[tex]g(x)=\frac{5+2x}{2+x} \\ \\ \implies g(4x)=\frac{5+2(4x)}{2+4x}=\boxed{\frac{5+8x}{2+4x}}[/tex]
Katie wants to buy a sundress priced at $40.00. If the sales tax is 6%, what is the total amount she must pay for the sundress?
Responses
Answer:
It should be 42.4
Aiden runs a farm stand that sells apples and strawberries. Each pound of apples sells
for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a
total of 35 pounds of apples and strawberries. Write a system of equations that could
be used to determine the number of pounds of apples sold and the number of pounds
of strawberries sold. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
what did the mathematization do to practice over winter break
Zoe rode her motorcycle down a straight freeway at 80kilometersperhour for a total of 4hours. There was a car behind her for one-half of that time. How far did Zoe ride while the car was behind her?
Write your answer as a whole number.
The distance that Zoe rode while the car was behind her was of:
160 kilometers.
How to obtain the distance?The relation between velocity, distance and time is that the velocity is the distance divided by time, hence the equation is presented as follows:
v = d/t.
The values of the parameters in this problem are given as follows:
Velocity of v = 80 km/h.Time of t = 4 h.(both of these measures are taken from the first sentence of the problem).
Then the total distance is obtained replacing the values into the equation as follows:
80 = d/4
d = 80 x 4
d = 320 kilometers.
The car was behind her for half the trip, hence the distance that the car spent behind her was of:
d = 0.5 x 320 = 160 kilometers.
More can be learned about velocity, distance and time at https://brainly.com/question/4931057
#SPJ1
A video streaming company offers two monthly plans. Plan A charges $3 per video viewed plus a flat rate of $8 per month. Plant B charges $5 per video viewed and no additional flat rate.
A write and solve an inequality to determine when the cost of viewing n videos using plan A is less that the cost of viewing n video using plan B _________________
Plan A is less expensive when ____________________
The inequality is 8 + 3 n < 5 n. Plane A is less expensive when n > 4
What is inequality ?
Inequality of wealth in major cities Economic inequality comes in many forms, but two stand out above the rest: wealth inequality as measured by the distribution of wealth and income inequality as measured by the distribution of income.
The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are universal.
Plan A: flat rate $8 per month and $3 per video viewed
Plan B: $5 per video viewed
The number of viewing videos is n
∵ The number of viewing videos is n
→ Plan A
∵ The cost per viewing is $3
∵ Cost per month is $8
∴ The cost = 8 + 3 n
→ Plan B
∵ The cost per viewing is $5
∴ The cost = 5 n
We need the cost of viewing n videos using Plan A is less than the
cost of viewing n videos using Plan B
→ Cost Plan A < Cost Plan B
∵ Cost Plan A is 8 + 3 n
∵ Cost Plan B is 5 n
∴ 8 + 3 n < 5 n
* The inequality is 8 + 3 n < 5 n
∵ 8 + 3 n < 5 n
Subtract 3 n from both sides
∴ 8 < 2 n
Divide both sides by 2
∴ 4 < n
∴ n > 4
* Plane A is less expensive when n > 4
The inequality is 8 + 3 n < 5 n. Plane A is less expensive when n > 4
To learn more about inequality from the given link
https://brainly.com/question/13393925
#SPJ1
pls answerrrr correctly
The rate of change from the hour 4 to hour 7 is equal to the slope of 0 miles per hour.
How to determine the rate of change of a segment of a graph
The rate of change of a segment of a graph is represented by its slope, the slope that can be determined by the secant line formula:
m = Δd / Δt
Where:
Δd - Change in distance, in miles.Δt - Time, in hours.First, determine the coordinates of the initial and final points of the graph:
(t₁, d₁) = (4, 120), (t₂, d₂) = (7, 120)
Second, find the rate of change of the segment:
m = (120 - 120) / (7 - 4)
m = 0 mi / h
To learn more on rates of change: https://brainly.com/question/861183
#SPJ1
Question
What is the value of x?
Enter your answer in the box.
x =
The value of x is 4/3
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangles be ΔRST and ΔQRT
Now , from the figure
∠S = 90° in the triangle ΔRST
And RS = 2/√3
∠T = 60° in the triangle ΔRST
Now ,
sin 60° = opposite / hypotenuse
= RS / RT
= ( 2/√3 ) / RT
We know , sin 60° = √3 / 2
Substituting the value of sin 60° in the equation , we get
√3 / 2 = ( 2 / √3 ) / RT
Multiply by RT on both sides , we get
RT x ( √3 / 2 ) = ( 2 / √3 )
Divide by ( √3 / 2 ) on both sides , we get
RT = ( 2 / √3 ) x ( 2 / √3 )
RT = 4 / 3
Therefore , the value of RT = 4/3
Now , from the figure
∠R = 90° in the triangle ΔQRT
and ∠T = 45° in the triangle ΔQRT
So ,
tan 45° = opposite / adjacent
We know tan 45° = 1
Substituting the value for tan 45° = 1 in the equation , we get
1 = opposite / adjacent
1 = x / RT
Multiply by RT on both sides , we get
x = RT
So , x = 4/3
Hence , The value of x is 4/3
To learn more about trigonometric equations click :
https://brainly.com/question/14746686
#SPJ1
Answer:
x = 3
Step-by-step explanation:
we are here given a figure in which we have to calculate the value of x . The given figure is made up of two right angled triangles , ∆RST and ∆QRT . So , firstly in ∆RST, we have ,
sinθ = p/h = RT/RS
sinθ = RT/2√3
and here θ = 60° , so that,
sin60° = RT/2√3
√3/2 = RT/2√3
RT = 2√3 * √3/2
RT = 3 . . . . . . . (1)
again in ∆RTQ , we have;
tanθ = p/b = RQ/RT
tanθ = x/3 ( from equation 1 )
and here , θ = 45° , so that ;
tan45° = x/3
1 = x/3
x = 3
and we are done!
help me pleaseee pleaseee pleaseee for a lot of points
Answer:
53 5/7
Step-by-step explanation:
2 + 5/21 = (42 +5)/21 = 47/21
47/21 : 1/12 = x : 2
x = 2 * 47/21 / 1/12
x = 2 * 47/21 * 12
x = 2 * 47/7 * 4
x = 8 * 47/7
x = 376/7
x = 371/7 + 5/7
x = 53 5/7
You are visiting Mexico and need to convert your U.S. dollar to the Mexican Peso. How many Mexican Peso will you have from $350?
Conversion Ratio:
$1 = Mex$20.16
Answer:
Mex$7,056
Step-by-step explanation:
$1 = Mex$20.16
$350 = x
cross multiply
$350 * Mex$20.60 = Mex$7,056
Answer: Mex$7056
Step-by-step explanation:
Make the proportion:
$1 - Mex$20.16
$350 - x
[tex]\displaystyle\\x=\frac{ 350(20.16)}{1} \\\\x=350(20.16)\\\\[/tex]
x=Mex$7056
pleaseeee help lol, will mark brainliest
Transforming the function f(x) = 2x by compression of a factor of 1/4 gives g(x) = 1/2x
Transformation of a FunctionTransformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x2 + 3 is obtained by just moving the graph of g(x) = x2 by 3 units up. Function transformations are very helpful in graphing the functions just by moving/expanding/compressing/reflecting the curve without actually needing to graph it from scratch.
In the given function;
f(x)= 2x;
After a compression by a factor of 1/4, the function becomes
g(x) = 2x * 1/4 = 1/2x
The compressed function g(x) is 1/2x
Learn more on transformation of function here;
https://brainly.com/question/22949459
#SPJ1
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answer:
[tex]18x-9=18x-9\\\\3(6x-3)=18x-9\\\\x=4.5[/tex]
Step-by-step explanation:
Each equation is =72. So for the first 4 options, just find equivalent expressions for the left side:
[tex]\frac{3}{5}(30x-15)=18x-9\\\\18x-15\neq 18x-9\\\\50x-25\neq 18x-9\\\\18x-9=18x-9\\\\3(6x-3)=18x-9[/tex]
For x=4.5, must solve original equation:
18x-9 = 72
18x = 81
x = 4.5
30 Points! Tell me everything you know about congruent polygons. How can we prove that triangles are congruent?
The polygons that are congruent are those whose vertices and sides line up perfectly. The 4 triangle congruence theorems that help in finding if the triangles are congruent or not are SSS, SAS, ASA, AAS, and RHS.
Define congruent polygons.The polygons that are congruent are those whose vertices and sides line up perfectly. Congruent polygons are polygons having the same size and shape, even if they can be rotations, translations, or mirror reflections of one another. This is another way to conceive of the idea.
A triangle's congruence can be established using the triangle congruence theorem or triangle congruence criterion. The definition of congruent is "absolutely equivalent in shape and size regardless of rotation, flipping, or turning." Congruent figures are described in geometry as shapes that are superimposed on one another, such as triangles and quadrilaterals.
The following are the triangle congruence criteria that aid in demonstrating triangle congruence.
SSS (Side, Side, Side)SAS (Side, Angle, Side)ASA (Angle, Side, Angle)AAS (Angle, Angle, Side)RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)To know more about congruency, visit:
https://brainly.com/question/7888063
#SPJ1
Given that m_G = 81°, what is m
Answer:
180-81=
Step-by-step explanation:
The scatter plot shows the daily oil production in
the United States in the years since 1994. The
equation y=-168x+6,750 is the trend line for the
data. According to the equation of the trend line,
how many thousands of barrels of oil will be
produced daily in the United States 6 years from
1994?
168
5.406
5.742
(3 Points)
6.750
5700
$100
$100
0
5/00
Answer:
Step-by-step explanation:
168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
The scatter plot shows the daily oil production in the United States in the years since 1994.
The equation y=-168x+6,750 is the trend line for the data.
According to the equation of the trend line, we need to find how many thousands of barrels of oil will be produced daily in the United States 6 years from 1994
In the equation y=-168x+6,750
The 168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994
Hence, 168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
Determine the intercepts of the line. Do not round your answers. -6x+3y=-7−6x+3y=−7minus, 6, x, plus, 3, y, equals, minus, 7 xxx-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis yyy-intercept: \Big((left parenthesis ,,comma \Big))
Answer:
is there a photo because this dosent help
Step-by-step explanation:
Can't do this write this number in standard forms 3,000 + 1,600 + 8/10 + 3 ones what how would you solve this problem
we get the desired result after solving as 4603.8 .
What is the rule of BODMAS?In mathematics, the BODMAS rule is a rule or order that is used to condense arithmetic expressions with several operators. When an equation has multiple operators, we must first determine the correct order in which to solve the expression. The BODMAS rule is always used to resolve the issue of using algebraic symbols.
For this type of problem,
We generally use BODMAS
Here,
B= Bracket
O= Off
D= Divide
M= Multiply
A= Addition
S= Subtraction
Given expression,
3,000 + 1,600 + 8/10 + 3
By following above steps we get,
First we going to divide,
3,000 + 1,600 + 0.8 + 3
Then we move to addition,
4603.8
Hence we get the desired result as 4603.8
To learn more about BODMAS, visit:
https://brainly.com/question/16738857
#SPJ1
(3×10³) (2× 10²)
Write your answer in scientific notation
find the slope-intercept equation of the line that passes through (3,-1) and has a slope of -1
Answer:
y= -x+2Step-by-step explanation:
slope formula: (y2-y1)/(x2-x1)at the point (3,-1), it is known that x=3 and y= -1.[y-(-1)]/(x-3)= -1 (y+1)/(x-3)= -1 (y+1)= -1(x-3) y+1= -x+3 y= -x+2HELPPPPPPPP! please!
Select all the statements that are true for any value of x.
A. 7x + (2x + 7) = 9x + 7
B. 7x + (2x - 1) = 9x + 1
C. 1/2x + (3 - 1/2x) = 3
D. 5x – (8 - 6x) = -x - 8
E. 0.4x - (0.2x + 8) = 0.2x - 8
F. 6x - (2x - 4) = 4x + 4
The statements that are true for any value of x are
A. 7x + (2x + 7) = 9x + 7C. 1/2x + (3 - 1/2x) = 3E. 0.4x - (0.2x + 8) = 0.2x - 8F. 6x - (2x - 4) = 4x + 4How to determine the true statements?The equations are given as
A. 7x + (2x + 7) = 9x + 7
B. 7x + (2x - 1) = 9x + 1
C. 1/2x + (3 - 1/2x) = 3
D. 5x – (8 - 6x) = -x - 8
E. 0.4x - (0.2x + 8) = 0.2x - 8
F. 6x - (2x - 4) = 4x + 4
Next, we solve one side of the equations and then compare them with the other side
So, we have the following representations
A. 7x + (2x + 7) = 9x + 7
Evaluate
9x + 7 = 9x + 7 --- true
B. 7x + (2x - 1) = 9x + 1
Evaluate
9x - 1 = 9x + 1 --- false
C. 1/2x + (3 - 1/2x) = 3
Evaluate
3 = 3 --- true
D. 5x – (8 - 6x) = -x - 8
Evaluate
11x - 8 = -x - 8 --- false
E. 0.4x - (0.2x + 8) = 0.2x - 8
Evaluate
0.2x - 8 = 0.2x - 8 --- true
F. 6x - (2x - 4) = 4x + 4
Evaluate
4x + 4 = 4x + 4 -- true
Hence, the true statements are (a), (c), (e) and (f)
Read more about expressions at
brainly.com/question/4344214
#SPJ1
Equation with one solution 8x-3x+2-x=
[tex]\fbox{4x+2}[/tex]
Simplify:
[tex]8x-3x+2[/tex]
[tex]8x+-3x+2+-x[/tex]
Combine Like Terms:
[tex](8x+-3x+-x)+(2)[/tex]
[tex]4x+2[/tex]
Given f(x)=2x-2, find f(-3)
PLEASE HELP!!!!
Answer:4
Step-by-step explanation:
replace x with -3
f(x) = 2x-2
find f(-3)
f(-3) = 2(-3) - 2
f(-3) = -6 -2
f(-3) = -8
What are the advantages and disadvantages of bases other than ten
The advantages and disadvantages of bases other than ten are shown below.
What is base ten?The base-10 system is a way to give numbers a place value. As the position of the decimal point determines a number's mathematical value, it is often referred to as the place value number system or the decimal system.
In software systems, number systems with a base of 16 are frequently used. They have the fundamental benefit of being quickly convertible to binary systems.
The advantage of using number bases on 60 is that 60 may be divided by 2, 3, 4, and 6. Its downside is that it is cumbersome.
Number systems based on 12 provide advantages comparable to those of number systems based on 60, but they give up the advantage of being divisible by 5 for the benefit of a less cumbersome system.
Therefore, base-10 number systems are not the best.
To know more about Base ten on:
https://brainly.com/question/20938069
#SPJ1
find the slope of the line passing through the points (-6,2) and (-7, 7).
Answer:
y-2=7(x+6)
Step-by-step explanation:
You got it there bro
Find two positive numbers whose difference is 23
23
and whose product is 3408
3408
The two positive numbers are 71 and 48
How to calculate for the two positive numbersWe shall apply algebra in finding the unknown numbers as follows;
Let us represent the two numbers with the letters x and y
so that;
x - y = 23...(1)
xy = 3408...(2)
from equation (1),
x = 23 + y {adding y to both sides}
putting the value 23 + y for x in equation (2) we get;
(23 + y)y = 3408 {by expansion}
23y + y² = 3408
y² + 23y - 3408 = 0 {we rearrange to get a quadratic equation}
we factorize as follows;
y² + 48y - 71y - 3408 = 0
y(y + 48) - 71(y + 48) = 0
(y + 48)(y - 71) = 0
so by factorization; y = -48 or y = 71
the numbers are positive hence we take y = 71
putting the value 71 for y in equation (2) we get;
x71 = 3408 {divide through by 71}
x = 3408/71
x = 48
Thus; 71 - 48 = 23 and 71 × 48 = 3408, and we can say that the two positive numbers are 71 and 23.
Learn more about algebra here: https://brainly.com/question/4344214
#SPJ1
An important formula from chemistry is PV = nRT. Solve the formula for n.
The solution for n in the chemistry formula is n = PV/RT
How to solve for n in the chemistry formula?From the question, we have the following parameters that can be used in our computation:
Important formula from chemistry is PV = nRT
Write out the formula
So, we have the following representation
PV = nRT
Divide both sides of the equation by R
So, we have the following representation
PV/R = nT
Divide both sides of the equation by T
So, we have the following representation
PV/RT = n
Rewrite the equation as
n = PV/RT
Hence, the solution is n = PV/RT
Read more about subject of formula at
https://brainly.com/question/657646
#SPJ1
The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y=3.9x+441 , and for women, the equation is y=14.3x+312, where x is the number of years after 1970
The point (12,489) will be the solution of our given equations.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
number of men given by y=3.9x+441 ,
and for women equation is y=14.3x+312,
Now, Let us find the coordinates of the point of intersection of both lines by equating our both equations as:
3.9x+ 441 = 14.3x + 312
14.3x - 3.9x = 441 - 312
10.4x= 129
x= 129/10.4
x = 12.40
and, y= 3.9(12.4)+ 441
y= 489.36
Hence, the point (12,489) will be the solution of our given equations.
Learn more about equation here:
https://brainly.com/question/11898177
#SPJ1
Decide whether the rates are equivalent 17 heartbeats in 15 seconds
What is the image of the point (-6, 2) after a rotation of 180° counterclockwise
about the origin?
Answer:
[tex](6,2)[/tex]
Step-by-step explanation:
When rotating 180° about the origin, [tex](x,y) \longrightarrow (-x, -y)[/tex].
There are 22 girls and 28 boys on the dukes team. Write the ratio of boys to total students on the dukes team
Answer:
28:50
Step-by-step explanation:
22+28=50, and that is the total amount of students. The number of boys go first in the ratio, then total students.
What is the second term in the binomial expansion of (2r – 3s)12?
–73,728r11s
73,728r11s
608,256r10s2
–608,256r10s2
The second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
(2r - 3s)¹²
Using nth term of the binomial expansion is:
= C (12, 2-1) (2r)¹²⁻²⁺¹ (-3s)²⁻¹
After solving
= -73728 r¹¹ s
Thus, the second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ1