5-4-3-2
16
6/ +
77?1?
x
Which is the general form of the equation of the circle
shown?
Ox²+²+4x-2y-4 = 0
Ox+y+4x-2y + 2 = 0
Ox² + y² 4x +2y-4 = 0
Ox² + y² 4x + 2y + 2 = 0
Answers
Answer:
1st option
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 2, 1 ) and r = 3 , then
(x - (- 2) )² + (y - 1)² = 3² , that is
(x + 2)² + (y - 1)² = 9 ← expand factors using FOIL
x² + 4x + 4 + y² - 2y + 1 = 9
x² + 4x + y² - 2y + 5 = 9 ( subtract 9 from both sides )
x² + 4x + y² - 2y - 4 = 0 , that is
x² + y² + 4x - 2y - 4 = 0 ← in general form
Answer:
[tex]\textsf{1)} \quad x^2+y^2+4x-2y-4=0[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusFrom inspection of the graph:
center of the circle = (-2, 1)radius of the circle = 3Substitute the found values into the formula:
[tex]\implies (x-(-2)^2+(y-1)^2=3^2[/tex]
[tex]\implies (x+2)^2+(y-1)^2=9[/tex]
Expand and simplify:
[tex]\implies (x+2)^2+(y-1)^2=9[/tex]
[tex]\implies x^2+4x+4+y^2-2y+1=9[/tex]
[tex]\implies x^2+y^2+4x-2y+5=9[/tex]
[tex]\implies x^2+y^2+4x-2y-4=0[/tex]
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Related Questions
need help asap willing to give a lot of points!
Answers
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
Question 1
Part (a) :
⇒ 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ
⇒ 6⁷ = 6ˣ
⇒ x = 7
Part (b) :
⇒ y² = 169
⇒ √y² = √169
⇒ y = ± 13
⇒ y = 13, y = -13
Question 2
Part (a) :
⇒ (√5)² × (√3)²
⇒ 5 × 3
⇒ 15
Part (b) :
⇒ (∛9)³ × (√30)²
⇒ 9 × 30
⇒ 270
dsfghjmbhjghcvjkjjbhvgjjbkjguy8uygiyugykfgjhgghgjk
Answers
The equation y = 1/3x - 2 passes through the diagonals of ZDRN
How to determine the end result?The points are given as:
Z = (-3, -1)
D= (3, -1)
R = (3, -3)
N = (-3, -3)
The equation of the line is given as:
y = 1/3x - 2
When the points and the line equation are plotted in a graph on the same coordinate (see attachment), we can see that the equation y = 1/3x - 2 passes through the points Z = (-3, -1) and N = (-3, -3)
These points are the diagonals of the shape formed by the four points
Hence, the equation y = 1/3x - 2 passes through the diagonals of ZDRN
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work out the length x in the triangle
Answers
Answer:
The length x is 16 m==============
Imagine the height of the triangle is h, which is perpendicular to 15 m side.
The area is:
A = bh/2Use this formula and given values and find the value of h:
60 = 15h/2h = 60*2/15h = 8 mSince h is opposite to 30° angle and x is the hypotenuse of the formed right triangle, we'll use the property of 30°x60°x90° triangle.
Hypotenuse is twice the length of the side opposite to 30° angle.In our case h is opposite to 30° angle, therefore we have:
x = 2h = 2*8 = 16 mAnswer:
x = 16
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] absinC
where a, b are 2 sides of the triangle and C the angle between them
here a = 15, b = x, C = 30° and A = 60 , then
[tex]\frac{1}{2}[/tex] × 15 × x × sin30° = 60
7.5x × [tex]\frac{1}{2}[/tex] = 60 ( multiply both sides by 2 to clear the fraction )
7.5x = 120 ( divide both sides by 7.5 )
x = 16
help me deadline today
Answers
Answer:
6
Step-by-step explanation:
The equation becomes 9 *4 * 1/6. Then you simplify and get 6.
Please mark me as Brainliest if it is correct, thx.
Prove the triangles a re similar
Answers
Step-by-step explanation:
LINE B.I is parallel to LINE O.D
therefore :Ô = Î ( alternate angles )
: Ď = B ( alternate angles )
In ️ B. I. G and ️ D O G
O = I ( alternate angles)D = B ( alternate angles)G = G ( 3rd angle of️ )️ BIG is similar to ️ DOG
PLEASE HURRY
Let p: A student plays basketball.
Let q: A student plays tennis.
How many students play both basketball and tennis?
Answers
Answer:
4
Step-by-step explanation:
4 is the intersecting point which states p intersect q giving both tennis and basketball players
10.
(06.01 MC)
Classify the expression: 5x3 + 2x − 3 (1 point)
Quadratic expression
Linear expression
Cubic expression
Exponential expression
Answers
The correct answer is option C which is the given expression is cubic.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given expression
5x³ + 2x − 3
The cubic expression is one in which the highest power of the variable is three or we can say that the degree of the expression is three so the expression will have three solutions.
Therefore the correct answer is option C which is the given expression is cubic.
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PLEASE HELP ASAP
(Picture shown)
Answers
Answer:
first blank: 3
second blank: 4
Step-by-step explanation:
The completed equation should say:
y = -3x + 4
This is slope-intercept form of the equation. It's a fill-in-the-blank equation. You put the slope in the first blank and the y-intercept in the second blank. Your math program put the negative sign in and it does need to be there. To find the slope, look at the points on the line. To get from one point to the next you go DOWN3 and over 1. DOWN3 and OVER1 is the slope -3/1, which is -3. This number goes beside (in front of) the x. The line crosses the y-axis at 4, fill that in at the end of the equation (the second blank).
The equation for the line is
y = -3x + 4
There are 19 animals on the farm which contains hens and goats. There are 68 legs in total. How many goats are there on the farm?
Answers
Answer: 15 goats
Step-by-step explanation:
h = hens - they have 2 legs
g = goats - they have 4 legs
The equations would be:
h + g = 19
2h + 4g = 68
To solve this, I personally prefer substitution, we're isolating h since we need to find g:
h + g = 19
h = 19 - g
Now that we have h, we can plug this into the second equation:
2h + 4g = 68
2(19 - g) + 4g = 68
38 - 2g + 4g = 68
2g = 30
g = 15
There are 15 goats.
Adding onto this, 19 - 15 = 4, so there are 4 hens.
Javier is comparing costs of two cars. Car A costs $130 per month for insurance and $0.10 per mile to run. Car B costs $108 per month for insurance and $0.15 per mile to run. He defines x as the number of miles driven each month and y as the total cost to run the car. Which set of equations can be used to find the number of miles Javier would need to drive to make the costs equal?
0.10 x = 130. 0.15 y = 108
y = 0.10 x + 130. y = 0.15 x + 108
0.10 x = 108. 0.15 y = 130
y = 0.15 x + 130. y = 0.10 x + 108
Answers
Answer:
y = 0.10 x + 130. y = 0.15 x + 108
Step-by-step explanation:
0.10 and 0.15 are the slope in the equation y = mx + b since it requires an input (number of miles) to spit out an output (number of miles*0.10 = price) and the x intercept is 130 and 108 creating the equation y = 0.10 x + 130. y = 0.15 x + 108.
someone help how do I
factor x^3-y^3
Answers
Answer:
(x - y)(x² + xy + y²)
Step-by-step explanation:
Since both are cubed (³),
we can apply the Difference of Cubes Formula:
A binomial that is of the form (something)³ – (something else)³
To factor any difference of cubes,
the formula a³ – b³ = (a – b)(a² + ab + b²).
hence, x³ - y³ = (x - y)(x² + xy + y²)
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A company ordered $6,000 worth of chairs. Some of the chairs ordered cost $20 each and the others cost $40 each. If twice as many $20 chairs as $40 chairs were ordered, how many chairs were ordered altogether
Answers
In total 180 chairs are ordered for the cost $6000.
The total cost of chairs=$6,000.
What are simultaneous equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Let x be the chairs ordered each at $20 and y be the chairs ordered each at $40.
Then equation will be 20x+40y=6000-------(1)
Given that, twice as many $20 chairs as $40 chairs were ordered.
That is 2x=y⇒2x-y=0--------(2)
Multiply equation (2) by 40.
That is 80x-40y=0--------(3)
By adding equation (2) and (3) we get
20x+40y+80x-40y=6000
⇒100x=6000
⇒x=60
Substitute x=60 in equation (2)
That is, 2x=y
⇒y=120
Total number of chairs=x+y=60+120=180 chairs.
Hence, in total 180 chairs are ordered for the cost $6000.
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How many calories does the bran muffin contain? 400 calories 200 calories 650 calories 800 calories
Answers
Answer:
400 calories
Step-by-step explanation:
A bran muffin has around 380 calories, when rounded off it is 400 calories.
Hope I helped
Answer:
A. 400 Calories.
Step-by-step explanation:
Look it up on the net.
If this is wrong, it is because there wasn't enough information given.
Hope this helps!
If not, I am sorry.
HELP I REALLY NEED HELP
Answers
Answer: 72 inches squared
Step-by-step explanation:
So, the real floor of a classroom is 36 feet by 32 feet.
And the scale drawing, has length of the classroom equal to 9 inches.
What is the area in square inches of the floor in the scale drawing
1 foot = 12 inches
The length of the classroom, measured in feet, has been multiplied by 12, to get converted in inches. After that, it has been divided by a number, a proportion, to get to 9 inches.
36feet * 12 / x = 9 inches
432 inches / x = 9 inches
Now, to solve for x, we can cross-multiply
432 inches = 9x inches
Divide 9 inches on both sides.
x = 48
To solve the exercise, we need to calculate the floor's area in the scale drawing.
We have the length = 9 inches.
Now, let's calculate the width
Width = 32 feet * 12 / 48
Width = 384 inches / 48
Width = 8 inches
Area = Length * Width
Area = 9 inches * 8 inches
Area = 72 inches squared
Hope I helped!
Solve |x| > -9.
1. no solution
2. all reals
3. {x | x < -9 or x > 9}
Answers
Answer:
2. All reals
Step-by-step explanation:
It covers everything as absolute value (distance from 0)
If you graph it you will see
Reason:
Absolute value represents distance on a number line. Specifically it's the distance from x to 0.
For example, |-2| = 2 means -2 is 2 units away from 0.
Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.
Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")
The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family. The t-test for two means is appropriate in this situation because Group of answer choices women and men are dependent samples. women and men are independent samples. women and men are matched samples. the observations are paired. None of these.
Answers
The t-test for the two means is appropriate in this situation because women and men are independent samples.
What are Independent Samples?Independent samples are chosen randomly, ensuring that their results are independent of other observations' values.
The premise that samples are independent underlies many statistical analyses. Others are made to evaluate non-independent sample sets.
The samples of men and women are independent since their results are independent of other observations' values.
The Independent Samples t-Test analyzes the means of two separate groups to see if there is statistical support that the population means values are statistically substantially different.
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[39/(15-2)|-(2*9)
please solve and show steps! thx!
Answers
Answer:
- 15
Step-by-step explanation:
1) Simplify 15 - 2 to 13.
39/13 - 2 × 9
2) Simplify 39/13 to 3.
3 - 2 × 9
3) Simplify 2 × 9 to 18.
3 - 18
4) Simplify.
- 15
ax +by = 16
3x+2y=64
In the system of equations, a and b are constants. if the system has infinitely many solutions, what's the value of ab?
Answers
Answer:
The system has infinitely many solutions when a = 3/4 and b = 1/2Given
System of linear equations
ax +by = 163x+2y=64To find Values of a and b that leads to infinitely many solutionsSolutionThe linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.
We can solve it in two different ways
1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.
4ax + 4by = 643x + 2y = 64When compared it gives us:
4a = 3 ⇒ a = 3/44b = 2 ⇒ b = 2/4 = 1/22. Convert both equations from standard to slope-intercept form and compare:
ax + by = 16by = -ax + 16y = - (a/b)x + 16/b3x + 2y = 642y = - 3x + 64y = - (3/2)x + 32Work out values of a and b:
16/b = 32 ⇒ b = 16/32 ⇒ b = 1/2- (a/b) = - 3/2 ⇒ a/b = 3/2 ⇒ a = 3b/2 ⇒ a = 3(1/2)/2 ⇒ a = 3/4
(a - b)(2x-3)+(6x+7)(a+b)
Factorise
Answers
Answer:
2(4ax+2bx+2a+5b)
Step-by-step explanation:
the population of blackbirds in a park is counted every year.
the population decreases by 24% to 323
what was the original population?
Answers
Answer:
the original population was 425
Step-by-step explanation:
Answer:
425
Step-by-step explanation:
Let the original population of blackbirds be x.
Original population decreases by New population
100 24 76
x 24 323
Now we can make an expression like this.
100 ⇒ 76
x ⇒ 323
And now let us use cross multiplication and solve for x.
Let us solve it now.
323 × 100 = 76x
32300 = 76x
425= x
There are 10 marbles in a bag. are red and the others are blue. 5 What is the ratio of red marbles to blue marbles? Question 11 * 1 There are 10 marbles in a bag . are red and the others are blue . 5 What is the ratio of red marbles to blue marbles ?
Answers
Answer:
%50 1÷2
if there is missing information. if there is 10 total marbels 5 would be red, 5would be blue.
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 point is deducted. Desiree did not leave any question unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
and the equation will have
.
Answers
Total number of multiple-choice questions that Desiree has to answer in Aptitude test = 50
Points given for every correct Answer = +3
Points deducted for every Incorrect Answer = -1
For every question unanswered ,
points Deducted = -0.5
Total Points Obtained by Desiree after Answering all the questions = 110
Number of Answers that Desiree answered correctly = x questions
Number of Incorrect Answers = (50 - x) questions
Then,the Equation representing above situation
→ 3 × x + ( -1 ) × ( 50 - x ) = 110
⇒3x - 50 + x = 110 ----------- equation that represents the given situation
⇒ 4x - 50 = 110
Adding 50, on both sides
→ 4x - 50 + 50 = 110 + 50
⇒ 4x = 160
Dividing both sides by, 4 we get
x = 40
Number of correct answers given by Desiree= 40 questions
Number of Incorrect Answers = 50 - 40
= 10 Questions .
Answer:
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 points is deducted. Desiree did not leave any questions unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
3(50 - x) + x = 110
and the equation will have
no solution
.
Step-by-step explanation:
(x - 4)/(x + 6) - (x - 6)/(x + 4)
Answers
Answer:
[tex]\frac{20}{(x+4)(x+6)}[/tex]
Step-by-step explanation:
assuming you require the expression simplified
[tex]\frac{x-4}{x+6}[/tex] - [tex]\frac{x-6}{x+4}[/tex]
multiply the numerator/denominator of the first fraction by (x + 4)
multiply the numerator/denominator of the second fraction by (x + 6)
= [tex]\frac{(x-4)(x+4)}{(x+4)(x+6)}[/tex] - [tex]\frac{(x-6)(x+6)}{(x+4)(x+6)}[/tex] ← expand and simplify numerators leaving the common denominator
= [tex]\frac{x^2-16-(x^2-36)}{(x+4)(x+6)}[/tex]
= [tex]\frac{x^2-16-x^2+36}{(x+4)(x+6)}[/tex]
= [tex]\frac{20}{(x+4)(x+6)}[/tex]
What is the constant in the expression?
Answers
Answer:
12
Step-by-step explanation:
A constant in an expression is the number that is not attached to any variable, and this includes the sign that comes with the number.
0.05m +12
In the expression above, m is the variable thus 0.05 is known as the coefficient of m instead of a constant. Coefficients are numbers that are multiplied to variables.
+12, which can simply be written as 12, is not multiplied to any variable and is thus the constant.
The value of the number 12 will not change no matter the value of m. The fact that the value stays the same makes it a constant.
Additional:
To learn more about constant, check out the following!
https://brainly.com/question/16517603Answer: 12 ✅
Step-by-step explanation:
Hii, I'd love to help you! (:
This problem is about finding the constant in the expression. This is fun! Let's start our search...
____________________________________________
Wait, how can we find a constant if we don't even know what it is?
No reason to panic!
ConstantsA constant is a number that is not added (or subtracted) from any variables (and a variable is a letter).
_____________________________________________
Ohh now it's easy as winking!
Because the only number in this particular expression that is not added to any letters at all is 12.
______________________________________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
WILL MARK BRAINLEST
Fill in the missing work and justification for step 5 when solving 4(x + 1) = 8.
Step Work Justification
1 4(x + 1) = 8 Given
2 4x + 4 = 8 Distributive Property
3 4x + 4 − 4 = 8 − 4 Subtraction Property of Equality
4 4x = 4 Simplify
5
6 x = 1 Simplify
A 4x − 4 = 4 − 4; Subtraction Property of Equality
B 4x + 4 = 4 + 4; Addition Property of Equality
c Four times x over four equals four over four; Division Property of Equality
d 4x(4) = 4(4); Multiplication Property of Equality
Answers
Answer:
c) Four times x over four equals four over four; Division Property of Equality===========================
Given equation and steps to solve it:
4(x + 1) = 84x + 4 = 84x + 4 - 4 = 8 - 44x = 44x/4 = 4/4 This is the missing stepx = 1All steps given above including the missing one. As we can see, we divided both sides by 4, so the justification for this step is Division Property of Equality.
Hence, the correct choice is C.
Answer:
Four times x over four equals four over four; Division Property of Equality
Option CStep-by-step explanation:
See on antepenultimate step
4x=4Now for getting x we have to divide each side by 4
We get.
4x)4=4/4x=1Which shows how to find the value of this expression when X=-2 and Y = 5?
(3x®y-2)2
32 (-2)
54
3(-2)6
54
32(5) 6
(-2)
3
(2) 854
Answers
Answer:
(3^2(-2)^6)/5^4
Step-by-step explanation:
See attached image.
Is this linear or non linear?
Answers
Answer: This represents a linear function.
Step-by-step explanation:
I used Desmos to plot them on a graph. You can see that this is linear because each point is in a line. I hope this helps!!
How many square feet of outdoor carpet will we need for this hole.
Answers
Step-by-step explanation:
area of rectangle= 12×6
=72ft^2
A2=9ft^2 whereby the base of the hole is 3ft
height is 6ft
therefore the square is 18 ft
PLEASE HELP! SO CONFUSED! 25 POINTS!!
Answers
Answer:
D
Step-by-step explanation:
(f • g)(x)
= f(x) × g(x)
= (x + 4)(3x² - 7)
each term in the second factor is multiplied by each term in the first factor , that is
x(3x² - 7) + 4(3x² - 7) ← distribute both parenthesis
= 3x³ - 7x + 12x² - 28
= 3x³ + 12x² - 7x - 28 ← in standard form
help me with math please grade 5
Answers
Answer:
15/7 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Answer:
15/21
Step-by-step explanation:
First do 5 times 3, which is 15 (5+5+5). Then do 7 times 3, which is 21 (7+7+7). Since the denominator is 7 and there is 3 models with 7 parts each, there are 21 total parts. Out of each model, only 5 parts are highlighted/colored out of the 7. Add all the parts that are colored together to get 15. To put it simpler, 15 out of 21 parts are colored. This cannot be further simplified, giving you 15/21
