Answer: y = 7/3 - (4/3)*x
Step-by-step explanation:
First, let's write our line in the notation:
y = f(x)
So we must isolate y in the equation:
4x + 3y = 12
3y = 12 - 4x
y = 12/3 - (4/3)*x = 4 - (4/3)*x
Now, we have two translations, one horizontal and one vertical.
Let's define them in general cases:
Horizontal translation.
When we have y = f(x) and we want to do a horizontal translation of A units to the right (A positive) we have:
y = g(x) = f(x - A)
So we replace our variable x by x - A.
Vertical translation.
When we have y = f(x) and we want to do a horizontal translation of A units up (A positive) we have:
y = g(x) = f(x) + A.
Then in this case we have:
y = f(x) = 4 - (4/3)*x
then, the horizontal translation of 1 unit to the right is:
y = f(x - 1) = 4 - (4/3)*(x - 1)
And the translation of 3 units down (a vertical translation) is:
y = f(x - 1) - 3 = 4 - (4/3)*(x - 1) - 3 = 1 + 4/3 - (4/3)*x
y = 7/3 - (4/3)*x
This equation represents the new line.
please answer i need help quick
Answer:
(-2, 6)
Step-by-step explanation:
Since you want a 1 to 7 ratio, you want to divide the line into 2 parts, where one part has a length of 1 and the other has a length of 7. So the total length of the line is 8.
Start by looking at the difference in the X and Y coordinates.
X = | -4 - 12 | = | -16 | = 16
Y = | 7 - -1 | = | 8 | = 8
You could calculate the length of the line using pythagorian's theorem, but that's not needed. Simply use similar triangles. We have a right triangle with legs of length 16 and length 8. We want a similar triangle that is 1/8th as large (to get the desired 1 to 7 ratio). So divide both legs by 8, getting lengths of 16/8 = 2, and 8/8 = 1.
Now add those calculated offsets to point A.
A has an X coordinate of -4 and B has an X coordinate of 12 and the X coordinate for C must be between those limits. So calculate -4 + 2 = -2 to get the X coordinate for C.
The Y coordinate of A is 7 and the Y coordinate of B is -1. And since the Y coordinate must be between then, you have 7 - 1 = 6.
So the coordinates for C is (-2, 6)
The length of the carpet is 2a2 and width is 3a. Find the area of the carpet.
HELP ME PLEASE
Answer:
[tex]6a^{3}[/tex]
Step-by-step explanation:This is a very simple question.
We all know that the equation or formula for area is...
A= L*W
So multiply...
[tex]2a^{2} *3a[/tex]= [tex]6a^{3}[/tex]
Since 3a has an exponent power of 1 and you add the exponent power when multiplying...
The result would be... [tex]6a^{3}[/tex].
Hope this helps:)
In the city of Lawrenceville, how many phone numbers are possible using the area code 678? The restrictions for the phone company are listed below. · The first digit of the phone number cannot be numbers 0-5. · The second number cannot be a zero. · The third and fourth numbers cannot be a zero or one · The fifth number cannot be a zero, one or two How many phone numbers are possible using the area code 678? a.2000 b.1,6128 c.1,612,800 d.300
Answer:
Hey there!
If there were no restrictions, there would be 10x10x10x10x10 phone numbers.
The first number can only be a 6-9, so that is four options.
The second number can have nine options.
The third and fourth numbers have eight options.
The fifth number has seven options
4x9x8x8x7=16128.
16128 numbers are possible.
Let me know if this helps :)
Canada has a population of 1/10 as large as the United States and Canada population is about 32 million about how many people live in United States explain how many zeros in your answer
Answer:
Step-by-step explanation: If Canada(C) is 32,000,000 and America is A and C x 10 = A then 32,000,000 x 10 = A
And to multiply any whole number by 10 you just add a zero to the end so
320,000,000 is the answer which is pronounced "Three hundred twenty million" And there is 7 zeros in the answer
hope this helps mark me brainliest
The length of a rectangle is four meters less than twice it's width. If the area of the rectangle is 96 square meters what is the width?
Answer: (I'm sorry if this is not the right answer)
The width = 8 meters
Step-by-step explanation:
The length: a (m)
The width: b (m)
We cannot have a negative length and a negative width: a>b>0
Eq. I: a=2b-4
Eq. II: ab=96
Substitute the value of a from Eq. I into Eq. II: (2b-4).b=96
Solve for b:
(2b-4).b=96
2[tex]b^{2}[/tex]-4b-96=0
[tex]b^{2}[/tex]-2b-48=0
[tex]b^{2}[/tex]+6b-8b-48=0
b.(b+6)-8.(b+6)=0
(b+6).(b-8)=0
b=8; b=-6
As mentioned above, b>0. Therefore, b=8
Conclusion: if the area of the rectangle is 96 square meters then its width is 8 meters.
The width of the given rectangle is 8 units.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the length of the rectangle is L and the width is W
Given that,
The length of a rectangle is four meters less than twice its width.
So,
L = 2W - 4
And,
Area = 96 square meter
LW = 96
Now by substituting
2W² - 4W = 96
W² - 2W - 48 = 0
W² -8W + 6W - 48 = 0
W(W - 8) + 6(W - 8) = 0
(W + 6)(W - 8) = 0
W = 8, -6 since distance cannot be negative so it will be 6 meters.
Hence "The width of the given rectangle is 8 units".
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6.9times 1.221 equals
Answer:
8.2429
Step-by-step explanation:
Answer:
8.4249
Step-by-step explanation:
Use calculator if you have.
x+3 divided by 5=30 i need help
Answer:
x = 147
147 + 3 = 150
150 ÷ 5 = 30
Answer:
See answer in the explanation below.
Step-by-step explanation:
x = 147
147 + 3 = 150
150 ÷ 5 = 30
2635 divided by 17 in long form
Answer:
155
Step-by-step explanation:
17 can go into 26. 1 time then 26-17=9
bring down the 3 and it turns into 93
17 can go into 93 5 times. that equals 85
93-85=8 then add the 5 that make 85
85 divided by 17 =5
so the answer is 155
True or False? The absolute value of any number the same as absolute value of its additive inverse
Answer:
true
Step-by-step explanation:
that is true i need twenty charcters
Abe has $253.33 in his checking account. He wants to buy items that cost $23.33, $25.09, $33.45, and $56.02. How much is Gabe planning to spend?
Answer:
Gabe is planning to spend $137.89.
Step-by-step explanation:
23.33 + 25.09 + 33.45 + 56.02 = 137.89
Please help me with some math im stuck
y = - 40
- 40 since theres no letters it gonna be -40.
The sum of three consecutive integers is 180. What is the largest integer?
Answer:
61
Step-by-step explanation:
Here's a neat trick when you have an odd number of consecutive numbers.
Call the middle number k
Then the smaller number is k-1
The larger number is k + 1
The two ones will cancel.
k-1 + k + k-1 = 180
3k = 180
k = 180/3
k = 60
Therefore the largest number is k + 1 = 60 + 1 =61
Which expression represents the greatest common factor (GCF) of 70 and 112? A. 2 x 2 x 2 x 7 B. 2 x 2 x 2 x 5 C. 2 x 7 D. 2 x 2 x 2 x 3 x 5
Answer:
[tex]\huge\boxed{C. \ \ GCF = 2 * 7}[/tex]
Step-by-step explanation:
Firstly, we'll do prime factorization of these numbers.
70 = 2 × 5 × 7
112 = 2 × 2 × 2 × 2 × 7
So, The Greatest Common Factor can be written as:
GCF = 2 × 7 [Since Only one 2 and one 7 is common]
Hope this helped!
~AnonymousHelper1807Answer:
C
Step-by-step explanation:
I got this correct on e d g e n u i t y thanks to the person above me :)
k=6
c=2
5 • k - 10c + 8
Answer:
22-10c
Step-by-step explanation:
The simplified value of the expression is 18
Given the expression :
5 * k - 10c + 8k = 6c = 2To solve , substitute the values of k and c into the equation
Now we have ;
5 * 6 - 10(2) + 8
5 * 6 - 20 + 8
30 - 20 + 8
30 - 12
= 18
Hence, the. simplified value of the expression is 18
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In 2002, a school population was 956. By 2006 the population had grown to 1160. 1) How much did the population grow between the year 2002 and 2006? Correct students 2) How long did it take the population to grow from 956 students to 1160 students? 3) What is the average population growth per year? 4) What was the population in the year 2000? students 5) Find an equation for the population, P , of the school t years after 2000. P = 6) Using your equation, predict the population of the school in 2011. students
Answer:
1) The population grew by 204 students between 2002 and 2006.
2) It took 4 years for the population to grow from 956 to 1160.
3) The average population growth is about 51 students per year.
4) In 2000 the population was 854.
Step-by-step explanation:
-x+7= -6x-13 how do you solve it
Answer:
-4=x
Step-by-step explanation:
Okay, let's do this step-by-step for the best results!
We need to make sure that common variables can be put together first. If you did not know this, look at PEMDAS.
-x+7=-6x-13
We need to add -x and -6x together. If we do that then you would get,
7=-5x-13
Let's add 13 to 7 now.
20=-5x
Lets divide -5 with 20.
-4=x
I hope this helped!
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - x + 7 = - 6x - 13}[/tex]
Move 6x to left hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x + 6x + 7 = - 13}}[/tex]
Move 7 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x + 6x = - 13 - 7}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ 5x = - 13 - 7}}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{5x = - 20}}[/tex]
Divide both sides by 5
[tex] \dashrightarrow{ \sf{ \frac{5x}{5} = \frac{ - 20}{5} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = - 4}}[/tex]
Hope I helped!
Best regards! :D
A triangle drawn on a map has sides of lengths 9 cm, 12 cm, and 15 cm. The shortest of the
corresponding real-life distances is 122 km Find the longest of the real-life distances,
Answer:
26
Step-by-step explanation:
what is the absolute value of 0.8
Answer:
0.8
The absolute value of 0.8 is 0.8!
Hope this helps!
Is the square root of 900 rational
Answer:
Yes it is rational
Step-by-step explanation:
The square root of 900 is a rational number if 900 is a perfect square. It is an irrational number if it is not a perfect square. Since 900 is a perfect square, it is rational number.
plsss help asap!!!! i need it i have a time limit
Answer:
32
Step-by-step explanation:
90 = 7y + 27
7y = 63
y = 9
180 = 58 + 7(9) + 27 + $
$ = 32
It might be wrong
What is the first derivative of the following function: f(x) = aexp(-bx)
Answer:
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Step-by-step explanation:
Step(i):-
Given f(x) = ae⁻ᵇˣ ...( i )
we will use differentiation formula
[tex]\frac{d(e^{ax}) }{dx} = a e^{a x}[/tex]
Step(ii)
Differentiating equation (i) with respective to 'x', we get
[tex]\frac{df(x)}{dx} = a e^{-b x} \frac{d}{dx} (-b x )[/tex]
= -ab e⁻ᵇˣ
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Final answer:-
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
How many 1-1 functions from a set with five elements to a set with 4 elements?
Answer:
The number is zero
Step-by-step explanation:
From the question we are told to state the number of on-to-one that exist from the set of 5 element to the set 4 element
Generally there are no one-to-one function from a set with a higher number of elements to a set with the lower number of elements
So the correct answer to the question is there are no one-to-one function from the set of 5 elements to the set of 4 elements
Maya runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?
Answer:
5.6 miles.
Step-by-step explanation:
7/80=x/64 is our equation
Cross multiply to solve for x
x=7*64/80
x=5.6mi
Hope this helps ^-^
Answer:
5.6 miles
Step-by-step explanation:
Let's set up a proportion using the following setup.
[tex]\frac{miles }{minutes}=\frac{miles }{minutes}[/tex]
We know Maya can run 7 miles in 80 minutes.
[tex]\frac{7miles }{80minutes}=\frac{miles }{minutes}[/tex]
We don't know how many miles she can run in 64 minutes. Let's say she can run x miles in 64 minutes.
[tex]\frac{7miles }{80minutes}=\frac{x miles }{64 minutes}[/tex]
[tex]\frac{7}{80}=\frac{x}{64}[/tex]
We want to solve for x (miles in 64 minutes). Therefore, we must isolate x on one side of the equation.
x is being divided by 64. The inverse of division is multiplication. Multiply both sides of the equation by 64.
[tex]64*\frac{7}{80}=\frac{x}{64}*64[/tex]
[tex]64*\frac{7}{80}=x[/tex]
[tex]64*0.0875=x[/tex]
[tex]5.6=x[/tex]
[tex]x= 5.6 miles[/tex]
Maya can run 5.6 miles in 64 minutes.
Which is the best description for the graph below? A graph decreases from (0, 3) to (9, 0). The graph increases everywhere. The graph decreases everywhere. The graph remains constant. The graph increases, then decreases.
Answer:
the graph decreases everywhere
Step-by-step explanation:
the left side of the line is higher than the right side which means its a negative slope so it is decreasing
Answer:B
Step-by-step explanation:
please help, i will give brainliest
Answer:
24
Step-by-step explanation:
hope i helped
Valleywood Golf course offers classes Monday through Saturday. The Saturday classes last 75 minutes. If they offered 705-minutes of classes last week, what was the maximum number of weekday classes?
Answer:
Step-by-step explanation:
To make the problem easier to solve, we will set it up as the equation of the length of time of each class times the number of classes equals the total amount of minutes. However, since we don't know the number of classes, we'll symbolize our two unknowns with two variables.
75x + 45y = 705
(75x + 45y)/15 = 705/15
5x + 3y = 47
y = (47-5x)/3
It looks like we can't simplify the equation any more, so now it is a matter of trial and error. The minimum number of Saturday classes means the maximum number of weekday classes. We first will test for the maximum by assuming there are no Saturday classes, then will work our way up until x is an integer.
If x = 0
(47-5(0))/3 = 47/3 = 15.6666
If x = 1
(47-5(1))/3 = 42/3 = 14
This works. Therefore, the maximum number of weekday classes is 14, or choice b.
Select a counterexample for the conclusion.
The difference between two even numbers is positive.
A
9-13
B
13-9
C
10-2
D
2-10
Se tiene un conjunto de triángulos equiláteros, cuya medida de lados están en progresión geométrica cuya razón es 2. Si se ordenan los triángulos de acuerdo a su tamaño, se tiene que el primer triángulo mide un 1 cm de lado , ¿cuánto medirá el lado del vigésimo triángulo equilátero?¿cuánto medirá su perímetro?
Responder:
Explicación paso a paso:
Dado el conjunto de un triángulo equilátero con cada uno de sus lados en progresión geométrica, si el primer triángulo mide un lado de 1 cm y una razón común de 2 cm, para obtener el lado del triángulo 29, usaremos la fórmula para calcular el enésimo término de la progresión geométrica. expresado como;
Tn = ar ^ (n-1)
a es el primer término
n es el número de términos
r es la razón común.
Dados los siguientes parámetros
a = 1, r = 2 y n = 20 (ya que estamos buscando el lado del vigésimo triángulo)
Sustituyendo los parámetros dados en la fórmula para obtener el lado del triángulo 20, tendremos;
T20 = 1 (2) ^ 20-1
T20 = 1 (2) ^ 19
T20 = 2 ^ 19
T20 = 524,288 cm
Por lo tanto, la medida de la longitud de un lado del vigésimo triángulo equilátero es 524,288 cm.
Perímetro del vigésimo triángulo equilátero = 3 × 524,288 = 1,572,864cm
Tenga en cuenta que todos los lados de un triángulo equilátero son iguales.
Why isn't 0 at the far left of the scales?
Step-by-step explanation:
Why isn't "0" far left of the scales? It's not on the far left side because it wouldn't allow us to be much more precise if it was at the far end. Being where it is, it gives us a closer approximation to the actual distance in the real world.
A bag contains 8 green, 4 black and 6 yellow marbles. How could you use the complement to determine the probability of randomly selecting a green or black marble?
Answer:
12/18=2/3
Step-by-step explanation:
You should add up every marbles to find out how many marbles are in total. Then, you should add the green and black marbles. There are 4 black marbles, and 8 green marbles, which results 12 black+green marbles. Then you should make a fraction 12/18, because you are finding the probability of the green+black marbles out of the total marbles. If you simplify, you get 2/3.
The probability of randomly selecting a green or black marble is 12/18.
What is probability?Probability is the ratio that determines how likely an event is to occur from a set of possible events.
We can find the probability of randomly selecting a green or black marble as shown below:Total number of green marbles = 8
Total number of black marbles = 4
Total number of yellow marbles = 6
Total number of marbles = Total number of green marble + Total number of black marbles + Total number of yellow marbles = 18
P(selecting a green marble) = Total number of green marbles/Total number of marbles
= 8/18
P(selecting a black marble) = Total number of black marbles/Total number of marbles
= 4/18
P(selecting a green or black marble) = (Total number of green marbles + Total number of black marbles)/Total number of marbles
= (8 + 4)/18
= 12/18
Therefore, we have found the probability of randomly selecting a green or black marble to be 12/18.
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