−5.25 > −6.
There are two of them.
These two numbers need to be compared.
A number's square root is always less than?A number's square root is never greater than the number itself.
According to the question, we have -
A = −5.25
B = −6.
Clearly, A > B
Hence,−5.25 > −6.
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In what sense is the regression line the straight line that best fits the points in a scatterplot?
The straight line along which the squared vertical distances from the data points are reduced is known as the regression line. minimization of the squared vertical distance between the points and the line for a straight line.
What does regression line mean?
An estimated linear relationship between two variables, which is known as the real but unobserved linear relationship, is shown by a regression line. A given value for the explanatory variable is used to predict (or estimate) the value of the response variable using the equation of the regression line.
What does the term "regression line" mean?
Regress, which is derived from the Latin verb "regressus" (to go back), is the root of the word "regression" (to something). Regression, in this sense, is a method that enables "going back" from muddled, difficult-to-interpret data to a more understandable and valuable model.
The degree to which both variables can move in unison is defined by correlation. Regression, however, identifies how a change in the unit of a known variable (p) affects a variable that is being evaluated (q).
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Felix built a ramp. If the height of Felix' ramp i 6 inche from the ground ,how long i the part of the ramp that i on the ground?
There is not sufficient data provided to answer the question. So it cannot be answered.
To find the length of the part of the ramp that is on the ground, we need to know the angle of the ramp and the height of the ramp. If the height of the ramp is 6 inches, and we know the angle of the ramp, we can use the Pythagorean theorem to find the length of the ramp.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the ramp in this case) is equal to the sum of the squares of the other two sides. If we call the length of the ramp "x", and the height of the ramp "h", we can write the equation as:
x^2 = h^2 + (6 inches)^2
We don't have the angle of the ramp, so we can't use the Pythagorean theorem. Therefore, we can't find the length of the part of the ramp that is on the ground with the information given. To find the length, we would need additional information, such as the angle of the ramp or the length of the ramp.
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a fitness coach needs to use 3 different exercises from a list of 25 in a workout. How many different groups of 3 exercises can she choose?
Answer:
This is a combination problem, where order doesn't matter.
We want to find the number of ways to choose 3 exercises from a list of 25, which is denoted as 25C3.
This is also equal to (252423) / (321) which is equal to 2300.
Therefore, there are 2300 different groups of 3 exercises the fitness coach can choose from the list of 25 exercises.
Step-by-step explanation:
25. Which correctly gives the center of dilation
and scale factor of the dilation below?
A. (-8,-1); k=3/4
B. (-8,-1); k=4/3
C. (0,-5): k = 3/4
D. (0,-5); k=4/3
The required center of dilation and scale factor of a dilation is given as (0, -5) and k = 4/3. Option D is correct.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
To determine the center of dilation,
Draw a straight line Joining BB' and AA', this line meets at a point (0, -5) so this point is the required center of dilation.
Now,
From the ceter of the dilation,
The scale factor of the dilation is given as,
SF = OB'/OB
SF = 4/3
Thus, the required center of dilation and scale factor of a dilation is given as (0, -5) and k = 4/3. Option D is correct.
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Find the range, mean, median, and mode of the following data set. 8, 4, 12, 10, 6, 25, 6
The range of the set is 21
The mean of the set is 10.1
The median of the set is 8
The mode of the set is 6
What is Median?The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Given data ,
The range of the set is the difference of the largest and the smallest value in the set
So , the range R = 26 - 4 = 21
The mean of the set be represented as A
The value of A = sum of observations / total number of values in the set
The mean of A = ( 8 + 4 + 12 + 10 + 6 + 25 + 6 ) / 7
The mean of A = 71 / 7
The mean of A = 10.14
Now , the median of the set be represented as B
For calculating the median of the set
Arrange the data points from smallest to largest
The number of elements in the set is 7 which is odd
So , B = { 4 , 6 , 6 , 8 , 10 , 12 , 25 }
The median of B = the middle term of the set
The median B = 8
Now , the mode of the set be represented as C
The mode C = the mode is the value that appears the most often in a data set
So , the number 6 is the value that appear more in the set
The mode C = 6
Hence , the mean , median and mode is 10.14 , 8 and 6 respectively
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how can you use proportional and nonproportional linear relationships to solve problems? what does it mean to solve a system of equations?
Answer: Proportional and nonproportional linear relationships can be used to solve problems by creating equations and using them to find unknown values. A proportional linear relationship is a relationship in which the ratio of the dependent variable to the independent variable is constant. For example, y = kx is a proportional linear relationship, where k is the constant of proportionality. Nonproportional linear relationships, on the other hand, have a variable ratio between the dependent and independent variables. For example, y = mx + b is a nonproportional linear relationship, where m is the slope and b is the y-intercept.
To solve a system of equations is to find the values that make all the equations in the system true simultaneously. This can be done by using methods such as substitution, elimination, or graphing.
A system of equations is a set of two or more equations with the same variables, and solving such a system is finding the values of the variables that satisfy all the equations in the system.
For example, if we have a system of two equations,
y = 2x+1
y = -x+5
we can solve it by finding the values of x and y that make both equations true at the same time.
In summary, proportional and nonproportional linear relationships can be used to solve problems by creating equations and using them to find unknown values. Solving a system of equations is finding the values of the variables that satisfy all the equations in the system.
Step-by-step explanation:
Can the sides of a triangle have lengths 5'7 and 13?
The sum of the lengths of any two sides of a triangle must exceed the length of the third side; therefore, 5+7 > x, which cannot happen if x = 13.
Which Cannot be sides of a triangle?Assume that a triangle has sides that measure 5, 7, and 11. Finding the sum of the squares on the triangle's two shorter sides and comparing it to the square on the longest side will reveal the type of triangle. The triangle is therefore not acute. Thirteen plus seven equals twenty, and twenty is more than nine. The Triangle Inequality Theorem is satisfied by this set of side lengths. A triangle is formed by these lengths. No, not in the traditional sense of the word (Euclidean geometry). A "degenerate triangle" is possible, but it isn't exactly a triangle in the sense that we often think of triangles 8 + 7 = 15 the length of any two sides added together.To learn more about sides of a triangle refer to:
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The table represents a function.
Xx
-4
-1
3
5
f(x)
-2
5
4
-8
What is f(5)?
-8
-1
1
8
Therefore , the solution to the given problem of function comes out to be f(5) = -8.
What does the word function mean?Mathematics encompasses variables and their changes, equations and related structures, form locations and forms themselves. The relationship between a number of inputs, each of which has an associated output, is referred to as a "function." An association between inputs and outputs that yields a single, distinct outcome is known as a function. Each function has a realm and with a requested request, or scope, allocated to it. The letter f is frequently used to represent , equation functions (x). An x is entered. The four primary kinds of activities that are offered are on activities, each functions, numerous features, within characteristics, and on functions.
Here,
Given :
x -4 -1 3 5
=> f(x) -2 5 4 -8
The value of f(x) at x = 5 is f(5).
=> f(5) = -8
Therefore , the solution to the given problem of function comes out to be f(5) = -8.
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Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 5(m∠Y) − 150°. Find m∠Y.
If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
Suppose you know that ∠S and ∠Y are complementary and that ∠S = 5(∠Y) − 150°.
Then the other equation is given as,
∠S + ∠Y = 90°
5(∠Y) − 150° + ∠Y = 90°
6 (∠Y) = 240°
∠Y = 40°
If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.
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Which of the following is not a polynomial ? a: √3x^2-2√3x+3 , b: 3x^3/2-5x^2-1/√2x-1 , c: x+1/x , d: 5x^2-3x+ √2 please give full explanation of answer !!!
Answer: A polynomial is a mathematical expression that is composed of a sum of powers in one or more variables (indeterminates) with non-negative integer exponents, and coefficients that are real numbers.
Out of the options given, option "b" is not a polynomial.
Option "a" √3x^2-2√3x+3 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (√3, -2√3, 3)
Option "c" x+1/x is not a polynomial , it's called a rational function, it consists of one polynomial divided by another polynomial, it's not a polynomial because of the fraction 1/x
Option "d" 5x^2-3x+ √2 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (5, -3, √2)
So, option "b" 3x^3/2-5x^2-1/√2x-1 is not a polynomial, because of the fraction and the non-integer exponent (3/2)
Step-by-step explanation:
A baseball is thrown upward in the air. The height of the baseball f seconds after it is released is approximated by the function.
h=-16t^2+64t+80
a. find the number of seconds that it takes for the baseball to reach the ground?
b. Find the number of seconds that it will take the baseball to be at its maximum height?
c. Find the maximum height of the baseball?
Show work!
The solution to the quadratic equations are
a) The number of seconds for the ball to reach the ground is t = 5 seconds
b) The number of seconds to reach the maximum height T = 2 seconds
c) The maximum height of the ball is h ( 2 ) = 144 feet
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as h ( t )
Now , the equation will be
h ( t ) = -16t² + 64t + 80 be equation (1)
a)
The number of seconds for the baseball to reach the ground be t
The height when the ball reaches the ground will be h = 0
Substituting the value of h ( t ) = 0 , we get
0 = -16t² + 64t + 80
On simplifying the equation , we get
16t² - 64t - 80 = 0
Divide by 16 on both sides of the equation , we get
t² - 4t - 5 = 0
On factorizing the equation , we get
t² + t -5t - 5 = 0
t ( t + 1 ) - 5 ( t + 1 ) = 0
( t - 5 ) ( t + 1 ) = 0
The value of t is time and it is not negative
So , when ( t - 5 ) = 0
Adding 5 on both sides of the equation , we get
t = 5 seconds
b)
The number of seconds the baseball to reach the maximum height be T
And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola
T = ( -b / 2a )
On simplifying the equation , we get
T = ( -64 / ( 2 ( 16 )
T = -64 / 32
T = 2 seconds
c)
The maximum height of the baseball is when T = 2
Substituting the value of t = 2 in the equation , we get
h ( t ) = -16t² + 64t + 80
h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80
On simplifying the equation , we get
h ( 2 ) = -64 + 128 + 80
h ( 2 ) = 64 + 80
h ( 2 ) = 144 feet
Hence , the equation is solved
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On July 27, 2018, Mars will be about 57.6 million km from the earth. It will not be that close again until 2035. If a manned spacecraft could travel 40,000 km/hr, approximately how long would it take the spacecraft to reach Mars from Earth?
The time it would take the space craft to reach earth from Mars would be: 1440 hours
How to solve for the time it would take the space craft to reach earththe distance from Mars to Earth = 57.6 million km
= 57, 600,000 km
The time it takes the space craft to travel per km = 40000
We would use the formula t = d / v
where t is the unknown time we want to find
d is the distance = 57, 600,000 km
v is the velocity or speed = 40000
Hence we have
t = 57,600,000 / 40000
= 1,440 hours
It would take the space craft 1440 hours to reach mars from earth
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Help me with this worksheet please give me he answer!
I'm in a hurry!
The approximate annual cost of raising a child born in 2013 at age 17 is 15230.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
a) Plot (2, 12,940), (5, 12,970), (8, 12,800), (11, 13,600) 1nd (14, 14420) on graph.
b) (8, 12800) and (14, 14420)
Here, slope m=(14420-12800)/(14-8)
= 1,620/6
= 270
Substitute m=270 and (x, y)=(8, 12800) in y=mx+c, we get
12800=270(8)+c
12800=2160+c
c=10640
Substitute m=270 and c=10640 in y=mx+c, we get
y=270x+10640
c) Now, substitute x=17 in y=270x+10640, we get
y=270×17+10640
y=15230
Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is 15230.
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For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
The graph of the Equation and Inequalities is attached below.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
1. 2y – 4x < 8
The region is shaded by red region.
and, the inequality intersect y axis at 4 and x axis at -2.
2. -4y > -x + 12
The region is shaded by red region.
and, the inequality intersect y axis at -3 and x axis at 12.
3. | x + 3 |= y
The vertex of the equation is (-3, 0)
4. |2x – 6| + 2 = y
The vertex of the equation is (3, 2)
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-1/3(12d+18) answer?
Answer:
-4d - 6
Step-by-step explanation:
-1/3(12d+18)
-4d - 6
That is the simplest we can simple the function
So, the answer is -4d - 6
Mia is rolling a pair of 666-sided dice. P(n)p(n)p, left parenthesis, n, right parenthesis models the probability of the event that the sum of the dice is nnn. Which number type is more appropriate for the domain of ppp?.
Mia is rolling a pair of 666-sided dice. P(n)p(n)p, left parenthesis, n, right parenthesis models the probability of the event that the sum of the dice is nnn. The number type is more appropriate for the domain of ppp is {n | n ∈ N, 2 ≤ n ≤ 12}
A perfect dice has six faces and is exactly cubical in shape. Each face has one of the numerals 1, 2, 3, 4, 5, or 6, and any two faces can have a different digit.
Now that two dice have been rolled, P(n) simulates the likelihood that the total of the two dice's faces will be n.
The domain of P is therefore given by,
{n | n ∈ N, 2 ≤ n ≤ 12}
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The figure below is translated down 4 Units and then reflected over the x-axis.what are the coordinates of the images of point E after these transformations?
The coordinates of the image of point Y following these modifications are thus -2.
How do we find the Cartesian coordinate plane?There are no boundaries to the two dimensions of the Cartesian coordinate plane. Any two-dimensional figure can be drawn on an unending 2D plane. In a Cartesian plane, every point has a specific place.The provided number has been rotated 180 degrees anticlockwise and increased in scale by two units.
After these adjustments, the image of point Y has coordinates that are -2.
The coordinates of the image of point Y following these modifications are thus -2.
The x-axis and y-axis intersect to produce the two-dimensional coordinate plane known as the cartesian plane in mathematics. The origin is the point at where the x- and y-axes cross perpendicularly.The complete question is,
The figure below is translated up 2 units and then rotated 180° counterclockwise. What are the coordinates of the image of point Y after these transformations?
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A wheelchair ramp is 10 feet long. The ramp sits up on a 2 foot platform.
How far is it from the end of the ramp to the bottom of the platform? (Round to the tenths place & include units!)
Answer: 9.8 feet!
Step-by-step explanation:
Understand Only 93% of the airplane parts being examined pass inspection. What is the probability that the next 5 part examinedwill all pass inspection?
Answer:
0.67 or 67%
Step-by-step explanation:
The probability that a single part will pass inspection is 0.93, so the probability that all 5 parts will pass inspection is (0.93)^5 = 0.67 or 67%.
The solution is 0.67 or 67%, is the probability that the next 5 part examined will all pass inspection.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
Understand Only 93% of the airplane parts being examined pass inspection.
now, we have to find that the probability that the next 5 part examined will all pass inspection.
now, we have,
The probability that a single part will pass inspection is 0.93,
so the probability that all 5 parts will pass inspection is :
(0.93)^5
= 0.67
= 67%.
Hence, The solution is 0.67 or 67%, is the probability that the next 5 part examined will all pass inspection.
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Why is the base of a exponential function not allowed to equal 1?
The base of a exponential function is not allowed to equal 1 because it would create a graph that would violate the properties of the exponential functions.
An exponential function cannot produce an increasing graph when base is taken as 1. This would lead to violation of its properties. However, an exponential function can have any positive number as its base, however some bases are more advantageous than others. The base 2 is useful, for instance, in computer science applications. The number represented by the letter e, however, is the most significant base. A function of the form is an exponential function, when:
f(x) = b^x
where x is any real value and b is a positive constant. B is frequently referred to as the base. Typically, the particular case b=1 is not considered because it would only produce the constant function f(x) = 1.
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Potatoes cost $3.64/lb. How much would 0.47 lb of potatoes cost?
Answer:
Step-by-step explanation:
1.7108 is the answer
Lisa's father is 42 years old. His age is two more than five times Lisa's age. How old is Lisa?
Answer:
Lisa is 8 years old.
Step-by-step explanation:
If Lisa's father is 42, then we can easily find out what Lisa's age is from the problem. We simply just have to create an equation and then solve it.
The equation:
5x + 2 = 42
Solving said equation:
5x = 42 - 2
5x/5 = 40/5
x = 8
What you do to one side, must be done to the other.
Hope this helps!
What’s the factored answer of 27w^5-75w
Answer:
3w(3w²+5)(3w²-5)
The product of two numbers is 20⅚.If one of the number is 6⅔ Find the other number.
Answer:
X=3+1/8
Step-by-step explanation:
X * 40/6 = 125/6
(Multiply each side by 6 to get rid of the denominator)
X *40=125
Divide each side by 40
X = 125/40
X= 25/8
X=3+1/8
Mrs. James buys 5 hat and glove sets for charity. She has coupons for $1.50 off the regular price of each set. After using the coupons, the total cost is $48.75.
Item Cost ($)
Hat and glove set p
Scarf 9.99
Which equation can be used to determine the regular price, p, of a hat and glove set?
Multiple choice question.
cross out
A)
5p+9.99=48.75
cross out
B)
5(p−1.50)=48.75
cross out
C)
5(p+9.99)=48.75
cross out
D)
5(p+9.99−1.50)=48.75
Part B
Determine the regular price of a hat and glove set.
$__
The equation used to determine the regular price is :
5(p - 1.50) = 48.75
Regular price of a hat and glove set = $11.25
The correct option is (B).
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.
Given,
No. of hat and glove sets Mrs. James bought = 5
Discount with each coupon = $1.50
Total cost after using coupons = $48.75
Regular price of Hat and glove set = p
Cost of hat and glove set = p - $1.50
Cost of 5 sets of hat and glove = 5(p - 1.50)
By the question,
5(p - 1.50) = 48.75
p - 1.50 = 9.75
p = 9.75 + 1.50
p = 11.25
Regular price of a hat and glove set = $11.25
Hence, $11.25 is regular price of a hat and glove set,
5(p - 1.50) = 48.75
is the equation used to determine the regular price.
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How many four-digit integers are even perfect squares and also perfect cubes?
The is 1 four-digit integers that is a perfect squares and perfect cube and it is 4096
What are perfect squares and perfect cubes?A perfect cube is the cube of a whole number, found by multiplying a whole number by itself three times. For example, the number 8 is a perfect cube because 2 × 2 × 2 = 8 .
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer. For example, 25 is a perfect square because it is the product of integer 5 by itself, 5 × 5 = 25.
The only four-digit integers that is a perfect square and a perfect cube is 4096
i.e 64² = 4096
16³ = 4096
Therefore the number of four-digit number that is a perfect square and a perfect cube is 1
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Subtract (5x + 1/3) - (3x - 1/6)
[tex] \\ \\ \\ \\ \\ \\ [/tex]
ty:-;
The subtraction of the expression (5x + 1/3) - (3x - 1/6) is given by 2x + 1/2
How to subtract expressions?Subtraction refers to one of the mathematical operations which involves finding the difference between expressions or values.
(5x + 1/3) - (3x - 1/6)
Open parenthesis
= 5x + 1/3 - 3x + 1/6
Collect like terms
= 5x - 3x + 1/3 + 1/6
= 2x + (2+1) / 6
= 2x + 3/6
= 2x + 1/2
In conclusion, 2x + 1/2 is the result of the given expression (5x + 1/3) - (3x - 1/6)
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Answer:
2x + (1/2)
Step-by-step explanation:
Given expression,
→ (5x + (1/3)) - (3x - (1/6))
Let's simplify the expression,
→ (5x + (1/3)) - (3x - (1/6))
→ 5x + (1/3) - 3x + (1/6)
→ (5x - 3x) + ((1/3) + (1/6))
→ (2x) + ((2 + 1)/6)
→ 2x + (3/6)
→ 2x + (1/2)
Hence, answer is 2x + (1/2).
23. Kumar wishes to cut the biggest possible squares
from a rectangular sheet of paper without any
leftover paper. The sheet of paper has a length of
65 cm and a breadth of 50 cm.
(1) What is the length of each square?
(ii) How many squares can he cut altogether!
The length of each square Kumar cuts is 10cm and 13cm, and altogether he cuts 130 squares.
What is the length of squares cuts?The perimeter of a square is really the total length of all of its sides. As a result, we can calculate the perimeter of a square by adding its four sides. A square's sides are all equal. As a result, the perimeter of a square is calculated by multiplying the side of a square by four.Given that,
Length of paper = 65 cm
Breadth of paper = 50 cm
The length of each square,
The greatest common factor of 65 and 50 is 5.
So,
50/5 = 10
65/5 = 13
Therefore the length of each square is 10cm and 13cm.
To find the number of squares cut altogether ,
10 x 13 = 130 squares.
Therefore altogether Kumar cuts 130 squares.
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What is called prime factorization method?
Answer:
The process of writing all numbers as a product of prime.
Step-by-step explanation:
For example, if we have something like the number 20. We can break that down into two factors. We can say, “well, that's 4 times 5.” And notice, 5 is a prime number. Hope it helps!
Graph the inequality on a number line:
x [tex]\geq[/tex] 11
The required graph has been attached below which represents the inequality x ≥ 11 on a number line.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question, as follows:
x ≥ 11
In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout.
A number line is typically shown horizontally and can be extended indefinitely in any direction.
Thus, the graph has been attached below which represents the inequality on a number line.
Learn more about inequalities here:
brainly.com/question/20383699
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