Composition of functions:
You combine two functions bycomposition by using one of the functions to substitute the independient variable in the other one.
To find (g o h)(n) you substitute the n in the function g(n) for the function h(n):
[tex](g\circ h)(n)=2(n^2+3n)-2[/tex]Simplify:
[tex](g\circ h)(n)=2n^2+6n-2[/tex]Find the missing value in theequivalent ratio 12:18 = 16:ChooseA.20B.24C.28
we have that
12:18 is the same that 12/18
simplify
12/18=6/9=2/3
Multiply by 8/8
(2/3)*(8/8)=16/24 ------> 16:24
therefore
the answer is the option BProblem N 2
we have that
each earbud costs 0.94
so
Multiply by 22
0.94*22=$20.68
the answer is $20.68A student
answered 72
questions
correctly and
scored a 90%. How
many questions
were on the test?
Answer: 80
Step-by-step explanation:
= 72/90
= 72/0.9
= 80
Write the slope-intercept form of the equation of each line.3) 10 = -2y-x
Recall that the slope-intercept form of the line equation is of the form y=mx+b, where m is the slope and b is the y-intercept.
To transform the equation 10=-2y-x into the slope-intercept form we should apply algebraic operations so we isolate the y on one side of the equation.
Let's add x on both sides, we get
[tex]-2y=10+x[/tex]Now, lets divide by -2 on both sides, we get
[tex]y=\frac{10}{-2}+\frac{x}{-2}=-\frac{1}{2}\cdot x-5[/tex]we see that this now has the slope-intercept form, where the slope is m=(-1/2) and b=-5
solve the system using any method
-x^2-10x-y=30
3x^2+30x-y=-66
Answer:
(-4,-6) (-6,-6)
Step-by-step explanation:
-y = x^2 + 10x + 30
y = -x^2 - 10x - 30
3x^2 + 30x -(-x^2-10x-30) = -66
3x^2 + 30x + x^2 + 10x + 30 = -66
4x^2 + 40x +30 + 66 = 0
4x^2 + 40x + 96 = 0
x^2 + 10x + 24 = 0
(x+6)(x+4) = 0
x = -6
x = -4
y = -x^2 - 10x - 30
y = -(-6)^2 - 10(-6) - 30
Y = -36+60 - 30
y= -6
y= -(-4)^2 - 10(-4) - 30
y = -16 + 40 - 30
y = -6
The water temperature of the Pacific Ocean vanes inversely as the water's depth. At a depth of 1000 meters, the water temperature is 4.4 degrees Celsius. What is the water temperature at a depth of 5000 meters?
Is this the correct solution for this question? I need help please
Given equation:
[tex]9x^2\text{ - 12x + 4 = 0}[/tex]Let's solve the question to identify the type of solution.
Using factorization method:
[tex]\begin{gathered} 9x^2\text{ - 12x + 4 =0} \\ 9x^2-6x\text{ -6x + 4 = 0} \\ 3x(3x-2)\text{ -2(3x-2)= 0} \\ (3x-2)(3x-2)\text{ =0} \end{gathered}[/tex]The solution is thus
[tex]\begin{gathered} 3x\text{ -2 = 0} \\ 3x\text{ = 2} \\ x\text{ = }\frac{2}{3} \end{gathered}[/tex]Hence, there is one solution and it is real.
Answer: 1 real (Option B)
Use the function y = 200tan x on the interval 0 deg <= x <= 141 deg Complete the ordered pair (x, 0). Round your answer to the nearest whole number.
The value of x for the ordered pair (x,0) is 0. B is the correct option.
What is ordered pair?
An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Given function is
y = 200 tan x.
Given ordered pair is (x,0).
The value of y for the given ordered pair is 0.
The value of tangent function is increasing with increase the value of degree.
The value of tangent at 0 degree is 0 that is tan 0 = 0.
If we multiply a number with zero it returns 0.
The possible value of x is 0.
Hence option B is the correct option.
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Solve each inequality. Then graph the solution.1. -6t-3-2t - 192. - 3(m - 4) <63. 4(1 - x) < 164. 2y <-35. 3(v - 4) 5V - 246. -X – 1 > 3x + 1Solve each inequality.7. 2(k + 4) – 3k < 148. 3(4c – 5) – 2c> 09. 15(j – 3) + 3j < 4510. 22 > 5(2y + 3) – 3y11. -53 > -3(3z + 3) + 3z12. 20(d – 4) + 4d < 813. -2(6 + s)< -16 + 2s14. 9 - 2x < 7 + 2(x – 3)Solve each inequality.If all real-number values of x are solutions of the inequality, write TRUE.If no real-number values of x are solutions of the inequality, write FALSE.15. 2(n − 3) < -13 + 2n16. -3(w + 3) < 9 - 3w17. The unit cost for a piece of fabric is $4.99 per yard including tax. You havto spend on material. How many whole feet of material can you buy?
7. The unit cost for a piece of fabric is $4.99 per yard including tax. You have $30 to spend on material. How many whole feet of material can you buy?
we know that
1 yard --------> cost $4.99
so
x yards ------> $30
Applying proportion or rule of three
x=30/4,99
x=6.01 yd
answer 6 yards
all you need is in the photo please answer fast only give the answer don't put step by step pleaseeeeeeeeeeeeeeeeeeeeee
The value of x1 = 7 and x2 = -2
From the question, we have
a=1
b=-5
c=-14
x= [-b ± √(b2 – 4ac)]/2a
substituting the value, we get
x= [5 ± √(-5² – 4*1*-14)]/2*1
=[5 ± √(25+56)]/2
=[5 ± √81]/2
=[5 ± 9]/2
x1 =[5 +9]/2=7
x2 =[5 -9]/2=-2
Quadratic Equation:
The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).It is a given that the quadratic equation has two roots. Roots might have either a true or made-up nature.
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Entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. How much would it cost for a car with 4 people in the vehicle to enter the park?
From the information given, the entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. Given that 4 people entered the one vehicle, the amount that would be paid for the vehicle is $5. Sinec it is $2 per person, the amount for 4 persons would be 2 * 4 = 8
Thus, the total cost would be
5 + 8 = $13
Identify the mistake
There is no mistake in Chase solving steps.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a equation :
(1/3)(g - 3) = 3
We can write -
(1/3)(g - 3) = 3
We can write -
g - 3 = 3 x 3
g - 3 = 9
g = 12
Therefore, there is no mistake in Chase solving steps.
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a system of equations is graphed on the set of axes below
You have to determine the solution of the equation system by looking at the graph.
For any equation system there are three possible scenarions, that the system has "no solution", that the system has "infinite solutions" and that the system has "one solution"
Looking at the graph you can determine which situation if:
- both lines are parallel, they never meet, which indicates that the system has no solution.
- both lines are superimposed, i.e. they seem as if there is only one line, the system has infinite solutions.
- both lines cross at one point, this indicates that the system has only one solution and the solution will be the point where the lines intersect.
In the given graph, the lines cross at one point, which means that the system has one solution. To determine said solution you have to read the x and y coordinates of the point in the grid.
The lines meet at x=4 and y=2, which means that the solution of this system is a
Sketch the graphs for each of the following equations. 7 a. y = 5-X+7 b.y=9 c. y= 3x + 6
a)
Given:
The equation is,
[tex]y=-\frac{7}{5}x+7[/tex]The objective is to sketch the graph of the equation.
Since, the highest degree of the equation is 1, it could be a straight line. The general equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the equation and c represents the y intercept. Then comparing the both equations,
[tex]\begin{gathered} \text{slope, m=-}\frac{\text{7}}{5} \\ y\text{ intercept, c=7} \end{gathered}[/tex]Substitute, y = 0 in the given equation.
[tex]\begin{gathered} 0=-\frac{7}{5}x+7 \\ \frac{7}{5}x=7 \\ x=7\cdot\frac{5}{7} \\ x=5 \end{gathered}[/tex]Thus, at y = 0, the value of x = 5.
Using the coordinates (5,0) and y intercept c = 7, the graph will be,
Hence, the required graph is obtained,
in point slope form: passes through (1, -3), slope = -1?
Explanation
Step 1
Let
P1(1,-3)
slope=-1
Step 2
use the formula
[tex]y-y_1=m(x-x_1)[/tex]replacing
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-1(x-1) \\ y+3=-x+1 \\ \text{subtract 3 in both sides} \\ y+3-3=-x+1-3 \\ y=-x-2 \end{gathered}[/tex]I hope this helps you
Find the length of RS to the nearest tenth of a meter
We were given a right triangle, with a known angle and a known hypothenuse, we want to find the nearest side to the known angle, so we must use the cosine relation, as shown below:
[tex]\begin{gathered} \cos (28)=\frac{RS}{QS} \\ 0.88=\frac{RS}{9.6} \\ RS=9.6\cdot0.88=8.45\text{ m} \end{gathered}[/tex]The length of the side RS is approximately 8.5 meters.
What is 5x2 (This is a joke)
Answer:
10 (duh)
Step-by-step explanation:
Solve the equation. 42 = d2 - 22 d = and d =
we have
[tex]42=d^2-22[/tex]solve for d
[tex]\begin{gathered} d^2=42+22 \\ d^2=64 \\ \text{square root both sides} \\ d=\pm\sqrt[]{64} \\ d=\pm8 \end{gathered}[/tex]therefore
d=+8 and d=-8A six-sided number cube is rolled. Event A consists of rolling an even number. Event B consists of rolling a number greater than four. Match the correct sample space to each event.
EXPLANATION :
From the problem, we have two events :
Event A : rolling an even number {2, 4, 6}
Event B : rolling a number greater than four {5, 6}
1. Union of A and B is the combination of Event A and B
Since there's a common element, 6, we will take this as one only.
That will be {2, 4, 5, 6}
2. Intersection of A and B is the common element between the two events.
So that is {6}
3. Complement of A is the set of elements that is NOT present in Event A.
Since a cube has 6 sides, the elements are {1, 2, 3, 4, 5, 6}
The complement of A will be {1, 3, 5}
4. Event B, from the data we have from above, B will have {5, 6}
Divide. Reduce your answer to lowest terms.- 2/3 divide 7/9
For the division, the fraction is reciprocated with change in sign from divison to multiplictaion.
Divide the expression.
[tex]\begin{gathered} -\frac{2}{3}\times\frac{9}{7}=-\frac{2\cdot3}{1\cdot7} \\ =-\frac{6}{7} \end{gathered}[/tex]So answer is -6/7.
if G(t)=(3t-5)^2 + 4t - 1 find each of the following g of a and g of a plus 2
For point A, you just have to replace t by a in the given function, like this
[tex]\begin{gathered} G\mleft(t\mright)=\mleft(3t-5\mright)^2+4t-1 \\ \text{ Replacing} \\ G\mleft(a\mright)=\mleft(3a-5\mright)^2+4a-1 \\ \text{ Solving you have} \\ G(a)=(3a-5)(3a-5)+4a-1 \\ G(a)=9a^2-30a+25+4a-1 \\ \text{ Add similar terms} \\ G(a)=9a^2-26a+24 \end{gathered}[/tex]For point B, you just have to replace t by a+2 in the given function, like this
[tex]\begin{gathered} G(t)=(3t-5)^2+4t-1 \\ \text{ Replacing} \\ G(a+2)=(3(a+2)-5)^2+4(a+2)-1 \\ \text{ Solving you have} \\ G(a+2)=(3a+6-5)^2+4(a+2)-1 \\ G(a+2)=(3a+1)^2+4a+8-1 \\ G(a+2)=(3a+1)(3a+1)+4a+8-1 \\ G(a+2)=9a^2+6a+1+4a+8-1 \\ \text{ Add similar terms} \\ G(a+2)=9a^2+10a+8 \end{gathered}[/tex]Zach bought a pair of jeans for $54.The next week he noticed that the price for the same pair of jeans was now $74. Find the percent of change.
Let's begin by listing out the information given to us:
Old Price = $54
New Price = $74
The percentage change is given by:
[tex]\begin{gathered} \text{\%}\Delta=\frac{|OldPrice-NewPrice|}{OldPrice}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|54-74|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|-20|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{20}{54}\cdot100\text{\%} \\ \text{\%}\Delta=37.04\text{\%} \\ \text{\%}\Delta\approx37\text{\%} \end{gathered}[/tex]Question 9 of 22Which number produces a rational number when added to5?O A. 5.38516480...B. 10C.O D. 0.22SUBMIT
A rational number can be said to be a number that is expressed as a quotient of s fraction. The denominator of a rational number must be a non-zero number.
You can simply say a rational number is any number that can be written as a fraction.
To find the number when added to 5 produces a rational number, we have:
A. 5.38516480...
This number has infinite decimal so it is an irrational number
B. 10
10 + 5 = 15
This is not a rational number
C. 0
0 + 5 = 5
This is not a rational number
D. 0.22
0.22 + 5 = 5.22
This is a rational number because it can be written as a fraction
[tex]5.22=\frac{522}{100}[/tex]Therefore, the number that produces a rational number when added to 5 is 0.22
ANSWER:
D. 0.22
Make a question similar (but not the same!) to those in #2 Post your question and full solution
Write a function with vertical asymptote x=4, horizontal asymptote y=1, y intercept at (0,2).
A possible function can be express as:
[tex]f(x)=\frac{x-8}{x-4}[/tex]Let's prove that this function fulfils our conditions. Let's start with the y-intercept, we know that this happens when x=0, then we have:
[tex]f(0)=\frac{0-8}{0-4}=2[/tex]Hence the y-intercept is at (0,2).
Now, we know that a rational function has horizontal asymptote y=b if:
[tex]\begin{gathered} \lim_{x\to\infty}f(x)=b \\ \text{ or } \\ \lim_{x\to-\infty}f(x)=b \end{gathered}[/tex]Let's find these limits:
[tex]\begin{gathered} \lim_{x\to\infty}\frac{x-8}{x-4}=\lim_{x\to\infty}\frac{\frac{x}{x}-\frac{8}{x}}{\frac{x}{x}-\frac{4}{x}} \\ =\lim_{x\to\infty}\frac{1-\frac{8}{x}}{1-\frac{4}{x}} \\ =\frac{1-0}{1-0} \\ =1 \end{gathered}[/tex]and:
[tex]\begin{gathered} \lim_{x\to-\infty}\frac{x-8}{x-4}=\lim_{x\to-\infty}\frac{\frac{x}{x}-\frac{8}{x}}{\frac{x}{x}-\frac{4}{x}} \\ =\lim_{x\to-\infty}\frac{1-\frac{8}{x}}{1-\frac{4}{x}} \\ =\frac{1-0}{1-0} \\ =1 \end{gathered}[/tex]This means that we have a horizontal asymptote y=1 as we wanted.
Now, a rational function has vertical asymptote at x=a if:
[tex]\begin{gathered} \lim_{x\to a^-}f(x)=\pm\infty \\ \text{ or } \\ \lim_{x\to a^+}f(x)=\pm\infty \end{gathered}[/tex]to determine the value of a we need to look where the function is not defined, that is, the values which make the denominator zero, in this case we have:
[tex]\begin{gathered} x-4=0 \\ x=4 \end{gathered}[/tex]Then we need to find the limits:
[tex]\begin{gathered} \lim_{x\to4^-}\frac{x-8}{x-4} \\ \text{ and } \\ \lim_{x\to4^+}\frac{x-8}{x-4} \end{gathered}[/tex]Now, if we approach the value x=4 from the left we notice that as x gets closer to 4 the function gets bigger and bigger, for example:
[tex]f(3.9999)=\frac{3.9999-8}{3.9999-4}=400001[/tex]if we follow this procedure, we conclude that:
[tex]\lim_{x\to4^-}\frac{x-8}{x-4}=\infty[/tex]Similarly, if we approach x=4 from the right the function gets smaller and smaller, for example:
[tex]f(4.0001)=\frac{4.0001-8}{4.0001-4}=-39999[/tex]Then we can conclude that:
[tex]\lim_{x\to4^+}\frac{x-8}{x-4}=-\infty[/tex]Hence, we conclude that the function we proposed has a vertical asymptote x=4 like we wanted.
the properties we gave can be seen in the following graph:
The cost in dollars of making x items is given by the function C(x)=10x+700.The fixed cost is determined when zero items are produced. Find the fixed cost for this item.fixed cost=What is the cost of making 25 items?C(25)=Suppose the maximum cost allowed is $2700. What are the domain and range of the cost function, C(x)?When you enter a number in your answer, do not enter any commas in that number. In other words if you want to enter one thousand, then type in 1000 and not 1,000. It's not possible to understand what the interval (1,000,2,000) means, so you should write that as (1000,2000).domain=range=
According to the situation, the domain of this function will contain all values that x can take. Since x is the number of items, it only can take values from 0 to a certain value.
To find this certain value, use the maximum cost allowed (2700) as C(x) and find x using the equation:
[tex]\begin{gathered} C(x)=10x+700 \\ 2700=10x+700 \\ 2700-700=10x \\ 2000=10x \\ x=\frac{2000}{10} \\ x=200 \end{gathered}[/tex]It means that the domain of the function is [0,200]
The range contains all the values that cost can take. We know that the fixed cost (which is the minimum cost) is 700 and the maximum cost is 2700.
It means that the range of the function is [700,2700]
Answer:
it is not clear
Step-by-step explanation:
Which player is more likely to score more than 18 points in a game?Who is more likely to have a very bad game and score less than 3 points?(sorry for all the equations next to the whisker plots)
The boxplot that shows points that Dwight scored in each game has a minimum value of 1 point and a maximum value of 20 points.
The box plot that shows the points that Ron scored in each game, has a minimum value of 4, and a maximum value of 18 points.
The values below the minimum point and above the maximum point of the data set can be considered "outliers", i.e. atypical observations, and the probability if them being observed is very low.
Ron's box plot goes from 4 to 18 points, it is very unlikely for him to score less than 3 points or above 18, both scores would be considered "outliers" for him.
But, Dwigth's box plot goes from 1 to 20, which means that "scoring less than 3 on a game" or "scoring more than 18 on a game" are more possible situations for him.
So Dwight is more likely to score more than 18 points on a game and he is also more likely to have a very bad game and score less than 3 points.
WILL GIVE BRANLIEST Use the graph to write a linear function that relates y to x (for both please)
Question:
Use the graph to write a linear function that relates y to x
Solution:
To find the linear function that relates y and x in the above graph, we have to know that a linear function is given by the following formula:
[tex]y\text{ = mx+b}[/tex]where m is the slope of the line and b is the y-coordinate of the y-intercept (when x = 0). Now, notice that in this case, when x = 0 then y= 2, thus we can conclude that b = 2 and:
[tex]y\text{ = mx+}2[/tex]On the other hand, by definition, the slope of the line is given by:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2, Y2) are any two points on the line. Take for example:
(X1,Y1) = (0,2)
(X2,Y2) = (6,10)
then, replacing this data in the equation of the slope, we obtain:
[tex]m\text{ = }\frac{10-2}{6-0}=\text{ }\frac{8}{6}[/tex]then, using the slope obtained above, we can conclude that the equation of the linear function is:
[tex]y\text{ = }\frac{8}{6}x\text{ + 2}[/tex]1 1/6cdx (-6/7c raised to the 9 power d raised to the 7 power.I'll upload a picture
ANSWER:
[tex]-c^{10}d^8[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]1\frac{1}{6}cd\cdot\mleft(-\frac{6}{7}c^9d^7\mright)[/tex]We simplify as follows:
[tex]\begin{gathered} 1\frac{1}{6}=\frac{6+1}{6}=\frac{7}{6} \\ \frac{7}{6}cd\cdot(-\frac{6}{7}c^9d^7) \\ \frac{7}{6}\cdot-\frac{6}{7}\cdot cd\cdot(c^9d^7)=-1\cdot c^{10}d^8=-c^{10}d^8 \end{gathered}[/tex]If 6 garbage trucks can collect the trash of 36 homes in a day. How many trucks are needed to collect in 180 houses?
In the question, we are given that 6 garbage trucks can collect the trash of 36 homes in a day. We can find how many trucks are needed to collect in 180 houses below.
Explanation
[tex]\begin{gathered} \text{If 6 trucks collect for 36 houses} \\ x\text{ truck will collect for }180\text{ houses} \\ \text{Therefore using direct proportion} \\ \frac{6}{x}=\frac{36}{180} \\ \frac{6}{x}=\frac{1}{5} \\ \text{cross multiply} \\ x=30 \end{gathered}[/tex]Answer: 30 trucks
Please use photo for better understanding Please also know this is 6th grade level math.
ANSWER
1/3
EXPLANATION
We know that 2/3 of all the students in the orchestra play stringed instruments and that of that fraction, 1/2 play violins. To find how many students in the orchestra play violins, we have to multiply the two fractions. In other words, we have to find what fraction is half of the two thrids who play stringed instruments,
[tex]\frac{2}{3}\times\frac{1}{2}[/tex]We have a number 2 in the numerator of the first fraction and the same number is in the denominator of the second fraction, thus these two numbers are canceled, and we have,
[tex]\frac{1}{3}\times\frac{1}{1}=\frac{1}{3}[/tex]Hence, 1/3 of the students in the orchestra play violins.
A.Ghamarvion earned $8.00 an hour and was given a 75% wage ge increase. How much does Ghamarvion earn per hour after his ae raise? B. A population increased from 328 569 people to 400,232 people. What was the percent of change in the population?