Answer:
Step-by-step explanation:
For a given function f(x), we define the domain as the set of the possible inputs of the function and the range as the set of the outputs of the function.
We will see that both domain and range are the set of all real numbers.
D = (-∞, ∞)
R = (-∞, ∞)
Here we have the function:
The first thing we need to do is find the domain.
We start by assuming that the domain is the set of all real numbers and then we try to find some given values of x that cause some undefined operation, and then we remove these values of x from the domain.
Where this would be something like a zero in the denominator or something like that. We also could have specific restrictions to the domain that are applied in some specific cases (for example if x represents a length we should remove the negative values from the domain).
Here we can see that we do not have any indetermination, thus the domain is the set of all real numbers.
Now to study the range we need to see the general function, we can see that as x tends to negative infinity y will also tend to negative infinity, while when x tends to infinity y will also tend to infinity.
Then the range will also be the set of all real numbers.
Please hurry I will mark you brainliest
It's a hot summer
day and the icecream truck is on it's way. The driver gives you two options:
1) You can have a cone that is doubled in radius but the same height as a regular cone.
OR
2) You can have a cone that is doubled in height but the same radius as a regular cone.
Which would you choose and why?
You can explain it or attach a picture of your work.
Answer:
Volume of a cone - πr^2(h/3)
Step-by-step explanation:
If radius doubled - π2r^2(h/3)
If height doubled - πr^2(2h/2)
Let's assume r and h to be 1.
Radius doubled = 2π(1/3) = 2.09439510239 (volume)
Height doubled = π(2/3) = 2.09439510239 (volume)
If radius and height equal for 1, does it mean it is equal for other values too?
Let's use 2 instead of 1 and find out:
8π(2/3) - Option 1
8π(2/3) - Option 2
Both are the same...
Answer:
2x on the radius...
Vol = [tex]\frac{1}{3} \pi r^{2} h[/tex]
[tex]\frac{1}{3} \pi[/tex] is constant (in this story)
[tex](2r)^{2}[/tex] vs. 2h ... the [tex](2r)^{2}[/tex] will most likely be bigger...
I say most likely because if the cone radius was super small and
the height was super long (like a straw, or a piece of spaghetti)
then the 2x on the height actually can be better
Step-by-step explanation:
4) If x/y = 7/3 then find the value of
[tex]3x ^{2} + 2y^{2} \3x^{2} - 2y {}^{2} [/tex]
Answer:
1011
Step-by-step explanation:
3x^2 + 2y^2 x^2 - 2y^2
3(7)^2 + 2(3)^2 3^2 - 2(7)^2
3(7^2 + 2 x 3 x 7^2 - 2 x 3)
3(7^2 +6 x 7^2 - 6)
3(7 x 7^2 - 6)
3(7^3 - 6)
3(343 - 6)
3(337) = 1011
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
a = 7.3 in.
b = 13.2 in.
c = 15.8 in.
A = 27.3°, B = 56.1°, C = 96.6°
No triangle satisfies the given conditions.
A = 29.3°, B = 54.1°, C = 96.6°
A = 25.3°, B = 56.1°, C = 98.6°
Answer:
A) A = 27.3°, B = 56.1°, C = 96.6°Step-by-step explanation:
Use the Law of Cosines:
A = arccos [(b² + c² - a²)/(2bc)] = arccos [(13.2² + 15.8² - 7.3²)/(2*13.2*15.8)] = 27.3° B = arccos [(a² + c² - b²)/(2ac)] = arccos [(7.3² + 15.8² - 13.2²)/(2*7.3*15.8)] = 56.1°C = 180° - (A + B) = 180° - (27.3° + 56.1°) = 96.6°Correct choice is A.
Three identical squares are placed side by side to form a rectangle with a perimeter of 104 inches. What is the area, in square inches, of each square?
Answer: 169 square inches
Step-by-step explanation:
If the squares are placed side by side, then their perimeter will equal 8x, x being the length of one side
If we set that equal to the perimeter, we get 104=8x, and x=13
So 13 is the length of one side, and A=l x w so A=169 square cm
* if my savings of $x grows 10% each year how much money would i have in 1 year
I WILL MARK BRAINLIEST
Answer:
10/100*$x
Step-by-step explanation:
You will multiply the $x by 10%
Need help! Please answer quickly! :)
Answer: a
Step-by-step explanation:
What is the total surface area (including the area of the floor) of a building shaped as a hemisphere with radius 106 ft ?
Round your answer to the nearest whole number.
Answer:
105897 ft²
Step-by-step explanation:
let, r be the radius, so r = 106 ft
Surface area of a hemisphere,
2πr²+πr²
= 2π×106²+π×106²
= 105897 (rounded to the nearest whole number)
what if 7 dogs are in a room a man with a dog coms in and takes two and leaves his which has 3 pups how many dong are there
Answer:
8
Step-by-step explanation:
7 - 2 + 3 = 8
Answer:
9
Step-by-step explanation:
9 / 7 - 2 = 5 + 3 = 8 plus the Dog the man left behind, it would be 9
Determine what type of model best fits the given situation: the temperature of a cup of coffee decreases by 5 F every 20 minutes.
A. liner
B. exponential
C. quadratic
D. none of these
Answer: T = -t / 4 + T0 where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature
Explanation: This is a linear equation in T and t
(-1 / 4 represents -5 deg / 20 min = - 1 deg / 4min
Find an explicit rule for the nth term of the sequence.
The second and fifth terms of a geometric sequence are 20 and 1280, respectively.
Step-by-step explanation:
in a geometric sequence there is a constant factor x that is multiplied with every previous term to create the next one.
a2 = 20
a5 = 1280 = a2×x×x×x = a2×x³ = 20x³
64 = x³
x = 4
=> a1 = 5
therefore
an = an-1×4 =
[tex]a1 \times {4}^{n - 1} [/tex]
n > 1
HI I NEED HELP WITH THIS QUESTION ASAP!!!!!! ITS URGENT PLEASE HELP
A group of rowdy teenagers near a wind turbine decide to place a pair of
pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.
a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.
b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.
a) The sinusoidal function is y = 7·sin(π/15(t - 2.5)) + 9
b) The height of the shorts at t = 10 minute is approximately 6 meters
The above answers were arrived at as follows
a) The general form of a sinusoidal equation is presented as follows;
y = A·sin(B(t - h)) + k
Where;
A = The amplitude of the graph of the function
The period, T = 2·π/B
h = The horizontal shift
k = The vertical shift
The maximum height of the blade = 16 meters
The minimum height of the blade = 2 meters
The time the blade moves from maximum height to minimum height = 25 s - 10 s = 15 s
Therefore, the time it takes the blade to move from maximum height to minimum height, the period, T= 2 × 15 s = 30 s
Therefore;
B = 2·π/30 = π/15
B = π/15
When B·(t - h) = π/2, t = 10
Therefore;
(π/15)·(10 - h) = π/2
10 - h = 15/2
h = 10 - 15/2 = 2.5
The horizontal shift, h = 2.5
The amplitude, A = (Max - Min)/2
∴ A = (16 - 2)/2 = 7
A = 7
The vertical shift, k = Min - (-Amplitude)
∴ k = 2 - (-7) = 9
The vertical shift, k = 9 Up
Therefore, the equation of the sinusoidal equation that describes the height of shorts in terms of time is given by plugging in the values of the variables, A, B, h, and k to get the following equation;
y = 7·sin(π/15·(t - 2.5)) + 9
b) The height of the shorts at exactly, t = 10 minutes = 600 seconds, is given as follows;
y = 7·sin(π/15·(t - 2.5)) + 9
10 minutes = 600 seconds
When t = 10 minutes = 600 seconds
∴ y = 7·sin(π/15(600 - 2.5)) + 9 = 5.5 ≈ 6
The height of the shorts at exactly t = 10 minutes ≈ 6 meters.
Get more information on sinusoidal functions here;
https://brainly.com/question/16820464
What numbers are divided by -10 that equal 5?
Answer:
-50
Step-by-step explanation:
x / (-10) = 5
Multiply both sides by -10:
x = -50
Answer:
50
Step-by-step explanation:
50/10=5
[tex]50 \div 10 = 5 \\ [/tex]
Susan wants to make pumpkin bread and zucchini bread for the school bake sale. She has 15 eggs and 16 cups of flour in her pantry. Her recipe for one loaf of pumpkin bread uses 2 eggs and 3 cups of flour. Her recipe for one loaf of zucchini bread uses 3 eggs and 4 cups of flour. She plans to sell pumpkin bread loaves for $5 each and zucchini bread loaves for $4 each. Susan wants to maximize the money raised at the bake sale. Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes. What is the objective function for the problem
Answer:
Objective Function z
z = 5*x + 4*y . to maximize
Step-by-step explanation:
eggs flour
P. Bread (x) 2 3
Z. Bread . (y) 3 4
Availability . 15 16
Constraints.
Eggs availability . 15
2*x + 3*y ≤ 15
Flour availability 16 cups
3*x + 4*y ≤16
Objective Function z
z = 5*x + 4*y . to maximize
The model:
z = 5*x + 4*y . to maximize
Subject to:
2*x + 3*y ≤ 15
3*x + 4*y ≤16
x ≥ 0 y ≥ 0 . integers
Answer: C
Step-by-step explanation:
Correct on edg 2020
Given f(x) = - 3/4x + 2, find f(16).
Answer:
-10
Step-by-step explanation:
Find the value of x.
Answer:
x = 110°
Step-by-step explanation:
The Outside Angle Theorem states that the measure of the angle formed by two secants or a secant and tangent from a point outside of a circle is half the difference between the two arcs.
This means that ½ (210 – x) = 50.
½ ( 210 – x ) × 2 = 50 × 2
210 – x = 100.
210 – x + x = 100 + x.
210 = 100 + x.
100 + x = 210.
100 + x – 100 = 210 – 100.
x = 110.
This value must be true because:
½ ( 210 – 110 ) = 50.
½ ( 100 ) = 50.
50 = 50.
A merry-go-round has 25 horses. Each horse
is labeled consecutively with a letter from A to
Y-the first horse is labeled A, the second
horse is labeled B, and so on. A child walks
around the merry-go-round, starting at horse
A and continuing in alphabetical order,
counting as she goes. She stops at the 337th
horse. What is the letter of that horse?
A. A
B. J
C. K
D. L
E. M
Answer:
M
Step-by-step explanation:
337 / 25 = 13.48
Round to the nearest whole number = 13
The 13th letter of the alphabet is m, so:
The answer is M.
Find the distance between points (a,b) and Q -a,-b)
Answer:
d = 2* sqrt(a^2 + b^2)
Step-by-step explanation:
Interesting question. You should begin by noting that 0 is not the answer although it looks like it should be.
P = (a,b)
Q= (-a,-b)
x1 = a
x2 = - a
y1 = b
y2 = - b
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
d = sqrt( (-a - a)^2 + (-b - b)^2 )
d = sqrt ( -2a)^2 + - (2b)^2 )
d = sqrt(4a^2 + 4b^3)
d = 2* sqrt(a^2 + b^2)
Explain how the Quotient of Powers Property was used to simplify this expression. 5 to the fourth power, over 25 = 52
If f(x) = 3x2 - 7x, what is the ordered pair for x = 1 ?
A (1.4)
B (1,-4)
C (1,7)
D(1,10)
Answer:
b option is the weight answer I think.
A circle is represented by the equation below:
(x − 9)2 + (y + 8)2 = 16
Which statement is true?
a) The circle is centered at (−9, 8) and has a radius of 8.
b) The circle is centered at (9, −8) and has a diameter of 8.
c) The circle is centered at (9, −8) and has a radius of 8.
d) The circle is centered at (−9, 8) and has a diameter of 8.
Answer:
The center is (9,-8) and the diameter is 8
Step-by-step explanation:
(x − 9)^2 + (y + 8)^2 = 16
A circle is in the form
(x − h)^2 + (y -k)^2 = r^2 where (h,k) is the center and r is the radius
(x − 9)^2 + (y - -8)^2 = 4^2
The center is (9,-8) and the radius is 4
The diameter is 2 times the radius so the diameter is 8
The center is (9,-8) and the diameter is 8
- 5x + x - 6x²
6x3 - 4 - 5 + 6x3 - 3x3
Is this all one equation?
If it isn't, here:
-6x ^ 2 - 4x <-- Equation 1
18 - 9 + 18 - 9 = 18 <-- Equation 2
If it is:
-5x + x - 6x ^ 2 + 6 * 3 - 4 - 5 + 18 - 9
-4x - 6x ^ 2 + 18 - 9 + 18 - 9
-4x - 6x ^ 2 + 18
Then we order it
-6x ^ 2 - 4x + 18
How many people can Liam buy lunch for
Answer:
At most, Liam can only buy lunch for 6 people.
Step-by-step explanation:
It isn't going to be a decimal answer because there can't be half of a person
All you have to do is divide 50 by 8 and round down because you don't want to spend more than 50 dollars.
Writing it mathematically, it would be:
p [tex]\leq[/tex] 6
I'LL GIVE BRAINLIEST !!!! FASTERR
please explain how do you get the answer !
Answer:
i) 37
ii) 120
iii) 157
Explanation:
i)
BCA = 180-ACD (Linear Pair)
BCA=180-60
BCA = 120
23+x+BCA=180
143+x=180 (Angle sum property)
x=37
ii) Since triangle ABD is equilateral all of its angles are 60
y+ADC=180
y = 180-ADC (Angles on straight line adds upto 180)
y=180-60
y = 120
iii) Using the values from part i and ii
x+y = 120+37
= 157
Must click thanks and mark brainliest
find the missing side of the triangle
Answer:
25
Step-by-step explanation:
[tex]a^2 + b^2 = c^2[/tex]
[tex]24^2 + 7^2 = x^2[/tex]
[tex]576 + 49 = x^2[/tex]
[tex]x ^ 2 = 625[/tex]
[tex]x = 25[/tex]
Answer:
Using Pythagoras theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](x)^{2} =(24)^{2}+(7)^{2}[/tex]
[tex]x^{2} =576+49=625[/tex]
[tex]x=\sqrt{625} =25[/tex]
[tex]x=25[/tex]
OAmalOHopeO
You and six friends play on a basketball team. A sponsor paid $100 for the league fee, x dollars for each player’s T-shirt, and $68.25 for trophies. Write an expression for the total amount paid by the sponsor
Answer:
Total amount paid by the sponsor = 175 + 6d
Step-by-step explanation:
You and 5 friends = 6 people
Cost of renting a bus = $75
Team entry fee = $100
Cost of each student t shirts = $d
Cost of 6 student t shirts = $d × 6= $6d
Write an expression for the total amount the sponsor paid.
Total amount paid by the sponsor = Cost of renting a bus + Team entry fee + Cost of 6 student t shirts
= $75 + $100 + $6d
= $175 + $6d
Total amount paid by the sponsor = 175 + 6d
Where,
d = cost of each student t shirts
Find f(-2).....................................
Answer:
1/25
Step-by-step explanation:
f(x) = 5^x
Let x = -2
f(-2) = 5^-2
We know a^-b = 1/a^b
f(-2) = 1/5^2
= 1/25
Answer:
[tex]\frac{1}{25} [/tex]
Step-by-step explanation:
[tex]f(x) = {5}^{x} \\ f( - 2) \\ f( - 2) = {5}^{ - 2} \\ = \frac{1}{ {5}^{2} } \\ = \frac{1}{25} [/tex]
7
Setting 3 equal to which ratio would result in a valid proportion?
9
49
18
42
织但
Answer:
000
Step-by-step explanation:
000
If a bicyclist rides for 100 minutes at an average speed of 14 miles per hour, how far was the ride, to 1 decimal place?
Answer:
23.3 miles
Step-by-step explanation:
- convert 1hour = 60minutes
14 miles per 1 hour , is the same as
14 miles per 60 minutes
-write an equivalent fraction to keep the proportion
14 miles/60 minutes = ? miles / 100 minutes
-cross multiply , and divide by 60
? = (14*100) / 60 = 23. 3333333...
-round to 1 decimal place
23.3 miles
Write the equation in standard form then factor the left side of the equation. 2x^2=28-x
Answer:
Step-by-step explanation:
Standard for is 5x=28. Factoring gives you x=28/5
SEE QUESTION IN IMAGE
Answer:
20Find the mean:
(2*1 + 1*2 + 2*3 + 1*4 + 2*5)/(2 + 1 + 2 + 1 + 2) = 3Find the variance:
[2*(1-3)² + (2 - 3)² + 2*(3 - 3)² + (4 - 3)² + 2*(5 - 3)²]/8 = 18/8 = 9/421Find the range:
10 - 2 = 8Find the mean:
(2 + 3 + 4 + 5 + 6 + 6 + 7 + 8 + 9 + 10)/10 = 6Find the variance:
[(2 - 6)² + (3 - 6)² + (4 - 6)² + (5 - 6)² + 2(6 - 6)² + (7 - 6)² + (8 - 6)² + (9 -6)² + (10 - 6)²]/10 = 6The difference:
8- 6 = 222The mean:
(0 + x + 2 + 3x + 6 + 4x + 8)/4 = 8Find the value of x and the data points:
8x + 16 = 328x = 16x = 2The points are:
0, 2 + 2 = 4, 3*2 + 6 = 12, 4*2 + 8 = 16The mean deviation:
(0 - 8 + 4 - 8 + 12 - 8 + 16 - 8)/4 = 0Note. Mean absolute deviation is different, this is the average of absolute values of mean deviations:
(8 + 4 + 4 + 8)/4 = 6