ng Composite Functions
Given: f(x) = x - 7 and h(x) = 2x + 3
Write the rule for f(h(x)).
Answer:
f(h(x)) = 2x - 4
General Formulas and Concepts:
Algebra I
Composite FunctionsCombining Like TermsStep-by-step explanation:
Step 1: Define
f(x) = x - 7
h(x) = 2x + 3
f(h(x)) is x = h(x)
Step 2: Find f(h(x))
Substitute: f(h(x)) = (2x + 3) - 7Combine like terms: f(h(x)) = 2x - 4Please help me solve this question will give you braisnlt !
Answer:
t = 54m + 160
Step-by-step explanation:
Input = m
Output = t
Equation of the function in slope-intercept form, is represented as t = km + b
Where,
k = slope/rate of change
b = y-intercept
Using two pairs, say, (2, 268) and (3, 322):
[tex] slope(j) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{322 - 268}{3 - 2} = \frac{54}{1} = 54 [/tex]
k = 54
Find b, by substituting m = 2, t = 268, and k = 54 into t = km + b.
Thus:
268 = (54)(2) + b
268 = 108 + b
268 - 108 = b (subtraction property of equality)
160 = b
b = 160
To find the equation of the function, substitute k = 54, and b = 160 into t = km + b.
Thus:
t = 54m + 160
find a number such that five more than one half the number is three times the number
Answer:
0.5
Step-by-step explanation:
A storage bin in the corner of Joe's room has the dimensions shown below. What is the volume of the bin?
Mars is 1.5 AU. How many miles apart is Mars from the Sun?
Answer:
It would be 142 million miles
Step-by-step explanation:
Answer:
Mars is about 142 million miles away from the sun.
Three questions Please HELP!
At which point do the equations y=−2x+10 and y=x+4 intersect?(1 point)
(1,6)
(2,6)
(2,5)
(1,5)
2.If the two lines y1=−12x+5 and y2=2x+5 were to be graphed, what would their intersection point represent?
(1 point)
Their intersection point is the only point where different inputs into both functions yield different outputs.
Their intersection point is the only point where the same input into both functions yields different outputs.
Their intersection point is the only point where different inputs into both functions yield the same output.
Their intersection point is the only point where the same input into both functions yields the same output.
3.Given an equation y=−13x+5, explain the steps for using slope-intercept form to graph this equation.(1 point)
Use the y-intercept to plot the point (5,0). Then, using the y-intercept as a reference point, move right 3 units and up 1 unit, and plot a second point.
Use the y-intercept to plot the point (0,5). Then, using the y-intercept as a reference point, move left 1 unit and up 3 units, and plot a second point.
Use the y-intercept to plot the point (0,5). Then, using the y-intercept as a reference point, move left 3 units and up 1 unit, and plot a second point.
Use the y-intercept to plot the point (5,0). Then, using the y-intercept as a reference point, move left 3 units and up 1 unit, and plot a second point.
Answer:
2,6
Step-by-step explanation:
Answer:
1. (2,6)
2. C
3. B
Step-by-step explanation:
y = - 2x + 10
y = x + 4
SInce the two equation both equal y, we can said they are equal.
- 2x + 10 = x + 4
- 10 - 10
- 2x = x - 6
- x - x
- 3x = - 6
/-3 /-3
x = 2
Then we plug the x value into the equations and we will get the point that intersects y=-2x+10 and y=x+4.
- 2(2) + 10 = 2 + 4
- 4 + 10 = 6
6 = 6
This is true since both sides are equal.
The point that intersects y=-2x+10 and y=x+4 is (2,6).
2. If the two lines y1=−12x+5 and y2=2x+5 were to be graphed, what would their intersection point represent?
C) Their intersection point is the only point where different inputs into both functions yield the same output.
Ex: y=-2x+10 and y=x+4 both have the same solution which is (2,6).
3. Given an equation y=−13x+5, explain the steps for using slope-intercept form to graph this equation.
y = - 1/3x + 5
y = - 1/3(0) + 5
y = 5
Point: (0,5)
Slope: - 1/3
Rise over run (y/x) so up 3 and left 1.
B) Use the y-intercept to plot the point (0,5). Then, using the y-intercept as a reference point, move left 1 unit and up 3 units, and plot a second point.
An adult seal at a marine park consumes 2,400 kilograms of food in one year. If it consumes the same amount of food every month, how many kilograms of food does the seal consume per month?
can you help me please
Answer:
2. A, the first option
3. A, first option
Step-by-step explanation:
A segment is the part of a line that connects two points. It is the shortest distance between the two points. It has a length.
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray. A ray is named using its endpoint first, and then any other point on the ray
I hope this helps!!! Have a wonderful day!!!
How would you describe the difference between the graphs of f(x) =2/3x^3 and g(x)=2/3(-x)^3
A. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the y-axis.
C. g(x) is a reflection of f(x) over the x-axis.
D. g(x) is a reflection of f(x) over the line y = 1.
EC - The ratio of three numbers is 2:7:1.
The sum of the numbers is 30. What are the
three numbers?
Answer: 6, 21, 3
Step-by-step explanation:
2:7:1
Also, 2x 7x and 1x or just x
2x+7x+x = 30
10x = 30
x=3
So the three numbers: 2(3):7(3):1(3) OR 6:21:3
How many solutions does the system have?
Pig Race
Time (seconds)
O zero
O one
O two
O infinite
Answer:
Step-by-step explanation:
I think it's 2
While printing material from the Internet, Greg used 10 pages of paper from a package of 500 sheets of paper. What percent of the paper did he use?
Answer:
2%
Step-by-step explanation:
The percentage of paper used is 2%
Two numbers have a sum of 117 and a difference of 43. Find the numbers.
a: 83, 40
b: 80, 37
c: 160, -43
d: 70, 47
Answer:
this kid grayson is deleting my answer and i dont know how when they arent even his questions and he is being a little brat
Step-by-step explanation:
so watch out for him
Will someone with brain bigs help thou with thy math problem?
10. A jar contains 12 caramels, 7 mints and 16 dark chocolates. What is the probability of selecting a mint expressed as a fraction? *
Answer:
1/5
Step-by-step explanation:
7/35 and that simplifies to 1/5
WILL GIVE BRAINLEST PLZ HELP PLZZZZZ
Answer:
If that means least common multiple it’s 24.
Step-by-step explanation:
Answer:
LCM OF 3 AND 8 IS 24
Step-by-step explanation:
since 3 and 8 have no common factors:
LCM (3,8) = 3×8= 24
please help me with the attachment below,will give brainliest
Answer:
(b) 8n-2n+14n
Hope this helps
Answer:
B) 8n - 2n - 14n
Step-by-step explanation:
What we know:
0 is our starting point.
We're going forward by 8n first, so that's the minuend. Indicate that with +8n.
We're going back twice. First by 2n, then by 14n, so those two are the subtrahends. Indicate these two as -2n and -14n respectively.
That completes the expression of 8n - 2n - 14n.
For the function F(x) = 1/x+2, which of these could be a value of F(x) when xis
close to 2?
A 0.01
B 2
C 10,000
D -0.01
Answer:
B 2
Step-by-step explanation:
The computation of the value of f(x) in the case when x = 2 is shown below
As per the question, following function is given
F(x) = (1 ÷ x) + 2
Based on this, the x = 2
Now put the x value in the above equation
So,
= (1 ÷ 2) + 2
= (1 + 4) ÷ 2
= 5 ÷ 2
= 2.5
Hence the closet number is 2
Therefore the value of f(x) in the case when x = 2 is 2
Hence, the correct option is b.
Answer:
C. 10,000
Step-by-step explanation:
Find the matrix A of the reflection in the line L in R2 that consists of all scalar multiples of the vector.
Answer:
hello your question is incomplete attached below is the complete question
answer : 2/13 6/13
6/13 3/13
Step-by-step explanation:
Firstly we will calculate the orthogonal basis L in R^2
attached below is the detailed solution
also assuming β to be the standard ordered basis
hence the matrix A of the reflection in the Line L in R2 =
2/13 6/13
6/13 3/13
The matrix A of the reflection in line L is given by [tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex] and this can be determined by first evaluating the value of [tex]\rm R^2[/tex] by using the given data.
The orthogonal basis L in [tex]\rm R^2[/tex] is given by:
[tex]r = [u_1,u_2] =\left[\dfrac{1}{\sqrt{39} }\binom{6}{3}, \dfrac{1}{\sqrt{39} }\binom{3}{-6}\right][/tex]
[tex]\rm T(u_1)=u_1[/tex]
[tex]\rm T(u_2)=0[/tex]
[tex]\rm [T]_r = \begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}[/tex]
[tex]\rm Q = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]
Now, matrix A is given by the formula:
[tex]\rm A=Q[T]_rQ^{-1}[/tex]
Now, substitute the value of known terms in the above equation.
[tex]\rm A = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}\begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}\dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]
Simplify the above expression.
[tex]\rm A = \dfrac{1}{{39} }\begin{bmatrix}6 & 18\\ 18 & 9\end{bmatrix}[/tex]
[tex]\rm A = \dfrac{3}{{39} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]
[tex]\rm A = \dfrac{1}{{13} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]
Multiply by 1/13 in the matrix.
[tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/16850761
24a – 30
____________________________________________
Answer:
6(4a-5)
Step-by-step explanation:
mark as brainly answer
thnks
Answer:
Can`t solve it you can`t put 24a-30.
Step-by-step explanation:
It is not the same term 24a is a different term than 30. you need a equal sign to even solve the equation.
Which is more, 8 yards or 287 inches?
Answer:287 inches are greater than 8 yards
this is because 36 inches=1 yard and 8 x 36 equals 288 inches ,and 288 inches is less than 287 inches.
The coordinate pairs could represent the the vertices of a triangles congruent to KLM?
PLEASE HELP THIS IS TIMED
Answer:
D
Step-by-step explanation:
Answer:
Your answer is D :)
Step-by-step explanation:
I hope this helped
PLEASE HELP ME QUICK!!
A company produces circular drink coasters. The equation x2 + y2 = 18.0625, with units in inches, represents the size of a coaster. Each coaster is cut from a square piece of cardboard. What is the minimum possible area of each cardboard piece?
4.25 in^2
8.5 in^2
18.0625 in^2
72.25 in^2
Answer:
D
Step-by-step explanation:
72.25 in^2
The minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².
What is the equation of a circle?The equation of the circle is the equation that is used to represent the circle in the algebraic equation form with the value of the center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle, and (r) is the radius of the circle.
A company produces circular drink coasters. the equation which represents the size of a coaster is,
[tex]x^2+y^2=18.06[/tex]
The units are in inches. This equation can be written as,
[tex]x^2+y^2=(280/16)[/tex]
[tex]x^2+y^2=(17/4)^2[/tex]
Compare it with the equation of the circle, we get,
h=0
k=0
r=17/4 inch
The radius of the circular coaster is 17/4. Its diameter of it is,
[tex]d=2\times \frac{17}{4}\\ \\d=\frac{17}{2}[/tex]
Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.
a=d=17/2 inch
The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,
A=a^2
A=(17/2)^2
A=75.25inch^2
Thus, the minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².
Learn more about the equation of circle here;
brainly.com/question/1506955
#SPJ2
The Alden Middle School girls' soccer team won 75% of its games this season. If the
team won 9 games, how many games did it play? Solve this problem using a table,
diagram or picture model.
Answer:
12
Step-by-step explanation:
75% = 3/4 = 9games
1/4 = 3games
4/4 = 12 games
Please help thank you
Answer: 3
Step-by-step explanation:
simply divide 1200 by 400. :)
(a) 3,235 ft? is about how many m??
Answer:
If you mean m as in miles, then approx 0.61 miles.
Step-by-step explanation:
There are 5280 feet in a mile, so divide 3235 by 5280.
Answer: About 986 meters.
Step-by-step explanation: You can multiply by the unit conversion
.3085 m/1 /ft × 3235ft = 986.028
Or divide 3235/3.281 Same thing. Round to "about 986 meters."
Which phrase could the expression x-4 represent?
a number less than 4
the difference of a number and 4
the sum of a number and 4
four less a number
A 1 3/4 inch candle burns down in 7 hours. If b represents how much of the candle, in
inches, has burned away at any time given in hours, t, write a proportional equation
for b in terms of t that matches the context.
Answer:
14 I THINK
Step-by-step explanation:
PLEASE HELP
If the spinner is spun, what are the ODDS that the pointer lands on the number 6 or greater?
Answer:
What's the spinner? How many numbers are on it?
Step-by-step explanation:
what is the mode for 9,4,4,4,3,2
Answer:
Mode 4
Step-by-step explanation:
Mean x¯¯¯ 4.3333333333333
Median x˜ 4
Mode 4
Range 7
Minimum 2
Maximum 9
Count n 6
Sum 26
Quartiles Quartiles:
Q1 --> 3
Q2 --> 4
Q3 --> 4
