The composite result function (h o g)(x) in the given functions g(x) = 9 + 4x and h(x) = x + 21/5 is 4x + 66/5.
What is the composite result function (h o g)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
g(x) = 9 + 4xh(x) = x + 21/5(h o g )(x) = ?To find (h o g)(x), first set up the composite result function h(g(x)).
h(x) = x + 21/5
h( g(x) ) = g(x) + 21/5
Plug g(x) = 9 + 4x
h( g(x) ) = ( 9 + 4x ) + 21/5
Simplify
h( g(x) ) = 9 + 4x + 21/5
h( g(x) ) = 4x + 9 + 21/5
h( g(x) ) = 4x + 66/5
Therefore, the composite function h( g(x) ) is 4x + 66/5.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
Ice is placed around a bowl of water to lower the temperature. The equation D=−75t+22 shows the time, t, measured in minutes and temperature, D, measured in degrees Celsius.
Answer:
Before cooling begins, the temperature of the water is 22°C.
Step-by-step explanation:
need steps??
have a good day
rate my answer
hich linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)
The function with the steepest slope is \(y = 7x - 3\).
The correct answer is C.
The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.
Let's compare the coefficients of x in each of the given functions:
\(y = -8x + 5\)
Slope: -8
\(y - 9 = -2(x + 1)\)
Simplifying, we get \(y - 9 = -2x - 2\)
Rearranging, we have \(y = -2x + 7\)
Slope: -2
\(y = 7x - 3\)
Slope: 7
\(y + 2 = 6(x + 10)\)
Simplifying, we get \(y + 2 = 6x + 60\)
Rearranging, we have \(y = 6x + 58\)
Slope: 6
Therefore, the steepest slope is the \(y = 7x - 3\).
For such more questions on steepest slope
https://brainly.com/question/10726891
#SPJ8
URGENT!!!
Sharon invested $5,000 in a bond for 2 years. The total interest earned on the investment was $600. What was the interest rate on the investment?
The interest rate required to pay a simple interest of $600 from an investment of $5000 in 2 years is 6%.
What is the interest rate on the investment?Simple interest is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $5,000Interest I = $600Elapsed time t = 2 yearsInterest rate r = ?Plug the given values into the above formula and solve for r.
I = P × r × t
r = I / Pt
r = 600 / ( 5,000 × 2 )
r = 600 / ( 10,000 )
r = 0.06
Interest rate = r × 100%
Interest rate = 0.06 × 100%
Interest rate = 6%
Therefore, the interest rate is 6%.
Learn more about simple interest here: brainly.com/question/25845758
#SPJ1
Referring to the figure, the two rectangles shown have
equal areas. Find the value of x.
Answer:
x = 2
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × breadth
given the rectangles have equal areas then equating the two areas gives
4x × 9 = 4(6x + 6) , that is
36x = 24x + 24 ( subtract 24x from both sides )
12x = 24 ( divide both sides by 12 )
x = 2
Need help on this pleaseeeeee
Answer:
I think it's C
Step-by-step explanation:
I just rotated point K 180 degrees and C was the only one with the coordinate points I got for K'
Restless Leg Syndrome and Fibromyalgia
People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent study indicates that people with fibromyalgia are much more likely to have restless leg syndrome than people without the disease. The study indicates that, for people with fibromyalgia, the probability is 0.33 of having restless leg syndrome, while for people without fibromyalgia, the probability is 0.03. About 2% of the population has fibromyalgia. Create a tree diagram from this information and use it to find the probability that a person with restless leg syndrome has fibromyalgia.
Answer:
The probability that a person with restless leg syndrome has fibromyalgia is 0.183.
Step-by-step explanation:
Denote the events as follows:
F = a person with fibromyalgia
R = a person having restless leg syndrome
The information provided is as follows:
P (R | F) = 0.33
P (R | F') = 0.03
P (F) = 0.02
Consider the tree diagram attached below.
Compute the probability that a person with restless leg syndrome has fibromyalgia as follows:
\(P(F|R)=\frac{P(R|F)P(F)}{P(R|F)P(F)+P(R|F')P(F')}\)
\(=\frac{(0.33\times 0.02)}{(0.33\times 0.02)+(0.03\times 0.98)}\\\\=\frac{0.0066}{0.0066+0.0294}\\\\=0.183333\\\\\approx 0.183\)
Thus, the probability that a person with restless leg syndrome has fibromyalgia is 0.183.
A men's suit is on sale for $175. If the original price of the suit was $250, what percent of
discount was used during the sale?
Answer:
75 percent
Step-by-step explanation:
250-175=75
0.75 X 250= 75perecent
Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. Find the weight per carton.
Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.
Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.
How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.
Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.
The weight per carton is 55 pounds.
For more such questions on pounds
https://brainly.com/question/30400939
#SPJ8
This week Jose played guitar for 3/4 of an hour on Tuesday, an hour and a half on Thursday, and 2.3 hours on Saturday. If Jose plays guitar for the same amount of time next week, how many hours will he have practiced over these 6 days?
Answer:
Jose will have played the guitar for 9.1 hours during those 6 days.
Step-by-step explanation:
Given that this week Jose played guitar for 3/4 of an hour on Tuesday, an hour and a half on Thursday, and 2.3 hours on Saturday, to determine, if Jose plays guitar for the same amount of time next week, how many hours will he have practiced over these 6 days, the following calculation must be performed:
3/4 = 0.75
1/2 = 0.5
(0.75 + 1.5 + 2.3) x 2 = X
4.55 x 2 = X
9.10 = X
Therefore, Jose will have played the guitar for 9.1 hours during those 6 days.
What’s Jake’s error
His error is that he added the denominators x+3 and 2x to get 3x+3. When adding fractions, the denominators must be the same and they stay the same the entire time. We only add the numerators over this common denominator. Often, we'll want the lowest common denominator (LCD).
For example, if we add 1/8 and 2/8, then we get 1/8+2/8 = (1+2)/8 = 3/8. Think of it like slicing up a cake into 8 slices. Person A takes 1 slice while person B takes 2 slices. Overall, 1+2 = 3 slices were taken out of 8, so that's one way to see how 1/8 + 2/8 = 3/8.
If we added something like 1/4 + 1/8, then we cannot say the answer is 2/12. It's like adding apples and oranges. They aren't like terms in a way. But we can convert 1/4 to 2/8 since the fractions are equivalent
1/4 + 1/8 = 2/8 + 1/8 = 3/8
Those two one-eighth slices combine to get a quarter slice. In this example, 8 is the LCD.
---------------------
To fix his error, Jake needs to find the LCD of the denominators x+3 and 2x. The LCD in this case is 2x(x+3). He'll need to multiply top and bottom of the first fraction by 2x, as this is the missing factor needed to get to the LCD.
The missing factor for the second fraction is (x+3). So he'll need to multiply top and bottom of the second fraction by (x+3). After these steps are done, he can then add the fractions.
Answer:
You have to have common denominators to add.
Step-by-step explanation:
You have to have common denominators to add.
2x-3y-6=0 in slope intercept form step by step
Answer:
\(y=\frac{2}{3}x-2\)Step-by-step explanation:
A linear function is represented by the following function in slope-intercept form:
\(y=mx+b\)Therefore, to reorganize in slope-intercept form the given equation, isolate y using inverse operations to solve equations;
\(\begin{gathered} 2x-3y-6=0 \\ -3y=-2x+6 \\ y=\frac{-2}{-3}x+\frac{6}{-3} \\ y=\frac{2}{3}x-2 \end{gathered}\)Move vertices A, B, and C to create a triangle of your choice. Record the measures of the interior angles α, β, and γ for three different triangles. Then find the sum of the angle measures for each triangle.
Answer:
α β γ Sum of Interior Angles
75.96° 50.91 53.13° 180°
45° 126.87° 8.13° 180°
26.57° 135° 18.43° 180°
Step-by-step explanation: cause I did it
Answer:
S.A for Questions 1 and 2 for Edmentum and Plato
Like and Rate
Opposite of Gain of 30 yards
Answer:
Step-by-step explanation:
-30
Find the compound interest and the amount after twelve seconds if the
interest is compounded every three seconds.
Principal = 20,000
Rate of interest = 800%
Total amount =
Compound interest =
Results:
Compound Interest (CI) = 27,280
Total Amount = 47,280
How do we calculate Compound Interest?We shall calculate Compound Interest using the formula:
Compound Interest: CI = P * \((1 + r/n)^{nt}\) - P
Where:
P = Principal amount
r = Rate of interest (in decimal)
n = The compounding periods in a year
t = Time (in years)
Given:
Principal (P) = 20,000
Rate of interest (R) = 800% = 8 (in decimal)
Time (t) = 12 seconds
Compounding frequency = every 3 seconds
We need to calculate the rate of interest in decimal and the number of compounding periods in a year.
Rate of interest (r) = R/100 = 8/100 = 0.08
Compounding frequency (n) = 1 / (compounding period in seconds) = 1 / 3 = 0.3333
CI = 20,000 * \((1 + 0.08/0.3333)^{0.3333*12}\) - 20,000
CI = 20,000 * \((1 + 0.24)^{3.9996}\) - 20,000
CI = 20,000 * \(1.24^{3.9996}\) - 20,000
CI = 20,000 * 2.364 - 20,000
CI = 47,280 - 20,000
CI = 27,280
So, the compound interest after twelve seconds = 27,280.
To calculate the total amount after 12 seconds, we can use the formula:
Total Amount = Principal + Compound Interest
Total Amount = 20,000 + 27,280
Total Amount = 47,280
Therefore, the total amount after 12 seconds = 47,280.
Learn more about Compound Interest at brainly.com/question/28020457
#SPJ1
Question 2: Which statements about functions g(xx² - 4x +3 and f(x) = x² - 4x are true? Select all
that apply.
The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:
The functions have the same range.
The functions have the same domain.
The functions have the same x-intercepts.
Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.
Here are the options:
The functions have the same graph.
The functions have the same range.
The functions have the same domain.
The functions have the same vertex.
The functions have the same y-intercept.
The functions have the same x-intercepts.
The functions have the same graph:
This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).
Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).
The functions have the same range:
This statement is true.
Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.
The functions have the same domain:
This statement is true.
The domain of both functions, unless restricted by any other factors, is all real numbers.
Quadratic functions have a domain of (-∞, ∞).
The functions have the same vertex:
This statement is false.
The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).
Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).
The functions have the same y-intercept:
This statement is false.
The y-intercept of a function is the value of y when x = 0.
For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.
For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3
= 3.
Their y-intercepts are different.
The functions have the same x-intercepts:
This statement is true.
To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.
The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.
Both functions have the same x-intercepts.
For similar questions on functions
https://brainly.com/question/11624077
#SPJ8
Find (f-g) (x)
f(x) = 2x²-2 and g(x) = 4x + 1
6x²-x
2x² + 4x-1
2x² + 4x +3
2x² - 4x - 3
Answer:Ask your teacher for help!
Step-by-step explanation:
Listen in class and you’d know!
A numerical expression is evaluated as shown. 20 + (8 x 9 + 18) ÷ 10 x 4 Step 1: 20 + (72 + 18) ÷ 10 x 4 Step 2: 20 + 90 ÷ 10 x 4 Step 3: 110 ÷ 10 x 4 Step 4: 11 x 4 In which step does the mistake first appear?
Answer:
hope it helps
ppz mark as brainliest
Please help I’ll mark you as brainliest if correct!
Answer:
12
Step-by-step explanation:
first see how much ways we can package the cookies using the 33 cookie packages:
33, 33
33, 11, 11, 11
33, 11, 11, 11 ones
33, 11, 22 ones
33, 33 ones
now only the 11 packages:
11, 11, 11, 11, 11, 11
11, 11, 11, 11, 11, 11 ones
11, 11, 11, 11, 22 ones
11, 11, 11, 33 ones
11, 11, 44 ones
11, 55 ones
now we have one more set, 66 ones.
if you count all the possibilities, you get 12
[Will Give Brainliest] What is the area of the trapezoid?
Enter your answer in the box.
Answer:
A = 378 in²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = \(\frac{1}{2}\) h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here b₁ = 6 + 15 + 6 = 27 , b₂ = 15 ( equal to middle section of b₁ ), h = 18, so
A = \(\frac{1}{2}\) × 18 × (27 + 15) = 9 × 42 = 378 in²
Jacob stated that he solved the equation 2x + 3 = 5 using the addition and multiplication property of equality. Which statement is true
Answer: First one
Step-by-step explanation:
if you roll a number cube 20 times. which scenario is least likely?
a) you find the experimental probability of rolling a 1 or 2 to be 0.3.
b) you find the experimental probability of rolling a 3 or 4 to be 0.4.
c) you find the experimental probability of rolling a 5 or 6 to be 0.5.
d) you find the experimental probability of rolling a number divisible by 3 to be 0.35
Pls solve this trigonometry question
Step-by-step explanation:
to solve this question you need to know that to find the angle you can use the inverse of a trigonometric function. henceforth, we can use arctan for this particular question.
arctan(11/5) is the answer.
the answer correct to 1 decimal point is 65.6 degrees.
comment if you have any doubts.
What should you substitute for x in the second equation (bottom equation) in order to solve the system by the substitution method?
We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
The given system of equations are 2x-1/3y = -2...(1)
3x+y=1...(2)
We solve this system of equations by using substitution method.
Let us solve for x in equation to substitute it in equation (2).
2x=-2+1/3y
Divide both sides of equation by 2.
x=-1+1/6y
Now plug in the value of x in equation 2.
Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Write the word sentence as an inequality.
A number x is greater than 0.
Answer:
x>0
I am very certain.
brainliest?
Factor 48-6 using GCF
Answer:
I think the answer is six i just searched it or it could be 12
Step-by-step explanation:
The greatest common factor (GCF) of 48 and 6 is 6, so:
48 - 6 = 42.
this isn't college level *laugh*
b) In a certain weight lifting machine, a weight of 1 kN is lifted by an effort of 25 N. While the weight moves up by 100 mm, the point of application of effort moves by 8 m. Find mechanical advantage, velocity ratio and efficiency of the machine
The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.
The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.
The problem has provided the following information:
Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m
We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage
The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;
Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;
Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5
Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.
For more questions on Velocity .
https://brainly.com/question/25749514
#SPJ8
Which math expression means "33 more than an unknown number"?
O A. 33. x
O B. X-33
O C. X+33
O D. X=33
In each case below find an equation for the line with the given information about the linear equation and
give the slope of each line.
a) Vertical line through point (2, -65)
b) Horizontal line through point (-2, 4)
a) The equation of a vertical line is x = k, where k is the x-coordinate of the point where the line intersects the y-axis. In this case, the point where the line intersects the y-axis is (2, -65), so the equation of the line is x = 2. The slope of a vertical line is undefined, since it has no slope.
b) The equation of a horizontal line is y = k, where k is the y-coordinate of the point where the line intersects the x-axis. In this case, the point where the line intersects the x-axis is (-2, 4), so the equation of the line is y = 4. The slope of a horizontal line is 0, since it has no slope.
Eliza took a friend for a birthday dinner. The total bill for dinner was $32.22 (including tax and a tip). If Eliza paid a 19.3% tip, what was her bill before adding the tip? (Round your answer to the nearest cent.)
Answer:
$27.01
Step-by-step explanation:
100% + 19.3% = 119.3%.
$32.22 = 119.3%
divide both sides by 119.3:
(32220/1193) = 1
multiply by 100 to get 100% ie the bill before the tip:
$27.01 = 100%
$27.01 is bill to nearest cent
if the mean of x,x+3,x-5,2x and 3x then find the value of x
The Value of x is 2/3.
The value of x, we need to determine the mean of the given values and set it equal to the expression for the mean.
The mean (average) is calculated by adding up all the values and dividing by the number of values. In this case, we have five values: x, x+3, x-5, 2x, and 3x.
Mean = (x + x+3 + x-5 + 2x + 3x) / 5
Next, we simplify the expression:
Mean = (5x - 2 + 3x) / 5
Mean = (8x - 2) / 5
We are given that the mean is also equal to x:
Mean = x
Setting these two expressions equal to each other, we have:
(x) = (8x - 2) / 5
To solve for x, we can cross-multiply:
5x = 8x - 2
Bringing all the x terms to one side of the equation and the constant terms to the other side:
5x - 8x = -2
-3x = -2
Dividing both sides by -3:
x = -2 / -3
Simplifying, we get:
x = 2/3
Therefore, the value of x is 2/3.
For more questions on Value.
https://brainly.com/question/843074
#SPJ8