for the function g(x)=3-8(1/4)^2-x
a) State the y-intercept
b) State the equation of the horizontal asymptote
c) State whether the function is increasing or decreasing.
d) State the domain and range
e) Sketch the graph
Could anyone help?
Answers
Using function concepts, it is found that:
a) The y-intercept is y = 2.5.b) The horizontal asymptote is x = 3.c) The function is decreasing.d) The domain is [tex](-\infty,\infty)[/tex] and the range is [tex](-\infty,3)[/tex].e) The graph is given at the end of the answer.------------------------------------
The given function is:
[tex]g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}[/tex]
------------------------------------
Question a:
The y-intercept is g(0), thus:
[tex]g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5[/tex]
The y-intercept is y = 2.5.
------------------------------------
Question b:
The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3[/tex]
--------------------------------------------------
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty[/tex]
Thus, the horizontal asymptote is x = 3.
--------------------------------------------------
Question c:
The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.
--------------------------------------------------
Question d:
Exponential function has no restrictions in the domain, so it is all real values, that is [tex](-\infty,\infty)[/tex].From the limits in item c, the range is: [tex](-\infty,3)[/tex]--------------------------------------------------
The sketching of the graph is given appended at the end of this answer.
A similar problem is given at https://brainly.com/question/16533631
Related Questions
Question 6 of 25
In APQR, m P= 60°, m_ Q = 30°, and m2 R = 90°. Which of the following
statements about APQR are true?
Check all that apply.
Answers
Answer:
A, E, F
Step-by-step explanation:
From the angles given, we can infer that ΔPQR is a 30-60-90 special triangle. In a 30-60-90 triangle, the leg opposite the 30 degree angle is 1/2 the hypotenuse and the leg opposite the 60 degree angle is √3 times the one opposite the 30. Using this, we can say:
PR = 1/2 PQ which is just 2 PR = PQ(E)
PR √3 = QR (A)
We can substitute in PR from the first equation to the second to get:
√3/2 PQ = QR(F)
Please help with question thank you
Answers
Answer:
The answer is 3x=50-10y
Explain the relationship of the meaning of the word isometric to the properties of an isometric or rigid transformation
Answers
Step-by-step explanation:
The iso parts of isometric means same, and It is similar becuase rigid trtransformation and the metric parts means measure. Basically isometric means same measure. Rigid transformation preserve "same measures" like angles and side lengths.
The product of two algebraic expression is 4x²-9.If one of the expression is (2x+3),find the other expression
Answers
Answer:
Solution given:
we have formula
a²+b²=(a+b)(a-b)
now
4x²-9
(2x)²-3²
using formula
(2x+3)(2x-3)
other expression is 2x-3.
Answer:
( 2x - 3 )
Step-by-step explanation:
4x² - 9 is a perfect square meaning it can be factored into 2 expressions,
( 2x + 3 ) ( 2x - 3 )
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answers
Answer:
Step-by-step explanation:
The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:
original new
length
width
And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:
original new
length L
width 2L
Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.
The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:
original new
length L 100%L + 50%L
width 2L
The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:
original new
length L 100%L + 50%L
width 2L 100%(2L) - 20%(2L)
And now we'll simplify that "new" column:
original new
length L 150%L = 1.5L
width 2L 80%(2L) = 160%L = 1.6L
Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:
248 = 2(1.5L) + 2(1.6L) and
248 = 3L + 3.2L and
248 = 6.2L so
L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)
A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet
Answers
Answer:
Step-by-step explanation:
starting point: 140 feet below sea level.=-140
she then decends= 7(4.5)=31.5
-140-31.5=-171.5
finally she ascends 112.2 feet
-171.5+112.2=-59.3 feet or 59.3 feet below sea level
Answer:
It's B
Step-by-step explanation:
help me please to solve this 2 questions pleasee faster.. i will mark you as brainliest
Answers
Answer:
1. x=72, y=, 108
2.x=30, y=72
Step-by-step explanation:
Brainliest please~
in how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively
Answers
Answer:
2520 ways
Step-by-step explanation:
Given
[tex]n = 10[/tex]
[tex]r = (2,3,5)[/tex]
Required
The number of selection
First, select 2 people from 10 in 10C2 ways.
There are 8 people, left.
Next, select 3 people from 8 in 8C3 ways.
There are 5 people left.
Lastly, select 5 from 5 in 5C5 ways
So, we have:
[tex]Total = ^{10}C_2 * ^8C_3 * ^5C_5[/tex]
Using combination formula
[tex]Total = 45 * 56 * 1[/tex]
[tex]Total = 2520[/tex]
A machine with velocity ratio of 5 is used to raise a load with an effort of 500N . If the machine is 80% efficient , determine the magnitude of the load.
Answers
Answer:
Solutions given:
Velocity ratio V.R =5
effort =500N
efficiency =80%
magnitude of load=?
mechanical advantage [M.A ]
we have
efficiency =M.A/V.R*100%
80=M.A./5*100
80/100*5=M.A
M.A.=4
again
we have
M.A =load/effort
4=load/500
load=500*4
load=2000N
the magnitude of the load is 2000N.Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)
Answers
Answer:
[tex]\displaystyle d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
*Note:
The distance formula is derived from the Pythagorean Theorem.
Step 1: Define
Identify
Point (5, 10)
Point (10, 12)
Step 2: Find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{29}[/tex]The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
Answers
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
https://brainly.com/question/22213822
1. 80 = -10b
2. 6 = 2n
3. -16r = 32
1.
2.
3.
Answers
Answer:
1. - 8
2. 3
3. - 2
Step-by-step explanation:
1.
80 = - 10b
- 10b = 80
b = 80 / - 10
b = - 8
2.
6 = 2n
2n = 6
n = 6 / 2
n = 3
3.
- 16r = 32
r = 32 / - 16
r = - 2
1. b = - 8
2. n = 3
3. r = -16
Step-by-step explanation:
we’re trying to solve for each variable
1. 80 = -10b
Divide both sides by -10
80/-10 = -10b/-10
-8 = b
2. 6 = 2n
Divide both sides by 2
6/2 = 2/2n
3 = n
3. -16r = 32
Divide -16 by both sides
-16r/-16 = 32/-16
r = -16
Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Answers
Answer: £21007.22
Step-by-step explanation:
First, find the interest amount using the formula SI = (P × R × T) / 100.
SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22
The total amount = principle amount + interest amount
= £18790 + £2217.22 = £21007.22
A hundred chickadees can eat 100 kg of seeds in 100 days. How many kg of seeds can 10 chickadees eat in 10 days?
Answers
Answer:
1 kg
Step-by-step explanation:
Number of chickadees = 100
Quantity of seed eaten = 100 kg
Number of days = 100
Quantity of seeds each chickadee eats per day =Number of chickadees ÷ Quantity of seed eaten ÷ Number of days
= 100 ÷ 100 ÷ 100
= 1 ÷ 100
= 0.01 kg of seed
How many kg of seeds can 10 chickadees eat in 10 days?
= Quantity of seeds each chickadee eats per day × number of chickadee × number of days
= 0.01 kg × 10 × 10
= 1 kg
10 chickadees eat 1 kg of seeds in 10 days
ASAP HELP!! PLEASEEEE!!
Answers
Answer:
Step-by-step explanation:
5.1, please this is just a guess from using my head to calculate
Express 3.023 in P form where p and q are integers and q= 0 D
Answers
Given:
The number is 3.023.
To find:
The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].
Solution:
The given number is 3.023. It can be written as:
[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]
[tex]3.023=\dfrac{3023}{1000}[/tex]
It cannot be simplified further because 3023 and 1000 have no common factors.
Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].
C=-(251x3+281)+3X251-(1-281)
Answers
Answer:
-1
Step-by-step explanation:
=-251x3+281 +251x3-1+281
=-1
aint the answer for this 10 just let me if im wrong
Answers
Answer:
Yup
Step-by-step explanation:
1 point (1) Three times a number minus two times a number* Your answer
Answers
Answer:
Three times a number minus two times a number
3x-2x
=x
factor x^2-3x-28 using the x method
Answers
Answer:
[tex] {x}^{2} - 7x + 4x - 28 \\ = x(x - 7) + 4(x - 7) \\ = (x - 7)(x + 4)[/tex]
In a jail cell, there are 5 Democrats and 6 Republicans. Four of these people will be
chosen for early release. How many 4-person groups are possible?
Answers
two because there is 11 people in total and you have two 4 person groups so that would leave 3 people left and you cant make a 4 person group w 3 people
Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.
If in a jail cell, there are 5 Democrats and 6 Republicans, the possible ways to form a group of 4 is 330.
The number of possible groups is 330.
What is combination?Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.
It is given as:
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
We have,
The total number of people:
5 Democrats and 6 Republicans = 5 + 6 = 11.
The number of persons in a group = 4.
The number of groups possible are:
= [tex]^{11}C_4[/tex]
= 11! / 4! ( 11-4)!
= 11! / 4! 7!
= 11 x 10 x 9 x 8 / 4 x 3 x 2
= 330
Thus,
The number of possible groups is 330.
Learn more about combination here:
brainly.com/question/2970011
#SPJ2
Can someone please help me with this I’m struggling
Answers
Answer:
Equation: [tex]70=(x+3)x[/tex]
x = -10 or x = 7
x = 7 (width can't be negative)
x + 3 = 10
Step-by-step explanation:
Represent the width of the rectangle by x. "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression x + 3.
Area = (length)(width)
70 = (x + 3)x
Multiply out the right side.
[tex]70=x^2+3x\\x^2+3x-70=0[/tex]
Factor the left side.
[tex](x+10)(x-7)=0[/tex]
Each binomial could equal 0, so
[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]
The negative solution does not make sense as the width of a rectangle.
x = 7, making the length, x + 3 = 10
Answer:
Pls mark this as brainiest
Step-by-step explanation:
Area of the rectangle = length x breadth
consider 'x' to be width
therefore length = x+3
area = (x+3)*x
Area = 70 square
x = 7
x+3 = 7+3
= 10
verification
7 x 10
= 70
What’s the answer? I don’t understand the question and I came to see if you all can help
Answers
Answer:
15/2 that is the answer man
What is the simplified form of the complex fraction? 2x2+7x+6x2+x−64x2−9x2−5x+6
Answers
Answer:
3x - 124
Step-by-step explanation:
kindly find solutions in the picture above
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is
-65x² + 2x + 6
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6
Combine all like terms.
(2x² + 6x² - 64x² - 9x²) + (7x - 5x) + 6
(8x² - 73x²) + 2x + 6
-65x² + 2x + 6
There are no common factors or like-terms to simplify.
So,
The simplified form is -65x² + 2x + 6
Thus,
The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is
-65x² + 2x + 6
Learn more about expressions here:
https://brainly.com/question/3118662
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[tex]\text{Solve for 'x':}\\\\3(x+1)=12+4(x-1)[/tex]
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = -5[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3(x+1)=12+4(x-1)\\----------\\\rightarrow 3x + 3 = 12 + 4x - 4\\\\\rightarrow 3x + 3 = 12 -4+4x\\\\\rightarrow 3x + 3 = 8 + 4x\\\\\rightarrow 3x + 3 = 4x + 8\\\\\rightarrow3x + 3 -3 = 4x + 8 - 3\\\\\rightarrow 3x = 4x + 5\\\\\rightarrow 3x - 4x = 4x - 4x + 5\\\\\rightarrow -x = 5\\\\\rightarrow \frac{-x=5}{-1}\\\\\rightarrow \boxed{x = -5}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=-5Step-by-step explanation:
3(x+1)=12+4(x-1)
3(x+1)=8+4x
3x+3=8+4x
3x+3−4x=8
-x+3=8
-x=8-3
-x=5
-x(-1)=5(-1)
-x(-1)=-5
x=-5
Second time posting this. Please help!! :)
Answers
Answer:
Step-by-step explanation:
[tex]\frac{480+24(x-40)}{x}[/tex]
The numerator of the rational expression the money he earned for 'x' hours
The rate at which William is paid for each hour in excess of 40 hours 24.
x = 50 hours = (40 + 10 ) hours
The amount paid for excess 10 hours = 24 *10 = 240
Total amount earned for the week = 480 + 240 = 720
The height of a baseball in feet can be found by the equation -4.982 – 20t + 1000. How far has the
baseball traveled at t = 6?
Answers
Answer:
875.018
Step-by-step explanation:
To solve this, we must plug in 6 for our t value. So, we have the equation:
-4.982 - 20(6) + 1000
Following the rules of PEMDAS, we have:
-4.982 - 120 + 1000 = 875.018
Find the value of both variables.
Answers
[tex] \cos(45) = \frac{5 \sqrt{2} }{x} \\ \frac{1}{ \sqrt{2} } = \frac{5 \sqrt{2} }{x} \\ x = 10 \\ \\ \tan(45) = \frac{y}{5 \sqrt{2} } \\ 1 = \frac{y}{5 \sqrt{2} } \\ y = 5 \sqrt{2} [/tex]
I hope I helped you ^_^
1/x^-2 x=7 yeet yeet
Answers
Answer:
49
Step-by-step explanation:
x = 7
1 / x^-2
= x^2
= 7^2
= 49
Answer: 49
Step-by-step explanation: yeet
Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?
Answers
Answer:
56
Step-by-step explanation:
Zoe : hanna
3 7
Zoe got 24
3*8 = 24
so multiply each side by 8
Zoe : hanna
3*8 7*8
24 56
Hanna got 56
