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Answer:
use symbolab it will help you with almost anything
Related Questions
Answer both please
Find the domain of the function. (Enter your answer using interval notation.)
f(x) =
4x³-3
x² + 4x - 5
7. [-/3 Points]
f(-8)
=
Evaluate f(-8), f(0), and f(4) for the piecewise defined function.
f(x) =
x+4 if x < 0
2-x if x 20
f(0) =
f(4) =
Answers
The solution is, the domain is: x ∈ (-∞, ∞).
Here, we have,
When we have two functions, f(x) and g(x), the composite function:
(f°g)(x)
is just the first function evaluated in the second one, or:
f( g(x))
And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:
f(x) = 1/(x + 1)
where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.
Now, we have:
f(x) = x^2
g(x) = x + 9
then:
(f ∘ g)(x) = (x + 9)^2
And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:
x ∈ (-∞, ∞)
(g ∘ f)(x)
this is g(f(x)) = (x^2) + 9 = x^2 + 9
And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:
x ∈ (-∞, ∞)
(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4
And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:
x ∈ (-∞, ∞)
(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18
And again, there are no values of x that cause a problem here,
so the domain is:
x ∈ (-∞, ∞)
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complete question:
Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat
Solve the equation.
22
= 6
2 =
Answers
Z/2=6
(Multiply both sides by 2)
Z=6*2
Z=12
b) The Median and Mode of the following wage distribution are known to be $33.5 and $34 respectively. Three frequency values from the table are, however, missing. Find the missing values. Wages (in $) 0-10 10- 20 20 - 30 30 - 40 40-50 50 - 60 60-70 Frequencies (f) 10 10 ? ? ? 6 4 230
Answers
The frequencies based on the information are are 100, 40, and 6.
How to explain the frequencyIn the formula of the median, we have to calculate cumulative frequencies and have to use cumulative frequency of the interval previous to the median class. Also, in the formula of mode, frequencies are used and not the cumulative frequencies.
140 - y = 100
y = 40
substituting y and x in equation 1 is:
x + y + z = 146
100 + 40 + z = 146
z = 6
Therefore, the missing frequencies are 100, 40, and 6.
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use the graph below to find the indicated function value
Answers
Answer:
Step-by-step explanation:
Bozo can read at a rate of 300 words every four minutes. what is his rate of reading in words per minute?
Answers
Answer:
Bozo's rate of reading in words per minute is 75 (300 words / 4 minutes = 75 words/minute).
Step-by-step explanation:
Mark Brainliest!!
Answer: 75 words per minute
Step-by-step explanation:
We will divide 300 words by 4 to find the rate of words per minute since the original rate is words per four minutes.
300 / 4 = 75 words per minute
A man is flying in a hot air balloon in a straight line at a constant rate of 5' per second while keeping it at a constant altitude. As he approaches the parking lot of a market. , he notices that the angle of depression from his balloon to a friend's car in the parking lot is 34ﾟ. A minute and a half later after flying directly over his friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36ﾟ At that time what is the distance between him and his friend?
Answers
The distance is given as 272.98 feet.
What is Angle of Depression?The measurement of the angle of depression relates to the formation between a horizontal line and the observer's sightline to an object or point that exists beneath their level.
Therefore, it demonstrates the formed degree between the observer's line of vision towards a subject and the horizontal flatness visible when looking downwards at it from afar.
This notion is prevalent throughout trigonometry and play a vital role in areas including surveying, navigation and architecture. The degrees obtained from this practice are generally calculated via angles, with a complete 90-degree measure indicative of viewing straight downward over the designated target.
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Helppp I need the ending numbers ?
Answers
The solution is, the simplification of the equation is :
4x^2 - 4 = (2x -2 ) (2x+2)
Here, we have,
given that,
the expression is:
4x^2 - 4
now, we have to simplify this.
we know that ,
The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.
It is one of the algebraic identities.
It is used to factorize the binomials of squares.
The a^2 - b^2 formula is given as:
a^2 - b^2 = (a - b) (a + b).
so, we have,
4x^2 - 4
= (2x)^2 - 2^2
= (2x -2 ) (2x+2)
Hence, The solution is, the simplification of the equation is :
4x^2 - 4 = (2x -2 ) (2x+2)
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using algebra prove that given any 3 consecutive whole numbers, the sum of the square of the smallest number and the largest number is always 2 more that twice the square of the middle number
Answers
Answer:
Let x, x + 1, and x + 2 be the three numbers.
x^2 + (x + 2)^2 = x^2 + x^2 + 4x + 4
= 2x^2 + 4x + 4
= 2x^2 + 4x + 2 + 2
= 2(x^2 + 2x + 1) + 2
= 2(x + 1)^2 + 2
What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
Answers
The value of Q₃ of the data represented by the box plot is,
⇒ Q₃ = 30
Given that;
A box plot is shown in figure.
Now, We have been given an image of a box plot and we are asked to find the value of third quartile represented by our given box plot.
Since, we know that the upper or 3rd quartile is represented by the last line of the box.
We can see that 1st line of our box is at 20 ,so it will be 1st or lower quartile.
And, The middle line is at 25, so median for our given box plot is 25.
The last line of the box is at 30, which is representing the upper or third quartile of our given box plot.
Therefore, the third quartile, is 30 for our given box-plot.
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Use Heron's formula to find the area of the triangle with side lengths 9, 12, and 18, as shown below.
Answers
A = sqrt(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, given by:
s = (a+b+c)/2
For the triangle with side lengths 9, 12, and 18, we have:
s = (9+12+18)/2 = 39/2
Using Heron's formula, we get:
A = sqrt((39/2)(39/2-9)(39/2-12)(39/2-18))
A = sqrt((39/2)(15/2)(27/2)(3/2))
A = sqrt(72915/16)
A ≈ 269.258
Therefore, the area of the triangle with side lengths 9, 12, and 18 is approximately 269.258 square units.
Answer: the answer is 48 or b
Step-by-step explanation:
Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:
A = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter, which is half the perimeter of the triangle:
s = (a + b + c) / 2
In this case, the side lengths are a = 9, b = 12, and c = 18. Therefore, the semiperimeter is:
s = (9 + 12 + 18) / 2 = 39 / 2
Using Heron's formula, we can now calculate the area of the triangle:
23=-8v-7+2v????????????????????
Answers
Answer:
v=-5
Step-by-step explanation:
Answer:
[tex]23 = 10v - 7 \\ 23 + 7 = 10v \\ 30 = 10v \\ v = 3 \\ \\ [/tex]
Based on a poll, 60% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among three randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? (Round to three decimal places as needed.)
Answers
The probability that at least one of the three users is more careful is 0.936.
How to find the probability that among three randomly selected Internet users, at least one is more carefulWe need to find the probability that a single randomly selected Internet user is more careful, which is 0.60.
The probability that none of the three users are more careful is (0.40)^3 = 0.064.
Therefore, the probability that at least one of the three users is more careful is 1 - 0.064 = 0.936.
Rounding to three decimal places, the answer is 0.936.
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The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answers
The average rate of change for function f(x) = 1.85x² to the nearest tenth over the interval 10 ≤ x ≤ 20 is equal to 55.5 (Rounding to the nearest tenth).
Function models the cost of a square carpet
f(x) = 1.85x²
The average rate of change of a function f(x) over an interval [a, b] is,
Average rate of change = [f(b) - f(a)] / (b - a)
The average rate of change of f(x) over the interval 10 ≤ x ≤ 20.
Using the given function, we have,
f(10) = 1.85(10)²
= 185
f(20) = 1.85(20)²
= 740
Now calculate the average rate of change,
average rate of change
= [f(20) - f(10)] / (20 - 10)
= (740 - 185) / 10
= 55.5 (Rounding to the nearest tenth)
Therefore, the average rate of change of function f(x) over the interval 10 ≤ x ≤ 20 is approximately 55.5.
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answers
As per the given percentage, the value of the loan 10 years after it starts is £4506.32.
We know the values of P and A for the first two years. So, we can use these values to find the value of r. Let's use the formula for the first year:
2645 = 2500(1 + r/1)¹ˣ¹
Simplifying the equation, we get:
1 + r = 2645/2500
1 + r = 1.058
r = 0.058 or 5.8%
Therefore, the interest rate per annum is 5.8% (to 1 decimal place).
Now, let's move on to finding the value of the loan after 10 years. We can use the same formula for compound interest, but we need to substitute the values of P, r, n, and t accordingly. Here's the formula:
A = P(1 + r/n)ⁿˣ
Where:
P = 2500
r = 0.058
n = 1 (as the interest is compounded annually)
x = 10
Substituting these values, we get:
A = 2500(1 + 0.058/1)¹ˣ¹⁰
A = 2500(1.058)¹⁰
A = 4506.32
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Joey's current monthly expenses include a rent payment of $1,100, a $178 car payment, and a combined minimum payment of $220 for his credit card debt. His current gross monthly income is $3,600. If Joey moves to a new apartment, what is the maximum monthly rent payment he can make and still maintain a DTI ratio of 36%?
a.
$702
b.
$898
c.
$922
d.
$960
Answers
Based on Joey's debt-to-income ratio, the maximum monthly rent payment he can make and still maintain the DTI ratio would be; b. $898.
WE are given that Joey has a DTI ratio of 36% which means that his maximum debt payment should be 36% of his income.
This amount would be:
= DTI x monthly income
= 36% x 3,600
= $1,296
Maximum monthly rent can be found as:
= Maximum monthly debt payment - Car payment - Credit card payment
= 1,296 - 178 - 220
= $898
In conclusion, option B is correct.
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Write an explicit formula for an, the nth term of the sequence 36, 32, 28, ....
WORTH 20
Answers
Answer:
an = 36 + -4(n - 1)
Step-by-step explanation:
Explicit formula:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
an = nth terma1 = first termd = common differenceHere, we are given the following:
Sequence: 36, 32, 28The first term is 36
To get to the next term, 4 is subtracted from the previous term so the common difference is -4.
So we have:
First term(a1) = 36Common difference = -4By plugging this into [tex]a_n=a_1+(n-1)d[/tex]
We acquire : [tex]a_n=36+(n-1)(-4)[/tex]
Trigonometry question. Please help me
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The apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
What is a rectangular base pyramidIn a rectangular base pyramid, the base is a rectangle and the apex (or top point) is directly above the center of the rectangle.
The apex angle is the angle formed by the edges of the pyramid at the apex. In a rectangular base pyramid, the apex angle depends on the dimensions of the rectangle base and the height of the pyramid. It can be calculated using trigonometric functions.
The apex angles bec and aed formed by the opposite width of the rectangle base are equal.
In conclusion, the apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
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Using any example of a 2 by 2 matrix;
Show that (A inverse) inverse = A; where A is a 2 by 2 matrix
Answers
The inverse of A is A^-1 (see picture), where A^-1 = (1/(determinant of A))*(adjoint of A). Note that the inverse of A only exists if ad - bc ≠ 0.
So, if ANY example of a 2 by 2 matrix is allowed… we use an example where a = 1, b = 2, c = -3, d = -5. The inverse matrix will have the terms -5, -2, 3, 1. (See photo)
To show that the inverse OF the inverse equals A, follow the same process. And.. yes, (A^-1)^-1 = A. We want to see the identity matrix 1, 0, 0, 1 since A*A^-1 = I (this is an uppercase i).
I’m on my phone so it’s harder to type. Refer to the picture to see my work:
I hope this helps!
what is the average rate of change for the following intervals?
[-5,-4]
[-4,-3]
[-4,-1]
[-3,-1]
Answers
The average rate of change for the given intervals are:
(-5, -5) and (-4, 0): 0(-4, 0) and (-3, 3): 3(-4, 0) and (-1, 3): 1(-3, 0) and (-1, 0): 0How to find the average rate of changeTo compute the average rate of change for any given interval, determine the change between the function values at the endpoints and divide this value by the difference in independent variable values. it can be expressed as follows:
Average Rate of Change = (f(b) - f(a)) / (b - a)
The average rate of change for each point in the interval is determined form the graphs and used to solve for the average rate of change
(-5, -5) and (-4, 0):
Average Rate of Change = (0 - 0) / (-4 - (-5)) = 0 / 1 = 0
(-4, 0) and (-3, 3):
Average Rate of Change = (3 - 0) / (-3 - (-4)) = 3 / 1 = 3
(-4, 0) and (-1, 3):
Average Rate of Change = (3 - 0) / (-1 - (-4)) = 3 / 3 = 1
(-3, 0) and (-1, 0):
Average Rate of Change = (0 - 0) / (-1 - (-3)) = 0 / 2 = 0
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Which of the following is equal to 6,000 mL can someone also like give me like a step to step explanation for i can write it down
Answers
6,000 mL is equal to 6 litres
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 6,000 mL is equal to 6L
One litre is equal to 1000 ml
1 l = 1000 ml
6 l=6000 ml
Hence, 6,000 mL is equal to 6 litres
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At their practices, the volleyball team ran a total of 10 miles in 14 days. The tennis team ran a total of 8 miles in 7 days. Which team ran more miles per day?
Answers
Answer:
tennis team
Step-by-step explanation:
because they ran 8 miles is 7 days to get equal amount of days you multiply by 2 on both 8 miles and 7 days so they ran 16 miles in 14 days thats y tennisbteam ran more miles
A construction team maintains a 52 mile long sewage pipe. Each day the team can cover 4/5 of a mile. How many days will it take the team to complete the maintenance of the entire sewage pipe
Answers
It will take the team 65 days to complete the maintenance of the entire sewage pipe
How many days will it take the team to complete the maintenance of the entire sewage pipeFrom the question, we have the following parameters that can be used in our computation:
Sewage pipe = 52 miles
Distance covered each day = 4/5 miles
Using the above as a guide, we have the following:
Number of days = Sewage pipe /Distance covered each day
Substitute the known values in the above equation, so, we have the following representation
Number of days = 52/(4/5)
Evaluate the quotient
Number of days = 65
Hence, the number of days is 65
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Round 2,561 to the nearest hundred.
Answers
Answer:
2,600.
Step-by-step explanation:
Rounding 2,561 to the nearest hundred means rounding it to the nearest multiple of 100.
To do this, we need to look at the digit in the tens place, which is 6. Since 6 is greater than or equal to 5, we round up the digit in the hundreds place, which is 25, by 1.
Therefore, rounding 2,561 to the nearest hundred gives us 2,600.
3.
You have two credit cards. If you budget $375 to pay off your credit card debt and you payoff the highest interest card first while maintaining the interest accrued on the other card, how many months does it take you to pay it off?
Card Name (APR %) Existing Balance Credit Limit
Murk (5.6%) $675.49 $1,500.00
Mini (9.85%) $902.43 $1,000.00
5 months
2 months
4 months
3 months
Answers
It takes A. 5 months to pay off (Mini) the highest interest card.
How many months to pay off the highest interest card debt?To determine the number of months it takes to pay off the credit card debt, we shall calculate the monthly payment to pay off the highest interest card first.
First, calculate interest accrued on each card per month:
Murk: (5.6/100)/12 * $675.49 = $2.98 per month
Mini: (9.85/100)/12 * $902.43 = $7.42 per month
Next, we determine the order in which to pay off the cards, which is highest interest card first, we can allocate the entire $375 to Mini and leave a minimum for interest accrued on Murk.
This should be a percentage of the balance.
Assuming it's 2% of the balance, which is $13.51.
So, in month 1, we will pay:
Mini: $375
Murk: $13.51
Leaving these balances:
Murk: $675.49 + $2.98 - $13.51 = $664.96
Mini: $902.43 - $375 + $7.42 = $534.85
In month 2:
Mini: $534.85 + $7.42 = $542.27
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $664.96 + $2.98 - $16.49 = $651.45
Mini: $542.27 - $375 + $7.42 = $174.69
month 3:
Mini: $174.69 + $7.42 = $182.11
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $651.45 + $2.98 - $16.49 = $638.94
Mini: $182.11 - $174.69 + $5.52 = $12.94
month4:
Mini: $12.94 + $7.42 = $20.36
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $638.94 + $2.98 - $16.49 = $625.43
Mini: $20.36 - $12.94 + $0.54 = $8.96
month 5:
Mini: $8.96 + $7.42 = $16.38
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $625.43 + $2.98 - $16.49 = $612.92
Mini: $16.38 - $8.96 = $7.42
So, Mini's balance is paid off here.
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Note:
And we can allocate the entire $375 budget to Murk.
This means we will pay off Murk in month 6:
Murk: $612.92 + $2.98 + $375 - $13.51 = $977.39
The insurance premium of a new bus is GH¢93.30 plus 15% of the insured value. What is the insurance premium of a bus whose insured value is GH¢250.00?
Answers
The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.
Let's first calculate 15% of¢250.00:
15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50
Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:
GH¢93.30 + GH¢37.50 = GH¢130.80
Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
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The length of one of the legs of a right triangle is 17. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides (the second leg).
Answers
The value of the smaller of the two missing sides (the second leg) is,
⇒ 144 units
We have to given that;
The length of one of the legs of a right triangle is 17.
And, The lengths of the other two sides are consecutive integers.
Hence, Let the smallest of the other legs be x,
And, the hypotenuse be x + 1.
So, By using the Pythagorean theorem as;
⇒ 17² + x² = (x + 1)²
⇒ 289 + x² = x² + 1 + 2x
⇒ 2x = 288
⇒ x = 144
Thus, The value of the smaller of the two missing sides (the second leg) is,
⇒ 144 units
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you collect $20.92 for selling 4 video games and 2 cellphones on a website. Your friend collects $23.44 for selling 4 video games and 3 cell phones on a website. How much do you collect for each videogame
Answers
Let's call the cost of each video game "x". We can set up two equations based on the information given:
4x + 2(0.01) = 20.92 (the 0.01 represents the commission fee for each phone)
4x = 20.92 - 0.02
4x = 20.90
x = 5.225
So each video game costs $5.225.
We can double-check our answer using the information about the friend's sales:
4(5.225) + 3(0.01) = 23.44
20.90 + 0.03 = 23.44
23.44 = 23.44
So our answer is correct.
4,12,44,176,890
which is odd one ?
Answers
Answer:
890 as it is not divisible by 4
Find the value of $x$ . Write your answer in simplest form. 9 squared 2
Answers
The value of the expression 9 squared will be 81.
How to explain the expressionIn Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value will be:
= 9²
= 9 × 9.
= 81
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Select the correct answer.
Which of these statements defines the term resources?
O A. materials that help you achieve your goals
OB. all the goods and services provided to people
OC. the government's ability to deal with economic problems
Reset
Next
Answers
The statements that defines the term resources is A. materials that help you achieve your goals.
What is resources?Resource can be described as all the materials available that is available in individual environment and can be seen as one that is technologically accessible.
It should be noted that resources do help us to achieve most of our goals and can be seen as one that is economically feasible as welll as culturally sustainable and they serves as things that can help us and thjat can satisfy our needs and wants which is needed on daily basis.
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