[tex]\\ \sf\longmapsto f(x+4)=3x+4[/tex]
[tex]\\ \sf\longmapsto f(x)=3x+4-4[/tex]
[tex]\\ \sf\longmapsto f(x)=3x[/tex]
Now
[tex]\\ \sf\longmapsto f(4)[/tex]
[tex]\\ \sf\longmapsto 3(4)[/tex]
[tex]\\ \sf\longmapsto 12[/tex]
EMERGENCY A speeding ticket costs $80 plus $10 for each mile per hour over the speed limit the violator was traveling. How much would someone going 12 miles per hour faster than the speed limit have to pay for their ticket?
Answer:
$200
Step-by-step explanation:
Fine calculated per mile = $10
Fine calculated for 'm' mile = 10 * m = 10m
Cost paid by violator = 80 + 10m
m = 12 miles
Cost paid by the violator = 80 + 10*12
= 80 + 120
= $ 200
Part B
Can image 2 be the reflected figure? Explain your answer.
Answer:
Yes it can be be the reflected figure
A movie with an aspect ratio of 2.35:1 is shown as a letterboxed image on an older 25-inch 4:3 television. Find the height of the image, the height of each black bar at the top and bottom of the screen, and the percent of the screen’s area that is occupied by the image. Use a variety of representations to justify your response. Based on your analysis of television aspect ratios, why do you think the consumer market has moved having wide screen TV in the home?
The aspect ratio represents the ratio of the width to the height of a television.
The height of the image on the 25-inch television is 15 inches The height of each black bar is 8.51 inches The percentage of the screen area occupied is 56.73%Consumers moved to screens with wide screen to get clearer images.The size of a TV is calculated using Pythagoras theorem. Assume the length ratio of the older 25-inch [tex]4:3[/tex] TV is x.
The ratio is represented as:
[tex]Width : Height = 4:3[/tex]
Using Pythagoras theorem, we have:
[tex]Width^2 + Height^2 = 25^2[/tex]
[tex](4x)^2 + (3x)^2 = 25^2[/tex]
[tex]16x^2 + 9x^2 = 625[/tex]
[tex]25x^2 = 625[/tex]
Divide both sides by 25
[tex]x^2 = 25[/tex]
Take positive square roots
[tex]x = 5[/tex]
So, the height of the image is:
[tex]Height = 3x[/tex]
[tex]Height = 3 \times 5 = 15[/tex]
While the width is
[tex]Width = 4x = 4 \times 5 = 20[/tex]
Hence, the height of the image is 15 inches
The height of each black bar is calculated as follows:
[tex]Width : Height = 2.35 : 1[/tex]
Where
[tex]Width = 20[/tex]
So, we have:
[tex]20 : Height = 2.35 : 1[/tex]
Express as fraction
[tex]\frac{Height}{20} = \frac{1}{2.35}[/tex]
Make Height the subject
[tex]Height = \frac{20}{2.35}[/tex]
[tex]Height = 8.51[/tex]
The height of each black bar at the top and at the bottom is 8.51 inches
The percentage of the screen’s area that is occupied by the image is calculated using
[tex]\% Screen = \frac{A_1}{A_2} \times 100\%[/tex]
Where
[tex]A_1 \to[/tex] Area of black bars
[tex]A_2 \to[/tex] Area of the 25-inch 4:3 television
So, we have:
[tex]A_1 =8.51 \times 20 = 170.2[/tex]
[tex]A_2 =15 \times 20 = 300[/tex]
[tex]\% Screen = \frac{A_1}{A_2} \times 100\%[/tex] becomes
[tex]\% Screen = \frac{170.2}{300} \times 100\%[/tex]
[tex]\% Screen = \frac{170.2}{3} \%[/tex]
[tex]\% Screen = 56.73 \%[/tex]
Hence, the percentage of the screen area occupied is 56.73%
Consumers moved to TV with a wide screen because a TV with wide screen shows bigger pictures than smaller dimension TV screens,
When the pictures are bigger, the consumers will have a clearer view of what they're watching.
Read more about aspect ratios at:
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what is the domain and range
f(x)=x^3
Answer:
Step-by-step explanation:
The domain is X value and range is Y so just put y=x^3 in desmos and the graph appears then check its range and domain from it. the range is positive and nevative infinity
The area of a campground is exactly halfway between 25.9 acres and 26 acres . What is the area of the compound?
We have an algebra problem. Here we want to find the mid-value between 25.9 acres and 26 acres, we will find that the area of the compound is 25.95 acres.
For two given numbers A and B, such that A < B, the mid-value between these is given by:
A + (B - A)/2.
In this case, our two numbers are 25.9 and 26.
Using the above formula we get:
25.9 + (26 - 25.9)/2 = 25.95
Then we can conclude that the area of the compound is 25.95 acres.
If you want to learn more, you can read:
https://brainly.com/question/16871453
Solving equations and inequalities.
I’m confused on the subtraction behind the one, am I supposed to turn the one into a negative?
1-(4+3x)<-3
Answer:
x>0
Answer to your question:
Because the subtraction sign is after the negative, it applies to the term in front of it, in this case because there is a parenthesis, it would multiply into that and your equation from there would be 1-4-3x<-3. Then combine like terms from there.
If f(x) = x (ln x), find f'(x).
A. e^(x + 1)
B. 1 + ln x
C. 1 + e^x
D. (ln x)^2 + x
Answer:
[tex]f'(x)=1+\ln x[/tex]
Step-by-step explanation:
[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].
Recall the product rule:
[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]
Therefore, we have:
[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]
Note that:
[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]
Simplify:
[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]
The derivative is:
[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]
[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]
[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]
[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]
[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]
[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]
MissSpanishJk=7x+9
Jl 114, and
Kl =9x+9
Answer:
KL=63
Step-by-step explanation:
Answer:
Step-by-step explanation:
Kl=63
Find the inverse of the following
F(x) = 1/2x-1
if angle c=60° , b=5 ,a=4 then find the value of the c ?
Answer:
c=sqrt21
Step-by-step explanation:
angle c is the angle between a and b, so use the cos law
c^2=a^2+b^2-2*a*b*cosC
c^2= 16+25-2*4*5*1/2
c^2=21
c=sqrt21
4 workers can dig 4 holes in 4 hours, how long will it take to dig 6 holes with 2 workers
Answer:
12 hours
Step-by-step explanation:
each worker digs a hole and takes 4 hours doing so
2 workers dig 3 holes each, 3*4=12, 12 hours
Answer:
12 hours
Step-by-step explanation:
4 workers can dig 4 holes in hours=4
1 worker ,, ,, 4 ,, ,, ,, =4×4=16
1 ,, ,, ,, 1 hole ,, ,, =16÷4=4
2 ,, ,, ,, 1 ,, ,, ,, =4÷2=2
2 ,, ,, ,, 6 holes ,, ,, =2×6=12
What is the square root of 1 to the second power
Answer:
1
Step-by-step explanation:
The second power and square root cancel each other (second power means squared by the way)
PLEASE HELP!!!!!! Im being timed
Answer:
9,6 hope this helps
please help me with this quickly
Explanation:
We follow PEMDAS in reverse to undo every operation that is applied to variable x
Doing so will lead to the following
t = 0.4x + c
t - c = 0.4x
0.4x = t - c
x = (t - c)/(0.4)
The last equation is the same as writing [tex]x = \frac{t-c}{0.4}[/tex] which is what choice B shows.
what is the sum for the 20th row and the 50th row
Answer:
Step-by-step explanation:
lkj
Given that
a
= 3 cm and
b
= 21 cm, work out
θ
rounded to 1 DP.
Answer:
I am sorry I not no
this question
Step-by-step explanation:
sorry dear friend
The diameter of a circle is 16 in. Find its area in terms of π
Answer:
64[tex]\pi[/tex]
Step-by-step explanation:
A=[tex]\pi r^{2}[/tex]
Divide 16 by two to get the diameter: 8
Square 8: 64
Since the answer is in terms of pi, the answer is 64[tex]\pi[/tex]
Answer:
64 π
Step-by-step explanation:
Diameter = 16 inches
Radius = 16/2 = 8 inches
Area of circle = πr²
= π(8)²
= 64 π sq inches
26-4x=9x
Solve the equation
Answer:
x = 2
Step-by-step explanation:
26-4x=9x
Add 4x to each side
26-4x+4x=9x+4x
26 = 13x
Divide each side by 13
26/13 = 13x/13
2 = x
Answer:
-26/5
Step-by-step explanation:
[tex]26 - 4x = 9x \\ 4x = 9x - 26 \\ - 5x = - 26 \\ \frac{ - 5x}{5} = \frac{26}{5} [/tex]
a.a + b.b = 612
And
a+b = 30
so a.b?
Pls help.
Answer:
ab = 144
Step-by-step explanation:
Assuming you mean a² + b² = 612, then
(a + b)² = a² + 2ab + b² , that is
30² = a² + 2ab + b² , so
a² + 2ab + b² = 900
a² + b² + 2ab = 900 ← substitute a² + b² = 612
612 + 2ab = 900 ( subtract 612 from both sides )
2ab = 288 ( divide both sides by 2 )
ab = 144
12^8/12^4=
or
12^8
----- =
12^4
Answer:
[tex] \frac{ {12}^{8} }{ {12}^{4} } \\ = \frac{ {12}^{4} \times {12}^{4} }{ {12}^{4} } \\ = {12}^{4} =20736 \\ thank \: you[/tex]
Here's the solution :
[tex] \hookrightarrow \dfrac{12 {}^{8} }{ {12}^{4} } [/tex]
[tex] \hookrightarrow 12 {}^{8} \times {12}^{ - 4} [/tex]
[tex] \hookrightarrow12 {}^{4} [/tex]
PLS HELP ITS URGENT
Answer:
Surface area=48 in^2
See the image for solution
Equation 2x²-5x+1 has roots alpha and beta. Form quadratic equation with roots (alpha² + 1/alpha²) and (beta²+1/beta²)
Step-by-step explanation:
please see in the picture below.All step by step procedure
How many significant figures are in
246.000m?
Answer:
6
Step-by-step explanation:
The zeroes after the comma/full stop are significant...providede there is a non zero value in from of them just like the question posted
another example is 2300>>4significant digits or 0.00678 which has 3 significant digits.
hope this makes sense
:)
Name two integers with different signs that have a sum of -28
Answer:
-35 and 7
Step-by-step explanation:
7 - 35 = -28
35 has a (-) sign, and 7 has a (+) sign
Addition can be defined as the process of adding two numbers. The two integers with different signs that have a sum of -28 are -29 and 1.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
An integer is a number that can be written without using a fractional component.
Given that the two integers with different signs have a sum of -28. Therefore, we can write,
-29 + 1 = -28-30 + 2 = -28-31 + 3 = -28-32 + 4 = -28-33 + 5 = -28-34 + 6 = -28-35 + 7 = -28Hence, the two integers with different signs that have a sum of -28 are -29 and 1.
Learn more about Addition here:
https://brainly.com/question/13167637
#SPJ2
A motorboat travels 275 kilometers in 5 hours going upstream. It travels 405 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Step-by-step explanation:
[tex]275 \times 5 = 1375 [/tex]
The rate of the motorboat on still water is 1375
[tex]405 \times 5 = 2025[/tex]
The current rate of the motorboat is 2025
Xian and his cousin Kal both collect stamps. Xian has 52 stamps, and Kal has 68 stamps. The boys recently
joined different stamp-collecting dubs. Xian's club will send him 20 new stamps per month. Kai's club will
send him 16 new stamps per month. After how many months will Xlan and Kal have the same number of
stamps? How many stamps will each have?
Answer:
In 4 months, they will both have 132 stamps.
Step-by-step explanation:
Let x = # of months
52 + 20x = 68 + 16x
4x = 16
x = 4
Plug x value into both expressions and see if it checks out
52 + 20(4) = 68 + 16(4)
52 + 80 = 68 + 64
132 = 132
Complete the simplified ratio.
40 min : 3 hours
Answer:
math question? u can ask on
wrie down the equation of the line that is parallel to 4x - 2y = 7 and passes through (9, -3)
Answer:
4x-2y =42 is the required equation
Step-by-step explanation:
given equation is,
4x-2y -7=0---------eqn1
parallel equation of given equation is
4x -2y+k =0-------eqn 2
now passing it through (9,-3), we get,
4×9 + 2×3 +k = 0
or,36+6+k =0
or,42+k =0
or, k= -42
putting the value of k in eqn2
4x-2y - 42=0
4x-2y = 42
help asap please, forgot how to do math :)
Answer:
x = 8
Step-by-step explanation:
A common pythagorean triplet is 7, 8, 9
Answer:
11.4
Step-by-step explanation:
Pythagorean theorem
[tex]7^{2}[/tex] + [tex]9^{2}[/tex] = [tex]x^{2}[/tex]
49 + 81 = [tex]x^{2}[/tex]
130 = [tex]x^{2}[/tex]
11.4 = x
NEED HELP ASAP
Find the length of the arc
Answer:
C
Step-by-step explanation:
There are two arcs a major and a minor arc. You should never have to rely on a diagram to get the right answer.
The circumference is 2 * pi * r
r = 6 km
C = 2* pi * 6
C = 12 pi
The arc size is
arc size = 135 / 360 * 12pi
arc size = 3/8 * 12 pi
arc size = 4 1/2 pi = 9 pi /2 km