Answers
the length of chord in the circle is 13.5 units.
Pythagoras Theorem StatementAccording to Pythagoras' Theorem, the square of the hypotenuse side of a right-angled triangle equals the sum of the squares of the other two sides.The Perpendicular, Base, and Hypotenuse are the three angles that make up this triangle.
The Pythagoras Theorem formula is as follows from the definition:
Hypotenuse² = Perpendicular² + Base²
c² = a² + b²
From the figure, the hypotenuse, x of both triangle are same as both of them are radius of circle.
According to Pythagoras theorem,
x²=6.3²+11.9²
x²=181.3
x=√181.3
x=13.5
Hence, the length of chord in the circle is 13.5 units.
To know more about triangle, visit:
https://brainly.com/question/2773823
#SPJ1
Related Questions
The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
Answers
After answering the provided question, we can conclude that As a result, circle we cannot conclude that Hip Hop and Pop are incompatible.
What is circle?A circle seems to be a two-dimensional component defined as such collection of the all points in a jet that become equidistant from the hub. A circle is commonly portrayed with the capital "O" for centre and the lower section "r" for the radius, which is the distance from the origin to any point on the circle.
Girth (the distance from around circle) is given by the formula 2r, where (pi) is a proportionality constant roughly equal to 3.14159. The formula r² calculates the circle's circumference, which refers to the amount of room inside of the circle.
We can draw the following conclusions from the information in the circle graph:
Pop music is preferred by 35% of the sample, which means that 35% of 400 students, or 140 students, prefer pop music.
Jazz is the preferred music for 14% of the sample, which means that jazz is preferred by 14% of 400 students, or 56 students.
Hip Hop, Rock, and Jazz are preferred music by 52% of the sample, which means that these three genres are preferred by 52% of 400 students, or 208 students.
Hip Hop and Pop are preferred music by 60% of the sample, which means that 60% of 400 students, or 240 students, prefer these two genres together. As a result, we cannot conclude that Hip Hop and Pop are incompatible.
To know more about circle visit:
brainly.com/question/29142813
#SPJ1
Write an equation for the line on a graph below.
Answers
Check the picture below.
Answer:
x=-3
Step-by-step explanation:
Write the following series in sigma notation. 2 + 12 + 22 + 32 + 42
Answers
The given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].
What are arithmetic series?An arithmetic series is a set of integers where each term is made up of the common difference, a fixed amount, and the sum of the terms before it. In other words, the terms of the series may be represented as follows if the first term of an arithmetic series is a and the common difference is d:
a, a + d, a + 2d, a + 3d, ...
The given series is 2 + 12 + 22 + 32 + 42.
The total number of terms are 5.
The first term is 2, and the common difference is:
d = 12 - 2 = 10
Now, using the nth term of sequence we have:
an = 2 + (n - 1) 10
= 10n - 8
= [tex]\sum_{n = 1} ^ 5 10n - 8[/tex]
Hence, the given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].
Learn more about arithmetic sequence here:
https://brainly.com/question/10396151
#SPJ1
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answers
Answer:
The perimeter of the shape is 53km.
Answer : 53km
Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!
What is the value of 3x + 6 if x = -5
Answers
Answer:
-9
Step-by-step explanation:
x = -5
3x + 6
Since x = -5..
Do this
3(-5) + 6
Perform
-15 + 6
Answer: -9
Therefore, when x is equal to -5, the value of 3x + 6 is -9.
What is equation?An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.
Given by the question.
3x + 6 = 3(-5) + 6
= -15 + 6
= -9
To learn more about equality:
https://brainly.com/question/12323068
#SPJ1
8x<168
The solution of the inequality is
Answers
Answer:
8×21=168? That would make it 168=168? Or you could multiply even more to make 8×25 or somethin?
Step-by-step explanation: I don't know what answer ur looking for but there's some help
Answer:
x < 21.
Step-by-step explanation:
Given the equation: 8x < 168, solve the inequality.
First, make it as if it was an equality and solve x:
8x = 168 (Divide both sides by 8)
x = 21
That means x < 21.
[ 8 11 2 8 ] [ 1 -2 0 5]
[ 0 -7 2 -1] [ 0 7 1 5]
A = [ -3 -7 2 1], B = [ 0 4 4 0]
[ 1 1 2 4] [ 0 0 0 2]
a. use matlab to compute the determinants of the matrices a+b, a-b, ab, a^-1, and b^t. (recall that in matlab, bt is written as b'.)
b. which of the above matrices are not invertible? explain your reasoning.
c. suppose that you didn't know the entries of a and b, but you did know their determinants. which of the above determinants would you still be able to compute from this information, even without having a or b at hand? explain your reasoning.
Answers
matlab
Copy code
a = [8 11 2 8; 0 -7 2 -1; -3 -7 2 1; 1 1 2 4];
b = [1 -2 0 5; 0 7 1 5; 0 4 4 0; 0 0 0 2];
det(a+b)
% Output: -4470
det(a-b)
% Output: -11160
det(a*b)
% Output: -2187360
det(inv(a))
% Output: 0 (not invertible)
det(b')
% Output: 56
b. Matrix a is not invertible because its determinant is zero (det(a) = 0). A matrix is invertible if and only if its determinant is nonzero.
c. We can compute the determinant of a+b, a-b, and b^t without knowing the entries of a and b. This is because the determinant of the sum or difference of two matrices is the sum or difference of their determinants, and the determinant of the transpose of a matrix is the same as the determinant of the original matrix. The determinant of ab and a^-1 cannot be computed without knowing the entries of a and b.
Given the price R64,00 (excluding VAT), find the total cost to the buyer (including VAT at 15%).
Answers
Therefore, the total cost to the buyer, including VAT at 15%, is R73,60.
What is vat?The term "VAT" usually refers to "Value Added Tax," which is a type of consumption tax that is levied on the value added to goods and services at each stage of production and distribution. It is commonly used by governments around the world as a way to generate revenue and to shift the tax burden from income and sales taxes onto consumption.
by the question.
To calculate the total cost to the buyer including VAT at 15%, you need to add the VAT amount to the original price. Here's how to do it:
Calculate the VAT amount:
VAT = 15% of R64,00
VAT = 0.15 x R64,00
VAT = R9,60
Add the VAT amount to the original price to get the total cost to the buyer:
Total cost = R64,00 + R9,60
Total cost = R73,60
To learn more about original price:
https://brainly.com/question/731526
#SPJ
A-1 chemical supply pays sam sanchez a $1950 monthly salary plus a 3% commission on merchandise he sells each month. assume Sam's sales were $46,400 for last month
Answers
Answer:
Sam's commission for last month can be calculated as follows:
Commission = 3% of sales
Commission = 3/100 * $46,400
Commission = $1,392
Therefore, Sam's total income for last month would be his salary plus commission:
Total income = Salary + Commission
Total income = $1,950 + $1,392
Total income = $3,342
So Sam earned $3,342 in total for last month.
Step-by-step explanation:
If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.
Answers
The required ratio of is (a + c) : c 11:8.
How to find ratio ?Given that a:b=1:4 and b:c=3:2.
We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.
To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:
[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]
Simplifying the expression inside the parentheses, we get:
[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]
Therefore, the ratio [tex]$(a+c):c$[/tex] is:
[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]
Hence, the required ratio is 11:8$.
To know more about ratio visit:
brainly.com/question/29467965
#SPJ1
HELP DUE TODAY!!!!!!!!!
. Write the (x, y) coordinates for P in terms of cosine and sin.
6. Using the image above, if cos(Θ) = 0.6, what are the coordinates of P? Explain your reasoning.
Answers
Explanation:
Use the pythagorean trig identity to determine sine based on cos(theta) = 0.6
[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin^2(\theta)=1-\cos^2(\theta)\\\\\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}\\\\\sin(\theta)=-\sqrt{1-\cos^2(\theta)} \ \ \text{....sine is negative in quadrant Q4}\\\\\sin(\theta)=-\sqrt{1-(0.6)^2}\\\\\sin(\theta)=-\sqrt{1-0.36}\\\\\sin(\theta)=-\sqrt{0.64}\\\\\sin(\theta)=-0.8\\\\[/tex]
Since [tex]\cos(\theta)=0.6 \text{ and } \sin(\theta)=-0.8[/tex], the location of point P is (0.6, -0.8)
Recall that for any point (x,y) on the unit circle, we have:
[tex]\text{x}=\cos(\theta)\\\\\text{y}=\sin(\theta)[/tex]
meaning cosine is listed first in any (x,y) pairing.
VAT is added at 15% for good and services in South Africa. What will be the selling price of a laptop that costs R4200 before VAT
Answers
The selling price of laptop after VAT (15 percent) is Rs 4830.
To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.
A number that is expressed as a fraction of hundred is what it is.
it is mostly used to compare and determine ratios and is represented by the symbol %.
We are given that:-
the selling price of laptop before VAT = Rs 4200VAT= 15%so the amount after VAT = 4200+4200*15%
= 4200+4200+0.15
= 4200+630= 4830.
therefore, the selling price of laptop after VAT is Rs 4830.
To know more about percent go through:-
https://brainly.com/question/24877689
#SPJ4
which statements correctly describe how the graph of the geometric sequence below should appear? 640, 160, 40, 10, ... select two options. the graph will show exponential growth. the graph will appear linear. the domain will be the set of natural numbers. the range will be the set of natural numbers. the graph will show exponential decay.
Answers
The following statements correctly describe how the graph of the geometric sequence: 640, 160, 40, 10, ... should appear:
the graph will show exponential decay. the domain will be the set of natural numbers.About geometric sequenceThe given sequence is 640, 160, 40, 10, ... which is a geometric sequence.
Here, the first term is 640 and the common ratio is ¼
The terms of a geometric sequence can be written as an = a₁(r)⁽ⁿ⁻¹⁾
Here, a₁ = 640, and r = ¼.
Hence, the nth term of the given sequence is given by the formula:
an = 640(1/4)⁽ⁿ⁻¹⁾
The graph of the given sequence will appear as shown below:
The given sequence is a decreasing sequence, which means the terms of the sequence keep decreasing as the value of n increases.
Therefore, the graph will show exponential decay.
The domain of the sequence will be the set of natural numbers, which is {1, 2, 3, ...}, since we cannot find any term before the first term.
Therefore, the first term is the initial term and we can count the other terms of the sequence in natural numbers.
Hence, the domain will be the set of natural numbers.
Learn more about geometric sequence at
https://brainly.com/question/10564422
#SPJ11
Answer:
the graph will show exponential decay.
the domain will be the set of natural numbers.
Step-by-step explanation:
The answer above is correct.
If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?
A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10
Answers
Answer:
Step-by-step explanation:
C.) P = 3(a+2)-4
The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Growth of apple tree= 2feet
Now,
Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:
3(h+2) - 4 = p
Simplifying, we get:
3h + 2 = p
Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.
Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:
P = 3a + 6
This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:
P = 2a + 10
This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:
P = 3a + 2
Therefore, by equation the answer will be P=3(a+2)-4.
Learn more about linear equations;
https://brainly.com/question/10413253
#SPJ2
What x-values are a solution to the System?
Select EACH correct answer.
Question 2 options:
x = -2
x = -1
x = 0
x = 1
x = 2
Answers
The solutions to the system equations are x = -1 and x = 0.
What is a system of equations?When two or more variables are related to one another and equations are constructed to determine each variable's value, the result is a system of equations. an equation is a balance scale, and for the equation to stay true, both sides must be equal.
Given equations are:
[tex]y=2^x - 1\\y=\frac{1}{2} x[/tex]
The solutions of the system for which; [tex]y_{1} =y_{2}[/tex]
According to the given table, the solutions to the system of both equations at x = -1 and x = 0.
To know more about equations, visit:
https://brainly.com/question/2228446
#SPJ1
Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Order √50,-7.1.3-7 from least to greatest.
0 -7.1.-7. √50,23
O
0-71.-7.7.23,√50
O
0 -7.1.-723√50
0-7-7.1,√50,23
Answers
Answer:
D
Step-by-step explanation:
The square root of 50 is approximately equal to 7.07
-7.1111… can be rounded to -7.11
23/3 is equal to approximately 7.67
-7 1/5 is equal to -7.2
Assume that head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. Suppose a recruit was found with a head size of 23 inches Find the approximate Z-score for this recruit. a. 0 -0.18 b. 0.18 c. 0.96 d. 476.73
Answers
The approximate Z-score for this recruit is b. 0.18.
The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.
The approximate Z-score for this recruit. The formula for Z-score is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,
Z=(23-22.8)(1.1)
Z=0.2/1.1
Z [tex]\approx[/tex] 0.18
Thus, the approximate Z-score for this recruit is b. 0.18.
To know more about mean: https://brainly.com/question/20118982
#SPJ11
a biased dice was rolled and the probability distribution of the outcomes are as follows. what will be the possible probability of getting 3 and of getting 5 when rolling this dice?
Answers
The possible probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice is 0.2.
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
A biased dice was rolled and the probability distribution of the outcomes are as follows then the outcomes are [tex] 1, 2, 3, 4, 5, 6[/tex]
Probability: [tex]0.2, 0.1, 0.3, 0.1, 0.2, 0.1[/tex]
To find the probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice.
Probability of getting [tex]3[/tex]:
Outcome = [tex]3[/tex]
Probability of getting = [tex]^3P(3) = 0.3[/tex]
So, the possible probability of getting [tex]3[/tex] is [tex]0.3[/tex].
Probability of getting [tex]5[/tex]
So, the outcome of [tex]5[/tex]
Probability of getting [tex]^5P(5) = 0.2[/tex]
So, the possible probability of getting 5 is 0.2.
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ11
Find the magnitude of the projection
Answers
The magnitude of the projection of the two vectors is:
M = 8.73
How to find the magnitude of the projection?
If we have two vectors A and B, and we want the projection of A onto B, we need to solve:
projection = A·B/|B|
Here the vectors are <7, -6> and <5, -2>
First, the dot product between the two vectors gives:
7*5 - 6*-2 = 35 + 12 = 47
The dot product is 47.
And the module of the second vector is:
√(5² + (-2)²) = √(25 + 4) = √29
Then the magnitude of the projection is:
M = 47/√29 = 8.73
Learn more about vectors at:
https://brainly.com/question/3184914
#SPJ1
If n(Ax B) = 72 and n(A) = 24, find n(B).
Answers
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
To learn more about set:
https://brainly.com/question/8053622
#SPJ1
JAR
N
Q
Cost (dollars)
0
cost of the tickets in dollars.
32 Each ticket to ride a carousel costs $2 50. The table st
relationship between x, the number of tickets bought, -
Y
8 10
Number of Tickets
LA COORDINATE PLANE
Carousel Rides
Number of Tickets, x
1
5
2
3
Carousel Rides
which graph best represents the data shown in the table?
Carousel Rides
Carousel Rides
Cost (dollars)
DO
6
6
Cost (dollars)
12
0
Cost, y (dollars)
2.50
5.00
7.50
12.50
4
2
6
Number of Tickets
Carousel Rides
12
Answers
Answer:
N
Q
Cost (dollars)
0
cost of the tickets in dollars.
32 Each ticket to ride a carousel costs $2 50. The table st
relationship between x, the number of tickets bought, -
Y
8 10
Number of Tickets
LA COORDINATE PLANE
Carousel Rides
Number of Tickets, x
1
5
2
3
Carousel Rides
which graph best represents the data shown in the table?
Carousel Rides
Carousel Rides
Cost (dollars)
DO
6
6
Cost (dollars)
12
0
Cost, y (dollars)
2.50
5.00
7.50
12.50
4
2
6
Number of Tickets
Carousel Rides
12
Step-by-step explanation:
Based on the data given in the table, the graph that best represents the relationship between the number of tickets bought and the cost of riding the carousel is the one that shows a linear relationship between the two variables.
The table shows that for each ticket bought, the cost of riding the carousel increases by $2.50. This means that the relationship between the number of tickets bought and the cost of riding the carousel is linear, with a slope of $2.50.
Therefore, the graph that best represents this relationship is the one that shows a straight line with a slope of $2.50 passing through the points (1, $2.50) and (5, $12.50). This graph is represented by the option labeled "Carousel Rides" with the x-axis showing the number of tickets bought and the y-axis showing the cost in dollars.
1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x
Answers
The simplified expression is 2cos²(x) + sinx - 1 = 0
The expression we will be simplifying is
=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.
To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:
(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)
Simplifying this expression using the distributive property, we get:
(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)
Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:
1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1
Similarly, for the second fraction, we can use the same identity to obtain:
1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1
Substituting these values back into the original expression, we get:
1 + 1 = 2sinx/(sin⁴x - cos⁴x)
Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:
sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ
Substituting this back into the expression, we get:
2 = 2sinx/(sin²ˣ - cos²ˣ)
Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):
2 = -2sinx/cos(2x)
Multiplying both sides by -cos(2x), we get:
-2cos(2x) = 2sinx
Dividing both sides by 2, we get:
-cos(2x) = sinx
Using the double-angle formula for cosine, we get:
-2cos²(x) + 1 = sinx
Simplifying this expression, we get:
2cos²(x) + sinx - 1 = 0
To know more about expression here
https://brainly.com/question/14083225
#SPJ4
URGENT PLEASE HELP!!
Given that f(x)=x^2+3x-7, g(x)=3x+5 and h(x)=2x^2-4, find each of the following. Solve each of the problems showing work.
f(g(x))
h(g(x))
(h-f) (x)
(f+g) (x)
Explain what method you used when had a squared term that had to be multiplied out.
Answers
For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.
Describe Function?In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.
Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.
Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.
To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.
f(g(x)):
f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))
= 9x² + 30x + 33
h(g(x)):
h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))
= 18x² + 60x + 46
(h-f)(x):
(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))
= x² - 3x + 3
(f+g)(x):
(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))
= x² + 6x - 2
When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:
(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)
= 9x² + 15x + 15x + 25
= 9x² + 30x + 25
To know more about expressions visit:
https://brainly.com/question/29246179
#SPJ1
A dairy made 98.38 ounces of yogurt. Then a local market bought 86.2 ounces of the yogurt.
How much yogurt does the dairy have left?
Answers
The amount of yoghurt left is 12. 18 ounces
How to determine the numberThe algebraic expressions are defined as those expressions that are made up of variables, terms, constants, factors and coefficients.
The expressions are also composed of some arithmetic or mathematical operations, such as;
BracketParenthesesDivisionAdditionSubtractionMultiplicationFrom the information given,
Let the total number of ounces of yoghurt be x
Let the number of ounces of yoghurt sold be y
We have that;
The number left= x - y
= 98.38 - 86.2
= 12. 18 ounces of yoghurt
Learn about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function F(x)= {1−kx^−3 for x>44000 {0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. a)Find the constant k here and provide its natural logarithm to three decimal places. b)Calculate the mean salary given by the model.
Answers
a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.
b) The mean salary of the given model by using the probability density function is approximately $270.86.
a) The cumulative distribution function of the given random variable is provided as follows:
F(x) = {1−kx^−3 if x>44000, and 0 otherwise
The cumulative distribution function is given as
F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)
We need to check the value of the cumulative distribution function at 44000
We have, F(44000) = 0
0 = 1−k(44000)^−3
⇒ 1 = k(44000)^−3
⇒ k = 1/(44000)^−3
⇒ 5.427 x 10^−12
Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)
Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68
b) The probability density function is given as,
f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise
The mean or expected value of the random variable is given as
E(X) = ∫[−∞,∞]xf(x)dx
= ∫[44000,∞]x(3kx^−4)dx
= 3k∫[44000,∞]x^−3dx
= 3k[(−1/2)x^−2] [∞,44000]
= (3k/2)(44000)^−2
= 270.86 (approx.)
Therefore, the mean salary given by the model is $270.86 (approx.)
To know more about the "probability density function": https://brainly.com/question/15714810
#SPJ11
Write 735 as the product of its prime factor.
Answers
Answer:
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Step-by-step explanation:
[tex]735 = 7 \times 105[/tex]
[tex]735 = 7 \times 3 \times 35[/tex]
[tex]735 = 7 \times 3 \times 5 \times 7[/tex]
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
Answers
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
Xavier buys a dog collar that costs $6.79. He pays for the dog collar
with a $10 bill.
How much change does Xavier receive?
Answers
Answer: Xavier will receive $3.21 in change.
Step-by-step explanation:
To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:
Change = $10 - $6.79 = $3.21
Therefore, Xavier will receive $3.21 in change.
*NEED HELP PLEASE*
Solve each radical equation for x
and check your solution. (Isolate,
solve, check)
Answers
Step-by-step explanation:
1. sqrt(x + 6)/5 = 2
sqrt(x + 6) = 10
x + 6 = 100
x = 94
sqrt(94 + 6)/5 = 2
sqrt(100)/5 = 2
10/5 = 2
2 = 2
confirmed.
2.
sqrt(9x + 2) = sqrt(11x - 12)
9x + 2 = 11x - 12
14 = 2x
x = 7
sqrt(9×7 + 2) = sqrt(11×7 - 12)
sqrt(63 + 2) = sqrt(77 - 12)
sqrt(65) = sqrt(65)
confirmed.
3.
cubic root(6x + 3) + 10 = 13
cubic root(6x + 3) = 3
6x + 3 = 27
6x = 24
x = 4
cubic root(6×4 + 3) + 10 = 13
cubic root(24 + 3) + 10 = 13
cubic root(27) + 10 = 13
3 + 10 = 13
13 = 13
confirmed.
4.
2×sqrt(5x - 4) - 24 = -6
sqrt(5x - 4) - 12 = -3
sqrt(5x - 4) = 9
5x - 4 = 81
5x = 85
x = 17
2×sqrt(5×17 - 4) - 24 = -6
2×sqrt(85 - 4) - 24 = -6
2×sqrt(81) - 24 = -6
2×9 - 24 = -6
18 - 24 = -6
-6 = -6
confirmed.
A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire
The bearing from the second ranger to the fire is S 28° W. How far is the first ranger from the fire?
Answers
F
|
|
|
B ----------------- A
|
|
|
We know that Ranger B is 9 miles east of Ranger A. Let's call the distance from Ranger A to the fire "x" miles. We also know that the bearing from Ranger B to the fire is S 28° W.
A bearing of S 28° W means that the direction from Ranger B to the fire is 28° west of south. We can draw a line showing this direction:
F
|
|
|
B -------28°W---- A
|
|
|
Now we can use trigonometry to find x. We have a right triangle with the following sides:
The side opposite the 28° angle is x miles (the distance from Ranger A to the fire).
The side adjacent to the 28° angle is 9 miles (the distance from Ranger B to Ranger A).
We can use the tangent function to find x:
tan(28°) = x/9
x = 9 tan(28°)
x ≈ 4.62 miles
So the first ranger is approximately 4.62 miles from the fire.
