In the xy-coordinate plane shown, line L passes through point C and has a slope of -2. A dilation of line {with center A and a scale factor of 3 will
produce a new line through point C'the image of point C,
with coordinates
and with a slope of
Answers
The solution is, New line slope will be -2 and, coordinates (-4. 2).
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
Dilation of a line about a point not on the line shifts the line but leaves the slope intact .
New line slope will be -2
As both A and C lie on a horizontal line y = 2, C' will also lie on the same line
The distance between A and C is 0 - 2 = -2
a scale factor of 3 means C' is -2(3) = -6 units left of A
C' = (2 - 6, 2)
= (-4. 2)
Hence, The solution is, New line slope will be -2 and, coordinates (-4. 2).
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Related Questions
Find the volume of the following square pyramid.
Answers
Check the picture below.
[tex]\textit{volume of a pyramid}\\ V = \cfrac{Bh}{3}~~ \begin{cases} B = \stackrel{\textit{area of its base}}{50\times 50}\\ h = \stackrel{\textit{its height}}{60} \end{cases}\qquad \implies V = \cfrac{50\cdot 50\cdot 60}{3}\implies \boxed{V= 50000}[/tex]
Integrate ∫2tan(2x+π)dx
Answers
Answer:
[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos (2x + \pi) \big| + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Trigonometric Integration
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = 2 \int {\tan (2x + \pi)} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for u-substitution.
Set u: [tex]\displaystyle u = 2x + \pi[/tex][u] Differentiate [Derivative Properties]: [tex]\displaystyle du = 2 \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = \frac{2}{2} \int {2 \tan (2x + \pi)} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = \frac{2}{2} \int {\tan u} \, du[/tex]Simplify: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = \int {\tan u} \, du[/tex][Integral] Trigonometric Substitution: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos u \big| + C[/tex][u] Back-Substitute: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos (2x + \pi) \big| + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
1) Which value is equivalent to 5+ 4 x 2? A) 11 B) 13 C) 18 D) 22
Answers
Answer:
Option B) 13 is correct
Step-by-step explanation:
5+4×25+813help asap whoever right get brainiest
Answers
Answer:
EF
Step-by-step explanation:
I think the answer is EF because turning the line counterclockwise and 80 degree angle would be that.
help pls//////////////////
Answers
Answer:
x = 6
Step-by-step explanation:
12(x -2) +3x = 1/3(x +12) +10x
12x -24 +3x = 1/3x +4 +10x . . . . . eliminate parentheses
15x = (10 1/3)x +28 . . . . . . . . . . add 24, collect terms
(4 2/3)x = 28 . . . . . . . . . . . . . subtract 10 1/3
x = (3/14)(28) = 6 . . . . . . . . multiply by 1/(4 2/3) = 3/14
The value x=6 satisfies the equation.
What is the equation of this line?
A. y= x - 3 =
B. y=-x-3 =
C. y= -2x - 3
D. y=2x-3 - - 3
Answers
Solve for x: 49.98+12x=61.98+7x
Answers
Answer:
X=2.436
Step-by-step explanation:
Just give me the answer please
Answers
Answer:
what
Step-by-step explanation:
Answer:
Appologies but Why do you have pOn open?
Step-by-step explanation:
umm that is inapropriate but idrc
Help what is thisss
GIVING OUT BRAINLY IF U ANSWER
idc if sum r wrong
Answers
Answer:
it is a b and c
Step-by-step explanation:
The volume of a gas in cubic centimeters, V, varies inversely with the
pressure of the gas in liters per square centimeter, p.
When the volume of the gas is 16 cm, its pressure is 20 L/cm2. Find the
volume of the gas when the pressure is 2.5 L/cm2
A. 322.5 cm
B. 800 cm3
C. 128 cm3
D. 0.008 cm
Answers
Answer:
C. 128 cm³
Step-by-step explanation:
16(20) = 320
320/2.5 = 128 cm³
Determine f –1(x) if f of x is equal to the quantity x plus 3 end quantity over the quantity x minus 4 end quantity where x 4.
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 4 times x plus 3 end quantity
f inverse of x is equal to the quantity 4 times x plus 3 end quantity over the quantity x minus 1 end quantity
f inverse of x is equal to the quantity x minus 4 end quantity over the quantity x plus 3 end quantity
f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 4 end quantity
Answers
Answer:
Option BStep-by-step explanation:
Given function:
f(x) = (x + 3)/(x - 4)Find its inverse, take f(x) as y and swap x with y
x = (y + 3)/(y - 4)x = (y - 4 + 7) / (y - 4)x = 1 + 7/(y - 4)x - 1 = 7 / (y - 4)y - 4 = 7 / (x - 1)y = 4 + 7 / (x - 1)y = (4x - 4 + 7)/ (x - 1)y = (4x + 3) / (x - 1)Replace y with f⁻¹(x):
f⁻¹(x) = (4x + 3) / (x - 1)Correct choice is B
A x is equal to the quantity x plus 3 end quantity over the quantity x minus 4 end quantity where x 4. at x = 0.5, the inverse function f²(-1)(x) f²(-1)(x) = 0.5
To determine the inverse of the function f(x) = (x + 3) / (x - 4), to follow these steps:
Replace f(x) with -1, since you're looking for the inverse at the point where f(x) = -1:
-1 = (x + 3) / (x - 4)
Solve for x in terms of -1:
Multiply both sides by (x - 4):
-1 ×(x - 4) = x + 3
Distribute the -1:
-x + 4 = x + 3
Solve for x:
Subtract x from both sides:
4 = 2x + 3
Subtract 3 from both sides:
1 = 2x
Divide by 2:
x = 0.5
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can someone pleaseeeee helppppp mee
Answers
yessssss I cannnnnnn helppppp youu
[tex] \frac{ - 12}{c} = 6 \\ [/tex]
Inverse both sides
[tex] - \frac{c}{12} = \frac{1}{6} \\ [/tex]
Multiply both sides by - 12
[tex]( - 12) \times - \frac{c}{12} = ( - 12) \times \frac{1}{6} \\ [/tex]
[tex]c = - 2[/tex]
There u go have a great day ❤
Answer: C = -2
Step-by-step explanation: Well if you times 2x3 that = 12. So -2= c.
I am really sorry if this is wrong. I tried my best. :-)
Hope you have a wonderful day !
Ayaan travels 90 miles at an average speed of 60 mph.
She then travels a further 40 miles.
The average speed for the entire journey is 59 mph.
Assuming Ayaan didn't stop, what was her average speed for the final 40 miles to 2 dp?
Answers
Step-by-step explanation:
Speed = distance / timeThereafter,
Distance :-
90 miles + 40 miles = 130 milesTime :-
90 / 60 + 59 = 60.5 mphAverage Speed :-
130 / 60.5 = 2.148ILL MARK BRAINLIEST HELP PLS
Answers
Answer:
Step 1, do math:
-13.6 >= 1.7x
-8 >= x
answer: C
If X = 3 units, then what is the volume of the cube shown above?
Answers
Answer:
The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.
F varies jointly as q1 and q2 and inversely as the square of d.
If F=8 when q1=2, q2=8, and d=4, find F when q1=28, q2=12, and d=2
Answers
Answer:
F =672
Step-by-step explanation:
joint variation is of the form
F = k *q1 * q2
Inversly means divide
F = k * q1 * q2
-------------------
d^2
We know F=8 when q1=2, q2=8, and d=4 so we can solve for k
8 = k * 2*8
-----------------
4^2
8 = 16k
----
16
8 = k
Substituting
F = 8 * q1 * q2
-------------------
d^2
Let q1=28, q2=12, and d=2
F = 8 * 28 * 12
----------------
2^2
F = 2688
-------
4
F =672
We are given:
F varies jointly (directly) with q1 and q2, which means that F is proportional to both q1 and q2. also,
F varies inversely with d², so F is inversely proportional to the square to d
Finding a mathemetical experssion:
using the above information, we can say that:
F ∝ q₁
F ∝ q₂
F ∝ 1/(d²)
joining these together, we get:
F ∝ q₁q₂ / d²
let's say that 'k' is the constant of proportionality in this case,
F = k (q₁q₂ / d²)
First case:
F = 8, q₁ = 2, q₂ = 8, d = 4
we can use these values in our expression to find k
[tex]8 = k\frac{2*8}{4^2}[/tex]
[tex]8 = k\frac{16}{16}[/tex]
k = 8
Finding F in the second case:
q₁ = 28, q₂ = 12, d = 2, k = 8
[tex]F = k\frac{q_{1}*q_{2}}{d^2}[/tex]
[tex]F = 8(\frac{28*12}{2^2})[/tex]
[tex]F = 8(\frac{336}{4})[/tex]
[tex]F = 2(336)[/tex]
F = 672 N
What is the y-intercept of the line shown?
Answers
Answer: 4
Step-by-step explanation:
It crosses on the y axis at the point (0,4)
Answer:
4
Step-by-step explanation:
The y-intercept of the line shown is 4.
Hope this helps :)
simplify 4 whole 2/7 + 5/7
Answers
Answer:
1
Step-by-step explanation:
2/7+5/7=7/7=1 because 7/7 would be a 1 whole
Answer:
35/7
Step-by-step explanation:
4 = 28/7
28/7 + 2/7 + 5/7 = 35/7
Mathew basketball team won 68% of the games they played if they won 17 games how many did they play
Answers
Answer:
25
Step-by-step explanation:
turn 68% into a decimal (or keep as a percentage, your choice) and divide
17 divided by 0.68 (68% as a decimal) = 25
1.
Find the value of 5x? if x = -3.
Answers
Answer:
-15
Step-by-step explanation:
5 * -3 = -15
x = -3
5x = 5(-3)
5(-3) = -15
If your income is constant, what will happen to your savings when your expenses increase?
PASAGOT PO!!!!!
Answers
Okay, suppose your income is about $100.
You might spend $70 & save $30.
Now, suppose your income remains constant at $100 but your expenses go up to, say, $90. You can see that your savings will reduce or decrease. Now, you'll only have about $10 to save.
=》 So, if your income is constant, then your savings will 'decrease' when your expenses increase.
_______
RainbowSalt2222 ☔
Zahara rides with her dad to her grandmother’s house. They travel 159 miles in 3 hours. Her uncle, Jorge, drives there separately from his home. a. At what speed does Zahara’s dad drive, in miles per hour? Draw a model to show your work.SOLUTION b. Jorge’s trip takes the same amount of time as Zahara’s, but he travels a shorter distance. Does Jorge drive faster or slower than Zahara’s dad?A store changes the cost of a package of batteries. Now customers pay more money for the same number of batteries. Did the cost per battery increase, decrease, or stay the same? Explain how you know. 3 4
Answers
Write the expression as the sum or difference of two logarithmic functions containing no exponents.
log(x/x + 1)
Answers
Hi how u doin ?
[tex] log( \frac{x}{x + 1} ) = \\ [/tex]
[tex] log(x) - log(x + 1) [/tex]
Have a great day ❤
−9 13−(−1 13) Enter the simplified answer in the box.
Answers
Step-by-step explanation: −913−(−113)
=−913−(−113)
=−913+113
=−800
PLEASE HELP !!! PICS DOWN BELOW
Answers
Answer:
262.25 $
Step-by-step explanation:
HELPP!!! I have a root test for a series but it's in n/2 power, help me out please ?
Answers
What is the output of a function when tha input is -9
Answers
Answer: f(-9)
Step-by-step explanation:
A function is described in the form of f(x)
Therefore, if this is how a function is stated we have x as the input.
Here, the x is equal to -9
So now:
f(-9) after substitution.
y = - 1/7x - 2 parallel to 7,6 ???
Answers
Answer:
y = - 1/7x - 7
Step-by-step explanation:
Given equation ,
=> y = -1/7 - 2
On comparing to slope intercept form of the line we get the slope as -1/7
Now as we know that the slope of two parallel lines are same . So the slope of parallel line will be -1/7 .
Using point slope form ,
=> y - 6 = -1/7( x -7)
=> y -6 = -1/7x +1
=> y -7 = -1/7x
=> y = -1/7x -7
Look at picture for question.
Answers
HEHEHEHE HELP LOL IM NOT SMART ENOUGH FOR THIS 3
Answers
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