Answers
k= 5.
Step-by-step explanation:1. Write the expression.\(ksin^{2} (x)+kcos^{2} (x)=5\)
2. Factorize k.\(k(sin^{2} (x)+cos^{2} (x))=5\)
3. Simplify using pythagorean identities.Check attached image 1.
\(k(1)=5\\ \\k=5\)
4. Verify.Let's graph the function to see if it's true that it equals 5 for any value of x and k=5.
Check attached image 2.
As we can see in the graph, for any value of x the function returns 5. Hence, the answer is correct.
Related Questions
h(x) = x + 1 k(x) = x - 2 (h + k)(2) =
Answers
\(h(x) = x + 1\)
\(k(x) = x - 2\)
_________________________________
\((h + k)(x) = h(x) + k(x)\)
\((h + k)(x) = (x + 1) + (x - 2) \\ \)
\((h + k)(x) = x + 1 + x - 2\)
\((h + k)(x) = 2x - 1\)
\((h + k)(2) = 2(2) - 1\)
\((h + k)(2) = 4 - 1\)
\((h + k)(2) = 3\)
_________________________________
And we're done.....♥️♥️♥️♥️♥️
Answer:it’s 5
Step-by-step explanation:
because it is
Paxton invests $4850 at 7.6%/a simple interest. If she wants the money to increase to $8000, how long will she need to invest her money?
Answers
Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.
To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (initial investment)
r = Interest rate per year (expressed as a decimal)
t = Time (in years)
Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:
4850 * 0.076 * t = 8000
Simplifying the equation:
369.8t = 8000
To find t, we divide both sides of the equation by 369.8:
t ≈ 8000 / 369.8 ≈ 21.62 years
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GEOMETRY 100 POINTS
Find the length of BC
Answers
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
Find g(x), where g(x) is the translation 6 units up of f(x)=x2. Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
Answers
Answer:
g(x) = x²+6
Step-by-step explanation:
g(x) = f(x)+6 = x²+6
Irene is making bags of trail mix for hiking club. She will use 22 ounces of walnuts, 11.2 ounces of
almonds, and 12.3 ounces of cashews. This amount makes 25 bags of trail mix. How many
ounces are in each bag?
Please help :/ if i dont finish theses questions i will go to summer school & i dont wanna go there
Answers
Answer:
In each bag there will be 1.82 ounces of mixture.
Step-by-step explanation:
Since Irene is making bags of trail mix for hiking club, and she will use 22 ounces of walnuts, 11.2 ounces of almonds, and 12.3 ounces of cashews to make 25 bags of trail mix, to determine how many ounces are in each bag you must perform the following calculation:
(22 + 11.2 + 12.3) / 25 = X
45.5 / 25 = X
1.82 = X
Thus, in each bag there will be 1.82 ounces of mixture.
What is the equation of the parabola with focus at (1, 1) and directrix y = -1?
Answers
The equation of the parabola having focus (1,1) and directix y = -1 is
y = x²/4 - x/2 + 1/4
The focus of the parabola (h , k + p) = (1,1)
The directrix of the parabola is y = -1
From, the focus
k + p = 1
k = 1 - p
The formula of directrix is
y = k - p (1)
Substituting the value of directrix and k
-1 = 1 -p -p
-1-1 = -2p
-2 = -2p
p = 1
Substituting the value p in equation (1)
k = 0
Now, we have got the vertex of the parabola (h ,k) is (1,0)
The equation of the parabola is
(x-h)² = 4p (y - k)
(x - 1)² = 4 (1) (y - 0)
( x -1 )² = 4(y )
x² - 2x + 1 = 4y
x²/4 - 2x/4 + 1/4 = y
y = x²/4 - x/2 + 1/4
which is the equation of the parabola.
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Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest?
Be sure to include in your response:
• the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
Answers
Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
To find out how many months it takes to pay off the credit card and the total amount paid including interest, we can use the following steps:
Step 1: Calculate the monthly interest rate
Divide the annual percentage rate (APR) by 12 to get the monthly interest rate.
Monthly interest rate = 14.5% / 12 = 0.145 / 12 = 0.01208 (rounded to 5 decimal places)
Step 2: Set up the equation for the number of months
Let's denote the number of months it takes to pay off the card as 'n'. The monthly payment is $1,200.00, and the initial balance is $3,287.90. The monthly interest rate is 0.01208. The equation for the number of months can be written as:
(1) $3,287.90 ×\((1 + 0.01208)^n\) - $1,200.00 ×\([(1 + 0.01208)^n\) - 1] = 0
Step 3: Solve the equation
To find the value of 'n', we need to solve equation (1). However, solving it algebraically can be complex. Instead, we can use numerical methods like trial and error, or we can use a spreadsheet or a calculator to find the solution.
Using a spreadsheet or a calculator, we can input the values and increment 'n' until we find the point where the equation equals zero.
After performing the calculations, it is determined that it takes approximately 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
Therefore, the answer to the original question is that it takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
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A kids pool had a small opening through which water sometimes leaked out. Water was poured into the pool from time to time. The graph shows the amount of water in the pool (y), in gallons, at certain times (x), in hours.
Which of the following statements best describes the amount of water in the pool ?
1) it is increasing during the time interval 4
2) it is increasing during the time interval 10
3) it is decreasing during the time interval 4
4) it is decreasing during the time interval 10
Answers
The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.
How to determine the the interval of the water in the pool?To determine the time interval of the water in the pool the following is carried out.
At 0 hour, the water is at the level of = 40 gallons
At 1 hour, the water decreased to = 25 gallons.
At 2 hours, the water decreased to = 10 gallons.
The water remained at a constant level till 4 hours.
Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.
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Which description matches the graph of the inequality y > |x + 4| – 1? a shaded region above a solid boundary line a shaded region above a dashed boundary line a shaded region below a dashed boundary line a shaded region below a solid boundary line
Answers
Answer:
Shaded region above a dashed boundary line
Step-by-step explanation:
> This is a greater than symbol. It has no "or equal to" underline under it, so it needs a dashed line for its graph. Because it is a greater than (as opposed to a less than< ) the shaded area will be above the dashed line.
Symbol-Line-Shade
< dashed, below
> dashed, above
<= solid, below
>= solid, above
How many terms of the arithmetic progression 2,5,8..Must be taken to get a sum of 392?
Answers
Answer:
Number of term = 48
Step-by-step explanation:
GIven:
Arithmetic progression
2,5,8..
Total sum of Arithmetic progression is 392
Find:
Number of term
Computation:
First term a = 2
Difference d = 5 - 2 = 3
Sn = [n/2][2a + (n-1)d]
392 = [n/2][2(2) + (n-1)3]
392 = [n/2][4 + 3n - 3]
784 = [n][1 + 3n]
784 = n + 3n²
3n² + n - 784
n = 48 , n = -49
Number of term = 48
A population of bacteria contains 80 bacteria in generation 1 and triples in
population every generation. This sequence represents the number of
bacteria for the first few generations:
80, 240, 720, ...
What is the explicit formula for the number of bacteria in generation n?
A. a(n) = 80 + (n - 1)3
B. a(n) = 3.801-1
C. a(n) = 3 + (n-1)80
D. a(n) = 80.30-1
Answers
Answer:
A
Step-by-step explanation:
Answer:a(n)=80•3n-1
Step-by-step explanation:
what's the inverse of f(x)=(x+3)^5
Answers
Answer:
The inverse is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x) = (x+3)^5
Finding the inverse,
\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)
We replace x with y and vice versa
so,
\(x = (y+3)^5\)
Solving for y,
the the 5th root,
\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)
hence the inverse function is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x)=(x+3)×5
Y=5X+15
now
interxchanging x and y we get,
x=5y+15
5y=x-15
y=x-15/5
therefor f~1(x)=x-15/5
Whats 2x2 i will give you 14 points
Answers
Answer:
4
Step-by-step explanation:
2×2=4
hope that helped
Answer: 4
Step-by-step explanation: 2 x 2 = 4 dummy
A = {3,5,7,9}
B = {2, 4, 6, 8, 10)
C = {12, 14, 18, 20, 24}
D = {21, 26, 31, 36}
Given the sets above, fill-in the blank: 7 €
Answers
find the vertex of the graph of the following quadratic equations y= -3x^2 -12x-13
Answers
Answer:
Step-by-step explanation:
The vertex is a point. The x value is defined as x = - b / 2a where
a = -3
b = - 12
x = - -12/ 2* -3
x = 12 / - 6
x = -2
what is y when x = - 2?
y = -3(-2)^2 - 12(-2) - 13
y = -12 + 24 - 13
y = -1
Does the graph agree? It should
The equation is written as
y = -3(x + 2)^2 - 1
Find the value of x.
x = ___
Answers
Solving steps In photo wrote down on paper
During the last week of the semester, students at a certain college spend on the average 4.2 hours using the school’s computer terminals with a standard deviation of 1.8 hours. For a random sample of 36 students at that college, find the probabilities that the average time spent using the computer terminals during the last week of the semester is a) At least 4.8 hours (Draw the bell curve) b)
Answers
Answer:
0.97725
Step-by-step explanation:
Given :
Population mean, μ = 4.2
Population standard deviation, σ = 1.8
Sample size, n = 36
Obtain the Zscore of x = 4.8
Zscore = (x - μ) ÷ (σ / √n)
Zscore = (4.8 - 4.2) ÷ (1.8 / √36)
Zscore = 0.6 ÷ 0.3
Z = 2
Hence,
P(Z ≤ 2)
Using the Z probability calculator :
P(Z ≤ 2) = 0.97725
Suppose you are traveling the world and want to visit Africa this month. The probability that you go to Africa is 23%. When you get to Africa, you can relax at a bar, a pool, or in your hotel room. The probability you relax at a bar is 19%. Assuming traveling to Africa and relaxing at a bar are independent events, what is the probability that you travel to Africa and relax at a bar? Round to the nearest thousandths
Answers
Answer:
0.044
Step-by-step explanation:
The joint probability of independent events is the product of their individual probabilities.
P(bar & Africa) = P(bar)×P(Africa) = 0.19×0.23 ≈ 0.044
Answer:
Step-by-step explanation:
A store opens at 8am. From 8 until 10am customers arrive at a Poisson rate of four an hour. Between 10am and 12pm they arrive at a Poisson rate of eight an hour. From 12pm and 2pm the arrival rate increases steadily from eight per hour at 12pm to ten per hour at 2pm; and from 2 to 5pm the arrival rate drops steadily from ten per hour at 2pm to four per hour at 5pm. Determine the probability distribution of the number of customers that enter the store on a given day.
Answers
The probability distribution of the number of customers that enter the store on a given day is described as follows:
Poisson with a mean of 70 customers.
What is the Poisson distribution?In a Poisson distribution, the mass function probability that X represents the number of successes of a random variable is given by the equation presented as follows:
\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number.\(\mu\) is the mean in the given interval or range of values of the input parameter.A combination of Poisson variables is a Poisson variable, hence the daily distribution is a Poisson variable with mean given by the sum of these following observations:
8 customers from 8 am to 10 am.16 customers from 10 am to 12 pm.18 customers from 12 pm to 2 pm. (the average over the interval is of 9 an hour).28 customers from 2 pm to 5 pm.Hence the mean is of:
8 + 16 + 18 + 28 = 70 customers.
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What is the maximum of f(x)=sin(x)
Answers
Answer:
1
Step-by-step explanation:
The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2. If you look at a graph of
y = sin(x) you can see this.
Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.
Step-by-step explanation:
Property of Sine function:
Sin(x)=0 when x=90°,180°,360°The maximum and Minimum value of Sin(x) is 1 and -1 respectively, when and x=270° respectively.The range of values of sin(x) is -1 to 1.Read more on the Sine function:
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Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which Ben agreed to pay $215 per month. Which of the following statements best gives the reasons that Ben’s rent payment is an essential (fixed) expense?
a.
It cannot be eliminated in a later budget, in order to save money.
b.
Living expenses have a higher priority than any other type of expense.
c.
The spender controls the amount of the rent by choice of apartment.
d.
He agreed to pay the same amount every month.
Answers
Answer:
this is late but it's d :))
Step-by-step explanation:
The statement that best gives the reasons that Ben's rent payment is an essential (fixed) expense is,
D. it is by contract the same amount every month.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which Ben agreed to pay $215 per month.
Since, this is his rent, the amount of money that he is legally bound to pay every month in order to keep on living in that location.
He has an agreement with his landlord to pay $215 each month and thus he has to do it.
Thus, The statement that best gives the reasons that Ben's rent payment is an essential (fixed) expense is,
D. it is by contract the same amount every month.
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Please help me solve #1
Answers
Answer:
domain x range y
Step-by-step explanation:
hopefully it helps
Solve for the valid solution set: x−3≥2 or x+5≥7
Answers
Answer: X ≥ 5 or X ≥ 2
Step-by-step explanation:
Add 3 to both sides for the first equation
x ≥ 5
and subtract 5 from both sides for the second one
x ≥ 2
Need help on this question
Answers
Answer:nhjhbghhnkjn hojn
Answer:
I dont really know for sure but I think its 5
Four 3-megawatt wind turbines can supply enough electricity to power 3,000 homes. How many turbines would be required to power 55,000 homes?
Answers
Answer:
74
Step-by-step explanation:
Lets explain how to solve the problem
- Four 3 megawatt wind turbines can supply enough electricity
to power 3000 homes
∴ The number of turbines is 4
∵ Each turbine give 3 megawatt
∴ The four turbines give ⇒ 4 × 3 = 12 megawatt
- This quantity give enough electricity to power 3000 homes
∴ The number of homes for the 12 megawatt is 3000
- We need to find how many turbines can cover enough electricity
to power 55,000 homes, so we must to know the quantity of
electricity that be enough to power 55,000 homes
* Lets use the cross multiplication to solve the problem
∵ megawatt : number of homes
12 : 3,000
? : 55,000
- By using cross multiplication
∴
∴ The enough electricity to power 3000 homes = 220 megawatt
∵ Each turbine gives 3 megawatt
- Find the number of turbines divides the total megawatt by the the
megawatt of one turbine
∴ The number of turbines = 220 ÷ 3 = 73.3
- If we take 73 only the electricity will not be enough to cover all
homes, so we must to take 74 turbines
∴ The number of turbines is 74
-15( - 18 -10x)
Please show your work!
Answers
Answer:
270+150x
Step-by-step explanation:
(-15)(-18)+(-15)(-10x)
270+150x
The parent absolute value function is reflected across the x-axis and translated right 2 units. Which function is represented by the graph?
–|x – 2|
–|x + 2|
|–x| – 2
|–x| + 2
Answers
The function represented by the graph with the given transformations is |–x| + 2.
The function represented by the given transformations is |–x| + 2.
Let's analyze the transformations step by step:
Reflection across the x-axis:
Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.
Translation right 2 units:
Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.
Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.
Thus, the function represented by the graph with the given transformations is |–x| + 2.
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Answer: -lx-2l
Step-by-step explanation:
Erica decides to paint the birdhouse. She has a pint of
paint that covers 32.5 ft2 of surface. How can you tell that Kali has
enough paint without calculating?
Answers
Answer:
Step-by-step explanation:
If the birdhouse is a cube that is 2 ft on each edge, the surface area is 6×2² = 24 ft². That's a pretty large birdhouse, and it will need about ¾ of a pint of paint.
mr drew wants to build a square sandbox with an area of 100 square feet. What is the length of wood Mr.Drew needs to.make the sides of the sandbox
Answers
10’ x 10’ x 10’ x 10’ sandbox.
Reason
Area of a square is Side^2.
We know the area of the square is 100
So take √100 = 10
Problem solved!
Which equation represents a function of x that is not linear?
Answers
Answer:
y = 4x+3x^2
Step-by-step explanation:
For an equation to be linear, x must have a power of 1
y = 4x+3x^2 has a power of x that is not x ( x^2) so this is not linear ( it is quadratic)