Which function is graphed below?
On a coordinate plane, an exponential decay function is shown. The curve starts in quadrant 2 and decreases into quadrant 1. It crosses the y-axis at (0, 3) and approaches y = 0 in quadrant 1.
1)y = one-third (3) Superscript x
2)y = 3 (one-third) Superscript x
3)y = (one-half) Superscript x Baseline + 2
4)y = (2) Superscript x Baseline minus 1
Answers
By solving a system of equations, we will see that the rational function is:
[tex]f(x) = \frac{12}{(x + 2)} -3[/tex]
Which rational function is graphed below?
First, we need to see the x-value of the vertical asymptote, here we can see that the vertical asymptote happens at x = -2, then the denominator will be something like:
d = (x - (-2)) = (x + 2).
Then our rational function will be something like:
[tex]f(x) = \frac{a}{(x + 2)} + c[/tex]
In the graph we can see two things, first:
f(0) = 3
f(1) = 1
Replacing that in our function, we get:
[tex]\frac{a}{(0 + 2)} + c = 3\\\\ \frac{a}{(1 + 2)} + c = 1[/tex]
This is a system of equations, that can be rewritten as:
a/2 + c = 3
a/3 + c = 1
Isolathing c in both equations, we get:
a/2 - 3 = -c = a/3 - 1
Then we have:
a/2 - 3 = a/3 - 1
Now we can solve this for a:
a/2 - a/3 = 3 - 1
a/6 = 2
a = 2*6 = 12
And the value of c is given by:
-c = a/3 - 1 = 12/3 - 1 = 4 - 1 = 3
c = -3
Then the rational function is:
[tex]f(x) = \frac{12}{(x + 2)} - 3[/tex]
If you want to learn more about rational functions, you can read:
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Answer:
B. 3(1/3)^x
Step-by-step explanation:
Edg 2022
Related Questions
in the similar triangle ABE and triangle CDE,AB=10cm,ED=4cm,CD=8cm find the length of BC
Answers
9514 1404 393
Answer:
BE = 5 cm
Step-by-step explanation:
Your problem statement asks for the length of BC. There is no segment BC. Points B and C are in different triangles.
The length of segment BE can be found from the proportion ...
BE/DE = AB/CD
BE = DE·AB/CD = (4 cm)(10/8)
BE = 5 cm
Find the value of x.
Answers
Answer:
x=10
Step-by-step explanation:
6(x+2)=8(x-1)
x=10
Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
[tex]8(x−1)=6(x+2)[/tex]
[tex]8x−8=6(x+2)[/tex]
[tex]8x−8=6x + 12[/tex]
[tex]2x−8=12[/tex]
[tex]2x=12+8[/tex]
[tex]2x=20[/tex]
[tex]x = \frac{20}{2} [/tex][tex]x = 10[/tex]
Hope it is helpful....What is the value of h(2)?
Answers
Step-by-step explanation:
answer is 0
because x= 2 and y =3 make a circle
Helppppppp me please
Answers
Given:
In [tex]\Delta QRS, \overline{QR}\cong \overline{SQ}[/tex] and [tex]m\angle Q=114^\circ[/tex].
To find:
The [tex]m\angle S[/tex].
Solution:
In [tex]\Delta QRS[/tex],
[tex]\overline{QR}\cong \overline{SQ}[/tex]
It means the triangle QRS is an isosceles triangle. We know that the base angles of an isosceles triangle are congruent and their measures are equal.
[tex]\angle R\cong \angle S[/tex] [Base angles of isosceles triangle QRS]
[tex]m\angle R=m\angle S[/tex] ...(i)
In [tex]\Delta QRS[/tex],
[tex]m\angle Q+m\angle R+m\angle S=180^\circ[/tex]
[tex]m\angle Q+m\angle S+m\angle S=180^\circ[/tex] [Using (i)]
[tex]114^\circ+2m\angle S=180^\circ[/tex]
[tex]2m\angle S=180^\circ-114^\circ[/tex]
[tex]2m\angle S=66^\circ[/tex]
Divide both sides by 2.
[tex]m\angle S=\dfrac{66^\circ}{2}[/tex]
[tex]m\angle S=33^\circ[/tex]
Therefore, the [tex]m\angle S[/tex] is 33 degrees.
Find f(2) if f(x) = 2x + 1.
Answers
2(2)+1
4+1=5
Answer is 5
Solve x2 − 3x = −8. (2 points)
Answers
Answer: x=3 plus or minus i square root 29 end root all over 2
PLEASE HELP
IT SAYS IN PROGRESS BUT ITS COMPLETED WHAT DO I DO???!!!!
Answers
Answer:
click on it and double check that all questions are 100% complete if so wait because it is quite possible it is a glitch this sort of thing happens often no need to be alarmed
!!PLEASE HELP 25 POINTS!! The graph of an absolute Value
Answers
Answer:
(-1, 8)
the value of a is 8
factoring polynominaly
Answers
Answer:
Most of the question is missing. If you could type out the rest, we might be able to help you.
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answers
Answer:
area =length× width
32 =length×4.
length=8 feet
3100 times 43 how much is this
Answers
Answer:
133,300
Step-by-step explanation:
3100 x 43 = 133,300
Answer: 133,300
Step-by-step explanation: 3100 x 43= 133300
HELP! What is the surface area of the right cone below?
12 6
A. 339 sq. units
B. 245 sq. units
C. 185 sq. units
D. 582 sq. units
Answers
The surface area of the right cone is,
⇒ 339 units²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Radius of right cone = 6 units
Slant height of right cone = 12 units
Now, We know that;
The formula for the total surface area of a right cone is,
⇒ T. S. A = πrl + πr²
Hence, We get;
The surface area of the right cone is,
⇒ 3.14 × 6 × 12 + 3.14 × 6²
⇒ 226.08 + 113.04
⇒ 339.1
⇒ 339 units²
Thus, The surface area of the right cone is,
⇒ 339 units²
Learn more about the mathematical expression visit:
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need help finding the value of f (7)
Answers
Answer:
f(7) = -4
Step-by-step explanation:
f(7) means f(x) when x = 7. The x is replaced with 7.
So we'll replace every x with 7 to go from x = 7 to 3 - x = 3 - 7 = -4
Put in another way:
f(x) = 3 - x
f(7) = 3 - 7
f(7) = -4
16. m + 5(m - 1) =
How do u solve this
Answers
Distribute 5
m+ 5m-5
Simplify
6m -5
Select the number line model that matches the expression
|8 - 1|
Answers
Answer:
B
Step-by-step explanation:
Trust
A truck is carrying pineapple juice, tomato juice, and cherryjuice bottles in a ratio of 3:5:4. If there are 80 tomato juice bottles, then how many juice bottles in total?
PLEASE HELP!!
Answers
Answer:
192
Step-by-step explanation:
The ratio of pineapple to tomato to cherry is 3 to 5 to 4.
That means for some number x,
we have 3x pineapple, 5x tomato, and 4x cherry.
We are asked to find the total number which is 3x+5x+4x which is equal to 12x.
We are given that there are 80 tomato and we also have 5x tomato. These two expressions are therefore equal and we need to solve 80=5x which leads to x=80/5=16.
So the total amount is 12x=12(16)=192.
Which of the following statements contain a variable? Check all that apply.
A. The amount of time you ran on the track.
B. How high you can jump.
C. The time school starts.
D. The temperature outside is 31 degrees.
Answers
please can anyone help me out!!
Answers
Answer:
1.39 m
Step-by-step explanation:
sin 63 = x/13.5 (x = CD)
sin 52 = x/13.5 (x=AC)
take the difference between the two
Sorry can someone help please…
Answers
26) -8
27) 0
28) -7
29)6
The solutions of x² = 16x - 28 are
1) -2 and -14
2) 2 and 14
3) -4 and -7
4) 4 and 7
Answers
hope this helps
A population of insects can be modeled by the equation y = 12,000 + 8000 sin(θ). What is the greatest number of insects you will find?
Answers
Answer:
20000
Step-by-step explanation:
The greatest value obtained by sin(x) is 1.
So the greatest amount of insects is 12,000 + 8000(1)=20000.
The greatest number of insects are 20000.
What is trigonometric function?"Trigonometric functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trigonometric functions.
The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. "
We have,
y = 12000+8000 sinθ
The possible greatest value of trigonometric function in sinθ is 1 i.e., at [tex]90^{0}[/tex]
∴ sinθ = 1
substitute sinθ = 1 in given equation
y = 12000+8000 (1)
⇒ y = 12000+8000
⇒ y = 20000
Hence, The greatest number of insects are 20000.
Learn more about trigonometric function here
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Name a Radius
A. AP
B. AB
C. DE
D. All of the above
please help I'll really appreciate it
Answers
Answer:
AP is the radius since it's a straight line extending from the center. CP and BP are radiuses as well
Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
Radius is the line segment that joins the centre of a circle and any point on its circumference. In the figure , AP is the radius. The plural form of radius of radii. All the radii of a circle are equal i.e AP , PB & PC are radii and they're equal.[tex] \large{ \tt{❁ \: LET'S \: CHECK \: THE \: OPTIONS: }} [/tex]
[tex] \large{ \tt{ \overline{AP}}}[/tex] - Yes! [tex] \tt{ \overline{AP }}[/tex] is a radius since it is the line segment which joins the centre of a circle and any point on the circumference. [tex] \large{ \tt{ \overline{ AB}}}[/tex] - No! It's a diameter since it is the line segment that passes through the centre of a circle and joins any two points on its circumference. Remember: The length of a diameter is two times radius i.e if the length of radius [ AP ] is 5 then the length of Diameter [ AB ] will be 5 × 2 = 10.[tex] \large{ \tt{ \overline{ DE}}}[/tex] - No! It's a chord since it is the line segment which joins any two points on the circumference of a circle.
[tex] \large \boxed{ \boxed{ \tt{☄OUR \: FINAL \: ANSWER : { \tt{ \overline{AP}}}}}} \: [/tex]
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
URGENT PLS!!
consider the system: 5x+3y = 12 , x-7y=10
using elimination method, what is the value of 38y?
Answers
Answer:
5x+3y=12
x-7y=10
first you want to make the x the same to 5 since you want to make the x = 0 so you can cancel out the x to find y
5x+3y=12
5x-35y=10
_________
38y = -38
y = -1
to find the x value substitute to any equations it can be the 1st or 2nd
5x+3(-1)=12
x = 3
Find the volume of the prism.
2 m
Answers
Answer:
12 cubic meters
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP ME WITH THIS QUESTION I KEEP GETTING SPAM ANSWERS, THANK YOU!
EXPLAINING YOUR ANSWER = BRAINLIEST
The area is 96 square units.
The length, x, of the base is ___ units.
Answers
Given :
Δ Area of the Triangle is 96 square units
Δ Height of the Triangle is 9.6 units
We know that:
[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base \times 9.6 = 96}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base = \dfrac{96}{9.6}}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base = \dfrac{960}{96}}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base = 10}[/tex]
[tex]\implies \sf{Base = 20 \ units}[/tex]
Figure ABCD was reflected across the x-axis to create figure A'B'C'D'.
On a coordinate plane, a quadrilateral has points A prime (2, negative 2), B prime (negative 8, 2), C prime (2, 6), and D prime (8, 2).
What are the coordinates of the pre-image of B'?
(2, –8)
(–8, –2)
(–2, 8)
(8, 2)
Answers
Answer:
i think it is b -8 -2
Step-by-step explanation:
Answer:
in picture
Step-by-step explanation:
Line l has a slope of −3. The line through which of the following pair of points is perpendicular to l? i will give brainliest for the answer
A. (−4,−3),(−3,−6)
B. (−18,−1),(−3,0)
C. (−6,−4),(−3,−3)
D. (−2,−3),(−3,−6)
Answers
Answer:
c. (−6,−4),(−3,−3)
Step-by-step explanation:
a). y2 - y1 / x2 - x1
-6 - (-3) / -3 - (-4)
-3/ 1
= -3
b). y2 - y1 / x2 - x1
0 - (-1) / -3 - (-18)
= 1/15
c). y2 - y1 / x2 - x1
-3 - (-4) / -3 - (-6)
= 1/3
d). y2 - y1 / x2 - x1
-6 - (-3) / -3 - (-2)
3
Answer:
D
Step-by-step explanation:
ALWAYS REMEMBER THIS EQUATION: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Find the slope of answer A
1. [tex]\frac{-6 - -3}{-3 - -4} = \frac{-3}{1}[/tex]
2. This answer is not perpendicular to "l" because it is equal to -3. (Even if it has a different y-intercept, it will just be parallel, not perpendicular.)
Find the slope of answer B
1. [tex]\frac{0 - -1}{-3 - -18} = \frac{1}{15}[/tex]
2. This answer is not perpendicular to "l".
Find the slope of answer C
1. [tex]\frac{-3 - -4}{-6--2} = \frac{1}{-4}[/tex]
2. This answer is not perpendicular to "l".
Find the slope of answer D
1. [tex]\frac{-6 - -3}{-3 - -2} = \frac{-3}{-1}[/tex]
2. This answer is perpendicular to "l" because 3 is the inverse of -3.
The graphs of f(x) and g(x) are shown below.
o o
00
f(x)
4
2
5
21
2
-2 -1
-2
3
-4
g(x)
-6
-8
-12
-147
What are the solutions to the equation f(x) = g(x)?
Answers
HELP I WILL AWARD BRAINLIEST
*Prove that corresponding angle bisectors in congruent triangles are congruent.
Answers
Answer:
CPCTC
Step-by-step explanation:
BESTIE MY CAPS LOCK KEY IS LIKE STUCK SO YEAH
ANYWAY, THIS IS GOING TO SOUND REALLY AGGRESSIVE
SO CONGRUENT TRIANGLES HAVE 3 EQUAL SIDES AND 3 EQUAL ANGLES
THEY ARE EXACTLY THE SAME
SINCE WE KNOW ALL OF THIS AWESOME INFORMATION, NOW WE CAN THAT THE ANGLE BISECTORS WILL BE CONGRUENT BY CPCTC -
CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT
WE CAN USE AN EXAMPLE TO UNDERSTAND BETTER
SAY YOU HAVE 2 CONGRUENT TRIANGLES
THE ANGLES ARE 50, 60, AND 70
SAY THAT THE ANGLE BISECTORS ARE ON 60
THEY WILL BE CONGRUENT BECAUSE THEY ARE THE CORRESPONDING ANGLES OF 2 CONGRUENT TRIANGLES
BUT WHEN YOU ARE ASKED FOR A REASON, IT IS BECAUSE OF CPCTC
CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT
a/2-8=-4
I have no idea how to do this!!
Answers
Answer:
a = 8
Step-by-step explanation:
a ÷ 2 - 8 + 8 = - 4 + 8
a ÷ 2 = 4
a ÷ 2 × 2 = 4 × 2
a = 8
Answer:
a = 8
Step-by-step explanation:
Given
[tex]\frac{a}{2}[/tex] - 8 = - 4 ( add 8 to both sides )
[tex]\frac{a}{2}[/tex] = 4 ( multiply both sides by 2 to clear the fraction )
a = 8