The GCF of 25 and 12 is 1, which means they are relatively prime. Another example of a pair of relatively prime numbers is 8 and 15, as their only common divisor is 1.
The greatest common factor (GCF) of 25 and 12 is 1. Numbers that have a GCF of 1 are called relatively prime. Another pair of numbers whose GCF is 1 could be 8 and 15. To verify, we look for any common divisors. The divisors of 8 are 1, 2, 4, and 8 while the divisors of 15 are 1, 3, 5, and 15. The only common divisor is 1, which confirms they are relatively prime.
HELP!! Given f(x)=5x squared and g(x) = x squared + 2x squared - 5x, what is F (x) * g(x)?
Mr woods is going to fence his garden, His garden is rectangular shaped with the length being 13 1/2 feet and the width 8 1/4 feet how many feet of the fence should mr woods buy to fence in his garden?
2m - nx = x + 4 with description
The equation 2m - nx = x + 4 is a linear equation solvable for x using algebraic manipulation. The solution is x = (2m - 4)/(nx + 1), requiring values for m and n to find x's specific value.
The given equation 2m - nx = x + 4 is a linear equation and can be solved for x by applying algebraic techniques. The question indicates that there is an element of differential equations involved, suggesting that it might be related to more advanced topics such as linear differential equations or characteristics equations. However, the provided context also mentions concepts like probability with positive and negative jumps, quadratic equations, and principles from physics, but these do not directly apply to the initial linear equation provided.
To solve for x in the given equation, we would rearrange the terms to isolate x:
2m - nx = x + 4
2m - 4 = x(nx + 1)
x = (2m - 4)/(nx + 1)
The solution for x is now expressed in terms of m and n. To find the specific value of x, values for m and n must be known.
Please help asap!! What is the rate of change from x = π to x = 3 pi over 2 ? (6 points)
How to find instantaneous and average velocity?
Instantaneous velocity is found by taking the derivative of the position function with respect to time, giving the velocity at a specific moment. Average velocity is calculated by dividing the total displacement by the total time elapsed.
To find instantaneous velocity, we take the derivative of the position function x(t) with respect to time t. This provides the velocity at any given moment. Mathematically, if the position x is a function of time t, then the instantaneous velocity v at time t is defined as:
v = lim_(Δt→0) (x(t + Δt) - x(t)) / Δt
For average velocity, we simply take the total displacement (the change in position) and divide it by the total time elapsed. Suppose we have an object that moves from position x1 to x2 over a time period from t1 to t2, the average velocity ū is:
ū = (x2 - x1) / (t2 - t1)
When the time interval becomes very small, the average velocity approaches the instantaneous velocity.
Hello pls help it's for pre calc composition of functions
The composite function that converts temperatures from degrees Kelvin to degrees Fahrenheit is:
K to F = 9/5 * K - 241.15
The image shows a question about how to convert temperatures from degrees Celsius to degrees Fahrenheit using composite functions. The question provides two functions:
[tex]$F(x) = \frac{9}{5}x + 32$[/tex] converts from degrees Celsius to degrees Fahrenheit
[tex]$C(x) = x - 273.15$[/tex]converts from degrees Kelvin to degrees Celsius
We are asked to find the composite function [tex]$C \circ F$[/tex] that converts from degrees Kelvin to degrees Fahrenheit.
To find the composite function, we simply substitute the output of the first function, [tex]$F(x)$[/tex], into the input of the second function, [tex]$C(x)$[/tex]. This gives us:
[tex]```(C \circ F)(x) = C(F(x)) = F(x) - 273.15 = \frac{9}{5}x - 241.15```[/tex]
Therefore, the composite function that can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit is:
[tex]```(C \circ F)(x) = \frac{9}{5}x - 241.15```[/tex]
A composite function is a function that is created by composing two or more other functions. In other words, it is a function that takes the output of one function as the input to another function. Composite functions are often used to solve complex problems that cannot be solved using a single function.
For example, the composite function that we found above,[tex]$(C \circ F)(x)$[/tex], can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit. This is a useful function for scientists and engineers who work with temperatures in different units.
Another example of a composite function is the product rule in calculus. The product rule states that the derivative of the product of two functions [tex]$u(x)$[/tex]and [tex]$v(x)$[/tex] is equal to the sum of the product of the derivatives of [tex]$u$[/tex] and [tex]$v$[/tex] and the product of [tex]$u$[/tex] and the derivative of [tex]$v$[/tex]. This can be expressed mathematically as follows:
[tex]```\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)```[/tex]
The product rule is a composite function because it takes the output of two functions, [tex]$u$[/tex] and [tex]$v$[/tex], and their derivatives,[tex]$u'$[/tex] and [tex]$v'$[/tex], and produces a new function, [tex]$\frac{d}{dx}[u(x)v(x)]$[/tex].
Composite functions are a powerful tool that can be used to solve a wide variety of problems in mathematics, science, and engineering.
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Mario has a number cube with sides numbered 1 through 6. He rolls the number cube twice. He rolls an odd number on the first roll. What is the probability that Mario will roll an even number on the second roll?
O coarda a unui cerc pentru O si raza r=20 cm, are lungimea de 32cm. DIstanta de la centru cercului la coarda este:
solve for h
ab - s - 2d - 3t = 4h
? = h
In the diagram, m < ACB = 65.
m < ECA =
A. 180
B. 115
C. 65
D. 90
The measure for <ECA is 115 degree.
What is Linear Pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.
Given:
m <ACB = 65 degree
m <ECA = ?
As. <ACB and <ECA forms a linear pair.
So, m<ACB + m<ECA = 180
64 + m <ECA = 180
m <ECA = 180 - 65
m <ECA = 115
Hence, the measure of <ECA = 115 degree.
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How do I do these only need to do 1 I just need to see how to do it!
I need help ASAP!!
Maria is doing a probability experiment. She has a bag containing marbles of different colors. The probability of selecting each color of marble is given below.
Blue - 1/2
Green - 1/8
Red - 5/16
Yellow - 1/16
What is the probability that Maria randomly selects a green marble, replaces the marble, and then randomly selects a red marble?
Luis can spend up to $240 buying men’s and women’s shirts for his club. Men’s shirts cost $8 each and women’s shirts cost $12 each. He needs to buy at least 3 men’s shirts and at least 8 women’s shirts. Also, the women’s shirts must be at least twice the number of men’s shirts.
The graph shows the feasible region, where x represents the number of men’s shirts and y represents the number of women’s shirts.
Which ordered pairs meet all the constraints and make sense in context of the situation?
Select each correct answer.
(4, 9)
(7, 13)
(2, 15)
(5,12)
(6, 15)
Let
x------> the number of men’s shirts
y-----> the number of women’s shirts
we know that
[tex]8x+12y \leq 240[/tex] ----> constraint A
[tex]x\geq 3[/tex] ----> constraint B
[tex]y\geq 8[/tex] ----> constraint C
[tex]y\geq 2x[/tex] ----> constraint D
using a graphing tool
see the attached figure N[tex]1[/tex]
The solution is the shaded area
Remember that
if an ordered pair meets all restrictions and makes sense in the context of the situation, then the ordered pair is a system solution
we're going to proceed to verify each pair ordered
case A) [tex](4,9)[/tex]
Substitute the value of x and y in each constraint
[tex]x=4\\y=9[/tex]
Verify constraint A
[tex]8*4+12*9 \leq 240[/tex]
[tex]140 \leq 240[/tex] -------> is true
Verify constraint B
[tex]4\geq 3[/tex] -------> is true
Verify constraint C
[tex]9\geq 8[/tex] ------> is true
Verify constraint D
[tex]9\geq 2*4[/tex]
[tex]9\geq 8[/tex] -----> is true
therefore
the ordered pair [tex](4,9)[/tex] is a system solution
case B) [tex](7,13)[/tex]
Substitute the value of x and y in each constraint
[tex]x=7\\y=13[/tex]
Verify constraint A
[tex]8*7+12*13 \leq 240[/tex]
[tex]212 \leq 240[/tex] -------> is true
Verify constraint B
[tex]7\geq 3[/tex] -------> is true
Verify constraint C
[tex]13\geq 8[/tex] ------> is true
Verify constraint D
[tex]13\geq 2*7[/tex]
[tex]13\geq 14[/tex] -----> is not true
therefore
the ordered pair [tex](7,13)[/tex] is not a system solution
case C) [tex](2,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=2\\y=15[/tex]
Verify constraint A
[tex]8*2+12*15 \leq 240[/tex]
[tex]196 \leq 240[/tex] -------> is true
Verify constraint B
[tex]2\geq 3[/tex] -------> is not true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*2[/tex]
[tex]15\geq 4[/tex] -----> is true
therefore
the ordered pair [tex](2,15)[/tex] is not a system solution
case D) [tex](5,12)[/tex]
Substitute the value of x and y in each constraint
[tex]x=5\\y=12[/tex]
Verify constraint A
[tex]8*5+12*12 \leq 240[/tex]
[tex]184 \leq 240[/tex] -------> is true
Verify constraint B
[tex]5\geq 3[/tex] -------> is true
Verify constraint C
[tex]12\geq 8[/tex] ------> is true
Verify constraint D
[tex]12\geq 2*5[/tex]
[tex]12\geq 10[/tex] -----> is true
therefore
the ordered pair [tex](5,12)[/tex] is a system solution
case E) [tex](6,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=6\\y=15[/tex]
Verify constraint A
[tex]8*6+12*15 \leq 240[/tex]
[tex]228 \leq 240[/tex] -------> is true
Verify constraint B
[tex]6\geq 3[/tex] -------> is true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*6[/tex]
[tex]15\geq 12[/tex] -----> is true
therefore
the ordered pair [tex](6,15)[/tex] is a system solution
therefore
the answer is
[tex](4,9)[/tex]
[tex](5,12)[/tex]
[tex](6,15)[/tex]
see the attached figure N[tex]2[/tex] to better understand the solution
Answer:
(4,9) (5,12) (6,15)
Step-by-step explanation:
Those were the correct options.
The sum of two trinomials ________.
Lixin intends to buy either Gift A, which costs $10 or Gift B, which costs $8, as Christmas gifts for each of her parents, 2 siblings, 13 relatives and 10 friends. Given that she intends to spend $230, find the number of each gift she should buy
Please help !! I need someone
The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight. what is the daily dose for a 34 lb child?
Answer: 1773.54 mg
Step-by-step explanation:
Given: The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight.
The weight of a child = 34 lb
We know that 1 pound = 0.453592 kg
Then , the weight of child in kilograms = [tex]0.453592\times34=15.422128\text{ kg}[/tex]
Now, the daily dose of ampicillin for the treatment of an ear infection for the child is given by :-
[tex]115\times15.422128=1773.54472\approx1773.54\text{ mg}[/tex]
Hence, the daily dose for a 34 lb child = 1773.54 mg
The conversion rate from Ib(pounds) to kg(kilograms)
1 Ib = 0.453592kg
Step 1
We convert the weight of the child to from lb to kg
1 Ib = 0.453592kg
34 lb = ?
Cross Multiply
34 x 0.453592kg
= 15.4221 kg
The weight of the child in kg = 15.4221 kg
Step 2
The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight.
Therefore the daily dose of ampicillin for the treatment of ear infection for the child = 15.4221 kg x 115 mg/kg
= 1,773.5415 mg
The daily dose for a 34 lb child is approximately to nearest whole number is 1,774 mg
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Any help appreciated!
For the third one is it translation, rotation, or reflection?
Thanks!
Find f(2) and f(a+h) when f(x)=3x^2+2x+4
Initially there were 2 liters of blue paint and 8 liters of crimson paint. a paint job uses 20% of the blue and 80% of the crimson paint. (a) what percentage of the total combined amount of paint is used during the job?
Final answer:
68% of the total combined amount of paint is used for the job, calculated by using 20% of the blue paint and 80% of the crimson paint from the initial amounts of 2 liters and 8 liters, respectively.
Explanation:
To calculate the percentage of the total combined amount of paint used during the job, we first identify the amount of blue and crimson paint used separately. From the question we know that there were initially 2 liters of blue paint and 8 liters of crimson paint.
20% of the blue paint is used, which is 0.20 × 2 liters = 0.4 liters.80% of the crimson paint is used, which is 0.80 × 8 liters = 6.4 liters.Now, we compute the total paint used and the initial total paint:
Total paint used = 0.4 liters (blue) + 6.4 liters (crimson) = 6.8 liters.Initial total paint = 2 liters (blue) + 8 liters (crimson) = 10 liters.To find the percentage of the total paint used, we divide the total paint used by the initial total paint and multiply by 100:
Percentage used = (Total paint used / Initial total paint) × 100
Percentage used = (6.8 liters / 10 liters) × 100 = 68%
Therefore, 68% of the total combined amount of paint is used for the job.
A function, h(x), is defined as shown.
h(x) =
Which graph represents h(x)? {image Attached)
Answer:
option B
Step-by-step explanation:
We have three different function for h(x)
[tex]h(x)= \frac{1}{4}x-4, x<=0[/tex]
WE have x<=0, so the graph starts at x=0 and goes down
Plug in 0 for x
[tex]h(0)= \frac{1}{4}(0)-4[/tex]
So h(0)= -4
When x=0, y= -4
The graph starts at (0,-4) and goes down
[tex]h(x)= \frac{1}{3}x-3, 0<x<=3[/tex]
x lies between 0 and 3, so the graph starts at x=0 and ends at x=3
Plug in 0 for x
[tex]h(0)= \frac{1}{3}(0)-3[/tex]
So h(0)= -3
When x=0, y= -4
Plug in 3 for x
[tex]h(3)= \frac{1}{3}(3)-3=-2[/tex]
When x=3, y= -2
The graph starts at (0,-4) and ends at (3, -2)
[tex]h(x)= \frac{1}{2}x-2, x>=4[/tex]
WE have x>=4, so the graph starts at x=4 and goes to the right
Plug in 4 for x
[tex]h(4)= \frac{1}{2}(4)-2[/tex]
So h(4)= 0
When x=4, y= 0
The graph starts at (4,0) and goes to the right.
SEcond graph is correct
Answer:
B
Step-by-step explanation:
One cubic foot holds 7.48 gallons of water, and one gallon of water weighs 8.33 pounds. how much does 6.26.2 cubic feetfeet of water weigh in pounds? in ounces
-138 greater than or equal to -6(6b-7)
To solve the inequality -138 greater than or equal to -6(6b-7), distribute the -6 to the terms inside the parentheses. Simplify the inequality by subtracting 42 from both sides. Divide both sides by -36, remembering to flip the inequality sign.
Explanation:To solve the inequality -138 ≥ -6(6b-7), we need to distribute the -6 to the terms inside the parentheses. This gives us -138 ≥ -36b + 42. Next, we can simplify the inequality by subtracting 42 from both sides, resulting in -180 ≥ -36b. To isolate b, we divide both sides of the inequality by -36. Remember when dividing or multiplying an inequality by a negative number, the inequality sign flips. So the final answer is b ≤ 5.
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Solve for x: 1 over 4 (2x − 14) = 4. 15 15 over 2 9 11
complete a prime factorization of 54 and write it as a product of primes
A coffee shop uses 4 liters of milk every day.If there are 15 liters of milk in the refrigerator, after how many days will more milk need to be purchased?
The table shows the steps for solving the given inequality for x.
7x + 16 < −5(4 − 5x)
Select the reason for each step from the drop-down menus.
7x + 16 < − 5(4 − 5x) - Given
7x + 16 < −20 + 25x - Distributive Property
16 < −20 + 18x - (Choose)
36 < 18x - (Choose)
2 < x - (Choose)
Answer:
Subtraction (addition) property of inequalityAddition property of inequalityDivision property of inequalityStep-by-step explanation:
You want the reasons for each of the final three steps in the solution of the inequality 7x +16 < -5(5 -5x).
Steps2. 7x +16 < -20 +25x . . . . . . . given step 2
3. 16 < -20 +18x . . . . . Subtraction property of inequality
7x was subtracted from both sides4. 36 < 18x . . . . . . . . . Addition property of inequality
20 was added to both sides5. 2 < x . . . . . . . . . . . . Division property of inequality
both sides were divided by 18__
Additional comment
Subtraction of 7x is the same as adding -7x, so you can say the reason for step 3 is either of "subtraction property" or "addition property" The same would be true of step 4.
To figure this out, you compare the inequality on each line with the one before, and determine what was changed. If the same thing is done to both sides of the inequality (addition, subtraction, multiplication, division), the reason is the corresponding property of inequality.
The multiplication and division properties of inequality tell you to reverse the comparison symbol when the factor used is negative. Here, the factor is 18, a positive number, so the inequality symbol remains untouched.
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A shop rents bikes for a $4.00 insurance charge plus $2.40 for each hour. for how many hours can a person rent a bike with $19.60?
If JK LM , which statement is true ?
47 is the result when 12 and x are added. what is the value of x?
For a large cooking project, Arthur needs to put 18 cups of water into a large pot. He can transport a maximum of 4 cups from the sink in a single trip. The pot already contains 5 cups of water. How many trips are required for Arthur to fill the pot to 18 cups?