The negative solution of the given statement is - 4.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the unknown number be 'n'.
∴ When 32 is subtracted from the square of a number, is n² - 32 and the result is 4 times the number which is equal to 4n,
So, n² - 32 = 4n.
n² - 4n - 32 = 0.
n² - 8n + 4n - 32 = 0.
n(n - 8) + 4(n - 9) = 0.
(n - 8)(n + 4) = 0.
n - 8 = 0 Or n + 4 = 0.
n = 8 Or n = - 4.
So, the negative solution is - 4,
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Points F, Q, and D are coplanar.
We can find whether three points are coplanar by using vector approach.
What is Coplanar?In geometry, a of group points in space are coplanar if there exists a geometric plane that contains them all. For instance, three points are always coplanar, and if the points are distinct and non-collinear, the plane they exist is unique.
We can check whether the given point F,Q and P are coplanar by first forming vectors of the each given point. The vector form for general point (a,b,c) can be written as [tex]a\hat{i}+b\hat{j}+c\hat{k}[/tex].
The vector forms of point F,Q and P can be given as 'f', 'q' and 'p'. The scalar triple product of the vectors 'f', 'q' and 'p' can be found out by finding the scalar product of vector 'f' with the cross product of the vectors 'q' and 'p' .
For the points F,Q and P to be coplanar the triple scalar product must be zero else the points are not coplanar.
This implies f·(q×p)=0 must be satisfied for three points to lie on the same plane.
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The correct question is " How can you say points F, Q and D are coplanar?"
For each equation, find the center and radius of the circle.
(x+3)²+(y-5)²=81
The equation of the circle (x + 3)^2 + (y - 5)^2 = 81 has a radius of 9 and a center located at (3 , 5).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 3)^2 + (y - 5)^2 = 81, is in standard form, then
h = -3
k = 5
r = 9
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Work out the length x in the triangle below.
If your answer is a decimal, give it to 1 d.p.
area = 26 m²
13 m
x
30°
PLEASE HELP WITH THIS QUESTION!!
Answer:
x = 8
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] absinC
where a and b are 2 sides of the triangle and C the angle between them
here a = 13 , b = x , C = 30° and A = 26 , then
[tex]\frac{1}{2}[/tex] × 13 × x × sin30° = 26 ( multiply both sides by 2 to clear the fraction )
13x × sin30° = 52 ( using the exact value of sin30° = [tex]\frac{1}{2}[/tex] )
13x × [tex]\frac{1}{2}[/tex] = 52 ( multiply both sides by 2 to clear the fraction )
13x = 104 ( divide both sides by 13 )
x = 8
Use the principle of superpositinn to explain why two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Angle is mistaken because triangles of two pairs of congruent sides and one pair of congruent angles do not always satisfy the SAS criterion.
What do we mean by the congruency of a triangle?If all three corresponding sides are equal as well as all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned. Two triangles are congruent if they satisfy the five congruence conditions. There are five of them: side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).In the given situation:
Angle is incorrect because triangles with two congruent sides and one congruent angle do not always satisfy the SAS criterion.Therefore, the angle is mistaken because triangles of two pairs of congruent sides and one pair of congruent angles do not always satisfy the SAS criterion.
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Find an explicit relation between x and y in the form f(x,y)=1 by eliminating the parameter
The explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.
Given that x=2sin, y=2cos, and 0 are constants,
Simplify the parametric functions that are presented. Add their squares after taking them. The following trigonometric identity can be used:
sin2θ+cos2θ=1sin2θ+cos2θ=1
x=2sinθ,
y=2cosθ,0≤θ≤2πsinθ
=x2cosθ,
=y2x
Y=2sinθ,
y=2cosθ,0≤θ≤2πsinθ=x2cosθ=y2
Square them now and add them:
(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)
(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)
A parameter in a parametric equation can stand in for anything, including an angle. When a parameter is an angle—as opposed to a non-angle parameter—the plane curve can be graphed by choosing values for the angle and computing the x- and y-values.
Hence, the explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.
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6
The endpoints of AB are -16 and -4. Find the coordinate of the point P that partitions the segment in
the ratio 2 : 1.
The coordinate of point P is
The coordinate of point P is -8.
We are given that the endpoints of AB are -16 and -4.
This means that A is at -16 and B is at -4
Therefore, the total length of the line AB will be-
-16 - (-4) = -12 units
But since length cannot be negative, we take only the absolute value, the length of AB comes out to be 12 units.
Now, point P divides AB in the ratio 2:1
The length of these two parts will be
12 × 2/3 and 12 x 1/3
= 8 units and 4 units
This means that AP = 8 units and PB = 4 units
Hence the coordinate of P will be (-16 + 8) or (-4 - 4)
Thus, the coordinate of point P is -8.
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Write an algebraic expression that models each situation.
You had 250 minutes left on your cell phone, and you talk an hour a week.
If you had 250 minutes left on your cell phone and you talk an hour a week, then the algebraic expression is 250-60x
Given,
The conditions
You had 250 minutes left on your cell phone You talk an hour a weekConsider the number of weeks as x
We know 1 hour = 60 minutes
Then, the algebraic expression = 250-60x
Hence, if you had 250 minutes left on your cell phone and you talk an hour a week, then the algebraic expression is 250-60x
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ALGEBRA Which equation is equivalent to 7 x-3(2-5 x)=8 x ?
F 2 x-6=8
G 22 x-6=8 x
H -8 x-6=8 x
J 22 x+6=8 x
According to this the given equation the correct option is G. 22x - 6 = 8x
What precisely is algebra?Algebra is a field of mathematics that aids in the depiction of issues or situations using mathematical expressions. To construct a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division.
What is the primary goal of algebra?Algebra is a generalized version of arithmetic in which variables stand in for nonspecific numbers. Its objective seems to be to solve algebraic equations including equation systems.
According to given data:The equation is = 7x-3(2-5x)=8x
Now simplifying the equation:
7x-3(2-5x)=8x
7x - 6 + 15x = 8x
22x - 6 = 8x
According to this the correct option is G. 22x - 6 = 8x
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A circle whose center is at (1, -3) passes through the point (7, 5). whats the radius?
The distance from the center to any point on the circle exists comprehended as the radius. The radius is 10cm.
What defines the radius of a circle?The radius of a circle is the separation between any two points on the circle and its center. The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it.
The distance along a line connecting a circle's center to a point on its perimeter is known as a circle's radius. Therefore, the radius is equal to half the diameter's length. Therefore, the radius is equal to half the diameter's length.
The radius of a circle is the separation between any two points on the circle and its center.
In this instance (using the Pythagorean Theorem)
r = [tex]\sqrt{(7-1)^{2}+(5-(-3))^{2} }[/tex]
= √(36 + 64)
r = 10
If a circle whose center is at (1, -3) passes through the point (7, 5) then the radius of the circle exists 10.
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At a swim meet, the order of the divers is randomly selected. If there are 12 divers, what is the probability that Danielle, Nora, and Li will dive first, second, and third, respectively?
The probability that Danielle, Nora, and Li will dive first, second, and third, respectively is 1/1320.
Since we are provided that in the meet, the orders of the drivers are randomly selected so, the total number of drivers is: 12
let A be the event in that Danielle was the first to dive.
B be the event that Nora been the second to dive.
and C is the event that Li has been the third to dive into.
P(A), probability of Danielle to dive first = 1/12
P(B), probability of Nora to dive second = 1/11
and P(C), probability of Li to dive in third = 1/10
So, the total probability that Danielle, Nora, and Li will dive first, second, and third, respectively = P(A) x P(B) x P(C)
= 1/12 x 1/11 x 1/10
= 1/ 1320
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Plane P contains lines a and b. Line c intersects plane P at point J.
Lines a and bare parallel, lines a and care skew, and lines band care not skew.
Draw a figure based upon this description.
Step-by-step explanation:
you cant make things in brainly
Write an equation of a parabola with vertex at the origin and the given focus.
focus at (0,7)
The equation that defines the parabola with vertex at the point (0, 0) and focus at (0, 7) is:
y = x²/28
A parabola is a quadratic function that can move on any axis, it is composed of:
vertexfocal axisdirectrixThe equation that defines a parabola can be given by:
(x - h)² = 4p(y - k)(y - k)² = 4p(x - h)This will depend on its aperture
In this case we have the vertex of the parabola at the point (0, 0) and the focus at the point (0, 7) this is displaced on the y-axis upward, so the parabola is of the form y = x²
(x - 0)² = 4p(y - 0)
Focus
f = (0, 0 + p)
0 + p = 7p = 0 + 7p= 7(x- 0)² = 4*7(y - 0)
(x - 0)² = 28(y - 0)
y = x²/28
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Tell whether each equation is in slope-intercept, point-slope, or standard form.
a. y+2=-2(x-1)
y+2=-2(x-1) is in point-slope form, it is neither in slope-intercept form nor standard form.
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope.
We know that point-slope form = y₂ - y₁ = m(x₂ - x₁)
the equation looks like this in point-slope form ⇒ y-(-2)= -2(x-1)
Here, the points are (x, y) and the points the line is passing through is
(1, -2)
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List all of the factors of 45 in pairs that
produce 45.
45: [?], [ ],
least
greatest
Remember that
every number has a
factor of 1!
Left Box (green)
[ ], [ ], [?]
least greatest
What number can
be multiplied by 1
to produce 45?
Right Box (yellow)
Enter
Determine the solutions of the equation: absolute value of the quantity one fourth times x plus 7 end quantity minus 3 equals 24. x = −136 and x = 136 x = −136 and x = 80 x = −112 and x = 80 x = −80 and x = 80
The solutions are x = 80 and x = -136
Given equation is [tex]|\frac{x}{4}+7|-3=24[/tex].
We need to solve for x.
Absolute value function is given by, [tex]|x| = \left \{ {{x\ if\ x\geq 0} \atop {-x\ if\ x < 0}} \right.[/tex]
So the equation may have two solutions.
We use the property of absolute value to solve [tex]|\frac{x}{4}+7|-3=24[/tex]
⇒ [tex](\frac{x}{4}+7)-3=24[/tex] and [tex]-(\frac{x}{4}+7)-3=24[/tex]
⇒ [tex](\frac{x}{4}+7)=27[/tex] and [tex](\frac{x}{4}+7)=-27[/tex]
⇒ [tex]\frac{x}{4}=20[/tex] and [tex]\frac{x}{4}=-34[/tex]
⇒ x = 80 and x = -136
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Answer:
The solutions are x = 80 and x = -136
Step-by-step explanation:
What are the solutions to the system of equations?
y = x² - 3
x - y = 1
Answer: x has no solutions, y has no solutions
Step-by-step explanation:
y = x² - 3
x - y = 1
x - x² - 3 = 1
- x² - x - 3 = 1
- x² - x - 4 = 0
- x² - x - 16/4 = 0
- x² - x - 1/4 - 15/4 = 0
- (x² + x + 1/4) - 15/4 = 0
- (x+1/2)^2 - 15/4 = 0
- (x+1/2)^2 = 15/4
(x+1/2)^2 = -15/4 ==> x has no solutions, y has no solutions
any number to an even power, in this case to the power of 2, has to be positive, but -15/4 is negative.
Find the length of a segment ab but a= -7 and b=9
The length of a segment ab is 16 units.
Given that, a= -7 and b=9.
We need to find the length of a segment ab.
What is a line segment?In geometry, a line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.
The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimetres (cm), millimetres (mm) or by conventional units like feet or inches.
Now, the length of a segment ab=a+b
=7+9=16
Therefore, the length of a segment ab is 16 units.
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Pls help for brainly 2 Figure JKLMN is reflected across the x-axis to form figure J'K'L'M'N'.
4
-6 <-4 -2 o
J
2
M'
4
M
6
N
8
Decide if each statement about figures JKLMN and J'K'L'M'N' is true or false.
Choose True or False for each statement.
a. The y-coordinate of J' is the
opposite of the y-coordinate of J.
b. L' is located at (-3,-4).
c. N and N' both are at the same
distance from the y-axis.
d. L' is located 3 units above the x-axis.
True False
OOOO
O
OO
O
50
Turn in 0. = AA
Page
The result of true and false is-
a) True: J and J' are opposite of y axis.
b) False: Location of L' is (-3, -4).
c) True: N and N' are at same distance.
d) False: L' is at 3 unit above x axis.
What is defined as the reflection on coordinates?The x-coordinates of a point remain constant when it is reflected across the X-axis. However, the Y-coordinates are changed into their inverse signs. As a result, the X-axis reflection of a point (x, y) is (x, -y).As per the given graph;
Part a: True: J and J' are opposite of y axis.
It is clear from the graph that J and J' lies on the opposite side of Y-axis.
The coordinate of J = (2, -6) and J' = (2, 6).
Part b: False: The location of L' is not (-3, -4)
The correct Location of L' is (3, 4) as seen from the graph.
Part c: True: N and N' are at same distance.
The coordinates of N and N' are (5, -5) and (5, 5).
Thus, they are at the same distance from the both axis.
Part d: False: L' is at 3 unit above x axis.
Point L' lies at the distance of 4 units from the x axis.
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Armando leans an 18 -foot ladder against the side of his house to clean out the gutters. The base of the ladder is 5 feet from the wall. How high up the side of the house does the ladder reach? Express your answer in feet, rounded to the nearest tenth.
The height of house to ladder reach is 17 ft
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
Given data; ladder = 18 ft
The base = 5 ft
In order to find out the height of house.
we know this is triangle shape so we apply here so we consider here x is ladder and y is base and z is height
By pythagoras theorem;
z² + y² = x²
z² = x² -y²
Then put value
z² = 18² - 5²
z² = 299
z = 17.29
z = 17
Therefore, the height of house to ladder reach is 17 ft
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Between 11 P.M. and 8:20 A.M., the water level in a swimming pool decreased by 4/9 in . Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
That means that each hour it drops about 0.0625 inches
Divide the decrease in water level by the length of the time interval.
decrease = 7/12 inches ≅ 0.583 inches
Time interval: From 11 pm to 8:20 am you have 9:20 hours = (9 + 20/60) hours ≅ 9.33 hours
So the water drops at a rate of about
0.583/9.33 inches/hour ≅ 0.0625 inches/hour
Therefore, each hour it drops about 0.0625 inches.
The rate constant, or the specific rate constant, is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.The rate constant is a proportionality factor in the rate law of chemical kinetics that relates the molar concentration of reactants to reaction rate. It is also known as the reaction rate constant or reaction rate coefficient and is indicated in an equation by the letter k.
Rate constant is dependent on the temperature. For zero-order reaction, rate constant's unit is mol L - 1 s - 1 . For first-order reaction, rate constant's unit is . For second-order reaction, rate constant's unit is mol - 1 L s - 1 .
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Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
15,20,24
The following set of numbers 15, 20, and 24 can be the measures of the sides of an acute triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 15, b = 20, and c = 24
a + b > c 15 + 20 > 24 35 > 24 True
a + c > b 15 + 24 > 20 39 > 20 True
b + c > a 20 + 24 > 15 44 > 15 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
15^2 + 20^2 = 625
2. Compare it to the square of the largest side.
24^2 = 576
625 > 576
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 15, 20, and 24 can be the measure of the sides of an acute triangle.
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An item sold for $500. three years later it was only worth $10. how much is the annual depreciation rate
The annual depreciation rate is $163.33.
Depreciation rate is calculated using the formula
Annual Depreciation Rate =(Total Depreciable Cost)/(time) ..where time is in years.
In the given Question
The original cost of item = $500
Cost of item after 3 years = $10
Total Depreciable Cost = (original cost of item) -(Cost of item after 3 years)
=500-10
=$490
So,
Annual Depreciation Amount = (Total Depreciable Cost)/(time)
Annual Depreciation Amount =490/3=163.33
Hence, the item cost would depreciate $163.33 per year.
which means every year the amount will depreciate by $163.33
Therefore, the annual depreciation rate is $163.33 .
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Use your results from Exercises 1-6 to determine whether the given measures define 0 , 1,2, or infinitely many acute triangles. Justify your answers.
a=10, b=10, m
An unlimited number of acute triangles can be formed from two sides without an angle measurement, such as a = 10 m and b = 10 m.
As an illustration -
If our side lengths are 10m and 10m, and our angle value goes from 0 to 90 degrees, how many different acute triangles can we create?
Construct a triangle with sides of 10 and 10 metres, an angle of 45 degrees, and a third side that can be extended to the desired length. You have built a triangle.
By changing the third side's length and angle, we can make a whole different triangle that is identical to this one.
Never forget to choose the side lengths and angles. There is a suggestion that you might decide to take a different step. The same angles can be used to make an unlimited number of different triangles.
As a result, with a single angle and a single side length, we can create an endless number of triangles.
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Match each expression with its translation.
1. 4 d
2. y-4
3. 4+x
4. 4÷n
NEXT ESTION
udentAssignment/index?eh-1005519587#
ASK FOR HELP
four divided by a number
four added to a number
the product of a number and four
the difference between a number
and four
Answer:
Step-by-step explanation:
division is ÷
addition is +
product is the word for the answer of multiplying numbers together
difference is the word for the answer of subtracting numbers
in this problem, any variable is called a number.
4 d : this is the product. you can write 4 x d, but a shortcut is to exclude the multiplication
y - 4 : this is subtraction, so the difference
4 + x : this is addition
4 ÷ n : this is division
Which equation is correct
a) 2 + 3 x 4 = 14
b) 2 + 3 x 4 = 20
Answer:
A. Is the correct answer
Step-by-step explanation:
Step 1: Multiply (3 x 4 = 12)
Step 2: Add (12 + 2 = 14)
I hope i was able to help you out :)
Identify the location of point P under translation (x+3, y+1) .
A. (0,6)
B. (0,3)
C. (2,-4)
D. (2,4)
The location of point P under the translation is (2, 4)
How to identify the location of point P under the translation?The complete question is added as an attachment
The location of point P is
P = (-1, 3)
The translation is given as:
(x+3, y+1)
So, we have
P' =(-1 + 3, 3 + 1)
Evaluate
P' = (2, 4)
Hence, the location of point P under the translation is (2, 4)
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ALGEBRA The measure of the larger acute angle in a right triangle is two degrees less than three times the measure of the smaller acute angle. Find the measure of each angle.
The measure of each angle is 23 degrees, 67 degrees, and 90 degrees.
What is Acute angle ?The acute angle can be defined as the angle less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle.
What is a Right triangle ?Right triangle is also known as right angled triangle. If a triangle has atleast one 90° angle then the triangle is said to be a right angled triangle. A right angle triangle always follows the Pythagoras theorem.
Now, According to statement given :
Let smaller acute angle = x,
and measure of larger acute angle = 3x-2
Since, it is right triangle the acute angles must be complementary
x + (3x-2) = 90
4x - 2 = 90
4x = 92
x = 23
i.e. smaller acute angle is 23
now second angle = 3x-2 = 3(23) - 2 = 67
and third angle is 90 , as this is a right angled triangle.
Thus, The measurement of each angle is 23 degrees, 67 degrees, and 90 degrees.
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I need help I don’t get it
Answer:
Step-by-step explanation:
Perimeter = 2(l + w)
Area = l x w
l = 6 - 3 = 3 (Difference in x cords from A to B)
w = 5 - (-1) = 6 (Difference in y cords from A to C)
Perimeter = 2(3 + 6) = 18 units
Area = 3 x 6 = 18 square units
Compare the two numbers. Use > or < .
4, √12
The value of √12 is equals to 3.46, and the number 4 is larger than the number 3.46.
What does "square root" mean?The square root of a number x in mathematics is a number y whose square (the result of multiplying the number by itself, or y y), equals x.The radicand is the expression (or number) whose square root is being considered.The phrase or number in this instance that appears under the radical sign is known as the radicand, and it is 9.Square roots of negative integers can be discussed in relation to complex numbers.In any circumstance where the idea of an object's "square" is stated, square roots can be considered more generally.These include, among other things, function spaces and square matrices.The value of √12 = 3.46, and the number 4 is larger than the number 3.46.
Therefore, 4 > √12.
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Select the reason that best supports statement 7
Answer:
C because ur adding
