Answer:
Option a represents a proportional relationship.
Step-by-step explanation:
A proportional relationship is a relationship where two variables are directly related to one another, meaning that their ratio is always the same. In other words, when one variable changes, the other variable also changes in the same ratio.
In the equation y = 2/3 * x, the value of y is directly proportional to the value of x, meaning that for every change in x, the corresponding change in y will always be 2/3 of that change. This is because the coefficient of x is a constant value, in this case 2/3. Therefore, as x increases or decreases, y will also increase or decrease at the same rate in proportion to x.
Option a represents a direct proportion.
Option b, c, and d are not proportional relationships because they include a constant or an operation like subtraction, addition or negative sign.
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a) Can a 3 × 4 matrix have independent columns? Independent rows? Explain.
b) If A is 4 × 3 and rank A = 2, can A have independent columns? Independent rows? Explain.
c) If A is an m × n matrix and rank A = m, show that m ≤ n.
d) Can a nonsquare matrix have its rows independent and its columns independent? Explain.
e) Can the null space of a 3 × 6 matrix have dimension 2? Explain.
f) Suppose that A is 5 × 4 and null(A) = x for some column x ≠ 0. Can dim(im A) = 2?
A) A 3 × 4 matrix can have independent columns but not independent rows.
B) A 3 × 4 matrix can have independent columns but not independent rows.
C) If A is an mxn matrix and rank A = m, it follows that m ≤ n.
D) A nonsquare matrix can have its rows independent.
E) The null space of a 3 × 6 matrix cannot have dimension 2.
F) If A is 5x4 and null(A) = x for some column x ≠ 0, dim(im A) cannot be 2.
Matrix Linear Independence RulesA) A 3 × 4 matrix can have independent columns but not independent rows. This is because a column vector can be linearly independent, meaning no linear combination of other columns in the matrix can create it, but a row vector can't be linearly independent because it can always be written as a linear combination of the columns.
B) If A is 4 × 3 and rank A = 2, it cannot have independent columns but it can have independent rows. This is because if rank A = 2, the number of linearly independent columns is 2, which is less than the number of columns, meaning that not all columns can be linearly independent. However, since rank A = 2, the number of linearly independent rows is also 2, which is less than the number of rows, meaning that some rows can be linearly independent.
C) If A is an mxn matrix and rank A = m, it follows that m ≤ n. This is because the rank of a matrix is the maximum number of linearly independent columns, which cannot be greater than the number of columns.
D) A nonsquare matrix can have its rows independent and its columns independent, as long as the number of rows is not equal to the number of columns.
E) The null space of a 3 × 6 matrix cannot have dimension 2. This is because the dimension of the null space is always less than or equal to the number of columns of the matrix, which is 6 in this case.
F) If A is 5x4 and null(A) = x for some column x ≠ 0, dim(im A) cannot be 2. This is because the dimension of the image of A is equal to the rank of A, which cannot be less than the dimension of the null space. Therefore, dim(im A) must be greater than or equal to the dimension of the null space, which is at least 1.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
9
Step-by-step explanation:
the square of 3 is 9
3 + 3 + 3 = 9
Next Finding the Reciprocal: Mastery Test Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Find the reciprocal of 4/5
The numerator is 3 and the denominator is 5. IN order to determine the reciprocal 4 becomes the denominator and 5 becomes the numerator. The reciprocal is 5/4.
What is Reciprocal?The definition of reciprocal in mathematics is the inverse of a value or a number. If n is a real number, then 1/n will be n's reciprocal. Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9. The result of multiplying a number by its reciprocal now equals one. Inverse multiplicative is another name for it. The Latin word "reciprocus," which means "returning," is where the word "reciprocal" originated. Therefore, if we take the reciprocal of an inverted number, it returns its original value. This article will teach you how to find the reciprocal of numbers, fractions, and decimals with multiple factors.
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Elias is adding and. He finds the lcd to be 10t2 and uses multiplication to find equivalent expressions. Which is the sum of ?.
The LCD (Least Common Denominator) of 10t2 is 10t2. To determine the equivalent expression is the sum of the fractions is 8t2.
A/B = C/D
Where A and B are the two fractions, and C and D are the equivalent fractions.
We will use this formula to determine the equivalent expression of the given fractions:
3t/20 = C/10t2
We can solve for C by multiplying both sides by 10t2, yielding:
30t2/20 = C/10t2
We can solve for C by multiplying both sides by 10t2, yielding:
30t2/20 = C/10t2
We can then simplify by cancelling out the 10t2 on the denominator, yielding:
C = 30t2/20
The equivalent expression for the given fractions is therefore 30t2/20.
To find the sum of the fractions, we first need to convert all fractions to equivalent fractions with a common denominator. In this case, the LCD is 10t2.
The equivalent expressions for the fractions are therefore:
3t/20 + 5/10t2 = 30t2/20 + 50/10t2
The sum of the fractions is then the sum of the numerators divided by the denominator, or:
30t2/20 + 50/10t2 = 80t2/10t2
We can simplify this expression by cancelling out the 10t2 on the denominator, yielding:
80t2/10t2 = 8t2
Therefore, the sum of the fractions is 8t2.
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The sum of 14t/10t^2 + (5t^2 + 40t)/10t^2 is (5t^2 + 54t)/10t^2
In this question we have been given that Elias is adding 7t/5t^2 and (t + 8)/2t
He finds the least common divisor (LCD) of 7t/5t^2 and (t + 8)/2t which 10t^2
He uses multiplication to find an equivalent expression.
7t/5t^2 = 7t/5t^2 * 2/2
= 14t/10t^2
and (t + 8)/2t = ((t + 8) * 5t)/(2t * 5t)
= (5t^2 + 40t)/10t^2
We need to find the sum 14t/10t^2 + (5t^2 + 40t)/10t^2
We know that if the base of two rational expressions a/b and c/b then the denominator of the result is same and we just add numerators i.e., a/b + c/b = (a + c)/b
So, 14t/10t^2 + (5t^2 + 40t)/10t^2
= [14t + (5t^2 + 40t)]/10t^2
= (5t^2 + 54t)/10t^2
Hence, 14t/10t^2 + (5t^2 + 40t)/10t^2 = (5t^2 + 54t)/10t^2
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complete the problems using synthetic division
Answer:
Step-by-step explanation:
Write k for the divisor.
Write the coefficients of the dividend.
Bring the leading coefficient down.
Multiply the leading coefficient by k.
Add the terms of the second column.
Multiply the result by k.
Repeat steps 5 and 6 for the remaining columns.
PLEASE HELP
The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ft, the liquid boils at 197.04°F. At an altitude of 4500 ft, the liquid boils at 202.8°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2300 ft?
Write an equation.
b= ??
The equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet is b = -0.0016a + 210
The boiling point of the liquid at 2300 ft is 206.32°F
How to determine the equation giving the boiling point b of the liquidFrom the question, we have the following parameters that can be used in our computation:
At an altitude of 8100 ft, the liquid boils at 197.04°F. At an altitude of 4500 ft, the liquid boils at 202.8°FThese parameters mean that
(a, b) = (8100, 197.04) and (4500, 202.8)
The relationship is a linear equation
So, we have
slope = (b2 - b1)/(a2 - a1)
Substitute the known values in the above equation, so, we have the following representation
slope = (202.8 - 197.04)/(4500 - 8100)
Evaluate
slope = -0.0016
The equation is then represented as
b = slope * a + c
Using one of the points, we have
197.04 = -0.0016 * 8100 + c
So, we have
197.04 = -12.96 + c
Evaluate
c = 210
This gives
b = -0.0016a + 210
What is the boiling point of the liquid at 2300 ft?This means that
a = 2300
So, we have
b = -0.0016 * 2300 + 210
Evaluate
b = 206.32
Hence, the boiling point is 206.32°F
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quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (4, -4)(4,−4). What is the vertex of the function defined as g(x)=f(x-2)g(x)=f(x−2)?
The vertex of the translated quadratic equation is:
(6, -4)
What is the vertex of the translated function?We know that we have a quadratic function f(x), such that the vertex is at (4, -4).
Here we have the translated function:
g(x) = f(x - 2)
Notice that this is a translation of 2 units to the right
Now, remember that the vertex of f(x) is at f(4), then the vertex of g(x) is at the value of x such that:
x - 2 = 4
x = 4 + 2
x = 6
So the vertex of g(x) is (6, -4)
(the y-value of the vertex does not change).
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SOMEONE PLEASE HELP ME. 20 POINTS PLEASE
Answer:
dupăStep-by-step explanation:
Este o rochie bleumarin[tex](4x^{2}-9y^{2})^3+(9y^{2} -16y^{2} )^3+(16z^{2} -4x^{2})^3/(2x-3y)^3+(3y-4z)^3+(4z-2x)^3[/tex]
The algebraic expression -
{ (4x² - 9y²)³ + (9y² - 16y²)³ + (16z² - 4x²)³ } / { (2x - 3y)³ + (3y - 4z)³ + (4z - 2x)³ } is simplified to give
undefinedHow to simplify the given expressionThe given algebraic expression is in fraction and we solve by breaking the fraction in to two: numerator and denominator and solve separately then bring them together.
The numerator
= (4x² - 9y²)³ + (9y² - 16y²)³ + (16z² - 4x²)³
bringing the powers together
= (4x² - 9y² + 9y² - 16y² + 16z² - 4x²)³
collecting like terms together
= (4x² - 4x² - 9y² + 9y² - 16y² + 16z² )³
= (0x² - 16y² + 16z² )³
= (16y² + 16z² )³
The denominator
= (2x - 3y)³ + (3y - 4z)³ + (4z - 2x)³
bringing the powers together
= (2x - 3y + 3y - 4z + 4z - 2x)³
collecting like terms
= (2x - 2x - 3y + 3y - 4z + 4z )³
= (0x - 0y - 0z )³
= 0
with a denominator of zero the solution is undefined, this may mean infinite many solutions
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The slope of the line that passes through the points \left( 2 , 3 \right) {and} \ \left( 5 , 9 \right)(2,3) and (5,9) is
Answer:
so here you'll get the formula
Slope (m) = y2 - y1 / x2 -x1
answer will be 2
correct if I'm wrong
Which of these relationships is a function?
The 3rd graph has a relationships which is a function as a vertical can be drawn through any point and it only intersects once.
What is function?A function is a particular kind of relationship in which inputs are mapped to just one output. Consider a function as a machine for useful insight. The domain of the function, which describes the types of input that the machine will accept, states that it will produce one and only one output for each input.
A function's fundamental notation is of the form f ( x), where x is the input variable and f is the function's name. "F of X" should be read as this. Any time you see this notation, f(x) generally refers to a function's output, though these letters are subject to change.
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Given right triangles efg and hjk. find the value of a that satisfies the congruency of the triangles. in two or more complete sentences, explain the relevance between the congruency of the triangles and the calculations made in finding the value of a.
The given triangles GEF and HKJ are congruent by the AAA test of congruency and the value of a = √2.
The two triangles are proved to be congruent and the value of a is to be determined.
Both triangles are right-angled triangles.
We know that similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
In triangle GEF,
since the sum of the angles in a triangle is 180
∠ G + ∠ F + ∠ E =180
90 + 45 + E = 180
∠ E = 45
similarly, ∠ J = 45
In Triangle GEF and Triangle HKJ,
∠ G = ∠ K (both are 90)
∠ F = ∠ H (both are 45)
∠ E = ∠ J (both are 45)
So, Triangle GEF and Triangle HKJ are congruent triangles by AAA congruency.
Now in triangle GEF,
cos 45 = 3a/6
1/√2 = a/2
a = √2
Thus, the given triangles are congruent by AAA . and the value of a = √2.
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The complete question is -
Given right triangles EFG and HJK. find the value of a that satisfies the congruency of the triangles. in two or more complete sentences, explain the relevance between the congruency of the triangles and the calculations made in finding the value of a.
The radius of a basketball hoop is 9 inches. Which expression can be used to find the
hoop's circumference in inches?
Answer:
C = 2πr, where C is the circumference, π is the mathematical constant pi (approx. 3.14), and r is the radius (9 inches). Therefore, the circumference of the basketball hoop is 2π(9) = 18π inches.
Step-by-step explanation:
In other words use C=2*pi*radius to find the circumference, here you are given the radius is 9 so when you plug that in it gives you a circumfrence of 18pi inches. Hope this helps!
can someone answer this question really quick
The expression 2.4x−3.9y−1.2x+ay is equivalent to 1.2x+1.2y.
What is the value of a?
Enter your answer as a decimal, like this: 42.5
Answer:
[tex]a=5.1[/tex]
Step-by-step explanation:
[tex]2.4x-1.2x-3.9y+ay=1.2x+y(a-3.9) \\ \\ \implies 1.2=a-3.9 \implies a=5.1[/tex]
can someone answer all that's question....I really² need the answer
1.
In the triangle that contains x (call the other 2 angles as a and b, where a is the angle that is supplemetary to the center angle.)
a = 180 - 110 = 70 (supplemetary angles add up to 180)
b = 30 (b and the angle measures 30 are in the same segment.)
-> x = 180 - 70 - 30 = 80.
2. In triangle PRT, v = 180 - 40 - 70 = 70.
Since P,Q,S,T all lies on the circumference, PQST is a cyclic quadrilateral.
-> w = 180 - PQS = 180 - (180 - 70) = 70.
3.
i) A 1:2 scale means that all sides of P must be shortened by twice the lengths.
Since D is the only shape with the sides shortened from P, it's the correct option.
ii) A 1:1/2 scale means that all sides of P must be enlarged by twice the lengths.
Therefore, the measures of the sides become sqrt(20),6,4,6 (clockwise from diagonal), which is B.
4. Using the Pythagoras' theorem, we can find the hypotenuse PR : [tex]\sqrt{12^{2} + 5^{2} } = 13[/tex]
sin(x) = QP/PR = 5/13 = 0.385 (rounded to 3 d.p)
tan(y) = QP/QR = 5/12 = 0.417 (rounded to 3 d.p)
A pizza is an example of a circular object. For each part of the circle in the table, provide a description of where you see that part in the pizza. A pizza cut into 8 slices.
For each part of the circle in the table, provide a description of where you see that part in the pizza is given below.
What is circle?A circle is a shape that has no sides or corners and is made up of only one curved line, which forms a perfect loop. It is the most basic and fundamental shape in geometry, and is used to create many other shapes, such as squares, rectangles, and triangles. It is also an important symbol in many cultures and religions, representing the cycle of life, eternity, and unity.
1. Arc: The arc is the curved edge of the pizza, starting at one end and ending at the other. This part can be seen along the outer circumference of the pizza.
2. Diameter: The diameter is the length of a straight line that passes through the center of the pizza and connects two opposite points on the circumference. It is the longest line that can be drawn on the pizza.
3. Radius: The radius is the distance from the center of the pizza to any point on the circumference. It is half the length of the diameter.
4. Chord: A chord is a straight line that connects two points on the circumference of the pizza.
5. Sector: A sector is a section of the pizza that is created when two radii are drawn from the center of the pizza to two points on the circumference.
6. Segment: A segment is a section of the pizza created when a chord is drawn between two points on the circumference.
7. Central Angle: A central angle is an angle formed by two radii drawn from the center of the pizza to two points on the circumference.
8. Circumference: The circumference is the outermost edge of the pizza. It is the line that forms the boundary between the inside and outside of the pizza.
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A. use this function to answer questions a-d f(x)=3x^3-7x^2-14x 24 using the fundamental theorem of algebra. how many possible complex roots with this polynomial have? explain. b. using descartes rule determine how many possible positive roots and how many possible negative roots this function will have c. use the same function f(x)=3x^3-7x^2-14x 24 using the rational roots theorem list all the possible rational roots for the function d. using possible roots you found on the previous question find all the possible zeros for this function (hint: you will use remainder theorem and synthetic division)
Answer:
Below in bold.
Step-by-step explanation:
I have assumed that it's + 24.
a. This is a cubic expression (highest power is 3).
By the theorem there are 3 roots with 2 possible complex roots.
b. f(x) = 3x^3-7x^2-14x+ 24
Using Descartes Rule of signs, the signs from left to right are:
+ - - +
Here there are 2 sign changes (+ - and - +)
So, the maximum number of positive real roots is 2.
f(-x)= 3(-x)^3 - 7(-x)^2 - 14(-x) + 24
Sign changes are:
- - + +
There is one change of sign so maximum number of possible negative real roots is 1.
c. Using the Rational roots theorem, the list of all possible rational roots is:
+/- (factors of 24 / factors of 3)
= +/- [1, 2, 3, 4, 6, 8, 12, 24) / (1, 3) ]
= +/- 1, +/-2, +/-3, +/- 4, +/-6, +/-12, +/- 8, +/-24, +/- 1/3, +/-2/3, +/-4/3, +/-8/3
d. Possible roots, using the Remainder theorem:
x = 1:
f(1) = 3 - 7 - 14 + 24 = 8 so 1 is not a root
f(-1) = 28 - so x = -1 not a root
f(2) = -8 so 2 not a root
f(-2) = 0 So, x = -2 is a root
So, x + 2 is a factor of f(x) so we divide
x + 2)3x^3 - 7x^2 - 14x + 24(3x^2 - 13x + 12 <--- Quotient
3x^3 + 6x^2
- 13x^2 - 14x
- 13x^2 - 26x
12x + 24
12x + 24
..............
So, we solve the following equation to find the other 2 roots:
3x^2 - 13x + 12 = 0
3x^2 - 9x - 4x + 12 = 0
3x(x - 3) - 4(x - 3) = 0
3x - 4 = 0 or x - 3 = 0
x = 4/3, 3.
The 3 roots are -2, 4/3, 3.
factorise x^2 + 3x - 54
The factorization of the quadratic equation:
x^2 + 3x - 54
Is (x + 9)*(x - 6).
How to factorize the expression?To factorize the quadratic equation we first need to find the roots:
x^2 + 3x - 54 = 0
Using the quadratic formula we will get:
[tex]x = \frac{-3 \pm \sqrt{3^2 - 4*1*(-54)} }{2} \\\\x = \frac{-3 \pm15 }{2}[/tex]
So the two roots are:
x = (-3 - 15)/2 = -18/2 = -9x = (-3 + 15)/2 = 12/2 = 6Then the factorized form of the quadratic equation is:
(x - (-9))*(x - 6)
(x + 9)*(x - 6)
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f(x) = 2x² + 4x - 5
g(x) = 6x³2x² + 3
Find (f + g)(x).
O A. (f+g)(x) = -6x³+4x² + 4x - 8
O B. (f+g)(x) = 6x² + 4x - 2
O C. (f+g)(x) = 6x³ - x² + 4x - 2
OD. (f+g)(x) = 8x³ + 2x - 2
If functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8
What is a function?A relation is a function if it has only One y-value for each x-value.
The given two functions are f(x) = 2x² + 4x - 5
and g(x) = - 6x³+2x² - 3
We need to find (f + g)(x).
(f + g)(x)=f(x)+g(x)
=2x² + 4x - 5 - 6x³+ 2x² -3
Now add the like terms
= 6x³+ 4x² +4x-8
(f + g)(x)=6x³+ 4x² +4x-8
Hence, if functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8
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Please help asap please I will make you the brainliest
Answer:
d= Deondre's age
d + 3
c = the number of people in the class
1/2c
w = wildcat's score
a = away team's score
w = 2a + 7
c = cost of the sweater
s = the regular cost of the sweater
c = 1/2s
y = total in the bank
x = number of weeks
y = 75x + 300
y = altitude
x = number of minutes
y = 200x + 1000
Step-by-step explanation:
Which of the following is divisible by 3?A. 1432B. 2132C. 2331D. 1453
PLEASE HELP WILL GIVE BRAINLIEST TO THE ANSWER THAT MAKES THE MOST SENSE
Answer:
go right 2 up 1 starting at (0,0)
Step-by-step explanation:
Find the length of the missing side in simplest radical form.
Answer: The best I could come up with is √65, −√65 or, 1, you pick!
(Decimal: 8.06225774…, −8.06225774…)
Step-by-step explanation:
Rewrite the equation as
x^2 = 8^2 + 1^2.
One to any power is one.
x^2 = 8^2 + 1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
x = ± √8^2 + 1
x = ± √64 + 1
Add 64 and 1.
x = ± √65
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
x = √65
Next, use the negative value of the ± to find the second solution.
x = −√65
The complete solution is the result of both the positive and negative portions of the solution.
x = √65, −√65
The result can be shown in multiple forms.
Exact Form:
x = √65, −√65
Decimal Form:
x = 8.06225774..., −8.06225774…
Answer:
[tex]x=\sqrt{65}[/tex]----------------------------
Given a right triangle with the missing hypotenuse.
Use Pythagorean to find the missing side:
[tex]x = \sqrt{8^2+1^2}=\sqrt{64+1} =\sqrt{65}[/tex]in a lottery drawing, tickets will be drawn randomly out of a hat. if 1/10 of the tickets in the hat are green. 1/2 of them are white, 1/4 of them are blue, and the remaining 30 tickets are pink, what is the number of blue tickets in the hat
The number of blue tickets is 50 tickets. The result is obtained by using the concept of operation with fractions.
How to add or subtract fractions?Find the least common denominator.Write the equivalent fraction with the least common denominator.Add or subtract the nominator without changing the denominator.In a hat, we have:
1/10 of the tickets are green.1/2 of the tickets are white.1/4 of the tickets are blue.The remaining, 30 tickets are pink.Find the number of blue tickets!
Let's say all tickets is a. Then,
Green tickets = 1/10 aWhite tickets = 1/2 aBlue tickets = 1/4 aThe remaining section (pink tickets) is
= 1 - (green + white + blue) tickets
= 1 - (1/10 + 1/2 + 1/4)
= 1 - (2/20 + 10/20 + 5/20)
= 20/20 - 17/20
= 3/20
All tickets are
3/20 = 30/a
a = (20 × 30)/3
a = 20 × 10
a = 200 tickets
The blue tickets are
= 1/4 a
= 1/4 (200)
= 50 tickets
Hence, the blue tickets in the hat are 50 tickets.
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Find the area of the isosceles
trapezoid.
Answer:
See answer below
Step-by-step explanation:
See drawing I made:
If x = 14 and y = 4, what is the value of the following expression? x - 7+ 5y St
Step-by-step explanation:
fill the data in the expression
(14)-7+5(4)
27
Evan cut a triangular piece of cloth to use in a quilt. The perimeter of the cloth is 934 cm. The base of the triangular cloth is 214cm. The remaining two sides are the same length.
The remaining two sides of the triangular piece are 360 cm each.
How to find the side of a triangle?Evan cut a triangular piece of cloth to use in a quilt. The perimeter of the cloth is 934 cm. The base of the triangular cloth is 214cm. The remaining two sides are the same length.
Therefore, the triangular piece is an isosceles triangle. This means the legs are equal.
Hence,
2x + 214 = 934
where
x = side of the isosceles triangleTherefore,
2x + 214 = 934
subtract 214 from both sides of the equation
2x + 214 - 214 = 934 - 214
2x = 720
divide both side by 2
x = 720 / 2
x = 360
Hence, the sides of the triangle are 360 cm each.
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Please help
Really stuck
Statement Reason
∠1 = ∠2, WX = ZY Given
WP = ZP converse of isosceles triangle theorem
△WXP ≅ △ZYP SAS
XP = YP CPCT
∠3 = ∠4 Isosceles triangle teorem
What is the isosceles triangle?
A triangle's corresponding angles are congruent if its two sides are.
Given that ∠1 = ∠2, WX = ZY.
Statement 1 is given.
According to the converse of the isosceles triangle theorem:
WP = ZP
SAS rule: If the two sides and an included angle of one triangle match the two sides and an included angle of the other, then two triangles are said to be congruent. This is referred to as SAS congruency.
In triangles △WXP and △ZYP:
∠1 = ∠2
WX = ZY.
WP = ZP
According to SAS rule, △WXP ≅ △ZYP
By CPCT, XP = YP
Again the isosceles triangle theorem ∠3 = ∠4.
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7 x 3/14 as a fraction in simplest form
Answer:
3/2
Step-by-step explanation:
7 x 3/14 can be simplified to 21/14, which is written in simplest form as 3/2.
Hope can help :)
The simplest form of the fraction of the expression is 3/2.
We have,
The expression:
7 x 3/14
Now,
14 is a multiple of 7.
i.e
7 x 2 = 14
So,
7 x 3/(7 x 2)
7 gets canceled.
= 3/2
Thus,
The simplest form of the fraction of the expression is 3/2.
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Either draw a full m-ary tree with 76 leaves and height 3, where m is a positive integer, or show that no such tree exists.
If and only if m is a divisor of 76, then there exists a full m-ary tree with 76 leaves and height 3. 1, 2, 4, 19, 38, and 76 are the divisors of the number 76.
One node at the root, 76 child nodes at the second level, and [tex]76^{2}[/tex] = 5776 child nodes at the third level make up the 5776 + 76 = 5852 nodes of a full 1-ary tree with 76 leaves and height 3. As a result, there is no whole 1-ary tree with 76 leaves and a height of 3.
There would be one node at the root, 38 child nodes at the second level, and [tex]38^{2}[/tex] = 1444 child nodes at the third level, making a total of 1444 + 38 = 1482 nodes in a full 2-ary tree with 76 leaves and height 3. As a result, there is a full 2-ary tree that is 3 in height and has 76 leaves.
There would be one node at the root, 19 child nodes at the second level, and [tex]19^{2}[/tex] = 361 child nodes at the third level, for a total of 361 + 19 = 380 nodes in a full 4-ary tree with 76 leaves and height 3. As a result, there is a full 4-ary tree that is 3 in height and has 76 leaves.
A full 19-ary tree with 76 leaves and height 3 would have a single node at the root, four children at the second level, and four and a half children, or 16 at the third level, for a total of 16 + four and a half and twenty nodes. As a result, there is a full 19-ary tree that is 3 in height and has 76 leaves.
A full 38-ary tree would contain a single node at the root, two child nodes at the second level, and two and a half child nodes at the third level, for a total of four + two + six nodes. Consequently, there is a complete 38-ary tree that is 3 in height and has 76 leaves.
There would be one node at the root, one child node at the second level, and [tex]1^{2}[/tex]= one child node at the third level, for a total of 1 + 1 = 2 nodes in a full 76-ary tree with 76 leaves and height 3. Consequently, there is a full 76-ary tree with 76 leaves and a height of 3.
As a result, for m = 2, 4, 19, 38, and 76, a full m-ary tree with 76 leaves and height 3 exists.
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