Step-by-step explanation:
y = 15 + x or x = y-15
and x sum to <= 85
x + y <= 85
(y-15) + y <= 85
2y <= 100
y <= 50 The maximum value of y is 50 minimum would be 16 ( since it must be 15 greater than a positive number x (which would be 1 ))
please help, 6 possible outcomes
Answer: Landing on X and heads, landing on Y and heads, landing on Z and heads, landing on X and tails, landing on Y and tails, landing on Z and tails
Step-by-step explanation:
There are three possible spinner options and 2 possible coin options. 3 * 2 = 6, leading to 6 possible outcomes.
The spinner could land on X, Y, or Z.
The coin could land on heads or tails.
If we type out all of these possibilities (each spinner section and heads, each spinner section and tails) we end up with;
➜ Landing on X and heads
➜ Landing on Y and heads
➜ Landing on Z and heads
➜ Landing on X and tails
➜ Landing on Y and tails
➜ Landing on Z and tails
Find the missing angles using trigonometry
The value of x is 24.426 degrees when the opposite side is 9 and adjacent side is 20 and value of x is 58.211 degrees degrees when the adjacent side is 17 and hypotenuse is 32
In the given triangle
We have to find the missing angle x
By tan function we know that tan is a ratio opposite side and adjacent side
tanx=9/20
tanx=0.45
x=tan⁻¹(0.45)
x=24.426 degrees
For example 2, we find x by using cosine function which is a ratio of adjacent side and hypotenuse
cosx=17/32
cosx=0.53
x=cos⁻¹(0.53)
x=58.211 degrees
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Please help me with these geometry questions
Answer:
a. 30 b. indeterminate, unless you're given the measure of either of the other sides.
Step-by-step explanation:
a. lazy solution: it's a 3-4-5 right triangle scaled up (18 is 3*6, 24 is 4*6, last side will be 5*6= 30. Less than lazy solution: it's a right triangle, pythagorean theorem applies:
[tex]x^2= 18^2+24^2 = 324+576 = 900\\x= 30[/tex]
b.problem is indeterminate as long as you don't know the measure of any of the other sides. the 30-60 triangle is half of an equilateral triangle and x is [tex]\sqrt3[/tex] times the short side, or [tex]\frac{\sqrt3} 2[/tex] times the long side. It's easily shown by mirroring the triangle along the vertical side, and if the short leg measures k, the hypotenuse measures 2k, and the vertical side measures [tex]x^2+k^2=(2k)^2\\x^2+k^2 = 4k^2\\x^2 = 3k^2 \implies x=\sqrt3\ k[/tex]
How do I find x? Please explain the process.
X=90 ....angles in a semi-circle
Angle B=A ...Radii
When simplifying a rational expression in the form ( a − b ) / ( a + b ), it always equals - 1.
True or False
The statement that the rational expression ( a − b ) / ( a + b ) always equals -1 is incorrect, it does not hold true for all values of a and b. Only specific values that satisfy ( a - b ) = -( a + b ) will lead to the result -1.
Explanation:The statement in the question is not correct. That is, it is False. The rational expression in the form ( a − b ) / ( a + b ) does not always equal - 1. For example, if a = 5 and b = 3, the rational expression ( a − b ) / ( a + b ) becomes ( 5 - 3 ) / ( 5 + 3 ), which evaluates to 2 / 8 = 0.25, not -1. The statement would only be true if (a - b) = -(a + b), which is not an assumption we can make for all values of a and b. So, while simplifying a rational expression it is necessary to substitute the values and check it out.
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In circle J with m/HJK = 48 and HJ = 11 units, find the length of arc HK.
Round to the nearest hundredth.
H
K
The length of arc HK is approximately 3.86 units.
To find the length of arc HK, we need to know the circumference of circle J.
The formula for the circumference of a circle is C = 2πr,
where C is the circumference and r is the radius.
Since we don't have the radius directly given, we can find it using the given information.
We know that the measure of angle HJK is 48 degrees, and HJ is 11 units. The angle at the center of a circle is twice the angle at the circumference that intercepts the same arc.
Therefore, angle HJK at the center of the circle intercepts an arc HK with the same measure.
So, the circumference of the circle is C = 2πr = 2π(11 units).
To find the length of arc HK, we need to find the fraction of the circumference represented by the angle HJK.
We know that the total angle at the center of a circle is 360 degrees (the full circumference), so the fraction of the circumference represented by angle HJK is 48/360.
The length of arc HK is then calculated by multiplying the fraction of the circumference represented by the angle HJK by the total circumference of the circle:
Arc HK = [tex](48/360) \times 2\pi (11 units)[/tex]
Calculating this value, we get:
Arc HK ≈[tex](48/360) \times 2 \pi \times 11[/tex] ≈ 1.234π
To find the numerical value, we can approximate π as 3.14:
Arc HK ≈[tex]1.234 \times 3.14[/tex] ≈ 3.86 units (rounded to the nearest hundredth)
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Help me out cause im so lost
1). 140cm²
2). angle QRT
3). angle ACB= 65°
4). radian measure of d°
Describe the relationship between the data points in the following scatter plot:
Positive Linear Relationship
Negative Linear Relationship
Nonlinear Relationship
No Relationship
Answer:
You have not provided a scatter plot for me to analyze. A scatter plot is a graph that shows the relationship between two variables by plotting data points on a coordinate plane. The relationship between the data points can be positive linear, negative linear, or nonlinear, or there may be no relationship. To determine the type of relationship between the data points in a scatter plot, I would need to see the plot itself. Could you please provide the scatter plot that you would like me to analyze?
MARK AS BRAINLIEST!!!
3x, 3x+7,4x,5x-8 What is the value of x
Hello
What is the value of x?^
[tex]\frac{3x}{4x} = \frac{3x+7}{5x-8} \\\\\frac{3}{4} = \frac{3x+7}{5x-8}\\\\\frac{3}{4}(5x-8) = 3x+7\\\\\frac{3(5x-8)}{4} = 3x + 7\\\\\frac{15x-24}{4} = 3x + 7\\\\15x - 24 = 4(3x + 7)\\\\15x - 24 = 12x + 28\\\\15x - 12x = 28 + 24\\\\3x = 52\\\\\boxed{x = 52/3}[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeee
Answer: All of the values for x would make the equation FALSE.
Step-by-step explanation:
To see if each value would fit x for this equation, we will need to check each of them.
If you said x = 1 would fit this equation, it would be 7 < 3 - 1. This would be false because when you evaluate this equation, it would be 2 is greater or equal to 7 which isn't true.
If you said x = 5 would fit this equation, it would be 7 < 3 - 5. This would be false because when you evaluate this equation, it would be -2 is greater or equal to 7 which also isn't true.
If you said x = -3 would fit this equation, it would be 7 < 3 - -3. This would be false because when you evaluate this equation, it would be 6 is greater or equal to 7 which is really close, but it isn't true.
Therefore, none of these values for x would fit this equation at all in any way. The value of x would have to be -4 or more to make this statement true. Hope this helps!
-From a Fifth Grade Honors Student
which point from the equation would you use? y-7=3(x+9)
Another point on the line is (-9, 7). Ultimately, the choice of which point to use depends on the context or specific requirements of the problem you are solving.
To determine which point to use from the equation y - 7 = 3(x + 9), we need more information.
The equation provided represents a linear equation in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Without additional context or specific instructions, we can choose any point that satisfies the equation to use as a reference.
For example, if we let x = 0, we can solve the equation for y:
y - 7 = 3(0 + 9)
y - 7 = 3(9)
y - 7 = 27
y = 27 + 7
y = 34
So, one point on the line is (0, 34).
Alternatively, if we let x = -9, we can solve the equation for y:
y - 7 = 3(-9 + 9)
y - 7 = 3(0)
y - 7 = 0
y = 7
So, another point on the line is (-9, 7).
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Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee.
In the given diagram, we have a pair of parallel lines intersected by a transversal line. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by parallel lines and a transversal.
From the diagram, we can observe the following angle relationships:
Angle A is alternate interior to the angle (4x - 10)°.
Therefore, we can write: A = (4x - 10)°.
Angle B is corresponding to the angle (4x - 10)°.
Therefore, we can write: B = (4x - 10)°.
Angle C is alternate interior to the angle 2x°.
Therefore, we can write: C = 2x°.
Angle D is corresponding to the angle 2x°.
Therefore, we can write: D = 2x°.
Since the sum of angles in a straight line is 180°, we can set up the equation:
A + B + C + D = 180°
Substituting the known values, we get:
(4x - 10)° + (4x - 10)° + 2x° + 2x° = 180°
Simplifying the equation, we can solve for x:
8x - 20 + 4x + 4x = 180
16x - 20 = 180
16x = 200
x = 12.5
Therefore, the value of x is 12.5.
Please note that this solution assumes the given diagram accurately represents the angle relationships.
If the three digits of a three-digit number are multiplied ou get 135. Which result to you get, by adding the three digits?
Answer:
Let's call the three digits of the three-digit number "a", "b", and "c". Since the product of the digits is 135, we know that:
a * b * c = 135
We need to find the value of a + b + c. One way to approach this is to try out different combinations of digits that multiply to 135 and see which one adds up to the correct sum. The possible combinations are:
1 * 3 * 45 = 135 -> 1 + 3 + 45 = 49
1 * 5 * 27 = 135 -> 1 + 5 + 27 = 33
1 * 9 * 15 = 135 -> 1 + 9 + 15 = 25
3 * 5 * 9 = 135 -> 3 + 5 + 9 = 17
So, the only combination of digits that adds up to a three-digit number is 1, 3, and 45, which add up to 49. Therefore, the answer is 49.
FIGURE A FIGURE B FIGURE C FIGURE D 2.1.1. Calculate the area of figure A 2.1.2. Calculate the area of figure 2.1.3. Calculate the area of figure C
D
Answer:
Step-by-step explanation:FIGURE A FIGURE B FIGURE C FIGURE D 2.1.1. Calculate the area of figure A 2.1.2. Calculate the area of figure 2.1.3. Calculate the area of figure C
Sure, here are the calculations for the area of each figure:
Figure A is a rectangle with a length of 4 cm and a width of 3 cm. The area of a rectangle is calculated by multiplying the length and the width, so the area of Figure A is 4×3=12 square centimeters.
Figure B is a triangle with a base of 4 cm and a height of 3 cm. The area of a triangle is calculated by multiplying the base and the height and dividing by 2, so the area of Figure B is (4×3)/2=6 square centimeters.
Figure C is a trapezoid with a top base of 4 cm, a bottom base of 6 cm, and a height of 3 cm. The area of a trapezoid is calculated by averaging the top and bottom bases and multiplying by the height, so the area of Figure C is (4+6)/2×3=15 square centimeters.
Figure D is a circle with a radius of 2 cm. The area of a circle is calculated by multiplying the square of the radius by π, so the area of Figure D is 2
2
π=4π square centimeters.
1. Write down the next three numbers and describe each pattern: b) 1; 8; 15; 22; c) 7; 9; 8; 10; 9:0 a) 3; 6; 9; 12; d) 4; 1; 16; 1; 64; 1; e) 2; 4; 8; 16; 32; f) 3; 9; 27; 81; 2. Draw the next diagram in each pattern. Explain the rule. a) b) P 3. The diagrams below show artwork that the Nguni people paint c their houses. Describe the pattern in the sequence of artwork.
I cannot describe the pattern in the sequence of artwork without visual representation.
Let's analyze each pattern:
The pattern appears to be adding 7 to each number to get the next number.
The next three numbers would be:
29, 36, 43.
The pattern alternates between adding 2 and subtracting 1.
The next three numbers would be:
11, 10, 12.
The pattern increments by 3 each time.
The next three numbers would be:
15, 18, 21.
The pattern alternates between squaring and taking the square root of the previous number.
The next three numbers would be:
1, 8, 1.
The pattern doubles each time.
The next three numbers would be:
64, 128, 256.
The pattern multiplies each number by 3 to get the next number.
The next three numbers would be:
243, 729, 2187.
As a text-based AI model, I am unable to draw diagrams.
I can describe the next diagram in each pattern:
The next diagram would consist of three rows, each containing four dots arranged in a square.
The next diagram would consist of a single dot positioned 7 units below the bottom dot of the previous diagram.
The next diagram would consist of two vertical lines with three dots each.
The next diagram would consist of a single dot positioned 4 units above the top dot of the previous diagram.
The next diagram would consist of a row of six dots arranged in a straight line.
The next diagram would consist of four rows, each containing three dots arranged in a square.
A text-based AI model, I am unable to see or analyze images or diagrams.
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Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.
There exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2.
To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use the concept of the longest path in a tree and the properties of odd integers.
First, let's consider the longest path in the tree T.
Since the tree has n vertices, the longest path can have at most n-1 edges.
Let's denote this longest path as P.
Since n is an odd integer, we have n = 2k + 1, where k is a non-negative integer.
This implies that n-1 = 2k, which is an even number.
Now, consider the middle vertex x of the longest path P.
If P has an odd number of vertices, then x is unique.
If P has an even number of vertices, then there are two possible middle vertices, but we can choose any one of them.
Next, let's consider the distance between v and x along the longest path P. Since x is the middle vertex, this distance can be at most (n-1)/2.
This is because the longest path P divides the tree into two parts, each containing (n-1)/2 vertices at most.
Now, let's consider the subtree rooted at x, which consists of all vertices that can be reached from x.
Since the distance between v and x is at most (n-1)/2, it implies that v is within this subtree.
Therefore, we have found a vertex u (in this case, x) in the subtree rooted at x such that the distance between u and v is at most (n-1)/2.
By proving the existence of such a vertex u, we have shown that for any vertex v in the tree T, there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.
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For this question “ followed by a number will mean to the power of.
I need the solution for x,y, and z with steps please
(3*5)”4*(2*3)”5*(2*5)”7= 2”x*3”y*5”z
Please and thank you
The solution for x, y, and z is x = 2, y = 2, and z = 2.
To solve the equation (35)"4(23)"5(25)"7 = 2"x3"y*5"z, let's break it down step by step:
Simplify the expressions within the parentheses using the power of operator ("^").
[tex](35)"4 = 15^4\\(23)"5 = 6^5\\(2\times5)"7 = 10^7[/tex]
Apply the power rule of exponents, which states that [tex](a^b)^c = a^{(b\times c).[/tex]
[tex]15^4 \times 6^5 \times 10^7 = (15610)^{(4+5+7)[/tex]
Simplify the expression within the parentheses.
[tex](15610)^{16 }= 900^{16[/tex]
Express both sides of the equation in terms of prime factors.
[tex]900 = 2^2 \times 3^2 \times 5^2[/tex]
quate the powers of the prime factors on both sides of the equation.
[tex]2^2 \times 3^2 \times 5^2 = 2"x \times 3"y \times 5"z[/tex]
From this, we can conclude that x = 2, y = 2, and z = 2.
Therefore, the solution for x, y, and z is x = 2, y = 2, and z = 2.
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Randall has been practicing his conversions. He said 40 cm is 400 m. Use reasoning to explain why his conversion is incorrect.
six ordered pairs of f(x)=-x^2+3x+2
The six ordered pairs for the function f(x) = -x^2 + 3x + 2 are:
(-2, -8), (-1, -2), (0, 2), (1, 4), (2, 4), (3, 2).
To find six ordered pairs for the function [tex]f(x) = -x^2 + 3x + 2[/tex], we can substitute different x-values into the function and evaluate the corresponding y-values.
Let's choose six x-values and calculate the corresponding y-values:
When x = -2:
[tex]f(-2) = -(-2)^2 + 3(-2) + 2 = -4 - 6 + 2 = -8[/tex]
Therefore, the ordered pair is (-2, -8).
When x = -1:
[tex]f(-1) = -(-1)^2 + 3(-1) + 2 = -1 - 3 + 2 = -2[/tex]
Therefore, the ordered pair is (-1, -2).
When x = 0:
[tex]f(0) = -(0)^2 + 3(0) + 2 = 0 + 0 + 2 = 2[/tex]
Therefore, the ordered pair is (0, 2).
When x = 1:
[tex]f(1) = -(1)^2 + 3(1) + 2 = -1 + 3 + 2 = 4[/tex]
Therefore, the ordered pair is (1, 4).
When x = 2:
[tex]f(2) = -(2)^2 + 3(2) + 2 = -4 + 6 + 2 = 4[/tex]
Therefore, the ordered pair is (2, 4).
When x = 3:
[tex]f(3) = -(3)^2 + 3(3) + 2 = -9 + 9 + 2 = 2[/tex]
Therefore, the ordered pair is (3, 2).
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Mrs. Matthews came up with an expression. Holly and Jim wrote the expression in their notebooks in order to simplify the expression. They compared their expressions.
Holly's expression is equal to 864, and Jim's expression is equal to 36. So, Jim's expression is 828 less than the other expression.
How to simplify expressions?Holly's notebook:
6 × (24 ÷ 2)²
= 6 × (12)²
= 6 × 144
= 864
Jim's notebook:
6 × 24 ÷ 2²
= 6 × 24 ÷ 4
using PEMDAS
P = parenthesis
E = exponents
M = multiplication
D = Division
A = Addition
S = Subtraction
6 × 24 ÷ 4
= 144 ÷ 4
= 36
Therefore, Jim's expression is less than Holly's expression.
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Classify the polynomial by degree and number of terms: 3x ^ 4 - 3x ^ 2 - 7x
Cubic Binomial
Quintic Trinomial
Cubic Trinomial
Quartic Trinomial
The polynomial 3x^4 - 3x^2 - 7x is classified as a Cubic Trinomial.
The polynomial 3x^4 - 3x^2 - 7x can be classified as a Cubic Trinomial.
Here's the breakdown of the classification:
Degree: The highest power of the variable x is 4, so the degree of the polynomial is 4. Since the degree is 4, the polynomial is not cubic (which would have a degree of 3) or quintic (which would have a degree of 5).
Number of terms: The polynomial consists of three terms: 3x^4, -3x^2, and -7x. A polynomial with three terms is called a trinomial.
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Answer:Quartic trinomial
Step-by-step explanation:
Don't listen to the other guy, I put cubic and I got the answer wrong thanks to the other guy.
Please help i need this done as soon as possible will mark brainly!!!!!!!!
The number 5730 represents
(**the number of years it takes for half of the carbon-14 to decay.**)
It is the half-life of carbon-14, which is the amount of time it takes for half of the substance to undergo radioactive decay.
A salad dressing is made by mixing lemon juice and vinegar in the ratio of 4 : 3. Vicky makes 700ml of the salad dressing. How much lemon juice does she use?
Answer:
Vicky uses 400 ml of lemon juice in the salad dressing.
Find a measure of angle cbd in regular octagon ABCDEFGH
The measure of angle cbd in regular octagon ABCDEFGH is 22.5°.
We are given that;
The octagon ABCDEFGH
Now,
To find the measure of angle CBD. Since ABCDEFGH is a regular octagon, triangle BCD is an isosceles triangle with BC = BD2. Therefore, the base angles of triangle BCD are congruent and have the same measure. Let x be the measure of angle CBD. Then, we have:
x + x + 135° = 180° (sum of angles in a triangle)
2x + 135° = 180°
2x = 180° - 135°
2x = 45°
x = 45°÷2
x = 22.5°
Therefore, by the angle the answer will be 22.5°.
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Please help i havent been able to get this for so long
Answer:
A) AAS
B) HL
C) SSS
E) SAS
Step-by-step explanation:
We cannot prove the triangles congruent by AAS because we would need another angle pair that is congruent to each other.
We can prove the triangles congruent by HL because the pairs of hypotenuses and shorter legs are shown to be congruent to each other.
We can prove the triangles are congruent by SSS because every side is congruent to its respective pair.
We cannot prove the triangles congruent by HA because we would need another angle pair that is congruent to each other, like with AAS.
We can prove the triangles are congruent by SAS because two pairs of sides in addition to their respective included angles (the right angles) are congruent to each other.
We cannot prove the triangles congruent by LA because we would need to know by the given information that ∠B≅∠E, but it's not provided.
Therefore, A, B, C, and E are the correct answers.
Area + Arc length equations of a circle, can someone help me out with this problem
To find the area of a sector, you can use the formula A = (θ/2π) × πr^2 = (θ/2) × r^2.
The area of a circle is given by the equation A = πr^2, where r is the radius of the circle. The arc length of a circle is given by the equation L = rθ, where θ is the central angle in radians and r is the radius of the circle.
To find the arc length of a portion of a circle, you can use the formula L = (θ/2π) × 2πr = (θ/2π) × C, where C is the circumference of the circle. This formula is useful when you have a fraction of a circle, such as a sector.
These equations are fundamental in geometry and are used in many applications such as architecture, engineering, and physics.
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Which linear graph represents a proportional relationship? a graph of a line that passes through the points 0 comma 2.5 and 1 comma 4 a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1 a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 1 a graph of a line that passes through the points 0 comma negative 3 and negative 1 comma negative 2 Question 13(Multiple Choice Worth 2 points)
The linear graph that represents a proportional relationship is the graph that passes through the origin, which is the second option;
A graph that passes through the points (0, 0), (4, -1)
What is a proportional relationship?A proportional relationship is one in which the output value is a multiple of the input value, such that, the graph passes through the origin.
The options in the question are;
The first option; A graph that passes through the points (0, 2.5), (1, 4)
The second option; A graph that passes through the points (0, 0), (4, -1)
The third option; A graph that passes through the points (0, -1), (1, -1)
The fourth option; A graph that passes through the points (0, -3), (1, -2)
The first option; A graph that passes through the points (0, 2.5), (1, 4)
A proportional relationship is a function of the form; y ∝ x
y = k·x
k = y/x
The graph of a function that has a proportional relationship, passes through the point (0, 0), therefore, the option that represents a function that is a proportional relationship is the second option, such that we get;
The ratio of proportionality, k = -1/4
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A man wants to borrow $125,000 for 30 years. He will pay 8.5% interest. What will be his monthly payments?
a) $961.25
b) $1231.25
c) $1080
d) $1085
it will be A .......................................
Given the inscribed polygon, find the value of both x .and y.
X =
y =
please help!!!
can someone help me solve this
Solution of expression 12 - |2x + 15| > 3 are,
⇒ - 12 < x < 3
And, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,
⇒ x ∈ [2, ∞) - {i, - i}
We have to given that;
Expressions are,
⇒ 12 - |2x + 15| > 3
And, (x - 3)² - x² + 3)/ (x² + 1) ≥ 0
Now, We can simplify as;
⇒ 12 - |2x + 15| > 3
⇒ 12 - 3 > |2x + 15|
⇒ 9 > |2x + 15|
⇒ |2x + 15| < 9
⇒ - 9 < 2x + 15 < 9
This gives,
⇒ - 9 < 2x + 15
⇒ - 9 - 15 < 2x
⇒ - 24 < 2x
⇒ - 12 < x
And, 2x + 15 < 9
⇒ 2x < 15 - 9
⇒ 2x < 6
⇒ x < 3
Hence, Solution of expression 12 - |2x + 15| > 3 are,
⇒ - 12 < x < 3
And, Simplify the expressions ,
⇒ (x - 3)² - x² + 3)/ (x² + 1) ≥ 0
⇒ (x - 3)² - x² + 3) ≥ 0
⇒ x² + 9 - 6x - x² + 3 ≥ 0
⇒ 12 - 6x ≥ 0
⇒ 12 ≥ 6x
⇒ 2 ≥ x
Hence, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,
⇒ x ∈ [2, ∞) - {i, - i}
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