The equation given is matched with the respective vertex forms.
What is the standard Equation for a circle ?The standard equation for a circle is given by
(x-h)² + (y-k)² = r²
The equation given in the question are
x² + y² − 4x + 12y − 20 = 0
(x − 6)² + (y − 4)² = 56
x² + y² + 6x − 8y − 10 = 0
(x − 2)² + (y + 6)² = 60
3x² + 3y² + 12x + 18y − 15 = 0
(x + 2)² + (y + 3)² = 18
5x² + 5y² − 10x + 20y − 30 = 0
(x+3)² + (y-4)² = 35
2x² + 2y² − 24x − 16y − 8 = 0
(x-1)² + (y+2)² = 11
The first equation is
x² + y² − 4x + 12y − 20 = 0
It can be written ad
x² -4x + 4 - 4 +y²+12y +36-36 -20 = 0
(x-2)² +(y+6)²= 60
The second equation is
x² + y² + 6x − 8y − 10 = 0
x² +6x +9-9 +y² -8y +16-16 -10 = 0
(x+3)² + (y-4)² = 35
The third equation is
3x² + 3y² + 12x + 18y − 15 = 0
(x + 2)² + (y + 3)² = 18
The fourth equation is
5x² + 5y² − 10x + 20y − 30 = 0
(x-1)² + (y+2)² = 11
The fifth equation is
2x² + 2y² − 24x − 16y − 8 = 0
(x − 6)² + (y − 4)² = 56
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Find the value of :
[tex] \sf log_{3 \sqrt{2} }(324) [/tex]
Answer:
4
Step-by-step explanation:
Is that a log with the base of 3√(2) ?
If so....my calculator says the answer is 4
Let's see if we can do it w/ou the calculator:
3 sqrt(2)^x = 324 = 3^4 * 2^2 Now 'LOG' both sides:
x log (3 sqrt 2) = log (3^4 *2^2) = 4 log ( 3 * 2^(2/4)) = 4 log (3 sqrt2)
now divide both sides by log (3 sqrt2 )
x = 4 (If I did the math correctly ! )
If point C is between points A and B, then ___ + CB = AB.
A. BC
B. CA
C. ABC
D. AB
Answer:
[tex]\fbox {B. CA}[/tex]
Step-by-step explanation:
Picture the line segment :
⇒ A ---------------- C ------------------ B
Then :
⇒ CA + CB = AB
Please helpppp !!!!!
Answer:
The answer is A
Box y, box y, and box z each contain a pencil and a highlighter. An item is drawn randomly from each box. A) Draw a tree diagram to represent the possible outcomes.
B) Determine the probability that the items drawn are two pencils and one highlighter.
The probability that the items drawn are two pencils and one highlighter is 0.25
How to draw the tree diagramTo do this, we make use of the following representations:
P represents PencilsT represents HighlightersSince there are three boxes, the number of possible outcomes is:
Outcomes = 2³
Outcomes = 8
See attachment for the tree diagram.
How to determine the probability?From the tree diagram, we have:
Outcomes = 8Two pencils and one highlighter (PPT) = 2So, the probability is:
P = 2/8
Evaluate
P = 0.25
Hence, the probability that the items drawn are two pencils and one highlighter is 0.25
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K'L'M'N' is a dilation image of KLMN. Which is the correct description of the dilation?
Answer:
d
Step-by-step explanation:
I finished all my other questions but i don't know how to do this one. could someone help me? I added 100 points. It is attached. :)
The answers are mentioned below.
What is Acceleration ?Acceleration is the change of speed with respect to time.
It is given that ,
The mass of the person is 50kg
Weight is 490 N
He has boarded an elevator with a bathroom scale.
1. The elevator is going down at constant speed , Force = 0N as acceleration is zero , The reading is 50kg.
2. The elevator is going up an slowing down . The magnitude of the acceleration is 4.9 m/sq.s , Force = mass * acceleration = 50 * 4.9 = 245N acting upward but the net force will be acting downward.
490 - 245 = 145N , reading 14.79 kg.
3.The elevator is free falling with an acceleration of 9.8m/sq.s force 0 N , as the gravitational force is pulling you down and the scale pushes up with the same force , Reading is 0 kg.
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Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$500 and $550.
Need the answer as a % !!!
Answer:
2.15%
Step-by-step explanation:
If you were to get the z-score for both 500 and 550 and then get the probability of both those z-scores. After getting the probability you would subtract both probability and get your answer.
Z-score:
550-400/2=3
500-400/2=2
Probability:
3 (from the Z-table) is .9987
2 (from the Z-table) is .9772
.9987-.9772= .0215
.0215 as a percentage is 2.15%
Mean: 400
Standard deviation: 50
Check to see if 500 and 550 fall within the standard deviations:
400+2(50) =500
400+3(50) =550
These values lie between the 2nd and 3rd deviations, so
the value is 0.0235
Percentage: 2.35%
Hope it helps!
What are the domain and range of the function represented by the set of
ordered pairs?
{(-7, 1), (-3, 2), (0, -2), (5,5)}
Answer:
see explanation
Step-by-step explanation:
the domain is the set of x- coordinates from the ordered pairs , that is
domain : { - 7, - 3, 0, 5 }
the range is the set of y- coordinates from the ordered pairs, that is
range : { - 2, 1, 2, 5 }
ABCD is a square. Triangle DEF is equilateral. Triangle ADE is isosceles with AD = AE. CDF is a straight line. Showing all your steps, calculate the size of angle AEF
Answer:
90°
Step-by-step explanation:
the sum of all angles in a triangle is always 180°.
in an equilateral triangle also all 3 angles are equal and therefore 180/3 = 60°.
angle EDF = 60°.
angle DEF = 60°
all angles in a square are 90°.
so, angle ADC = 90°.
and therefore, ADF = 90°.
the angle ADE is then 90-60 = 30°.
the triangle ADE is isoceles (both legs are equal, and both angles of the legs with the baseline are equal).
so, the angle AED = angle ADE = 30°
the angle AEF is then angles AED + DEF = 30 + 60 = 90°
-(x − 2)(3x2 + 4x − 5)
The simplification of the algebraic expression to its simplest form is -3x³ + 2x² + 13x - 10
What is the simplest form of an algebraic expression?The simplest form of an algebraic expression is a stage at which the expression can no longer be further simplified.
From the given expression:
= -(x − 2)(3x² + 4x − 5)
= (-x +2)(3x² + 4x − 5)
Open brackets
= -3x³ - 4x² + 5x +6x² + 8x - 10
= -3x³ + 2x² + 13x - 10
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marcus needs to paint a large wall with a window centered in the middle of the wall (shown below).what is the area (in square feet)that marcus will need to paint.
A 336ft
B 256ft
C 300ft
D 264ft
To calculate the area that Marcus needs to paint we must calculate the area of the window and subtract it from the total area of the wall.
How to calculate the area of a wall?To calculate the area of a rectangular wall we must use the following formula:
area = a × bWhere a is the length of the height, and b is the length of the width.
Next, we need to calculate the area of the window. If it is a square or rectangular window we use the same formula "area = a × b".
If the window is circular we use this formula:
Area of the circle = π r²Once we know the area of the wall and the area of the window, we subtract the area of the window from the area of the wall and we will know what is the total area that Marcus must paint.
Note: This question is incomplete because some information is missing. However I can answer it based on my general prior knowledge.
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How would you describe the graph of y< - lxl?
A dashed line up V on the (0,0) with the shading on the inside of the V.
A solid line up V on the (0,0) with shading outside the V.
A dashed line down V on the (0,0) with the shading inside the V.
Answer:
A dashed line down V on the (0,0) with the shading inside the V.
Step-by-step explanation:
- graph of y = -|x| is an upside down V
- less than sign means that there is dashed lines only
- plug in an x-value to determine whether the graph is shaded within the V or outside
1 peasant changed rabbits to hens and 2 rabbits were equal to 3 hens, each hen produced the eggs that were equal to ⅓ of the total number of hens, the peasant sold the eggs, 9 eggs will cost as many pennies as each hen that produced the eggs and totally he got 72 pennies so how many hens and how many rabbits he had?
The peasant had 28 hens and 42 rabbits
How to determine the number of hens and rabbits?Represent hens with h, eggs with e and rabbits with r.
So, we have:
2r = 3h
e = 1/3h
Make h the subject in e = 1/3h
h = 3e
He got 72 pennies.
So, we have:
r + h = 72
Multiply through by 2
2r + 2h = 144
Substitute 2r = 3h in 2r + 2h = 144
3h + 2h = 144
Evaluate the sum
5h = 144
Divide by 5
h = 28.8
Remove decimal
h = 28
Recall that:
2r = 3h
So, we have:
2r= 3 * 28
Divide by 2
r = 3 * 14
Evaluate the product
r = 42
Hence, the peasant had 28 hens and 42 rabbits
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(c) Find the number of sets where all three cards are the same for exactly $0$ attributes. (d) Find the number of sets where all three cards are the same for exactly $1$ attribute.
C. For the first card, there are three ways to choose the number of card.
For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.
Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.
D. The cards may have the same number, color, shapess, orshading.
However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.
If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.
what is Probability?
Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.
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Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
Answer:
From the graph in the attachment, it is clear that Option A is correct.
Step-by-step explanation:
The given inequalities are x - 4y ≤ 4 and y < x + 1.
Let us take the first line x - 4y ≤ 4 and remove the inequality and add equality, x - 4y = 4.
Now, we will find the intercept points. Putting y = 0 we will get x = 4 and putting x = 0 we will get y = -1. So, the points are (4,0) and (0,-1).
When we will solve the inequality, we find that portion above the graph satisfies this inequality.
Let us take the second line y < x + 1 and remove the inequality and add equality, y = x + 1.
Now, we will find the intercept points. Putting y = 0 we will get x = -1 and putting x = 0 we will get y = 1. So, the points are (-1,0) and (0,1).
When we will solve the inequality, we find that portion below the graph satisfies this inequality.
All these conditions satisfy the Option A.
The diagram is in the attachment.
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An elevator in a tall building goes up 7 floors, then
down a floors, down 4 floors, up 8 floors, and
down 2 floors. Now it is on floor 14. On what
floor did the elevator start?
If $5x-7=13x+17$, what is $6(x-4)$?
Answer:
0(x-4)
Step-by-step explanation:
in my working system i mean just when i try on the place of 4 any number can be inserted
$5x-7=13x+17$,here both gives -22 as a result so
$6(x-4)$=6x-24 and to give the same result or 0
$6(x-4)$=0(x-any number )
x=y²-1
2x - y = 4
Which of the following equations could be the result of using substitution to solve the system?
2y²-y-5=0
2y2-y-6=0
2y2-2y-5=0
Answer:
B) 2y² - y - 6 = 0
Given following:
x = y² - 1 ___equation 12x - y = 4 ___equation 2Insert equation 1 into 2:
2(y² - 1) - y = 42y² - 2 - y = 42y² - y - 2 - 4 = 02y² - y - 6 = 0Put in second
2x-y=42(y²-1)-y=42y²-2-y=42y²-y-6=0At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality.
The mistake she had done is she should have reversed the inequality as per the division property of inequality.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
The inequality is:
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
Given:
Jamie had $500 in her savings account.
She wants to have at least $200 left in the account at the end of the school year.
The inequality she had done is
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
But when she was dividing she should have reversed the inequality as per the division property of inequality.
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Function g is a transformation of function f.
Graph shows 2 exponential functions. First curve f enters quadrant 3 at (minus 6, minus 2) rises through (0, minus 1) and (1, 0) and (2, 2) in quadrant 1. Second curve g enters quadrant 2 at (minus 6, 6) falls through (0, 3) and (1, 0) in quadrant 1.
What is the equation of function g?
g(x) = f(x)
The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given:
genera form of an exponential function is y=aeᵇˣ
Now, equation for f(x) is
f(x) = [tex]e^{(log \;2)x} -2[/tex]
Similarly, graph for g(x) is
g(x) = [tex]-3e^{(log \;2)x} +6[/tex]
Comparing the two function a relation can be establish
g(x) = -3[f(x)]
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Answer:
shifted to the left two units
g(x)=-f(x+2)
Step-by-step explanation:
What function represents this graph??
The required piecewise function that represents the graph is given as:
[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]
Piecewise functionsThe graph consists of 3 lines with different equations and slopes. In order to determine the function it represents, we will create a piecewise function.
For the line crossing the negative x-axis
Using the coordinate points (-4, 2) and (-2, -4)
Slope = -6/2
Slope = -3
2 = -3(-4) + b
2 - 12 = b
b = -10
The equation of the line will be y = -3x-10
For the line crossing the negative y-axis
Using the coordinate points (-2, -4) and (2,-2)
Slope = 2/4
Slope = 1/2
-2 = 1/2(2) + b
-2 - 1 = b
b = -3
The equation of the line will be y = -1/2x-3
For the line crossing the positive x-axis
Using the coordinate points (2, -2) and (3, 0)
Slope = 2/1
Slope = 2
0 = 2(3) + b
0 - 6 = b
b = -6
The equation of the line will be y = 2x-6
The required piecewise function that represents the graph is given as:
[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]
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evaluate the expression below when x is 4
3x^2 +5 =
Answer:
[tex]\fbox {53}[/tex]
Step-by-step explanation:
⇒ 3x² + 5
Substitute x = 4 :
⇒ 3(4)² + 5
⇒ 3(16) + 5
⇒ 48 + 5
⇒ 53
Find the range of the given function y = 8x + 1, where x > 2.
The range of the function will be all values that are greater than 17 that is y > 17
Range of a functionThe range of a function is the dependent variable of the function for which it exists,
Given the linear function
y = 8x + 1
If the value of x is 2, hence;
y = 8(2) + 1
y = 17
Hence the range of the function will be all values that are greater than 17 that is y > 17
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If you apply the changes below to the quadratic parent function, f(x) = x²,
which of these is the equation of the new function? Shift 1 unit left.
Vertically stretch by a factor of 5.
Reflect over the x-axis.
A. g(x) = -5(x-1)²
B. g(x) = -5x² - 1
C. g(x) = -5(x + 1)²
D. g(x) = (-5x + 1)²
Answer:
Step-by-step explanation:
Comment
Do the most mechanical part first. Moving 1 unit left will mean that x becomes (x + 1). It is anti intuative, but that is the correct answer.
So far what you have is y = a(x + 1)^2
The reason that you want to do it this way is any answer with a minus sign is wrong which eliminates A and B
When you stretch the parabola, a becomes 5 so now you have another part of the puzzle. and the equation becomes
y = 5(x + 1)^2
The 5 goes on the outside of the brackets which eliminates D
When you reflect this over the x axis, you invert the parabola which means you turn it upside down. The sign in front of the 5 becomes a minus.
Answer
y = - 5(x + 1)^2 or C.
Help plssssss I need this today
Answer:1 is exponential. 2 is linear. 3 is neither. 4 is linear. 5 is linear. 6 is exponential. 7a is exponential. I think 7b could be 10x + y = 10 but I'm not too sure. 7c is (8,4).
Step-by-step explanation:1. the coordinates are moving in an exponential way or something im not sure the correct wording but that is what exponential graphs look like. 2 is a straight line so it is linear. 3 is neither because the graph isn't exponential or linear. 4 is linear because the coordinates are subtracting at the same number. 5 is linear for the same reason at 4. 6 is exponential because the coordinates are multiplied by 2 each time. 7a is exponential because the coordinates are divided by 2 each time. 7b I'm not sure on. 7c is 8/4 because August is the 8th month and the month before (7) is 8 so 8 divided by 2 equals 4. So the 8th month would have to be 4. I hope that helps!
What is the initial value of the function represented by this table?
Answer: 3
________________________________
initial value = starting value when x is 0
as you can see when x is 0 y is 3
so your initial value is 3
________________________________
Hoped this helped.
simplify the following polynomial expression. (5^4-9^3+7x-1)+(-8^4x^2-3x+2)-(-4x^3+5x-1)(2x-7)
The simplified expression is 5[tex]x^{4}[/tex] -37 x³ - 6x² +41x -6.
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Given:
(5[tex]x^{4}[/tex] - 9x³ + 7x -1) + ( -8[tex]x^{4}[/tex]+ 4x² - 3x + 2) - ( -4x³ + 5x -1) (2x - 7)
Now,
5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2 - ( -4x³ + 5x -1) (2x - 7)
=5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2-(-8[tex]x^{4}[/tex]+28x³ +10x² - 35x -2x +7
= 5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2 +8[tex]x^{4}[/tex]- 28x³ - 10x² + 35x + 2x - 7
= 5[tex]x^{4}[/tex] -37 x³ - 6x² +41x -6
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what is the equation of x2 + 6x + 8 + 0 algebraically
Answer:
x = - 4 , x = - 2
Step-by-step explanation:
x² + 6x + 8 = 0
consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 6)
the factors are + 4 and + 2 , since
4 × 2 = 8 and 4 + 2 = 6 , then
(x + 4)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x + 2 = 0 ⇒ x = - 2
If 15 members vote to choose 4 group leaders, what is the probability that 4 candidates will be chosen for 4 positions
Answer:
[tex]\frac{4}{60}[/tex] = [tex]\frac{1}{15}[/tex]
Step-by-step explanation:
Find the value of y.
The value of y from the equation is 12
What is a triangleA triangle is a shape that has three sides and angles
From the given diagram, the equation is true based on angle bisector theorem
8/4 = y/6
Cross multiply
4y =48
y = 12
Hence the value of y from the equation is 12
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