The inequality is |x-9| ≥ 4, and its solution set is (5,13).
What is inequality?An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality of the form |x-a| ≥ k means that the distance between x and a is greater than or equal to a certain value, k.
If the solution set is (5,13), it means that x is a number between 5 and 13, but not including 5 or 13. In other words, 5 < x < 13.
To find the value of a and k, we need to look for the midpoint of the solution set, which is (5+13)/2 = 9.
The distance between 9 and either endpoint (5 or 13) is 4, which is the value of k.
Thus, the inequality is |x-9| ≥ 4, and its solution set is (5,13).
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(Hari Bahadur sold a watch after allowing 20% discount and then adding 13% VAT. If the discount amount is Rs.192 more than VAT amount then find the marked price and selling price of the watch.)
Answer: Let's assume that the marked price of the watch is M.
The discount amount would be 20% of M, which can be calculated as:
0.2 * M = 0.2M
The selling price after the discount would be:
M - 0.2M = 0.8M
The VAT amount would be 13% of the selling price after the discount, which can be calculated as:
0.13 * 0.8M = 0.104M
Now, as the discount amount is Rs.192 more than the VAT amount, we can write an equation:
0.2M = 0.104M + 192
0.096M = 192
M = 192 / 0.096 = 2000
So, the marked price of the watch is Rs.2000 and the selling price after the discount and VAT is 0.8M = 0.8 * 2000 = 1600.
Step-by-step explanation:
The value of a motorcycle changes according to the equation V=5,000(1.03)t^, where V= value in dollars and t= time in years.
Use the dropdowns to complete the statements.
In the equation, the number 5,000 represents the ________ of the motorcycle. The value of the motorcycle is __________ at a rate of ________ per year.
In the equation, the number 5,000 represents the initial value of the motorcycle. The value of the motorcycle is increasing at a rate of 3% per year.
What are Exponential Functions?Exponential functions are functions where the independent variable, x is in the exponent.
The given exponential equation is,
V = 5,000 (1.03)^t
Here V represents the value of the motorcycle in t years.
When t = 0,
V = 5000 (1.03)⁰ = 5000
So 5000 represents the initial value of the motorcycle.
V = 5,000 (1 + 0.03)^t
At t = 0, V = 5000
At t = 1, V = 5000 (1.03)¹ = 5150
At t = 2, V = 5000 (1.03)² = 5304.5
So the value of the motorcycle is increasing.
The rate is 0.03 or 3%.
Hence, 5,000 represents the initial value of the motorcycle and the value of the motorcycle is increasing at a rate of 3% per year.
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Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=
don't spam ;-;
The linear function for the amount of store credit he will have left after purchasing x video games is given as follows:
f(x) = 299 - 60x.
How to obtain alinear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
b = 299, which is the initial credit that he has.m = -60, as for each videogame purchased, the amount of credit decays by $60.Hence the function is given as follows:
f(x) = 299 - 60x.
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which point is a solution for the system of inequalities shown in the graph below?
Answer: The answer to your problem is choice b
1 1/2 + 3 2/3 + 2/3 equals what?
Answer: 35/6 or 5 and 5/6
Step-by-step explanation:
Answer:
35/6
Step-by-step explanation:
Dodi has 2 cups of liquid starch and will use the entire amount. She plans to store the slime in containers that each hold a maximum of 6 fluid ounces how many containers will she need (hint 2 cups = 16 fluid ounces
The number of containers needed is given as follows:
3 containers.
How to obtain the number of containers needed?The number of containers needed is obtained applying the proportions in the context of this problem.
She has 2 cups, hence the number of fluid ounces that she has is given as follows:
16 fluid ounces.
Each container holds a total of 6 fluid ounces, hence the number of containers needed is given as follows:
16/6 = 3 containers.
(rounding up).
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A. 188.5in²
B. 94.25in²
C. 133.5in²
D. 149.25in²
Answer:B
Step-by-step explanation:
area of triangle is (10*11)/2=55
area of semicircle is
[tex]d=2r\\r=10/2=5\\s=\pi r^{2} /2=25\pi /2=39.25\\39.25+55=94.25[/tex]
Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where
P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4).
The volume of the parallelopiped is 4
How to solve for the volumeWe have to solve this with the use of matrix system in math
PQ, PR, PS where
P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4)
we have to find
Q - P
(-1, 6, 5) - (-3, 3, 2)
= (2, 3, 3)
R - P
R(-4, 2, 1) - (-3, 3, 2)
= ( -1 , -1, -1)
S - P
S(3, 1, 4) - (-3, 3, 2)
= (6 , -2, 2)
we would have [tex]\left[\begin{array}{ccc}2&3&3\\-1&-1&-1\\6&-2&2\end{array}\right][/tex]
the determinant of the matrix is the volume
2[(-1 * 2) - 3[(-1x2)-(6x-1)] + 3[(-1x-2) -(6 x -1)]
= -8 - 12 + 24
= 4
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Verify the Identity.
Step-by-step explanation:
[tex] \frac{ \tan( \alpha ) }{1 + \sec( \alpha ) } = - \cot( \alpha ) + \csc( \alpha ) [/tex]
Multiply by 1-sec(a)
[tex] \frac{ \tan( \alpha ) (1 - \sec( \alpha ) }{(1 + \sec( \alpha ) )(1 - \sec( \alpha ) )} [/tex]
[tex] \frac{ \tan( \alpha ) - \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]
[tex] \frac{ \tan( \alpha ) }{1 - \sec {}^{2} ( \\ \alpha ) } - \frac{ \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]
[tex] \frac{ \tan( \alpha ) }{ - \tan {}^{2} ( \alpha ) } + \frac{ \tan( \alpha ) \sec( \alpha ) }{ \tan {}^{2} ( \alpha ) } [/tex]
[tex] - \frac{1}{ \tan( \alpha ) } + \frac{ \sec( \alpha ) }{ \tan( \alpha ) } [/tex]
[tex] - \cot( \alpha ) + \frac{ \frac{1}{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } [/tex]
[tex] - \cot( \alpha ) + \frac{1}{ \sin( \alpha ) } [/tex]
[tex] - \cot( \alpha ) + \csc( \alpha ) [/tex]
PLEASE HELP WILL GIVE BRAINIEST!!
At what point does the graph of a function of this form start?
The start point the graph of a function of this form is (h, k)
How to determine the start of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = a√(x - h) + k
The domain is given as
x ≥ h
This means that the initial x value is h
From the question, we have the following parameters that can be used in our computation:
f(h) = a√(h - h) + k
Evaluate
f(h) = k
Hence, teh initial point is (h, k)
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How do you solve the problem: 5/8 * a/b = - 1/4?
Answer:a=-2
b=5
Step-by-step explanation:
[tex]\frac{a}{b} =\frac{\frac{-1}{4} }{\frac{5}{8} } \\\frac{a}{b} =\frac{-1}{4}*\frac{8}{5}\\\frac{a}{b}=-2/5[/tex]
in a certain test, there is a multiple choice question with the possible answers a, b, c, d, and e. By randomly guessing, the chances of getting the correct answer are stated as "1 in 5."Express the indicated degree of likelihood a a probability value between 0 and 1 inclusive
Linda and Rob charged a $67.44 restaurant bill on their credit card. They gave the card to the waitress, who accidentally transposed two digits and charged them $76.44. They did not notice this until they received their statement later that month. Their card has an 18% APR.
They plan to pay their monthly statement amount in full, but they need to deduct the amount they were overcharged, plus the finance charge that was based on the incorrect amount. If the overcharged amount was on their statement for 18 of the 31-day billing cycle, how much should they deduct from this monthly statement, including the amount they were overcharged?
Answer:
Step-by-step explanation:
a
What is the circumference of this circle?
Use π = 3.14
6 cm
A dolphin is at the surface of the ocean.What is the dolphin’s elevation?
Answer:
0
Step-by-step explanation:
surface of ocean = sea level = elevation of zero
A student's course grades and their corresponding weights are given in the table.
What is the minimum grade needed on the final exam to earn an overall grade of 83% in the class
Answer: 75%
Step-by-step explanation: To calculate,
(0.1 x 100) + (0.3 x 80) + (0.2 x 95) + (0.4 x 75) = 83%
Every day Guido eats one Jolly Rancher. He can select from any of 5 choices each day. How many ways can Guido select candy for one week?
Guido can choose his Jolly Rancher in 78,125 different ways over the course of a week.
Guido chooses one sweet per day from a selection of five options; there are a total of five possible selections for a single day. Since there are seven days in a week, the sum of the ways Guido can choose candy over the course of a week equals the sum of the methods for each day.
Using the multiplication principle of counting
Total number of ways = 5 x 5 x 5 x 5 x 5 x 5 x 5
Simplifying this expression gives:
Total number of ways = 5^7
Using a calculator or by hand, we can compute:
Total number of ways = 78,125
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What is the doubling time for the investment? Round answer to 1 decimal place.
The amount of money in an investment is modeled by the function A(T)=650(1.0455)^T. The variable A represents the investment balance in dollars, and T the number of years.
The doubling time for the investment as required to be determined is; 15.58 years.
What is the value of the investments doubling time?It follows from the task content that the model function is;
A(T)=650 (1.0455) ^T
For doubling time;
2 = (1.0455)^T
ln (2) = T ln (1.0455)
T = ln 2 / ln (1.0455)
T = 15.58 years.
Ultimately, the doubling time of the investment as required is; 15.58 years.
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That are a valid decomposition of c (x )such that c equals f ring operator g g (x )equals x squared f (x )equals cube root of x plus 1 end root g (x )equals x squared plus 1 f (x )equals cube root of x g (x )equals x plus 1 f (x )equals cube root of x squared end root g (x )equals cube root of x plus 1 f (x )equals x squared
By using the composition of functions, we can find valid decompositions of c(x) using f(x) = [tex](x+1)^{1/3}.[/tex] and g(x) = x²
A function is a rule that takes an input value and produces an output value.
One way to do this is to use the composition of functions. The composition of two functions f(x) and g(x) is denoted as f(g(x)). This means that we first apply g(x) to the input, and then apply f(x) to the output of g(x). In other words, we first evaluate g(x), and then plug that result into f(x) to get the final output.
Using this concept, let's look at the first set of functions. We are given
=> c(x) = f ◦ g (x) = (x²) f(x) = [tex](x+1)^{1/3}.[/tex]
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x², and f(x) = [tex](x+1)^{1/3}.[/tex] This is a valid decomposition of c(x).
Similarly, in the second set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x² + 1.
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x² + 1, and [tex](x+1)^{1/3}.[/tex] This is also a valid decomposition of c(x).
In the third set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x + 1, and f(x) = [tex](x^2)^{1/3}=x^{2/3}[/tex]
This is another valid decomposition of c(x).
Finally, in the fourth set of functions, we have
=> c(x) = f ◦ g (x) = x² g(x) = [tex](x+1)^{1/3}[/tex], and f(x) = [tex]x^{2/3}[/tex].
This is yet another valid decomposition of c(x).
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A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $9 the average attendance has been 28000. When the price dropped to $7, the average attendance rose to 33000. Find a demand function D(q), where q is the quantity/number of the spectators. (Assume D(g) is linear) D(q) =
The demand function of the question is expressed as;
D(q) = -²/₅₀₀₀q + 14.6
How to find the Demand Function?The formula to find the slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
The coordinates we are given are;
(28000, 9) and (33000, 7)
Thus;
Slope; m = (7 - 9)/(33000 - 28000)
m = -2/5000
Now, the equation of a line in point slope form is;
y - y1 = m(x - x1)
Where (x1, y1) is (28000, 9)
y - 9 = (-2/5000)(x - 28000)
y - 9 = -²/₅₀₀₀x + 5.6
y = -²/₅₀₀₀x + 14.6
This can be rewritten as a demand function; D(q) = -²/₅₀₀₀q + 14.6
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The area of a certain desert (Desert 1) is six times the area of another desert (Desert 2). If the sum of
their areas is 21,000,000 square miles, find the area of each desert.
Area of desert 1 is 18,000,000 square miles and area of desert 2 is 3,000,000 square miles.
What is meant by Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Let A₁ and A₂ be the area of Desert 1 and Desert 2 respectively.
Given,
Area of a Desert 1 is six times the area of Desert 2.
A₁ = 6 A₂
The sum of their areas is 21,000,000 square miles.
A₁ + A₂ = 21,000,000
Substituting A₁ = 6 A₂ in A₁ + A₂ = 21,000,000 ,
6 A₂ + A₂ = 21,000,000
7 A₂ = 21,000,000
A₂ = 21,000,000 / 7
A₂ = 3,000,000 square miles
A₁ = 6 A₂
= 6 × 3,000,000
= 18,000,000 square miles
Hence the areas of each desert is 18,000,000 square miles and 3,000,000 square miles.
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does the equation y^2-y^2x = 6 describe y as a function of x
The equation y² - y²x = 6 can be describe as a function of x as:
y = √(6/(x - x)).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y² - y²x = 6
Taking y² as common.
y²(1 - x) = 6
Divide both sides with (1 - x).
y² = 6/(1 - x)
Square root on both sides.
y = √(6/(x - x))
This is a function of x.
Thus,
y = √(6/(x - x)) is a function of x.
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Consider the two triangles. How can the triangles be proven similar by the SSS similarity theorem?
Answer:if their corresponding sides are proportional.
Step-by-step explanation:
Help please! Which of the following tables represents a relation that is a function? Explained answer please
A
B
C
D
Answer:
Step-by-step explanation:
THE ANSWER TO YOUR QUESTION IS C.
A sign for truck drivers states that the road ahead has a constant slope of 2 in 11. This means that for every 11m horizontally its rises 2m.
a. Over what horizontal distance will the road rise 300m?
b. What is the length of the road [AB]?
Alba Isabel bought a Bluray disc player on sale for $219.99. What is the sales tax if Alba lives in Kingston, New York, where the state tax is 4% and the county tax is 4%?
The sales tax on the Bluray disc player is $17.60.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
To calculate the sales tax on the Bluray disc player, we need to add the state tax and county tax to the sale price of the player.
First, we can calculate the amount of the state tax. The state tax rate is 4%, which can be expressed as a decimal by dividing by 100:
State tax rate = 4% = 0.04
To find the amount of state tax, we can multiply the sale price by the state tax rate:
State tax = 0.04 x $219.99 = $8.80
Next, we can calculate the amount of the county tax. The county tax rate is also 4%, so we can use the same method as above to find the county tax:
County tax rate = 4% = 0.04
County tax = 0.04 x $219.99 = $8.80
Now, we can find the total sales tax by adding the state tax and county tax:
Total sales tax = State tax + County tax
= $8.80 + $8.80
= $17.60
Therefore, the sales tax on the Bluray disc player is $17.60.
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A student moves into a bigger apartment that rents for $750 per month. That rent is $200 less than twice what she had been paying. Find her former
rent in dollars.
Answer:
$475
Step-by-step explanation:
x = former rent
2x - 200 = 750
2x = 750 + 200 = 950
x = 950/2 = 475
Rafael and Lucy, married taxpayers, each contribute $2,850 to their respective § 401(k) plans offered through their employers. The AGI reported on the couple's joint return is $40,500. Determine their credit for retirement plan contributions (the Saver’s Credit).
Answer:
Rafael and Lucy's credit for retirement plan contributions is $570.
Step-by-step explanation:
The Saver's Credit is a tax credit for low and moderate-income taxpayers who make contributions to a retirement plan. The credit is worth between 10% and 50% of the taxpayer's contributions, up to a maximum credit of $1,000 ($2,000 for married taxpayers filing jointly).
To determine the credit amount, we need to calculate the taxpayers' adjusted gross income (AGI) and their credit rate.
For the tax year in question, the AGI is $40,500 and the contribution limit is $2,850 per person. The total contribution amount is $2,850 x 2 = $5,700.
The credit rate is determined by the taxpayer's AGI and filing status, as follows:
For AGI up to $19,750 for married taxpayers filing jointly, the credit rate is 50%.
For AGI between $19,750 and $32,000 for married taxpayers filing jointly, the credit rate is 20%.
For AGI between $32,000 and $40,000 for married taxpayers filing jointly, the credit rate is 10%.
For AGI above $40,000 for married taxpayers filing jointly, the credit is not available.
Since the taxpayers' AGI is $40,500, the credit rate is 10%. The credit amount is calculated as follows:
Credit amount = Credit rate x Contribution amount
Credit amount = 10% x $5,700 = $570
So, Rafael and Lucy's credit for retirement plan contributions is $570.
The graph below is the function f(x)
The value of lim x -> -1- f(x)= -1
What is the Limit of a function?The behavior of a function at a specific input is described by its limit, a crucial concept in calculus and analysis.
Hence,
As x approaches -1 from the left, the graph of f(x) leads you to the point (-1, 3), so the limit from the left is 3.
As x approaches -1 from the right, the graph leads to the point (-1, -3), so the limit from the right is -3.
The one-sided limits do not match, so the two-sided limit does not exist.
But f(x) is still defined at x = -1; this is indicated by the point (-1, -1). So f (-1) = -1.
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The graph below is the function f(x)
Find lim x -> -1- f(x)=
h(n) =4n+2
g(n)= n³ +5 - 2n
Find 3h(n) + 2g(n)
The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-
E = 3h(n) + 2g(n)
E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)
E = 12n + 6 + 2n³ + 10 -4n
E = 2n³ + 8n + 6
Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.
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