The system of equation will have one solution.
The correct answer is an option (B)
What is a system of equation ?It is a collection of one or more linear equation involving the same variable.
For given question,
Two equations have negative reciprocal slope .
Which means if one equation have slope = m
then slope of other equation will be = -1/m
This means, both the lines are perpendicular to each other , hence both the lines must be intersecting each other at one point.
In system of equation , the solution of the two equation is the point where they intersect .
Since, both the lines are intersecting at one point . Hence, it will have only one solution.
Therefore, the correct answer is an option b) the system will have one solution
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Misaka solved the radical equation x – 3 = square root of 4x-7 but did not check her solutions. (x – 3)2 = square root of 4x-7^2 x2 – 6x + 9 = 4x – 7 x2 – 10x + 16 = 0 (x – 2)(x – 8) = 0 x = 2 and x = 8 Which shows the true solution(s) to the radical equation x – 3 = square root of 4x-7 x = 2 x = 8 x = 2 and x = 8 There are no true solutions to the equation.
Answer:
x=8 is a true solution of the radical equation
Step-by-step explanation:
we have
[tex]x-3=\sqrt{4x-7}[/tex]
Solve for x
squared both sides
[tex](x-3)^{2}=4x-7\\\\x^{2}-6x+9=4x-7\\\\ x^{2}-10x+16=0[/tex]
Convert to factored form
[tex]x^{2}-10x+16=(x-2)(x-8)[/tex]
The solutions are x=2 and x=8
Verify the solutions
For x=2
Substitute in the original equation
[tex]2-3=\sqrt{4(2)-7}[/tex]
[tex]-1=1[/tex] ----> is not true
therefore
x=2 is not a true solution of the radical equation
For x=8
Substitute in the original equation
[tex]8-3=\sqrt{4(8)-7}[/tex]
[tex]5=5[/tex] ----> is true
therefore
x=8 is a true solution of the radical equation
The true solution to the radical equation is x = 8, after checking the potential solutions by substituting them back into the original equation.
Explanation:The student is asked to find the true solution(s) to the radical equation x – 3 = square root of 4x-7. The student has solved the equation, but it is essential to check the solutions by substituting them back into the original equation to ensure they are not extraneous. The student got x = 2 and x = 8 as potential solutions. We must substitute these values back into the original equation to determine their validity:
For x = 2: 2 – 3 does not equal the square root of (4(2) – 7), so x = 2 is not a solution.For x = 8: 8 – 3 does equal the square root of (4(8) – 7), so x = 8 is a solution.Hence, the only true solution to the radical equation x – 3 = square root of 4x-7 is x = 8.
which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15). Check all that apply.
a. Divide 1 by 15
b. Count by hand
c. Add the endpoints
d. Divide 15 by 2
The methods that we can use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15) are: Option B: Count by hand, Option D: Dividie 15 by 2
What is the midpoint of a line segment?Midpoint of a line segment that lies in the mid of that line segment, as the name 'midpoint' suggests.
If the endpoints of the considered line segments are (a,b), and (c,d), then the coordinates of the midpoint would be:
[tex](x,y) = \left(\dfrac{c-a}{2}, \dfrac{d-b}{2}\right)[/tex]
We're specified here that:
The line segment in consideration is vertical.The endpoints of the line segment are (0,0) and (0,15).Since the line is vertical, we can easily find its midpoint by going up by half of the length of the line segment.
The y-coordinate starts from 0 and goes to 15 and x-coordinate is still all along the line as the line is vertical, so the length's half is (15-0)/2 =15/2 = 7.5 units. This gives the y-coordinate of the midpoint as visible in the formula specified above.
If we go this units up, we will reach the midpoint. Since x-coordinates of the points in the line segment are fixed to 0, so the midpoint's coordinates are (0, 7.5)
We can also count by hand as there is motion only in y-coordinates, so move half of the total motion upwards from (0,0) or half of the total length downwards from (0,15).
So we see, that the second method and the fourth method listed in the option can be used.
Thus, the methods that we can use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15) are: Option B: Count by hand, Option D: Dividie 15 by 2
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Final answer:
To find the y-coordinate of a vertical line segment midpoint between (0,0) and (0,15), you can count by hand to get an approximate location, add the y-coordinates of the endpoints and then divide by 2, or simply divide 15 by 2 to get the correct value of 7.5.
Explanation:
To calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15), you can use the following methods:
Count by hand, which means visually looking at the line and counting to the middle point between 0 and 15, which is 7.5.Using the formula for the midpoint of a segment, add the endpoints together and then divide by 2. For the y-coordinate, this means adding 0 and 15 and then dividing by 2: (0 + 15) / 2 = 7.5.Divide 15 by 2, as this is equivalent to the method above without including the initial step of adding 0 to 15 since 0 has no effect on the outcome.Option d is the most direct mathematical approach to finding the midpoint's y-coordinate. Option b is a valid but less precise method that relies on visual estimation. Option c is essentially part of the formula used in option d.
A(n)_______ (rational /irrational) number answer is desired.
Answer: rational number answer is desired
Step-by-step explanation:
Find the GCF of 52 and 84.
Answer:
4
Step-by-step explanation:
The GCF of 52 and 84 is 4.
52 = 2 × 2 × 13
84 = 2 × 2 × 3 × 7
Therefore, GCF = 2 × 2
GCF = 4
The GCF of 52 and 84 is found by finding the prime factors of each number and identifying the common factors. The GCF is 4.
Explanation:The GCF (Greatest Common Factor) of two numbers is the largest number that can evenly divide both numbers. To find the GCF of 52 and 84, we need to find the prime factors of each number and then find the highest common factor of these sets of prime factors.
Prime factors of 52: 2 x 2 x 13 Prime factors of 84: 2 x 2 x 3 x 7
The common factors are 2 and 2, so the GCF of 52 and 84 is 2 x 2, which equals 4.
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What is the conjugated expression?
Show that the LHS = RHS.
Step-by-step explanation:
:
2-csc²A
▬▬▬▬▬▬▬
csc²A + 2cotgA
2 - 1/sin²A
= ▬▬▬▬▬▬▬▬▬▬
1/sin²A + 2cosA/sinA
2sin²A - 1
= ▬▬▬▬▬▬▬
1 - 2cosAsinA
sin²A + sin²A - 1
= ▬▬▬▬▬▬▬▬▬▬▬▬
sin²A - 2cosAsinA + cos²A
sin²A - cos²A
= ▬▬▬▬▬▬▬
(sinA - cosA)²
(sinA - cosA)(cosA + sinA)
= ▬▬▬▬▬▬▬▬▬▬▬▬
(sinA - cosA)²
sinA + cosA
= ▬▬▬▬▬▬ <-- Let check "+" and "-"
sinA - cosA
By taking a common Equation denominator and simplifying, we will see that LHS = RHS. To prove that the given equation is true, we can simplify both sides step by step and show that they are equal.
To show that the left-hand side (LHS) is equal to the right-hand side (RHS) of the given equation, let's simplify both sides step by step.
LHS = 2 - cosec²A / cosec²A + 2cotA
= 2 - (1/sin²A) / (1/sin²A) + 2cosA/sinA
= 2 - 1/sin²A / 1/sin²A + 2cosA/sinA
RHS = sinA - cosA / sinA + cosA
By taking a common denominator and simplifying, we will see that LHS = RHS.
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The probable questionShow that the LHS = RHS.
2-cosec^2A/cosec^2A+2cotA=sinA-cosA/sinA+cosA may be:
What are the zeros of the function f(x)=x^2+x-6 divides by x^2-x-6?
Answer:
It is B.
Step-by-step explanation:
x^2+x-6 / x^2-x-6 = 0
The numerator equates to zero:
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
the zeroes are {-3, 2).
The zeroes of the function f(x) = (x² + x - 6)/(x² - x - 6) are -3, 2.
Hence, option B. is the right choice.
What are functions?A function (say f(x)) is defined over x, when an expression in x, gives only one value f(x) for all the x in its domain.
What are zeroes of function?A zero of a function (say f(x)) is the value x, where f(x) = 0.
How do we solve the given question?We are asked to find the zeroes of the function
f(x) = (x² + x - 6)/(x² - x - 6).
To find the zeroes, we put the value of f(x) = 0, in the above equation to get:
(x² + x - 6)/(x² - x - 6) = 0
or, (x² + 3x - 2x - 6)/(x² + 2x - 3x - 6) = 0
or, {x(x + 3) -2(x + 3)}/{x(x + 2) -3(x + 2)} = 0
or, {(x - 2)(x + 3)}/{(x - 3)(x + 2)} = 0
Zeroes are where the numerator = 0, as the denominator can not be 0.
∴ (x + 3)(x - 2) = 0
∴ Zeroes of the function x + 3 = 0 ⇒ x = -3, and x - 2 =0 ⇒ x = 2, that is
-3, 2. Hence, option B. is the right choice.
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which graph represents a function with direct variatio?
Answer:
In short, you are looking a diagonal line passing through the origin. And yes diagonal line is a straight-edged line that is running diagonally.
Step-by-step explanation:
If you want a better answer you can post the graphs.
I will tell you the trick, direct variations is another words for the relation is proportional.
The graph will have equation y=kx where k (k can't be zero) is the slope and your y-intercept is 0. The graph should be a diagonal line.
In short, you are looking a diagonal line passing through the origin. And yes diagonal line is a straight-edged line that is running diagonally.
Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?
Step-by-step explanation:
[tex]4x^3+x^2-8x-2\qquad\text{distributive}\\\\=x^2(4x+1)-2(4x+1)\\\\=(4x+1)(x^2-2)[/tex]
Identify the number that is NOT the same as the others when rounded to the nearest tenth.
a. 34.62 c. 34.49 b. 34.59 d. 34.56
Please select the best answer from the choices provided
A
B
C
D
Answer:
c. 34.49
Step-by-step explanation:
Note that the nearest tenth place value is directly next to the decimal point (located on the right). Round each number to the nearest tenth. Look at the number in the hundredth place value. If it is 5 or greater round up, if 4 and less, round down.
a. 34.62 rounded to the nearest tenth is 34.6
c. 34.49 rounded to the nearest tenth is 34.5
b. 34.59 rounded to the nearest tenth is 34.6
d. 34.56 rounded to the nearest tenth is 34.6
This makes it so that C. 34.49 is your answer.
~
PLEASE HURRY
In the diagram of circle O, what is the measure of ∠ABC?
I WILL GIVE BRAINLIEST
Answer:
The measure of angle ABC is 34°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
∠ABC=(1/2)[major arc AC-minor arc AC]
∠ABC=(1/2)[major arc AC-146°]
Find the measure of major arc AC
major arc AC=360°-146°=214°
substitute
∠ABC=(1/2)[214°-146°]=34°
To pass science, a student must earn at least a grade of 70. How many students failed this science class?
Answer:
7 students.
Step-by-step explanation:
To pass science, a student requires at least 70 grades so students who scored below 70 will be failed.
From the given bar chart we can calculate the number of students who scored below 70 grades
Students who earned 50 - 59 = 2
Students who earned 60 - 69 = 5
Therefore, number of students who failed were
2 + 5 = 7 students.
Answer:7 students
Step-by-step explanation:
What is the vertex of the graph of f(x) = |x + 5| – 6? (–6, –5) (–6, 5) (–5, –6) (5, –6)
Answer:
(-5, -6)
Step-by-step explanation:
The general form of absolute function is, and
its vertex form is given by:
.....[1]
where, (h, k) is the vertex
As per the statement:
we have to find the vertex of the graph of f(x).
On comparing given equation with [1] we have;
we have;
h =-5 and k = -6
⇒Vertex = (-5, -6)
Therefore, the vertex of the graph of f(x) = |x + 5| – 6 is, (-5, -6)
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Answer:
The answer is (-5, -6)
what would N be in this problem 9=8n
Answer:
9/8 = n
Step-by-step explanation:
9=8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
Point W is located on QR so that QW/QR = 3/4. What are the coordinates of point W?
Answer:
(9,9)
Step-by-step explanation:
I like to use similar triangles.
To take some confusion out of of this let's translate the line down 3 units and left 3 units.
Alright from the drawing we get:
a/8 = b/8 and a/8 = 3k/4k (or b/8=3k/4k )
We don't need the k's, they cancel.
a/8 = b/8 and a/8=3/4
So the first equation means a=b.
Now let's see what a and b are by solving a/8 = 3/4.
Cross multiply:
[tex]\frac{a}{8}=\frac{3}{4}[/tex]
[tex]a(4)=8(3)[/tex]
[tex]4a=24[/tex]
a=6
So if a=b and a=6, then b=6.
The ordered pair is (6,6).
Now let's move the line back.
We have to move it up 3 units and right 3 units which gives us the point (9,9).
Examine the first two steps used to solve the equation.
3 4 (20y − 8) + 5 = 1 2 y + 1 4 (20y + 8)
15y − 6 + 5 = 1 2 y + 5y + 2
15y − 1 = 11 2 y + 2
Which would be a good third step to solve the equation?
A. Combine like terms 11/2 and 2
B. Distribute 15 to each term on the left side.
C. Subtract 11/2y from each side of the equation.
D. Divide each side of the equation by 2.
Answer:
C.
Step-by-step explanation:
Your fractions are missing there fraction bars:
3/4 (20y − 8) + 5 = 1/2 y + 1/4 (20y + 8)
15y − 6 + 5 = 1/2 y + 5y + 2
15y − 1 = 11/2 y + 2
A. 11/2y and 2 aren't like terms because one contains the variable y and the other contains no variable
B. The distribute property can't be used there because you don't have 15(y-1) you have 15y-1
C. Subtracting 11/2y sounds like a good step because there is a y term on the opposing side.
15y-1=11/2y+2
Subtracing 11/2y on both sides
9.5y-1=2
That looks pretty good because then you would add 1 on both sides giving:
9.5y =3
Last step would get the y by itself which is dividing both sides by 9.5 giving you 6/19.
D. You could actually do this but it doesn't help you get x by itself. The equation would look like this: 15/2 y-1/2=11/4 y+1
Answer:
C. Subtract 11/2y from each side of the equation.
Step-by-step explanation:
A rectangle has a base length of 14 inches and an unknown height, h. The area of the rectangle is less than 56 square inches.
Which inequality represents the possible values of h, the height of the rectangle?
on-14> 56
14-h <56
14h> 56
14h <56
Answer:
14h <56
Step-by-step explanation:
The area of a rectangle is given by
A =bh
We know the area is less the 56
bh <56
The base length is 14
14h <56
Answer:
D
Step-by-step explanation:
i got this question right on edgeinuity
In each function, x is the horizontal distance the ball travels in meters, and y
represents the height.
Whose soccer ball reaches a greater height?
Soccer ball reaches its highest position when its equation turns from positive slope to zero and then negative. Mathematically it is where the derivative of the its function equals to zero. so:
d(-3x^2 + 6x + 3) / dx = -6x + 6
-6x + 6 = 0 -> x = 1 ->
[tex]y = 6[/tex]
it seems Paige's ball reaches higher than Viaola's with only 6 meters height.
The point slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y-1=1/4(x-12) what is the standard formula equation for this line?
Answer:
x - 4y = 8Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
============================================
We have the points (-4, -3) and (12, 1).
Substitute:
[tex]m=d\frac{1-(-3)}{12-(-4)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]
Put the volume of a slope and the coordinates of the point (12, 1) to the equation of a line:
[tex]y-1=\dfrac{1}{4}(x-12)[/tex]
The standard formula of an equation of a line:
[tex]Ax+By=C[/tex]
Convert:
[tex]y-1=\dfrac{1}{4}(x-12)[/tex] multiply both sides by 4
[tex]4y-4=x-12[/tex] add 4 to both sides
[tex]4y=x-8[/tex] subtract x from both sides
[tex]-x+4y=-8[/tex] change the signs
[tex]x-4y=8[/tex]
Find the coordinates when the parallel lines AB and PQ are reflected over the x-axis. The points are A(1, 1), B(1,4), and
P(3, 1). Q(3, 4).
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Hence
A(1, 1 ) →A'(1, - 1 )
B(1, 4 ) → B'(1, - 4 )
P(3, 1 ) → P'(3, - 1 )
Q(3, 4 ) → Q'(3, - 4 )
I Need The Answer Plz Geometry Is Hard!!!
Answer:
∠F = 106°
Step-by-step explanation:
The opposite angles of a parallelogram are congruent, hence
∠F = ∠J = 106°
(3 1/6 - 1 5/8) divided by (8 3/4 - 1.35)
The answer to the given expression when [3(1/6) - 1(5/8)] divided by [8{3/4} - 1.35) will be equal to 0.00896.
Convert mixed numbers to fractions:
[tex]3(\frac{1}{6}) = \frac{(3 \times 6 + 1) }{6} = \frac{19 }{ 6}\\\\8(\frac{3}{4}) = \frac{(8 \times 4 + 3) }{ 4} = \frac{35 }{ 4}[/tex]
Substitute the fractions into the expression:
[tex]\frac{[ (\frac{19}{6}) - 1(\frac{5}{8}) ] }{ [ (\frac{35}{4}) - 1.35 ]}[/tex]
Simplify the expression:
Numerator:
Common denominator for (19/6) and (5/8) is 24
19/6 - 1(5/8) = (19/6) - (15/8) = (19*4 - 6*15)/24 = 1/24
Denominator:
Convert 1.35 to fraction: 1.35 = 135/100 = 27/20
Common denominator for (35/4) and (27/20) is 20
(35/4) - 1.35 = (35/4) - (27/20) = (35 * 5 - 27 * 1) / 20 = 123/20
Divide the numerator and denominator by their greatest common divisor (GCD):
GCD(1, 24) = 1
GCD(123, 20) = 1
Simplify the expression:
[tex]\frac{(\frac{1 }{ 24}) }{ (\frac{123 }{ 20})}\\\\ = \frac{1 }{ \frac{24 \times 123 }{ 20}}\\\\ = \frac{1 }{ 111.6}[/tex]
1 / 111.6 ≈ 0.00896
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Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM.
Answer:
1. W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3. E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.O(10,1),P(6,7),Q(14,9) and R(16,7).
Step-by-step explanation:
We are given that a quadrilateral JKLM with vertices J(8,4),K(4,10),L(12,12) and M(14,10)
We have to match a quadrilateral with its correct transformation of given quadrilateral JKLM
1.a transformation 3 units down and 3 units left
By using transformation rule [tex](x,y)\rightarrow (x-3,y-3)[/tex]
The new vertices of quadrilateral is (5,1), (1,7),(9,9) and (11,7).
Hence, the quadrilateral WXYZ with vertices W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A sequence of reflection across x- axis and y-axis in order
Reflection across x- axis
The transformation rule [tex](x,y)\rightarrow (x,-y)[/tex]
By using this rule
The vertices of quadrilateral are (8,-4),(4,-10),(12,-12) and (14,-10).
After the reflection across y- axis
The transformations rule
[tex](x,y)\rightarrow (-x,y)[/tex]
By using this rule
We get the new vertices of quadrilateral are (-8,-4),(-4,-10),(-12,-12) and (-14,-10).
Hence, the quadrilateral ABCD with vertices A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3.a translation 3 unit left and 2 units up
The transformation rule [tex](x,y)\rightarrow (x-3,y+2)[/tex]
By using this rule
The new vertices are (5,6),(1,12),(9,14) and (11,12).
Hence, the quadrilateral EFGH with vertices E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.a translation 2 units right and 3 units down
The transformation rule
[tex](x,y)\rightarrow (x+2,y-3)[/tex]
By using this rule
The new vertices are (10,1),(6,7),(14,9) and (16,7)
Hence, the quadrilateral OPQR with vertices O(10,1),P(6,7),Q(14,9) and R(16,7).
Evaluate the expression, given functions f,g, and h:
Answer:
-1
Step-by-step explanation:
So you are asked to find 3f(1)-4g(-2).
In order to find this you must first find f(1) and g(-2).
So f(1) means what is the value of the expression 3x-2 for when x=1.
f(1)=3(1)-2
f(1)=3-2
f(1)=1
And g(-2) mean what is the value of the expression 5-x^2 for when x=-2.
g(-2)=5-(-2)^2
g(-2)=5-(4)
g(-2)=5-4
g(-2)=1
So both of those function values were 1.
Our problem of 3f(1)-4g(-2) becomes 3(1)-4(1)=3-4=-1.
If h(x) is the inverse of f(x), what is the value of h(f(x))?
оо
0 1
ООО
o f(x)
Answer:
x.
Step-by-step explanation:
If h(x) is the inverse of f(x) them h(f(x)) = x.
If h(x) is the inverse of f(x) then the the value of h(f(x)) is x.
What is a function?A relation is a function if it has only One y-value for each x-value.
The inverse function of a function f is a function that undoes the operation of f.
If h(x) is the inverse of f(x), then by definition we have:
h(f(x)) = x
This is because the composition of h and f is the identity function, which means that applying h to f(x) gives us back x.
Therefore, the value of h(f(x)) is x.
Hence, If h(x) is the inverse of f(x) then the the value of h(f(x)) is x.
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What is the vertex form of y=x^2-6x+6
[tex]y=x^2-6x+6\\y=x^2-6x+9-3\\y=(x-3)^2-3[/tex]
The vertex form of the quadratic equation is y = (x-3)^2 + 3.
Explanation:The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. To convert the quadratic equation y = x^2-6x+6 into vertex form, we need to complete the square.
First, let's group the terms with x together: y = (x^2-6x) + 6.To complete the square, take half the coefficient of x (-6), square it (-6/2)^2 = 9, and add it inside the parentheses: y = (x^2-6x+9) - 9 + 6.Simplify the equation: y = (x-3)^2 + 3. This gives us the vertex form of the quadratic equation.Learn more about Vertex form of quadratic equation here:https://brainly.com/question/31546205
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When figures (including points) are rotated 270° counterclockwise about the origin, it is also the same rotating figures clockwise by what other degree amount? Please help!
Answer: 90 degrees.
Step-by-step explanation: since 360 degrees is a whole circle, subtract 360 from 270 to get 90 degrees.
Drag the titles to the boxes to form correct pairs .not all titles will be used. Match the pairs of equation that represents concentric circles. Pleaseeeeeeee help
Answer:
The concentric circles are
[tex]3x^{2}+3y^{2}+12x-6y-21=0[/tex] and [tex]4x^{2}+4y^{2}+16x-8y-308=0[/tex]
[tex]5x^{2}+5y^{2}-30x+20y-10=0[/tex] and [tex]3x^{2}+3y^{2}-18x+12y-81=0[/tex]
[tex]4x^{2}+4y^{2}-16x+24y-28=0[/tex] and [tex]2x^{2}+2y^{2}-8x+12y-40=0[/tex]
[tex]x^{2}+y^{2}-2x+8y-13=0[/tex] and [tex]5x^{2}+5y^{2}-10x+40y-75=0[/tex]
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
where
(h,k) is the center and r is the radius
Remember that
Concentric circles, are circles that have the same center
so
Convert each equation in standard form and then compare the centers
The complete answer in the attached document
Part 1) we have
[tex]3x^{2}+3y^{2}+12x-6y-21=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](3x^{2}+12x)+(3y^{2}-6y)=21[/tex]
Factor the leading coefficient of each expression
[tex]3(x^{2}+4x)+3(y^{2}-2y)=21[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]3(x^{2}+4x+4)+3(y^{2}-2y+1)=21+12+3[/tex]
[tex]3(x^{2}+4x+4)+3(y^{2}-2y+1)=36[/tex]
Rewrite as perfect squares
[tex]3(x+2)^{2}+3(y-1)^{2}=36[/tex]
[tex](x+2)^{2}+(y-1)^{2}=12[/tex]
therefore
The center is the point (-2,1)
Part 2) we have
[tex]5x^{2}+5y^{2}-30x+20y-10=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](5x^{2}-30x)+(5y^{2}+20y)=10[/tex]
Factor the leading coefficient of each expression
[tex]5(x^{2}-6x)+5(y^{2}+4y)=10[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]5(x^{2}-6x+9)+5(y^{2}+4y+4)=10+45+20[/tex]
[tex]5(x^{2}-6x+9)+5(y^{2}+4y+4)=75[/tex]
Rewrite as perfect squares
[tex]5(x-3)^{2}+5(y+2)^{2}=75[/tex]
[tex](x-3)^{2}+(y+2)^{2}=15[/tex]
therefore
The center is the point (3,-2)
Part 3) we have
[tex]x^{2}+y^{2}-12x-8y-100=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-12x)+(y^{2}-8y)=100[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}-12x+36)+(y^{2}-8y+16)=100+36+16[/tex]
[tex](x^{2}-12x+36)+(y^{2}-8y+16)=152[/tex]
Rewrite as perfect squares
[tex](x-6)^{2}+(y-4)^{2}=152[/tex]
therefore
The center is the point (6,4)
Part 4) we have
[tex]4x^{2}+4y^{2}-16x+24y-28=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](4x^{2}-16x)+(4y^{2}+24y)=28[/tex]
Factor the leading coefficient of each expression
[tex]4(x^{2}-4x)+4(y^{2}+6y)=28[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]4(x^{2}-4x+4)+4(y^{2}+6y+9)=28+16+36[/tex]
[tex]4(x^{2}-4x+4)+4(y^{2}+6y+9)=80[/tex]
Rewrite as perfect squares
[tex]4(x-2)^{2}+4(y+3)^{2}=80[/tex]
[tex](x-2)^{2}+(y+3)^{2}=20[/tex]
therefore
The center is the point (2,-3)
Part 5) we have
[tex]x^{2}+y^{2}-2x+8y-13=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-2x)+(y^{2}+8y)=13[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}-2x+1)+(y^{2}+8y+16)=13+1+16[/tex]
[tex](x^{2}-2x+1)+(y^{2}+8y+16)=30[/tex]
Rewrite as perfect squares
[tex](x-1)^{2}+(y+4)^{2}=30[/tex]
therefore
The center is the point (1,-4)
Part 6) we have
[tex]5x^{2}+5y^{2}-10x+40y-75=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](5x^{2}-10x)+(5y^{2}+40y)=75[/tex]
Factor the leading coefficient of each expression
[tex]5(x^{2}-2x)+5(y^{2}+8y)=75[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]5(x^{2}-2x+1)+5(y^{2}+8y+16)=75+5+80[/tex]
[tex]5(x^{2}-2x+1)+5(y^{2}+8y+16)=160[/tex]
Rewrite as perfect squares
[tex]5(x-1)^{2}+5(y+4)^{2}=160[/tex]
[tex](x-1)^{2}+(y+4)^{2}=32[/tex]
therefore
The center is the point (1,-4)
Part 7) we have
[tex]4x^{2}+4y^{2}+16x-8y-308=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](4x^{2}+16x)+(4y^{2}-8y)=308[/tex]
Factor the leading coefficient of each expression
[tex]4(x^{2}+4x)+4(y^{2}-2y)=308[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]4(x^{2}+4x+4)+4(y^{2}-2y+1)=308+16+4[/tex]
[tex]4(x^{2}+4x+4)+4(y^{2}-2y+1)=328[/tex]
Rewrite as perfect squares
[tex]4(x+2)^{2}+4(y-1)^{2}=328[/tex]
[tex](x+2)^{2}+(y-1)^{2}=82[/tex]
therefore
The center is the point (-2,1)
Part 8) Part 9) and Part 10) in the attached document
18 is what percent of 24?
The number 18 expressed as a percentage of 24 is; 75%
To determine what percentage of 24 is 18;
We must evaluate the percentage as follows;
(18/24) × 100%= 0.75 × 100%= 75%Read more;
https://brainly.com/question/2236179
Find the equation of the line through (2,9)(1,6)(-7,-6)
Answer:
y=(3/2)x+6
If your equation is in a different form, let me know.
Step-by-step explanation:
So the slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
Parallel lines have the same slope, m (different y-intercept (b) though).
So we need to find the slope going through (1,6) and (-7,-6).
To do this you could use [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Or, what I like to do is line the points up vertically and subtract vertically then put 2nd difference over first difference. Like so:
( 1 , 6)
-( -7, -6)
---------------
8 12
So the slope of our line is 12/8.
Let's reduce it! Both numerator and denominator are divisible by 4 so divide top and bottom by 4 giving 3/2.
Again parallel lines have the same slope.
So we know the line we are looking for is in the form y=(3/2)x+b where we don't know the y-intercept (b) yet.
But we do know a point (x,y)=(2,9) that should be on our line.
So let's plug it in to find b.
y=(3/2)x+b with (x,y)=(2,9)
9=(3/2)2+b
9=3 +b
Subtract 3 on both sides:
9-3=b
6=b
So the equation in slope intercept form is y=(3/2)x+6