalez earns his living as a salary plus commission employee. His annual salary is $18,000. He makes 4% commission on all of his sales. Mr. Gonzalez wants to earn $60,000 this year. If his earnings are divided evenly throughout the year, how much in monthly sales would Mr. Gonzalez need to have?
a.
$37,500
b.
$87,500
c.
$100,000
d.
$125,000
Answers
In order for Mr. Gonzalez to reach his goal of $60,000, if his base salary is $18,000 and he earns a 4% commission on sales, he would need to make about $87,500 in sales per month.
Explanation:In this question, Mr. Gonzalez has a base salary of $18,000 and wishes to earn a total of $60,000 for the year. This means he needs to earn an additional $42,000 ($60,000 - $18,000) from sales commission.
The commission rate is 4%, which means for every $100 he sells, he earns $4. Therefore, to find out how much he needs to sell to make the required commission, we require to divide the target commission by the commission percentage.
Therefore, he will need to sell $42,000 / 0.04 = $1,050,000 for the whole year. If this is divided evenly over the year for monthly targets, then it would be $1,050,000 / 12 (months), which results in approximately $87,500 per month.
So, the correct answer option should be b. $87,500 per month.
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Carrie is an American teaching English in Mexico, and she currently has 45,000 pesos in her bank account. If the exchange rate changes from 1 U.S. dollar = 12.94 Mexican pesos to 1 U.S. dollar = 13.09 Mexican pesos, what happens to the value in U.S. dollars of the money in Carrie's bank account?
Answers
Answer:
Because of change in conversion rates, the value in Carrie's account decreases by $39.85.
Step-by-step explanation:
Total money in Carrie's bank account = 45000 pesos.
If exchange rate is 1 USD = 12.94 pesos, then in dollars the money in account is :
[tex]\frac{45000}{12.94}[/tex] = $3477.588 ≈ $3477.59
If exchange rate is 1 USD = 13.09 pesos, then in dollars the money in account is :
[tex]\frac{45000}{13.09}[/tex] = $3437.738 ≈ $3437.74
Now, if the conversion rate is 12.94 pesos then the amount in dollars is more, than when the conversion rate is 13.09 pesos.
The difference is [tex]3477.59-3437.74=39.85[/tex] dollars.
So, because of change in conversion rates, the value in Carrie's account decreases by $39.85.
A round cookie cake, divided into 8 equal pieces, has a diameter of 16 inches. Marty eats one piece of cake. What is the area of the piece of cake that Marty eats? Leave your answer in terms of pi. A)4π in2 B) 8π in2 C)16π in2 D) 64π in2
Answers
What is the area of the entire cookie cake?
The area of a circle is π*r²
The diameter is 16 inches, so the radius is 8 inches.
Area = π * 8²
Area = 64 π in²
The entire cookie has an area of 64 π in².
To find the area of Marty's piece, divide this number by 8:
64 π in² ÷ 8 = 8 π in²
Answer is B
Answer:
8
Step-by-step explanation:
An apple pie uses 4 cups of apples and 3 cups of flour. An apple cobbler uses 2 cups of apples and 3 cups of flour. You have 16 cups of apples and 15 cups of flour. When you sell these at the farmers market you make $3.00 profit per apple pie and $2.00 profit per apple cobbler. Use linear programming to determine how many apple pies and how many apple cobblers you should make to maximize your profit.
1. let ×= the number of apple pies you make and y= the number of apple cobblers you make. Write an inequality to show the constraint on the amount of apples you have?
2. Write an inequality to show the constraint on the amount of flour you have .
3. Write any non negativity contraints on x and y
Answers
Given that x represents the number of apple pies that can be made and y represents the number of apple cobblers that can be made.
Given that an apple pie uses 4 cups of apples and an apple cobbler uses 2 cups of apples and there are 16 cups of apples available.
An inequality to show the constraint on the amount of apples available is given by:
4x + 2y ≤ 16
Part 2:
Given that an apple pie uses 3 cups of flour and an apple cobbler uses 3 cups of flour and there are 15 cups of flour available.
An inequality to show the constraint on the amount of flour available is given by:
3x + 3y ≤ 15
Part C:
The non negativity contraints on x and y are:
x ≥ 0 and y ≥ 0
What is the value of the expression when n=3?
–2n(5 + n – 8 – 3n)
Answers
When n=3, the value of the expression is 54.
Explanation:To find the value of the expression when n=3, we substitute n=3 into the expression: –2n(5 + n – 8 – 3n).
First, we simplify the expression:
–2n(5 + n – 8 – 3n) = –2(3)(5 + 3 – 8 – 3(3))
= –2(3)(5 + 3 – 8 – 9)
= –2(3)(-9)
= –2(-27)
= 54.
Therefore, when n=3, the value of the expression is 54.
1. State the domain of the rational function. (2 points)
f(x) = thirteen divided by quantity ten minus x.
a) All real numbers except -10 and 10
b) All real numbers except 13
c) All real numbers except 10
d) All real numbers except -13 and 13
2. State the vertical asymptote of the rational function. (2 points)
f(x) = quantity x minus six times quantity x plus six divided by quantity x squared minus nine.
a) x = 6, x = -6
b) x = 3, x = -3
c) x = -6, x = 6
d) None
3. State the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus four x minus seven divided by quantity x minus seven.
a) None
b) y = -4
c) y = 7
d) y = 6
4. State the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus eight x minus two divided by quantity x minus two.
a) None
b) y = 1
c) y = -8
d) y = 2
5. Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at
x = 2 and x = 1.
Answers
f(x) = 13 / (10-x)
The only x value that would not produce a real number for f(x) is 10, since you
cannot divide a number by zero. Answer is C
2)
F(x)
=(x-6)(x+6)/(x2 - 9)
The vertical asymptotes are x=3 and x=-3. Graph the function on a graphing
calculator to observe the behavior of the function at these points. There is
both a positive and negative vertical asymptote a both x=3 and x=-3. Keep in
mind that the denominator approaches zero at these points, and thus f(x) approaches
either positive or negative infinite, depending on whether the denominator, however small, is a positive or
negative number. Answer is B) 3, -3
3)
F(x) = (x2
+ 4x-7) / (x-7)
Although there is a vertical asymptote as x=7, there is no horizontal asymptote.
This makes sense. As X gets bigger, there is nothing to hold y back from
getting greater and greater. X2 is the dominant term, and it’s only
in the numerator. A) none
4)
(x2 +
8x -2) / (x-2)
This function is very similar in structure to the previous one. Same rules
apply. Dominant term only in the numerator means no horizontal asymptote.
A)None
5)
Our
function approaches 0 as x approaches infinite, and has a vertical asymptote at
x=2 and x=1.
Here’s an easy example: 10 / ((x-2)*(x-1)). At x=2 and x=1, there is both a
positive and negative vertical asymptote. As x approaches infinite, the
numerator is dominated by the denominator, which contains x (actually x2 ),
and thus y approaches zero.
c) All real numbers except 10
Compare the denominator to zero and it will give you the point where there is no f(x) because it is impossible to divide anything by 0.
10-x=0 ⇔ x=10
The function has a domain containing all real numbers except 10 → x<10 or x<10.
2. Considering f(x)=[tex] \frac{(x-6)(x+6)}{x^{2}-9 } [/tex]
b) x = 3, x = -3
Once more, compare the denominator to zero and it will give you the point/points where there is no f(x) because it is impossible to divide anything by 0, and there is where you can find the vertical asymptotes.
x²-9=0 ⇔ x=-3, x=3
The vertical asymptotes are x=3 and x=-3.
3. Considering [tex] \frac{x^{2}+4x-7}{x-7} [/tex]
a) None (of those presented)
Apply long division on the function.
The horizontal asymptote is y=x+11.
4. Considering [tex] \frac{x^{2}+8x-2}{x-2} [/tex]
a) None (of those presented)
Once more, apply long division on the function.
The horizontal asymptote is y=x+10.
5. The polynomial in the numerator has to have a smaller degree than the polynomial in the denominator. The polynomial in the denominator needs to have factors of x-1 and x-2. This factors should not be part of the polynomial in the numerator. An example of such a function could be: f(x)=[tex] \frac{8x-2}{ x^{2} -3x+2} [/tex]
Brent has $3.35 in quarters and dimes. if he has 23 coins in all, find the number of quarters and dimes.