f(x) = 4x + 6 and g(x) = 1/2 x f (x)
What is the function rule for function g?
g(x) = ____ x+_____
The function rule for function g is g(x)=2x+3.
We are given the function f(x).In mathematics, a function is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are used all the time.The function f(x) equals 4x + 6.The function g(x) equals (1/2)*f(x).We see that the function g(x) is just a modification of the function f(x).In the definition of the function g(x), substitute the value of the function f(x).The function g(x) becomes (1/2)*(4x + 6).Open the brackets and simplify.The function g(x) becomes 2x + 3.To learn more about similar functions, visit :
https://brainly.com/question/12431044
#SPJ1
Division in Base Three: 22011/12
Answer: 1122
Step-by-step explanation:
Members of a baseball team raised $1187.25 to go to a tournament. They rented a bus for $783.50 and budgeted $21.25 per player for meals. Which tape diagram could be used to represent the context if xx represents the number of players the team can bring to the tournament?
The tape diagram that could be used to represent the context is A.
What is a tape diagram?It should be noted that a tape diagram is simply used to show number relationships. It so used to illustrate ratios, addition, etc.
In this case, the baseball team raised $1187.25 to go to a tournament and they rented a bus for $783.50 and budgeted $21.25 per player for meals.
Let x represents the number of players the team can bring to the tournament.
This will be illustrated as 783.50 + 21.25x = 1187.25. The tape diagram that illustrates this is A.
Learn more about tape diagram in:
brainly.com/question/15656029
#SPJ1
a motor racing track has lenght 5 5/6
a straigt section is 1 1/4
what fraction is the straight section
[tex]\frac{3}{14}[/tex] is the straight section.
What is fraction?A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is 12. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.
Given Data
Length = 5[tex]\frac{5}{6}[/tex]
Length = [tex]\frac{35}{6}[/tex]
Straight section = 1[tex]\frac{1}{4}[/tex]
Straight section = [tex]\frac{5}{4}[/tex]
Dividing them:
= [tex]\frac{35}{6}[/tex] ÷ [tex]\frac{5}{4}[/tex]
= [tex]\frac{35}{6}[/tex] ×[tex]\frac{4}{5}[/tex]
= [tex]\frac{6}{28}[/tex]
= [tex]\frac{3}{14}[/tex]
[tex]\frac{3}{14}[/tex] is the straight section.
To learn more about fraction, visit:
https://brainly.com/question/10354322
#SPJ9
7x-3y=13
9x+10y=-11
help me
Answer:
Step-by-step explanation:
it's below
Answer:
(1, - 2 )
Step-by-step explanation:
7x - 3y = 13 → (1)
9x + 10y = - 11 → (2)
multiplying (1) by 10 and (2) by 3 and adding will eliminate y
70x - 30y = 130 → (3)
27x + 30y = - 33 → (4)
add (3) and (4) term by term to eliminate y
97x + 0 = 97
97x = 97 ( divide both sides by 97 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (2)
9(1) + 10y = - 11
9 + 10y = - 11 ( subtract 9 from both sides )
10y = - 20 ( divide both sides by 10 )
y = - 2
solution is (1, - 2 )
Evaluate the function as indicated, and simplify.
g(x) = 2x² - 3x + 1
g(x) = 2x² - 3x + 1 =
-2 = 2[tex](x+2)^{2}[/tex]+ 3(x+2) - 1
-2 = 2( [tex]x^{2}[/tex] + 4x + 4) + 3(x+2) - 1
-2 = 2[tex]x^{2}[/tex] + 8x + 8 + 3x + 6 - 1
-2 = 2[tex]x^{2}[/tex] + 11x + 13
0 = 2[tex]x^{2}[/tex] + 11x + 15
0 = ( 2x + 5 )(kx + 3 )
2x + 5 = 0 ---> kx= -5/2
x+3=0 ----> x = -3
Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output.
one of them sums up a function the best?
Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output. So, this is the best choice.
The function's type is f/x)= 2x 2 + 3x 1.
Explanation: Since the polynomial f(x)=2x33x+1 is continuous and contains continuous derivatives of all orders for all real x, it unquestionably meets the theorem's hypotheses.
to learn more about g(x) = 2x² - 3x + 1 refer to:
https://brainly.com/question/17146672
#SPJ13
The amount of time light takes to travel one meter in a vacuum is 3.3 nanoseconds. To travel one mile it takes 5.4 microseconds.
How many times longer, to the nearest tenth, does it take for light to travel one mile than one meter?
The time to travel one mile is 1636.4 times the time to travel one meter.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent.
The amount of time light takes to travel one meter = 3.3 nanoseconds = 3.3 * 10⁻⁹ s
Time to travel one mile = 5.4 microseconds = 5.4 * 10⁻⁶ s
Ratio of time to travel one mile to time to travel:
one meter = 5.4 * 10⁻⁶ s / 3.3 * 10⁻⁹ s = 1636.4one mile is 1636.4 times the time of one meter.Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
HELP HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ ~~ y^{\frac{3}{4}} ~~ }{y^{\frac{1}{2}}}\implies \cfrac{ ~~ y^{\frac{3}{4}}y^{-\frac{1}{2}} ~~ }{1}\implies y^{\frac{3}{4}-\frac{1}{2}}\implies y^{\frac{1}{4}}\implies \sqrt[4]{y^1}\implies {\Large \begin{array}{llll} \sqrt[4]{y} \end{array}}[/tex]
PLS HELP i’m stuck on this question
Answer:
I djdhdhdh47747
Step-by-step explanation:
jrhrhdhrhdbdndbdbdjdjdjfjfjfjfjfjfjfjffuufufurtuhrbrbrnrntjrjfjfjdjfufufjfjfjfjffiitiririfiififig
Solve the system using matrices. Enter fractional answers in decimal form.
x + 5y + 3z = 6
4y -z = 3
6x - 2y + 4z = 12
The solution to the system of three linear equations is the ordered triple
Answer:
f
Step-by-step explanation:
find the difference using the number line 3-1
The area of a rectangle whose length is 7ft is 14ft squared. Use the equation 14=7w, where w represents the width of the rectangle, and these values for w: 2, 4, 98. Determine the width of the rectangle.
The most appropriate choice for area of rectangle will be given by:
Width of rectangle is 2 ft
What is area of rectangle?
Area of rectangle is the total space taken by the rectangle.
If the length of rectangle be [tex]l[/tex] ft and breadth of rectangle be [tex]b[/tex] ft, area of rectangle [tex]l \times b[/tex] [tex]ft^2[/tex]
Here,
Let the width of the rectangle be w ft
Length = 7ft
Area = 7 x w [tex]ft^2[/tex]
By the problem,
7 x w = 14
w = [tex]\frac{14}{7}[/tex]
w = 2 ft
Width of rectangle is 2 ft
To learn more about area of rectangle, refer to the link:
https://brainly.com/question/25292087
#SPJ9
triangle ABC has vertices A(-2,-1), B (1,2) and C (2,-4), if triangle A'B'C' is a dilation of triangle ABC with a scale factor of 2,5 and center of dilation (0,0), give the coordinates of the vertices of triangle A'B'C'
After a dilation with a scale factor of 2.5 and center of dilation (0, 0), the coordinates of the vertices of triangle A'B'C' are A' (-5, -2.5), B' (2.5, 5), and C' (5, -10).
What is dilation?Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
What is scale factor?A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as triangles.
For the given coordinates, the dilation with a scale factor of 2.5 and center of dilation (0, 0) should be calculated as follows:
Point A (-2, -1) → Point A' (-2 × 2.5, -1 × 2.5) = Point A' (-5, -2.5).
Point B (1, 2) → Point B' (1 × 2.5, 2 × 2.5) = Point B' (2.5, 5).
Point C (2, -4) → Point C' (2 × 2.5, -4 × 2.5) = Point C' (5, -10).
Read more on dilation here: brainly.com/question/20482938
#SPJ1
Exit Ticket
Donnie earns extra money as a lifeguard. He earns $52.50 for
5 hours. Identify the constant of proportionality, and write an
equation for the proportional relationship.
Answer:
10.5
10.5x = 52.50
Step-by-step explanation:
To identify the constant of proportionality, divide money by hours.
52.50 ÷ 5 = 10.5
Use the constant of proportionality to write the equation.
10.5x = 52.50
5 3/4 - 2 1/4
help me please love
Answer:
3 2/4Step-by-step explanation:
5 3/4 - 2 1/4
whole numbers
5 - 2 = 3
fractions
3/4 - 1/4 = 2/4
so
3 2/4 is the answer
what is the answer 67+2=?
Answer:This is 69
Step by step explanation:67 +2 is 69
Explain how using
basic facts can help you find 10 x 20 x 30 x 40 mentally.
Answer: 240,000
Step-by-step explanation: Ok so to get the answer we first do
10 x 20 which is 200 then you do 200 x 30 which is 6,000 then we times the last number which is 40 which would look like 6,000 x 40 which equals 240,000. Hope this helps but also a quicker way in your head could be lining them up straight and down in your head with all the numbers and with all the zeros you will no the answer will have 4 zeros on the end of the answer then do 1 x 2 = 2 x 3 = 6 x 4=24 so then add the four zeros on the end and there you go you get your final answer of 240,000.
Find the value of x.
(3x + 3) (5x + 1)
Please help me :)
Answer:
22
Step-by-step explanation:
The angles form a linear pair, and thus add to 180°.
[tex]3x+3+5x+1=180 \\ \\ 8x+4=180 \\ \\ 2x+1=45 \\ \\ 2x=44 \\ x=22[/tex]
3. John and Savanah are saving money to go on a trip to Mexico. They need at least $2,545 in order to go. John tutors English and Savanah works as a babysitter to raise money. John charges $15 per hour and Savanah charges $20 per hour. The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hours.. Write a set of constraints to model the problem, with x representing the number of hours John tutors and y representing the number of hours Savanah babysits.
The set of constraints to model the problem include
y < 5x and y ≥ 40 hoursHow to write a set of constraints to model the problemThe following is data given in the problem
They need at least $2,545 x representing the number of hours John tutorsy representing the number of hours Savanah babysitsThe number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hoursThe constraints to model the problem is as follows:
The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled.
no more than means it is not greater that which implies it is less thany < 5xSavanah will babysit at least 40 hours
at least 40 hours means a minimum of 40 hours this is 40 hours and above simplified further to greater than or equal to 40 hoursy ≥ 40 hoursThe two constraints required is modelled using inequalities and represented as follows y < 5x and y ≥ 40 hours
Read more on constraints here: https://brainly.com/question/14309521
#SPJ1
PLEASE HELP AGAIN PLS
Answer:
(5,0)
Step-by-step explanation:
Let y=0. Then, x=5.
Kevin and Randy Muise have a jar containing 69 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.25 How many of each type of coin do they have?
Taking into account the definition of a system of linear equations, Kevin and Randy Muise have 19 quarters and 50 nickels.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In this way, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of quarters and nickelsIn this case, a system of linear equations must be proposed taking into account that
"q" is the amount of quarters."n" is the amount of nickels.You know that:
Kevin and Randy Muise have a jar containing 69 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.25The system of equations to be solved is
q + n= 69
0.25q + 0.05n= 7.25
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "q" from the first equation:
q= 69-n
Replacing this expression in the second equation:
0.25(69 - n) + 0.05n= 7.25
Solving:
0.25×69 - 0.25n + 0.05n= 7.25
17.25 - 0.25n + 0.05n= 7.25
- 0.25n + 0.05n= 7.25 - 17.25
-0.2n= -10
n= (-10)÷ (-0.2)
n= 50
Remembering that q= 69 -n, you get:
q=69 - 50
q= 19
Finally, there are 19 quarters and 50 nickels.
Learn more about system of equations:
brainly.com/question/11087158
brainly.com/question/14323743
brainly.com/question/1365672
brainly.com/question/20533585
brainly.com/question/20379472
#SPJ1
if 7(n-m) = 3m, what is m/n
Answer:
10m/7n
Step-by-step explanation:
distribute the
7n-7m=3m
7n=
HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT )I HAVE OTHER QUESTIONS TOO HELP PLS)
The equation of the line perpendicular to the given line and passing through (-3, 7) is; y = (-2/3)x + 5
What is the equation of the Line in slope intercept form?
We are given the equation of a line as; y = (3/2)x - 1
Now, the general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, for our given equation we have;
Slope; m = 3/2
y-intercept; c = -1
Now, for a line perpendicular to this, will have a slope of -1/(3/2) = -2/3
Thus, equation of the line perpendicular to the given line and passing through (-3, 7) is;
y - 7 = (-2/3)(x - (-3))
y - 7 = (-2/3)(x + 3)
y = 7 - 2 - (2/3)x
y = (-2/3)x + 5
Read more about Equation in slope intercept form at; https://brainly.com/question/1884491
#SPJ1
Find the value of x and y
Answer:
a
Step-by-step explanation:
Vertical angles are congruent, so:
[tex]7x+7=112 \\ \\ 7x=105 \\ \\ x=15[/tex]
Using linear pairs,
[tex]112+4y=180 \\ \\ 4y=68 \\ \\ y=17[/tex]
You have saved $24 towards the purchase of your own laptop. you get a job at the corner store cleaning after hours on sundays that pays $40 per week. the laptop you want costs $850 and includes everything you'll need to start college.
The number of weeks needed to get $850 is 21 weeks.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.
Let the number of weeks be represented by w
Amount saved = $24
Amount needed = $850
Number of weeks = w.
This will be illustrated as:
24 + 40w = 850
Collect like terms
40w = 850 - 24
40w = 826
Divide
w = 826 / 40
w = 20.65 = 21 approximately
There'll be 21 weeks.
The complete question is written below.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
You have saved $24 towards the purchase of your own laptop. you get a job at the corner store cleaning after hours on sundays that pays $40 per week. the laptop you want costs $850 and includes everything you'll need to start college. How may weeks are needed?
13) Three adjacent angles are at a point. The first angle is represented by x, the second angle is 20° more than the
first, and the third angle is 20° more than the second angle. Find the measurements of all three angles.
Answer:
x=40 degrees
Step-by-step explanation:
adjacent angles add up to 180 degrees
First angle=x
second angles=x+20
third angle =x+40
add all and equate to 180 degrees i.e.
x+x+20+x+40=180
3x=180-60
x=40 degrees
x+20=40+20=60 degrees
x+40=40+40=80 degrees
Find the distance between each pair of points
Answer: [tex]\sqrt{82}[/tex]
Step-by-step explanation:
Points are (4,-4) and (3,5)
We find the difference between the numbers
5- - 4 = -9
3 - 4 = -1
Then find the length between them using a triangle [tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]\sqrt{-9^{2} +-1^{2} } =\sqrt{82}[/tex]
I have a test tomorow and I dident study i need help what is 2 + 8 ples help
Answer:
10
Step-by-step explanation:
lol XD are you trolling?
HELPP ME ASAP
Which point is located on the y axis iready
Answer: The first option (0,-3)
3(x-2)+2x=1/2(10x-12)
Answer:
this equation is always true
Step-by-step explanation:
3(x-2)+2x=1/2(10x-12)
3x - 6 + 2x = 5x - 6
5x - 6 = 5x -6
5x - 5x = 6 - 6
0 = 0
this equation is always true
Answer:
Infinitely many solutions
Step-by-step explanation:
[tex]\sf 3(x - 2) + 2x = \dfrac{1}{2}*(10x - 12)\\\\ 3x - 3*2 + 2x = \dfrac{1}{2}*10x - \dfrac{1}{2}*12 \ [\bf distributive \ property]\\\\ 3x - 6 + 2x = 5x - 6[/tex]
Combine like terms,
3x + 2x - 6 = 5x - 6
5x - 6 = 5x - 6
There are infinitely many solutions for this equation.
Please Simplify
√81x¹²y³
Answer:
9x^6y√y
Step-by-step explanation:
√81x¹²y³ = √9*9* x^6* x^6 * y*y*y = 9x^6y√y