Answer:
Step-by-step explanation:
Given the original coordinate as C (-6, 9) and new coordinates after dilation as C' (-2, 3), we can see that the value of the new coordinates has reduces by a factor. Let the factor be k
For the x coordinates:
C' = kC
x' = kx
-2 = k(-6)
-2 = -6k
Divide both sides by -6
k = -2/-6
k = 1/3
For the y-coordinates:
y' = ky
3 = 9k
Divide both sides by 9:
3/9 = 9k/9
1/3 = k
k = 1/3
Hence the scale factor of the dilation is 1/3
Answer:
The scale factor from C' to C is
3
But the scale factor from C to C' (the one you may have asked for in the question) is
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
What we already know is that we have line segments C and C' and we know their lengths.
C = (-6, 9)
C' = (-2, 3)
So the scale factor from C' to C can be easily known if we simply use the rules of division
-6 ÷ -2
and
9 ÷ 3
They both are equal to the outcome, 3.
So we now know that the scale factor from C' to C is 3.
But what about C to C'??
Yes we still have to do division, BUT (you may have guessed it already but), we must switch the positions that the numbers for dividend and divisor were.
-2 ÷ -6 =
0.33333333... or [tex]\frac{1}{3}[/tex]
3 ÷ 9 =
0.33333333... or [tex]\frac{1}{3}[/tex]
So we can decisively conclude that the scale factor of C to C' is [tex]\frac{1}{3}[/tex]
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Write the exponential equation for the given situation. A tennis tournament starts with 128 participants. Each round, half of the participants gets eliminated from the tournament
Answer:
y= 128(1-.5)^t
Step-by-step explanation:
2\3n = -12 what value of n makes this equation true
Answer:
-0.055555555555556
Step-by-step explanation:
Simplify the expression
Answer:
B
Step-by-step explanation:
3 boys shared a whole pizza. Andrew ate 25% of the pizza. alonso ate 5/8 of the pizza. Tyler ate .1255 of the pizza. who are the most?
Answer:
Alonso ate the most
Step-by-step explanation:
mark braniest pls
Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min. (The same conditions as in the previous problem). After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank.
(a) Find the concentration, in kilograms per liter, of salt in the tank after 10 min. [Hint: Let A denote thenumber of kilograms of salt in the tank at t minutes after the process begins and use the fact that rate of increase in A = rate of input - rate of exit.
(b) After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank. What will be the concentration, in kilograms per liter, of salt in the tank 20 min after the leak develops?
Answer:
(a) 0.288 kg/liter
(b) 0.061408 kg/liter
Step-by-step explanation:
(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute
The mass of salt exiting the tank per minute = 5 × (5 + x)/500
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
Δ/dt = x - 5 × (5 + x)/500
The increase, in mass, Δ, after an increase in time, dt, is therefore;
Δ = (x - 5 × (5 + x)/500)·dt
Integrating with a graphing calculator, with limits 0, 10, gives;
Δ = (99·x - 5)/10
Substituting x = 1 gives
(99 × 1 - 5)/10 = 9.4 kg
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)
∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter
(b) With the added leak, we now have;
Δ/dt = x - 6 × (14.4 + x)/500
Δ = x - 6 × (14.4 + x)/500·dt
Integrating with a graphing calculator, with limits 0, 20, gives;
Δ = 19.76·x -3.456 = 16.304
Where x = 1
The increase in mass after an increase in = 16.304 kg
The total mass = 16.304 + 14.4 = 30.704 kg
The concentration of the salt in the tank then becomes;
Concentration = 30.704/500 = 0.061408 kg/liter.
Calculating the salt concentration per liter of water we will find:
(a) [tex]0.288 kg/liter[/tex]
(b) [tex]0.061408 kg/liter[/tex]
The mass of salt entering the tank per minute:
[tex]X= (0.2)( 5) = 1 kg/minute[/tex]
The mass of salt exiting the tank per minute:
[tex]\frac{5 * (5 + x)}{500}[/tex]
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
[tex]\frac{\Delta}{dt} = \frac{x - 5 * (5 + x)}{500}[/tex]
The increase, in mass, Δ, after an increase in time, dt, is therefore;
[tex]\Delta = (x - 5 * (5 + x)/500)dt[/tex]
Integrating with a graphing calculator, with limits 0 at 10, gives;
[tex]\Delta = (99X - 5)/10[/tex]
Substituting x = 1 gives:
[tex](99)( 1 - 5)/10 = 9.4 kg[/tex]
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank). The concentration of the salt and water in the tank after 10 minutes:
[tex](5 + 9.4)/500 = (14.4)/500 = 0.288[/tex]
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter.
(b) With the added leak, we now have;
[tex]\frac{\Delta}{dt} = \frac{ (x - 6 ) (14.4 + x}{500} \\\Delta = \frac{(x - 6)(14.4 + x)}{500} dt[/tex]
Integrating with a graphing calculator, with limits 0 at 20, gives;
[tex]\int\limits^{20} _0 {\frac{(x - 6)(14.4 + x)}{500} dt}[/tex]
Where x = 1:
[tex]\Delta = 19.76(1) -3.456 = 16.304[/tex]
The increase in mass after an increase in = 16.304 kg. The total mass:
[tex]16.304 + 14.4 = 30.704 kg[/tex]
The concentration of the salt in the tank then becomes;
[tex]30.704/500 = 0.061408 kg/liter[/tex]
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Express your answer as a polynomial in standard form.
f(x) = 3x² + 4x – 7
g(x) = 2x – 11
Find: g(f(x))
Answer:
g(f(x)) = 6x^2 + 8x - 25
Step-by-step explanation:
So, first we have to substitute f(x) into the place of x in the g(x). This will be shown as g(f(x)) (which is what we need to solve). Next, we have to substitute 3x^2 + 4x - 7 into the place of x in 2x - 11. We do this because we had to substitute f(x) into the place of x in g(x).
So this is how your equation should look, and then solve:
g(f(x)) = 2(3x^2 + 4x - 7) - 11
g(f(x)) = 6x^2 + 8x - 14 - 11
g(f(x)) = 6x^2 + 8x - 25 < ---- This is your answer
Hope this helps!
Can someone please me how to solve [tex]|a|\ \textgreater \ 2[/tex]
Answer:
[tex]|a| \to \: is \: the \: absolute \: value \: of \: a .[/tex]
Step-by-step explanation:
[tex]|a| \to \: is \: the \: absolute \: value \: of \: a \\ if \: a \: is \: - 5 : then : \\ |a| = | - 5| = 5.\\ if \: a \: is \: 5 : then : \\ |a| = | 5| = 5. \\ \\ but \: \\ when \: its \: - |a| \\ if \: a \: is \: - 5 : then : \\ - |a| = - | - 5| = - 1 \times 5 = \boxed{ - 5}.\\ if \: a \: is \: 5 : then : \\ - |a| = - | 5| = - 1 \times 5 = boxed{ - 5}. [/tex]
♨Rage♨
Step-by-step Answer:
Whenever we have a problem like this, we can have 2 solutions (either one can work) because, in absolute equations, we need to find how far away the number is from 0.
So the answer would simply be that a>2 and a<-2
a can be anything greater than 2 or a can be anything less than 2
The image below might help to better understand
Write sec 325° in terms of the secant of'a positive acute angle.
Answer:
sec35°
Step-by-step explanation:
sec325° = sec(360 - 325)° = sec35°
The secant of a positive acute angle of sec 325° = sec 35° = 1.22077
What are Trigonometric Ratios?
Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios.The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given data ,
The trigonometric ratio is = sec 325°
Now , to express the ratio in terms of a positive acute angle , we take the four quadrants of the graph and express the angle in the first quadrant.
And , 325° lies on the 4th Quadrant , where all cosines and secants are positive.
Therefore , sec 325° = sec ( 360° - 35° )
= sec ( 35° )
=1.22077
Hence , the secant of a positive acute angle of sec 325° = sec 35° = 1.22077
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A billboard on level ground is supported by a brace as shown in the accompanying diagram the measure of angle is 15° greater than twice the measure of angle b determine the measure of angle a in the measure of angle b
Answer:
has a right angle to hold the billboard upright. Since a triangle is 180, and there' s a right angle, then when you add angle A and angle B together, they should add up to 90.
Step-by-step explanation:
A = 2B + 15
A + B = 2B+15 + B = 90
3B + 15 = 90
3B = 75, so B = 25 degrees
90 - B = A, so A = 65 degrees
The class can contain at most 28 students.
Which difference is closest to 12?
A. 89−1112
B. 67−19
C. 1516−38
D. 35−611
Answer:
b
The rest are at least 500 numbers away from 12
Step-by-step explanation:
Give 5 reasons explaining why math is your favorite subject.
Give 5 reasons why you dont like math.
Give 5 areas that math can help you now or in the future.
Answer:Math is important
Step-by-step explanation:
It could help you get into collage and get a good job and with that you could start your life.
Answer:
1.)
I love working with numbers
I love math because of what a challenge it is
I love math because I can become a engineer
I love math because I can also become a doctor with it
I love math because it is useful
2.)
I don't like math because of the word problems
I don't like math because it sometimes gets too easy
I don't like math because I usually have to help others
I don't like math because people call me a nerd
I don't like math because it makes me explain in words
3.)
when your in the store and it helps you with knowing how much your spending
lets you know about if the discount in the store is really good or bad
helps you with becoming certain things when you grow up
it will help you with most of your jobs
Will help others if you know it, you can share your knowledge
Step-by-step explanation:
brainlist pls :>
I need help with this question
Answer:
I think it is D
Step-by-step explanation:
please 5 stars
Answer:
the answer is b 24
Step-by-step explanation:
12,24
8,16,24
need help pease its due at 11;59pm today explian
Answer:
65
Step-by-step explanation:
you add all the numbers inside.
80+35= 115
You have to make sure it equals to 180 to find angle 1.
Therefore, 180-115=65.
A rectangle has a length that is 4 ft more
than its width. What are the length and
width of the rectangle if the rectangle has
a perimeter of 48 ft?
Answer:
length = 14 width = 10
Step-by-step explanation:
48/4=12
10+10+14+14=48
what is the answer a, b, c, or d
Answer: Choice B
(-2, 5)
==================================================
Explanation:
The original system is
[tex]\begin{cases}-4x+3y = 23\\ x-y = -7\end{cases}[/tex]
Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations
[tex]\begin{cases}-4x+3y = 23\\ 3x-3y = -21\end{cases}[/tex]
Now add straight down
The x terms add to -4x+3x = -1x = -x
The y terms add to 3y+(-3y) = 0y = 0
The terms on the right hand sides add to 23+(-21) = 2
We end up with the equation -x = 2 which solves to x = -2
Now use this to find y. You can pick any equation with x,y in it
----------------
-4x+3y = 23
-4(-2)+3y = 23
8+3y = 23
3y = 23-8
3y = 15
y = 15/3
y = 5
Or
x-y = -7
-2-y = -7
-y = -7+2
y = -5
y = 5
Either way, we get the same y value.
So that's why the solution is (x,y) = (-2, 5)
A pet store was selling 2 lizards for
$14.48. If they ended up selling 6
lizards, how much money would they
have earned?
Answer:
43.44
Step-by-step explanation:
If they are selling 2 lizards for 14.48 you would divide
14.48 by two which is 7.24.
This means the lizards are 7.24 each.
7.24x6 is 43.44
Answer:
$43.44
Step-by-step explanation:
If two lizards are worth $14.48, then you just need two multiply the cost by three.
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. Without
looking, what is the probability that Fiona pulls out a marble that is not white?
Answer:
85%
Step-by-step explanation:
The probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
What is the probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1. Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event.
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. The total number of marbles in the bowl is,
[tex]n=5+2+10+3\\n=20[/tex]
The number of white balls in the bowl is 3. Thus, the probability that Fiona pulls out a marble that is white, is,
[tex]P=\dfrac{3}{20}[/tex]
The probability that Fiona pulls out a marble that is not white is,
[tex]P^{-1}=1-\dfrac{3}{20}\\P^{-1}=\dfrac{20-3}{20}\\P^{-1}=\dfrac{17}{20}[/tex]
Thus, the probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
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What is the slope intercept form of this line?
Answer:
the desired equation is y = (-3/4)x + 7
Step-by-step explanation:
If you start at (0, 7) and move along the line to (4, 4), you'll see that x increases by 4 (this is the 'run') and y decreases by 3 (this is the 'rise'). Thus, the slope of this line is m = rise/run = -3/4.
Let's use this m = -3/4 and the point (0, 7) to write the equation of this line.
(0, 7) is actually the y-intercept.
Thus, the desired equation is y = (-3/4)x + 7.
HELP PLEASE!!!
I’ll give brainlest
What is the image of (-5, 6) after a reflection over the line y = -2
Answer:
I'm pretty sure it would be (5,6)
Step-by-step explanation:
Reflecting a point over the Y-axis would change the x-coordinate, but not the y-coordinate
Kieran made 42 pizzas while working 7 hours at Sam's. If Kieran has made
60 pizzas so far, how many hours has he been working at Sam's today?
Answer:
answer is 10hours
42pizzas= 7hours
60pizzas =xhours
x hours =(60*7)/42
x hours = 10 hours
If f(1) = 1, what is f(3)?
Answer:
would be 3
Step-by-step explanation:
if 1 is 1 ,3 would be 3 ;-;
PLZ HELP !!!!!!
28x+36y=2520 Write this in slope intercept form or graph!!
Answer:
y= -7/9 x+70
Step-by-step explanation:
28x+36y=2520
36y=-28x+2520
y= -7/9 x+70
The teacher separated her group of 28 students into 2 groups. One group has 4 more than twice as many students as the other group. How many students are in each group?
Answer:
one group has 12. one has 16. 12 + 16 = 28. 16 is 4 more than 12
3b) Two pizzas are made to the same dimensions. The only difference is that
Pizza 1 is cut into pieces at 30° angles and Pizza 2 is cut at 45° angles. They are
sold by the slice. The slices for Pizza 1 sell for $1.45/slice and the slices for Pizza 2
sell for $1.75/slice. What is the difference in total sales between Pizza 2 and Pizza
1?
Step-by-step explanation:
$0.30 because they only sell 30 cents less/more than each other
Given f(x) = -5(2x-7 )- 19, what is the
value of f(-2)?
Answer:
X=1.8
Step-by-step explanation:
f(X)=-2
-5(2x-7)-19=-2
-10x+35-19+2=0
-10x=-18
X=-18÷(-10)
X=1.8
What should be the first step to solve the equation?
2x + 9(x – 1) = 8(2x + 2) – 5
Combine like terms on each side of the equation.
Use the distributive property on each side of the equation.
Use the subtraction property of equality to subtract 5 from each side of the equation.
Use the addition property of equality to add 2x to each side of the equation.
Answer: B
(Use the distributive property on each side of the equation.)
Step-by-step explanation:
123476870975 divide by 5
Answer: 24695374195
Step-by-step explanation: did you really need this?
Find the cos of angle c
A.3/5
B.6/5
C.5/3
D.1