Identify the rational function whose graph is given below. Note the x-intercept of the graph is x=4 and the y-intercept of the graph is y=−3. The graph has one vertical asymptote at x=2
Answers
Using the vertical asymptote of the function, it is found that it is given by:
[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the x-intercept of the graph is x=4, hence the numerator is a(x - 4).
The graph has one vertical asymptote at x=2, hence the denominator is x - 2.
Hence:
[tex]f(x) = \frac{a(x - 4)}{x - 2}[/tex]
The y-intercept of the graph is y=−3, hence:
[tex]-3 = \frac{a(0 - 4)}{0 - 2}[/tex]
[tex]-4a = 6[/tex]
[tex]a = -1.5[/tex]
Thus, the function is:
[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]
More can be learned about asymptotes at https://brainly.com/question/16948935
Related Questions
Find the measure of the reflex angle, B.
A
75%
B
B = [?]°
Enter
Answer
Answers
Answer:
285
Step-by-step explanation:
I could be wrong but if i remember you subtract 75 from 360 which would be 285
solve for x ~
[tex]32x - 16 +48 = 0[/tex]
thankyou ~
Answers
Answer:
[tex]\boxed{ \bold{x = -1 }}[/tex]
Explanation:
[tex]\rightarrow \sf 32x-16+48=0[/tex]
simplify
[tex]\rightarrow \sf 32x+32=0[/tex]
subtract both sides by 32
[tex]\rightarrow \sf 32x+32-32=0-32[/tex]
simplify
[tex]\rightarrow \sf 32x=-32[/tex]
divide both sides by 32
[tex]\rightarrow \sf \frac{32x}{32} =\frac{-32}{32}[/tex]
final answer
[tex]\rightarrow \sf x=-1[/tex]
[tex]32x - 16 + 48 = 0 \\ 32x - 16 = - 48 \\ 32x = 16 - 48 \\ 32x = - 32 \\ x = - \frac{32}{32} \\ x = - 1[/tex]
x = -1
The width of a rectangle with the area 55in^2 depends on its length. Write the formula that describes the width of the rectangle as a function of its length.
Answers
The width of the rectangle as a function of its length is w = 55/l
How to find the area of a rectangle?The formula for finding the area of a rectangle is expressed as:
A = lw
where
l is the length
w is the width of the rectangle
Given that A = 55 square inches, then;
55 = lw
w = 55/l
Hence the width of the rectangle as a function of its length is w = 55/l
Learn more on area of rectangle here; https://brainly.com/question/2607596
What's the answer to 0.02x + 0.1 (6000) = 0.08 (x + 6000)
Answers
Answer:
X=2000
Step-by-step explanation:
[tex]0.02x + 0.1(6000) = 0.08(x + 6000)[/tex]
[tex]0.02x + 600 = 0.08x + 480[/tex]
[tex]600 - 480 = 0.08x - 0.02x[/tex]
[tex]120 = 0.06x[/tex]
[tex]x = \frac{120}{0.06} [/tex]
[tex]x = \frac{120 \times 100}{0.06 \times 100} [/tex]
[tex]x = \frac{120}{6} \times 100[/tex]
[tex]x = 20 \times 100 = 2000[/tex]
X=2000
−6146.153846154
Step-by-step explanation:
0.02x+6=0.8(x+6000)
0.02x+6=0.8x+4800
0.02x+6−0.8x=4800
−0.78x+6=4800
−0.78x=4800−6
−0.78x=4794
x=4794/-0.78
x=479400/-78
x=- 79900/13
A triangle has a perimeter of 16x + 4. If Side 1 is 3x + 2, Side 2 is 8x + 7, what is the measure of Side 3?
Answers
Answer:
5x - 5
Step-by-step explanation:
To find the missing side, add the two sides together and subtract them from the perimeter.
side 1 + side 2
3x + 2 + 8x + 7
combine like terms
11x + 9
Subtract from the perimeter
16x + 4 - (11x + 9)
rewrite as an addition problem, so you need to change the signs inside the parentheses.
16x + 4 + (-11x -9)
Now combine like terms
5x - 5
Let a represent a non zero rational number and let b represent an irrational number. Which expression could represent a rational number?
Answers
The operation between a rational and a irrational number that results in a rational number is a multiplication, hence the expression ab could represent a rational number.
What are rational and irrational numbers?If a number can be represented by a fraction, it is rational, otherwise, it is irrational.
The addition/subtraction of a rational and an irrational numbers is irrational, while the multiplication is rational, hence the expression ab could represent a rational number.
More can be learned about rational numbers at https://brainly.com/question/10814303
The graph of the equation x ^ 2 + y ^ 2 - 16x + 6y + 14 = 0 is a circle. An equivalent form of this equation is (x - 8) ^ 2 + (y + 3) ^ 2 = M
What is the value of M?
Answers
Answer:
author link
ghanami
Ace
2.9K answers
12.1M people helped
hello :
note :
an equation of the circle Center at the w(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : x²+y²-16x+6y+53=0
(x²-16x) +( y²+6y ) +53 = 0
(x² -2(8)x +8² - 8²) +(y² +2(3)x -3²+3² ) +53=0
(x² -2(8)x +8²) - 8² +(y² +2(3)x +3²)-3² +53=0
(x-8)² +( y+3)² = 20
the center is : w(8,-3) and ridus : r = √20
Still stuck? Get 1-on-1 help from an expert tutor now.
Step-by-step explanation:
sales representative can take one of 4 different routes from City B to City E and any one of 4 different routes from City E to City H. How many different routes can she take from City B to City H, going through City E?
Answers
Answer:
16
Step-by-step explanation:
4 x 4 = 16 because you have to go through city E
Pls figure out the question
Answers
Answer:
w=2
Step-by-step explanation:
Step-by-step explanation:
first simplified by dividing both sides by -5.
then, at
w - 5 = -3
add 5 to both sides.
and we get
w = 2
6 is 15% of what amount
Answers
Answer:
6 is what percent of 15? = 40.
I hope this answers your question
6/x = 15/100
You cross multiply (6x100=600) and then divide by 15
Once you divide 600 by 15 you should get 40
Hopefully this makes sense :)
A rectangular sheet of metal measures 8 inches by 12 inches. The metal is worth $2.00 per square inch. How much is the sheet of metal worth?
Answers
Answer:
Step-by-step explanation:
Find the area of the sheet metal
Area = L * w
L = 12
w = 8
Area = 12 * 8
Area = 96 square inches.
Find the value of the sheet metal
1 square inch costs $2.00
96 square inches cost 2 * 96 = $192.00
a company puts 23 buttons in each of its containers. how many buttons are needed for 562 containers?
Answers
Answer:
12,926
Step-by-step explanation:
23 x 562 = 12,926
What is the measure of angle A in the triangle below?
us
B
18
9
A
A
С
30°
o 45°
60°
90°
Answers
To find the measure of Angle A, we'll need to use a trigonometric function.
Remember: SOH-CAH-TOA
Looking from Angle A, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.
sin(A) = 9 / 18
---To solve for A, you'll need to use the inverse sin function on your calculator. It should look like so: sin^-1()
The inverse sin of 1/2 = 30
Answer: first option, 30 degrees
Hope this helps!
Find the area
(Please would mark Brainily
Answers
Answer:
195.5 m²
Step-by-step explanation:
A = bh/2
A = (23)(17)/2
A = 391/2
A ≈ 195.5 m²
MAPS A map of the eastern United States has a scale
where 3 inches = 25 miles. If the distance on the map
between Columbia, South Carolina, and Charlotte, North
Carolina, is 11.5 inches what is the actual distance
between the cities?
Answers
Answer:
[tex]95\frac{5}6{[/tex] miles
Step-by-step explanation:
First, find base. 1 inch = [tex]\frac{25}{3}[/tex] miles.
multiply the map distance by base.
[tex]11.5\cdot\frac{25}{3} = 95.8\overline{3}=95\frac{5}{6}[/tex] miles
Use the distributive property to remove the parentheses.
7w3(2w5+9w)
Simplify your answer as much as possible.
Ó
Х
Х
5
?
Answers
Answer:
14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]
Step-by-step explanation:
7w³ (2[tex]w^{5}[/tex] + 9w) ← multiply each term in the parenthesis by 7w³
= 14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]
[ using rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] ]
Answer:
7w⁴ (2w⁴ + 9)
Step-by-step explanation:
Given
7w³ (2w⁵ + 9w)Let's simplify.
Using the distributive property, 7w³ is distributed to 2w⁵ and 9w7w³ * 2w⁵ + 7w³ * 9w14w⁸ + 63w⁴The common factor of the two terms is : 7w⁴⇒ 7w⁴ (2w⁴ + 9)Dianne has $0.95 in dimes and nickels . She has a total of 11 coins . How many of each kind does she have ?
Answers
Answer:
8 dimes and 3 nickels
Step-by-step explanation:
If we change $0.95 to $0.9 + $0.05, we get 9 dimes and 1 nickel. However, that is only 10 coins. We can then try 8 dimes and 3 nickels. When you add them up, they equal $0.95. Also, there are 11 coins in total. Therefore, 8 dimes and 3 nickels is the answer.
I hope this helps and please mark me as brainliest!
Name the theorem or postulate that justifies the congruence.
JAJSAS
[B] ASA
[C] AAS
[DJ HL
Answers
can someone help me solve this?
Answers
Answer:
[tex]\dfrac{7\pi}{18}[/tex]
Step by step explanation:
[tex]70^{\circ}=\dfrac{70\pi}{180}~~\text{radians}=\dfrac{7\pi}{18}~~\text{radians}[/tex]
pls help this is important ty <3
Answers
Below are the score of 30 students in an oral interview. use the information to find the average score.
Score: 1 2 3 4 5
frequency: 7, 7, 7, 12, 3
Answers
Step-by-step explanation:
the average score would be 3 i think
Which letter on the number line represents one and eighty five hundredths?
A number line partitioned into tenths, starting at zero and ending at five. There are nine tick marks between each whole. There is a dot labeled A between the fifth and sixth tick mark after zero. A dot labeled B is between the eighth and ninth tick mark after one. A dot labeled C is between the fourth and fifth tick mark after 2. A dot labeled D is between the second and third tick mark after 3. A dot labeled E is between the seventh and eighth tick mark after three. A dot labeled F is between the fifth and sixth tick mark after four.
A
B
C
D
Answers
Do you think you could attach a photo?
∞You start at (10, 5). You move left 5 units. Where do you end?
Answers
We have the following point:-
[tex]\sf{(10,5)}[/tex]
where 10 is the x-coordinate & 5 is the y-coordinate.
If we move 5 units to the left, then we subtract 5 from the x-coordinate:-
[tex]\sf{(10-5,5)}[/tex]
Hence, the point is:-
[tex]\bigstar{\boxed{\pmb{5,5}}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Help! Surface area!!!
Answers
Answer:
6656 cm²
Step-by-step explanation:
6656 cm² is the required answer
Find the equation of the line that contains the point (4, - 2) and is perpendicular to the line y = - 2x + 5.
Answers
y=1/2x
Solution:The slopes of perpendicular lines are opposite reciprocals of each other.The simplest way to determine a number's reciprocal is to flip it over, like so:[tex]-2 ~ - > -\displaystyle\frac{1}{2}[/tex]Now, change the sign:[tex]\displaystyle\frac{1}{2}[/tex]So we have the slope of the line that's perpendicular to the given line.Now, let's find the line's equation.First, let's write it in Point-Slope Form:y-y1=m(x-x1)y-(-2)=1/2(x-4) y+2=1/2x-2 (Point slope)Now, convert to slope-intercept:y=1/2x+2-2y=1/2xHope it helps.
Do comment if you have any query.
Answer:
y=1/2x
Step-by-step explanation:
Salim receives a gift card for a bookstore. He does not know the value of the gift card.
Salim buys a book for $7.50. Then he has $12.50 remaining on the gift card.
• What is the unknown in this situation?
*) the price of the book
the amount of money remaining on the gift card
the amount of money on the gift card when Salim receives it
Answers
Answer:
1: The amount on the card, 2:$7.50, 3: $12.50, 4: $20
Step-by-step explanation:
Consider the principle
N{A ∪ B} = N{A} + N{B} − N{A ∩ B}.
An interview of 50 women in a residential subdivision reveals that 22 are gardeners while 31 are avid readers. How many are both gardeners and avid readers?
Answers
3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Step-by-step explanation:[tex]31+22-50[/tex]
____________________________________________
Calculate
[tex]53-50[/tex]
____________________________________________
Calculate the sum or difference
[tex]3[/tex]
I hope this helps you
:)
find the equation of the tangent to the circle whose equation is given below at the point (1,2)
(x-3)^2 + (y+2)^2 = 20
give answer in form ax+by+c=0 where abc are integers
Answers
Answer:
[tex]x-2y+3=0[/tex]
Step-by-step explanation:
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the centre, and r is the radius)
Given equation: [tex](x-3)^2+(y+2)^2=20[/tex]
Therefore, the centre is (3, -2) and the radius is √20
To find the equation of the tangent
The tangent of a circle is perpendicular to the radius at the point.
Therefore, first find the gradient (slope) of the line that passes through the centre of the circle and the given point.
[tex]\textsf{let}\:(x_1,y_1)=(1,2)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(3,-2)[/tex]
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{3-1}=-2[/tex]
If two lines are perpendicular to each other, the product of their gradients will be -1.
Therefore, the gradient of the tangent is:
[tex]m_t \cdot-2=-1\implies m_t=\dfrac12[/tex]
Now use the point-slope formula of a linear equation to find the equation of the tangent:
[tex]\implies y-y_1=m_t(x-x_1)[/tex]
[tex]\implies y-2=\dfrac12(x-1)[/tex]
[tex]\implies 2y-4=x-1[/tex]
[tex]\implies x-2y+3=0[/tex]
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
y = -x - 4
Step-by-step explanation:
brayden saves 1500 at a yearly simple interest rate of 2.5. how many years doess it take for the amount he has served to be double the original
I WILL GIVE U 100 POINTS
Answers
Answer:
80 years
Step-by-step explanation:
(.025)*n = 2 solve for n
