Answer:
To solve the equation f(x) = 3, we can set the expression for f(x) equal to 3 and then solve for x. In other words, we want to find the values of x that make the equation 5 - \frac{x}{r^2} + 5 + 6 = 3 true.
We can start by simplifying the left side of the equation by combining like terms. This gives us
5 - \frac{x}{r^2} + 5 + 6 = 5 + 5 - \frac{x}{r^2} + 6 = 10 - \frac{x}{r^2} + 6
Next, we set this expression equal to 3 and solve for x:
10 - \frac{x}{r^2} + 6 = 3 \quad \Rightarrow \quad 10 - 6 = 3 - \frac{x}{r^2} \quad \Rightarrow \quad \frac{x}{r^2} = 7
To solve for x, we can multiply both sides of the equation by r^2:
x = 7r^2
Therefore, the solutions to the equation f(x) = 3 are $x = 7r^2$. Note that this is a general solution, and it may not give all the possible values of $x$ that make the equation true. It's also possible that there are no solutions, depending on the value of $r$.
The expected annual returns are 15% for investment 1 and 12% for investment 2. The standard deviation of the first investment’s return is 10%; the second investment’s return has a standard deviation of 5%. Which investment is less risky based solely on standard deviation? Which investment is less risky based on coefficient of variation? Which is a better measure given that the expected returns of the two investments are not the same?
a) Investment B is less risky based solely on the standard deviation.
b) Based on the coefficient of variation, Investment B is less risky.
c) The better measure of expected returns of the two investments is the coefficient of variation.
What is the coefficient of variation?The coefficient of variation shows how spread out or variable the standard deviation is to population mean.
It is a ratio of the standard deviation compared to the population mean.
A higher coefficient of variation shows a greater dispersion or risk.
The formula for the coefficient of variation is given as follows:
Coefficient of Variation (CV) = (Standard Deviation/Mean) × 100.
Investments A B
Expected annual returns 15% 12%
Standard deviations 10% 5%
Coefficient of variation = Standard deviation ÷ Expected annual returns x 100
Investment A = 66.67% (0.10/0.15 x 100)
Investment B = 41.67% (0.05/0.12 x 100)
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solve this
6/7 × 1/2 = ?
Answer:
To solve this problem, we need to first perform the multiplication. In mathematics, multiplication is performed before division, so we should calculate the product of 6/7 and 1/2 before dividing it by any other number. To find the product, we simply multiply the numerators together to get 6 and the denominators together to get 14. So the product of 6/7 and 1/2 is 6/14.
Step-by-step explanation:
Which expression is equivalent to 2 (x -2 ) -5 (2x -3)
A: 2x - 4 - 10x - 15
B: 2x - 4 - 10x + 15
C: 2x - 2 - 10x - 3
D: 2x - 2 - 10x +15
The expression equivalent to the given expression 2(x -2)-5(2x -3) is
(2x-4-10x+15)
What is an expression?An expression in maths, a sentence with a minimum of two numbers or variables and at least one maths operation.
Given is an expression, 2(x -2)-5(2x -3)
Using distributive property,
a(b+c) = ab+bc
2(x -2)-5(2x -3) = 2x-4-10x+15
Hence, The expression equivalent to the given expression 2(x -2)-5(2x -3) is (2x-4-10x+15)
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In the diagram below of triangle BCD, E is the midpoint of BD and F is the midpoint of CD. If EF = 43-4x, and BC = 32-2x, what is the measure of EF?
The measure of the length EF of the triangle is; 21
How to solve similar triangles?We are given the the triangle BCD and we are told that;
E is the midpoint of BD.
F is the midpoint of CD
Now, since we have those midpoints, it means that by the concept of similar triangles, that;
DF/DC = EF/BC
Since F is the midpoint of DC, then it means that;
2DF = DC
We are given;
EF = 43 - 4x, and BC = 32 - 2x
Thus, we now have;
DF/(2DF) = (43 - 4x)/(32 - 2x)
1/2 = (43 - 4x)/(32 - 2x)
Cross multiply to get;
32 - 2x = 43 - 4x
4x - 2x = 43 - 32
2x = 11
x = 11/2
x = 5.5
Thus;
EF = 43 - 4(5.5)
EF = 43 - 22
EF = 21
Thus, we conclude that the side length EF is 21.
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The assets and liabilities of a local surf shop are listed below.
Building Mortgage $109,850
Other Debt $35,988
Accounts Receivable $10,760
Property Value $162,974
Long Term Investments $238,000
Small Business Loan $62,700
Long Term Liabilities $38,000
Owned Inventory $72,980
Cash $215,083
Savings Account $128,721
Owned Equipment $30,971
The surf shop owner receives notice that the property value has increased by $20,000. What is the net worth of the surf shop?
$859,489
$879,489
$612,951
$632,951
PLEASE HELP
Answer: $879,489
Step-by-step explanation:
When it comes to a business net worth is simple:
assets - liabilities = net worth.
Assets are an expenditure that has utility through multiple future accounting periods. For example, a company pays its electrical bill. This expenditure covers something (electricity) that only had utility during the billing period; therefore, it is recorded as an expense.
Conversely, the company buys a machine, that it expects to use for the next five years. Since this expenditure has utility through multiple future periods, it is recorded as an asset.
Cash, savings, inventory, investments, equipment, and receivables are also assets. Basically, anything that is owned and could be liquidated for cash.
Accounts Receivable $10,760Property Value $162,974Long-Term Investments $238,000Owned Inventory $72,980Cash $215,083Savings $128,721Owned Equipment $30,971In simple terms a liability is something that is owed to someone else:
Building Mortgage $109,850Other Debt $35,988Small Business Loan $62,700Long-Term Liabilities $38,000A factory made 3 jars of creamy peanut butter and 97 jars of chunky peanut butter. What percentage of the jars of peanut butter were creamy?
Answer:
3%
Step-by-step explanation:
They made 97+3 total jars, 3 out of 100 is 3 percent.
3. There are five different tables in the class and five students. Each table can be occupied by only onestudent. Their
studying year consists of 200 days. As a small prank on their teacher students would like to sit in a new way every
day, so there are no two days during their studying year such that all students are occupying the same tables.
They would like to see whether this is possible. How many ways are there for them to sit in the class?
There are 3,125 different places to sit if they don't mind sharing s desk sometimes and there are 120 different places to sit, if they all sit on separate tables.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that there are five different tables in the class and five students
Each table can be occupied by only one student
There are 200 days of studying years.
As a small prank on their teacher students would like to sit in a new way every day, so there are no two days during their studying year such that all students are occupying the same tables.
5×4×3×2×1 = 120
There are 120 different places to sit, if they all sit on separate tables.
5×5×5×5×5 = 3,125
There are 3,125 different places to sit if they don't mind sharing s desk sometimes.
Hence, there are 120 different places to sit, if they all sit on separate tables and there are 3,125 different places to sit if they don't mind sharing s desk sometimes.
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what is the additive inverse of -17-25
Answer: 42
Step-by-step explanation: ik additive inverse
Zachary purchased a computer for $1100 on a payment plan. three months after he purchased the computer, his balance was $710. four months after he purchased the computer, his balance was $580. What is an equation that models the balance y after x months?
Answer:
y = 1,100 - 130x
Step-by-step explanation:
Zachary purchased a computer for $1100 on a payment plan. three months after he purchased the computer, his balance was $710. four months after he purchased the computer, his balance was $580. What is an equation that models the balance y after x months?
(1,100 - 710)/3 = he pays $130 per month
(1,100 - 580)/4 = he pays $130 per month
when balance = y and x = months
y = 1,100 - 130x
If A = {x|x is an odd integer), B = {2, 3, 4, 5), list the elements of the set AUB.
Choose the correct answer below.
O A. {x x is an even integer or x = 2 or x = 4}
O B. {x|x is an even integer or x = 3 or x = 5}
OC. {x|x is an odd integer or x = 3 or x = 5}
OD. {xx is an odd integer or x = 2 or x = 4}
Answer:
D) {x: | x is an odd integer or x = 2 or x = 4}-----------------------------
Given two sets:
A = {x: | x is an odd integer}, B = {2, 3, 4, 5}Both sets include 3 and 5 so the combination is all the elements of the A and two unique elements of the B:
A∪B = {x: | x is an odd integer or x = 2 or x = 4}The matching choice is D.
#19 i
Solve the system of linear equations by elimination.
1.5x - 9y = -21
-1.5x - 3y = 9
The solution is:
Answer:
to solve a system of linear equations by elimination, we need to eliminate one of the variables, for example, we could add the two equations together to eliminate the variable y. However, we need to make sure that the coefficients of the two equations are the same before we can add them together. We can do this by multiplying the first equation by -1.5 and the second equation by 1.5. This gives us the following system of equations:
-2.25x - 13.5y = -31.5
2.25x - 4.5y = 13.5
We can now add these two equations together to eliminate the variable y, which gives us the following equation:
0 = -18
This equation is not possible, so the system of equations does not have a solution.
Answer:
Math can help you get your answer it has a linear equation by option
Step-by-step explanation:
A door is 2 feet off the ground and a contractor needs to develop a wheelchair ramp to go on it. Ramps have to be in a ratio of 1:12 slope. How far away from the house would the ramp have to start. Explain
The slope of the ramp is the ratio of the y and x coordinates thus it will be 24 feet.
What is the slope?A slope is a tangent or angle at a point or a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The situation is making a right-angle triangle as shown below.
The slope of the wheelchair = 2 feet / x
2/x = 1/12
x = 2 x 12 = 24 feet
Hence "The ramp will be 24 feet long since the slope is determined by the ratio of the y and x variables".
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18. Which of the following is an equation of the line parallel to y = 5x+8 that passes through the point
(4, -3)?
Answer:
y=5x-23
Step-by-step explanation:
y=mx+b is the slope intercept form
m is slope
And b is y intercept
We know the line will have a slope of 5 since they are parallel both lines will have the same slope
y=5x+b
To find b we put in the given coordinates (4,-3)
-3=5(4)+b
-3=20+b
-20 -20
-23=b
Now we just plug in b
y=5x-23
Hopes this helps
The y-intercept of the line y=-4 x-7 is
a. -7
c. 4
b. -4
d. 7
B
A
D
C
The y-intercept of a line is where it meets the y-axis.
This y-axis occurs at x = 0.
Simply input x = 0 into the line y = -4x - 7
y = -4(0) - 7
y = -7
y - intercept (we also like to abbreviate that y-int) = -7
Hope this helps :)
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- Jeron
Answer: -7
Step-by-step explanation:
Since the answer is already in slope intercept form x=-4 and y = -7
2 people paint at the rate of 45 m² per hour to finish painting the
house on schedule.
At what rate would 6 people have to paint at, in m², to finish exactly
on schedule?
The rate at which 6 people will paint the house will be 135 [tex]m^{2}[/tex] per hour
What is Unitary Method ?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
According to the Given information
Applying Unitary Method
House painted by 2 people at the rate = 45 [tex]m^{2}[/tex] per hour
House painted by one person at the rate = [tex]\frac{45}{2}[/tex] [tex]m^{2}[/tex] per hour
House painted by 6 people at the rate = [tex]\frac{45}{2}[/tex]× 6 [tex]m^{2}[/tex] per hour
= 135 [tex]m^{2}[/tex] per hour
Hence
The rate at which 6 people will paint the house will be 135 [tex]m^{2}[/tex] per hour
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If a triangle has lengths of 11tf and 24ft, check all the possible lengths for the third side
All the possible lengths for the third side lie between 13 to 35 feet.
What is a triangle Inequality Theorem?
In Euclidean geometry, the theorem is that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.
Therefore, 24 − 11 < x < 24 + 11
13 < x < 35 is the possible length of the third side of a triangle.
13 < x < 35 satisfies the triangle inequality theorem.
Hence, all the possible lengths for the third side lie between 13 to 35 feet.
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NO LINKS!! Help me with the 2-Column Proof Part 3aa
Here is the two column proof:
Statement Reason
RD bisects OS GivenA is the point of intersection Shown on the diagramOA ≅ AS Definition of a segment bisectorProved
x (4.4) (1.4)
x=5
Help me solve this question please
Solve x(4.4)(1.4) given that x = 5
Plug x into equation
5(4.4)(1.4)
Distribute 5 into 4.4
22(1.4)
Distribute 22 into 1.4
30.8
Hope this helps :)
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Help plsssssssssssss
Answer: thanks for the ponts
Step-by-step explanation: ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Which of the following numbers are irrational?
-4.8237, π/2, ³√/4, 4+√25
π/2 and ³√4
-4.8237 and 4+√25
-4.8237 and π/2
³√4 and 4+√25
The irrational numbers are option (A) π/2 and [tex]\sqrt[3]{4}[/tex]
The rational numbers are the numbers that can be expressed in the p/q form
The irrational numbers are the numbers that cannot be expressed in the p/q form.
The first number is -4.8237
This can be expressed in p/q form
It is a rational number
The second number is π/2
This cannot be expressed in p/q form
It is an irrational number
The third number is [tex]\sqrt[3]{4}[/tex]
We cannot express this in p/q form
It is an irrational number
The fourth number is 4 + [tex]\sqrt{25}[/tex]
Find the square root
4 + 5 = 9
This is a rational number
Therefore, the rational numbers are π/2 and [tex]\sqrt[3]{4}[/tex]
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Evaluate and match each expression on the left to its value on the right, when x = 6 and y = 5.
12 + x
3x + y
4y - 10
xy
10
15
18
23
Answer:
Step-by-step explanation:
The values of the expressions 12 + x is 18, 3x + y is 21, 4y - 10 is 14,
xy is 30.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Finding the value of given expression when x = 6 and y = 5 is simply replacing x and y with their numeric values.
Given,
12 + x.
= 12 + 6.
= 18.
3x + y.
= 3(5) + 6.
= 15 + 6.
= 21.
4y - 10.
= 4(6) - 10.
= 24 - 10.
= 14.
xy.
= (5)(6).
= 30.
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Cashews cost $63.00 per 5 pound bag. How much would a 2 pound bag of cashews cost?
Cassidy has 10 feet of thread. She wants to cut the thread into 1 1/6 foot pieces to make necklaces. How many full necklaces can Cassidy make? 
Answer:8
Step-by-step explanation: 10/ 1 1/6 so the equals to 8 4/7 but the problems says whole necklaces to the answer is 8
The general form of a hyperbola is 6x2−5y2+12x+50y−149=0.
What is the standard form of this hyperbola?
Enter your answer by filling in the boxes.
The quadratic equation (x + 1)² / 46.667 - (y - 5)² / 56 = 1 represents the hyperbola in standard form.
How to derive the standard form of the equation of a hyperbola
In this question we find the equation of a hyperbola in general form, that is, a quadratic equation of the form A · x² + B · y² + C · x + D · y + E = 0, and we need to obtain the standard form of the hyperbola:
(x - h)² / a² - (y - k)² / b² = 1
Where:
(h, k) - Coordinates of the center.a, b - Length of the semiaxes.We can switch from general form into standard form by completing the square, an application of algebra properties:
6 · x² - 5 · y² + 12 · x + 50 · y - 149 = 0
(6 · x² + 12 · x) - (5 · y² - 50 · y) = 149
6 · (x² + 2 · x) - 5 · (y² - 10 · y) = 149
6 · (x² + 2 · x + 1) - 5 · (y² - 10 · y + 25) = 149 + 6 + 125
6 · (x + 1)² - 5 · (y - 5)² = 280
(x + 1)² / 46.667 - (y - 5)² / 56 = 1
The equation of the hyperbola in standard form is (x + 1)² / 46.667 - (y - 5)² / 56 = 1.
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Type the correct answer in each box. Use numerals instead of words.
3^1/5
The expression above can also be written in the form (image because I can't type it).
For this expression,
a =
and b =
.
The value of a is 3.
The value of b is 5.
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,
[tex]3^{1/5}[/tex]
This expression can be written as 5 roots of 3.
[tex]\sqrt[5]{3}[/tex]
Thus,
The value of a and b from the expression [tex]3^{1/5}[/tex]are 3 and 5.
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Simplify.
√3/√8
Responses
√6/8
√6/4
√3/4
√24/8
Answer:
1/8
Step-by-step explanation:
To simplify the expression √3/√8, we can first simplify the square root terms by finding the prime factorization of each number under the square root. The prime factorization of 3 is 3, and the prime factorization of 8 is 2 * 2 * 2.
We can then rewrite the square root terms as follows:
√3/√8 = √(3) / √(2 * 2 * 2)
Next, we can use the property of square roots that says that the square root of a number is equal to the square root of each of its prime factors. This means that we can rewrite the square root term as follows:
√(3) / √(2 * 2 * 2) = √(3) / √(2) / √(2) / √(2)
Since the square root of a number is the same as the number itself, we can simplify the expression further by removing the square root symbols from the prime numbers 2:
√(3) / √(2) / √(2) / √(2) = √(3) / 2 / 2 / 2
Finally, we can use the rules of division to simplify the expression even further:
√(3) / 2 / 2 / 2 = √(3) / (2 * 2 * 2)
Since any number divided by itself is equal to 1, we can simplify the expression one last time to get our final answer:
√(3) / (2 * 2 * 2) = 1/2 * 1/2 * 1/2 = 1/8
Therefore, the simplified form of the expression √3/√8 is 1/8.
Answer: 6/4
Step-by-step explanation:
Pull terms out from under the radical.
3
(
8
√
8
)
Multiply
8
by
3
.
3
√
8
The result can be shown in multiple forms.
Exact Form:
6
√
4
Decimal Form:
0.61237243....
What’s
: -4 (2x + 4) = 5
Please explain step by step to get picked brainliest!
Answer:
[tex]x=-\frac{21}{8}[/tex]
Step-by-step explanation:
[tex]-4(2x+4)=5 \\ \\ 2x+4=-\frac{5}{4} \\ \\ 2x=-\frac{21}{4} \\ \\ x=-\frac{21}{8}[/tex]
Which values of m
b and b will create a system of equations with no solution? Select two options.
y = mx + b
y=-2x+3/2
Answer:
m = -2; b can be any number other than 3/2
Step-by-step explanation:
There is no solution when the lines are parallel.
To have parallel lines you need equal slopes and different y-intercepts.
Answer: m = -2; b can be any number other than 3/2
In the scale used on a blueprint, inch represents 2 feet. On the blueprint what is the length of a room with an actual length of 20 feet?
On the blueprint what is the length of a room is 5square inch.
What is square?
A square is a quadrilateral because it has four equally sized sides. Our immediate surroundings is filled with many square-shaped things. Equal sides and interior angles of 90 degrees help you identify each square form. A closed form known as a square has four equal sides and two interior angles that are both 90 degrees. A square has a wide range of characteristics.
Given the square bedroom have 3 feet side
The area of the bedroom is = 3² = 9 sq inch
1 inch = 2 feet
1 square inch = 4 square feet
20 square feet = 5square inch
Hence, On the blueprint what is the length of a room 5square inch.
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the product of 0.8 and a number is 12represent the statement as an equation determine the solution set using the replacement set 0 8 1 7 15
Answer:
The product of 0.8 and a number is 12, so the equation representing this statement is: 0.8 * x = 12.
To solve this equation, we need to find the value of x that makes the equation true. We can do this by using the replacement set {0, 8, 1, 7, 15}.
If we substitute 0 for x in the equation, we get: 0.8 * 0 = 12. This equation is not true, so 0 is not a solution.
If we substitute 8 for x in the equation, we get: 0.8 * 8 = 12. This equation is not true, so 8 is not a solution.
If we substitute 1 for x in the equation, we get: 0.8 * 1 = 12. This equation is not true, so 1 is not a solution.
If we substitute 7 for x in the equation, we get: 0.8 * 7 = 12. This equation is not true, so 7 is not a solution.
Finally, if we substitute 15 for x in the equation, we get: 0.8 * 15 = 12. This equation is true, so 15 is a solution.
Therefore, the solution set for this equation is {15}.
Answer: 0.8x=12
x=15
Step-by-step explanation:
0.8x=12
x=15
15*0.8=12