Answer:
the square of hypotenuse rs eqaul to the sum of the square of the legs
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?
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
Find the height of the room 15m long amd 10 m wide . The area of whose floor and ceiling together is equal to the area of 4 walls
Answer:
first
you
do15 multiply 10 =150 then divide by 4 walls with 150 =37.5 then mutiply with 4
Apples are cut into 8 pieces to be shared among some children. Twenty-two bags of seven apples are used. How many pieces of apple are cut?
Answer: 1232 pieces
Work Shown:
1 bag = 7 apples
22 bags = 22*7 = 154 apples
So we have 154 apples to work with in total.
Each of those apples is cut into 8 pieces, giving us 8*154 = 1232 pieces
We can write it as one single calculation to say 22*7*8 = 1232
Point S lies between points R and T on Line segment R T. A line contains points R, S, T. The space between R and S is 2 x. The space between S and T is 3 x. If RT is 10 centimeters long, what is ST?
Answer:
[tex]ST = 6cm[/tex]
Step-by-step explanation:
Given
[tex]RS =2x[/tex]
[tex]ST = 3x[/tex]
[tex]RT = 10[/tex]
Required
Find ST
From the question, we understand that S is between R and T.
So:
[tex]RS + ST = RT[/tex]
Substitute known values
[tex]2x + 3x = 10[/tex]
[tex]5x =10[/tex]
Divide both sides by 5
[tex]x =2[/tex]
Given that:
[tex]ST = 3x[/tex]
[tex]ST = 3 * 2[/tex]
[tex]ST = 6cm[/tex]
Answer:
C or 6 centimeters
Step-by-step explanation:
7 x ..... = 364 whats the missing number ?
To find the missing number divide 364 by 7
364 / 7 = 52
The missing number is 52
Answer:
52
Step-by-step explanation:
In this equation, you would have to use inverse operations.
Since this equation is a multiplication equation, you need to do the opposite, division. So, 364 ÷ 7 = 52
Hope this helps! :)
Find the number of possible ways one can choose marbles from a bag containing three marbles: a) if the order is important b) if the order is not important.
Answer:
There are 3 marbles, that we assume are different.
Let's define them as marble 1, marble 2, and marble 3.
a) If the order is important, and we select the 3 marbles, then:
for the first marble, we have 3 options.
For the second marble, we have 2 options (because one is already taken)
for the third marble is only one option.
The total number of combinations is equal to the product between the numbers of options, so in this case, we have:
C = 3*2*1 = 6 combinations.
Now, if we only select 2 marbles from the bag, we have:
for the first marble, we have 3 options.
For the second marble, we have 2 options
Here the number of different combinations is:
C = 3*2 = 6 combinations.
And if we select only one marble from the bag, we have:
for the first marble, we have 3 options.
Then here are only 3 combinations.
the total number of combinations is:
C' = 6 + 6 + 3 = 15 different combinations.
b) If the order is not important, then there is only one combination when we draw the 3 marbles.
When we draw one marble there are 3 combinations (one for each marble)
When we draw two marbles, again there are 3 combinations (one for each marble that we do not draw)
then the total number of combinations in this case is:
C = 1 + 3 + 3 = 7
How many 9 digit palindromes are there with all the digits being even and each digit appearing no more than once
Answer:
96
Step-by-step explanation:
We have to find number of 9 digit palindromes when all digits are even and each digit appearing not more than twice.
Digits used here
0,1,2,3,4,5,6,7,8,9
Total number of even digits=0,2,4,6,8=5
Now,
0 cannot be used for first place if number is 9-digit number.
Firs place can be filled by number of ways=4
Second place can be filled by number of ways=4
Third place can be filled by number of ways=3
Fourth place can be filled by number of ways=2
Fifth place can be filled by number of ways=1
Total number of ways=[tex]4\times 4\times 3\times 2\times 1[/tex]
Total number of ways=96
Hence, total number of 9-digits palindromes when all digits are even and appearing not more than twice=96
Please help me out with math will mark like brainlist if answers ASAP
Answer:
13/16
Step-by-step explanation:
To add these two fractions multiply the first fraction by 2 to get equivalent denominators so 6/16+7/16 then add the numerators to get 13/16.
Answer:
13/16
Step-by-step explanation:
3/8 + 7/16
Get a common denominator
3/8*2/2 + 7/16
6/16 + 7/16
13/16
PLEASE HELP! I HAVE BEEN AT THIS FOR A LONG TIME!.
For each investement, 25 000 is deposited in an account. How much is each payment?
(a. 8% per annum, compounded annually, with annual payments starting in a year.
Answer:
Annual payment wil be 2,001 and total amount after compounded annually will be 27,001
solve the quadratic equation
give your answer to 2 decimal places
: 3x^2+x-5=0
Given:
The quadratic equation is:
[tex]3x^2+x-5=0[/tex]
To find:
The solution for the given equation rounded to 2 decimal places.
Solution:
Quadratic formula: If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]3x^2+x-5=0[/tex]
Here, [tex]a=3,b=1,c=-5[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-1\pm \sqrt{1^2-4(3)(-5)}}{2(3)}[/tex]
[tex]x=\dfrac{-1\pm \sqrt{1+60}}{6}[/tex]
[tex]x=\dfrac{-1\pm \sqrt{61}}{6}[/tex]
[tex]x=\dfrac{-1\pm 7.81025}{6}[/tex]
Now,
[tex]x=\dfrac{-1+7.81025}{6}[/tex]
[tex]x=1.13504167[/tex]
[tex]x\approx 1.14[/tex]
And
[tex]x=\dfrac{-1-7.81025}{6}[/tex]
[tex]x=-1.468375[/tex]
[tex]x\approx -1.47[/tex]
Therefore, the required solutions are 1.14 and -1.47.
-8z^{-2} Write the expression using only positive exponents. Assume no denominator equals zero.
Answer:
Step-by-step explanation:
-8z⁻² = -8/z²
evelins room has an area of 45 squar feet. the length of her room is 5. what is the perimeter of her room?
Answer:
28 feet
Step-by-step explanation:
Since the area is 45 and length is 5.In order to find the width we divide the area by the side given
45 ÷ 5 = 9 is the width
Perimeter is the sum of all the side of a figure.
9 + 9 + 5 + 5
= 28
I hope this helps :)
Does this graph show a function? Explain how you know.
O A. Yes; there are no y values that have more than one x-valuer
O B. No, there are y-values that have more than one x-value.
O C. Yes, the graph passes the vertical line test.
O D. No, the graph fails the vertical line test. SUBMIT
Answer: D) No. The graph fails the vertical line test.
Explanation:
We are able to draw a single vertical line that passes through more than one point on the red curve. For example, we could draw a vertical line through x = 5 and have it cross the red curve at (5,4) and (5,-4).
So this is one example where the graph fails the vertical line test. It passes this test when such a thing doesn't happen. In other words, a function is only possible if any x input leads to exactly one and only one y output.
In this case, x = 5 leads to multiple outputs y = 4 and y = -4 at the same time. There are other x values which this occurs as well (any x values such that x > 1). So this is why we don't have a function.
What kind of shape will you see if you cut a cross section parallel to the base of a cylinder
Answer:
Hexagons, Cross sections parallel to the base will be hexagons. It is also possible to take cross sections using planes that are neither parallel not perpendicular to the base
Answer:
The cross-section parallel to the base is a hexagon congruent to the hexagonal bases. The cross-section perpendicular to the base is a rectangle. The cross-section parallel to the base is a pentagon similar to the pentagonal base. The solid is a cylinder.
Lucy's dog sleeps 14 hours a day. What percent of the day does her dog spend sleeping?
Answer:
58.3333
Step-by-step explanation:
make 14/24 into a fraction with a denominator of 100, and you get 58.333333 over 100
Lucy's dog sleeps for 58.3% of the whole day.
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, Lucy's dog sleeps 14 hours a day, we need to find that how much percent of the total day, her dog sleeps.
We know, there are 24 hours in a day,
Percentage = 14% of 24
= 24x14/100
= 58.3333333333 ≈ 58.3%
Hence, Lucy's dog sleeps for 58.3% of the whole day.
Learn more about percentage,
https://brainly.com/question/29306119
#SPJ6
The sum of two integers equals twelve, while their product equals thirty-five. Which two numbers are they?
Answer: 5 and 7
Step-by-step explanation:
Given
Sum of the integers is 12
Product of the integers is 35
Suppose the integers are [tex]x[/tex] and [tex]y[/tex]
[tex]\Rightarrow x+y=12\\\\\Rightarrow y=12-x\\\Rightarrow xy=35\\\text{Substitute y}\\\Rightarrow x(12-x)=35\\\Rightarrow 12x-x^2=35\\\Rightarrow x^2-12x+35=0\\\Rightarrow x^2-7x-5x+35=0\\\Rightarrow (x-7)(x-5)=0\\\Rightarrow x=5\ or\ 7[/tex]
[tex]\therefore \text{y can be }7\ or\ 5[/tex]
Hence, the numbers are 5 and 7.
Tìm m để hàm số sau là hàm số bậc nhất:
(2m-1)x+2018
Answer:
2mx-x+2018
Step-by-step explanation:
multiply each term in the parentheses by x
Fastest answer will be declared the brainliest
Answer:
All whole numbers are rational numbers.
False
All integers are whole numbers.
True
There are integers that are not rational numbers.
True
There are whole numbers that are not integers.
True.
please answer fast urgent
Determine, to one decimal place, the length, width & height of the rectangular prism that would have the greatest volume, with a surface area of 200 cm^2.
Answer:
The length = The width = The height ≈ 5.8 cm
Step-by-step explanation:
The volume of a rectangular pyramid, V = l × w × h
The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200
∴ l × h + w × h + l × w = 200/2 = 100
We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;
At maximum volume, l = w = h
∴ l × h + w × h + l × w = 3·l² = 100
l² = 100/3
l = 10/√3
Therefore, the volume, v = l³ = (10/√3)³
The length = The width = The height = 10/√3 cm ≈ 5.8 cm
How high does rent have to be to be an outlier
Answer:
congratulate you have Windows 11
Find the length of BW
A.132.59
B.134.24
C.21.26
D.3.33
Answer:
BW = 132.59
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 9 = 21 / BW
BW tan 9 = 21
BW = 21/ tan 9
BW = 132.5887818
BW = 132.59
Answer:
Step-by-step explanation:
Side BW is the height, aka as the side adjacent to the reference angle of 9 degrees. We have the side opposite the reference angle (21) and we are looking for the side adjacent to the reference angle. The trig ratio that we use for this, the one that relates the sides opposite and adjacent, is the tangent ratio, namely:
[tex]tan(9)=\frac{21}{BW}[/tex] and solving for BW:
[tex]BW=\frac{21}{tan(9)}[/tex] so
BW = 132.59
5 + 8n = 7(-7 + 4n) -6
Answer:
n = 3
Step-by-step explanation:
Given
5 + 8n = 7(- 7 + 4n) - 6 ← distribute parenthesis on right side
5 + 8n = - 49 + 28n - 6 ( subtract 28n from both sides )
5 - 20n = - 55 ( subtract 5 from both sides )
- 20n = - 60 ( divide both sides by - 20 )
n = [tex]\frac{-60}{-20}[/tex] = 3
giai bat phuong trinh: 10x + 3 - 5x_< 14x + 12
Answer:
x>_-1
10x + 3 - 5x_< 14x + 12
-9_<9x
Answer:
Step-by-step explanation:
10x +3-5x < (nhỏ hơn hoặc bằng) 14x=12
10-14x-5x< bằng 12 -3
-9x< bằng 9
x > bằng -1
Please help me on this assignment, I will brainly to the person with the correct answer!
Answer:
Step-by-step explanation:
I'm not sure if you have learned this yet, but using dimensional analysis (DA) for this problem makes everything so. much. easier! (I'll share a good video in the comments if you don't know what it is)
Okay, so we're given a 50,145 [tex]cm^{3}[/tex] statue, and we want to see how much it'll cost if it's $0.35 per kg, with a conversion factor of 2.6 [tex]g/cm^{3}[/tex].
First, with the conversion factor, I'll set up a dimensional analysis.
[tex]50,145 cm^{3} * \frac{2.6 g}{cm^{3} }[/tex]
cancel out the cm^3, and multiply the top two numbers. I used a calculator:
130377 g
We're not done yet! The question asks for how much it is in kg, not g. We could use D.A. , but g to kg is pretty easy. just put a decimal three paces in.
130.377 g = 130.377 kg
Now, either use D.A. to show your work, or just simply multiply.
130.377*0.35= $45.63
I think this is the right answer... Any questions, please comment!
The definition of parallel lines requires the undefined terms line and plane, while the definition of perpendicular lines requires the undefined terms of line and point. What characteristics of these geometric figures create the different requirements?
Answer:
Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.
Step-by-step explanation:
Its correct trust me.
Answer:
Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.
Step-by-step explanation:
find the exact value of the indicated trigonometric functions for the acute angle a:
Given: cot a= 3 3/7, find: cos a and tan a?
Answer:
cot a = 3 3/7
or, cot a = 24/7
or, tan a = 7/24
So,
cos a = 24/25
tan a = 7/24
Answered by GAUTHMATH
Anyone Answer Please
Answer:
shift of 6 units left
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
f(x) = 3 | x + 6 | + 9
Represents a horizontal shift of the parent function 6 units left
PLEASE Help! I need this by tomorrow!
Answer:
18m
Step-by-step explanation:
6 times 3 = 18
Find dy /dx of x² - 2x + 5 - 6x
Answer:
Step-by-step explanation:
If [tex]y=x^2-2x+5-6x[/tex] then
[tex]y=x^2-8x+5[/tex] by combining like terms. (I'm thinking you might have mistyped the problem because this representation is weird).
[tex]\frac{dy}{dx}=2x-8[/tex]
