The sides 7 cm, 24 cm and 25 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.
From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angles triangle.
Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. Then the equation, can be written as,
CA² = AB² + BC²
Now, let us check this rule for the above given sides of the triangle.
Longest side² = Sum of squares of other two sides
25² = 24² + 7²
625 = 625
Thus, the sides 7 cm, 24 cm and 25 cm can form a right-angled triangle.
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Star Finish charges $3.45 to develop a roll of film and $0.33 for each photo that it prints. Create a ration function giving the mean cost c per print when p prints are made.
The rational function to define this situation would be p = 3.45 + 0.33c.
What is rational function?A rational function in mathematics is any function that can be expressed as a rational fraction, which is an algebraic fraction in which the denominator and numerator are both polynomials. It is not necessary for the polynomials' coefficients to be rational numbers; they can be taken from any field K.
In this instance, a rational function and a rational fraction over K are used. The variables' values can be entered into any field L that contains K. In this case, L is the codomain and the domain of the function is the collection of variable values for which the denominator is not zero.
They charge $3.45 to develop a roll of film and $0.33 for each photo that it prints.
The rational function define this situation would be
p = 3.45 + 0.33c
Thus, the rational function to define this situation would be p = 3.45 + 0.33c
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Which of the following is not a solution of the pair of equations 3x−2y=4 and 6x−4y=8?A) x=2,y=1B) x=4,y=4C) x=6,y=7D) x=5,y=3
As the value of x(=5) and y(=3) does not satisfies any of the given equation, hence (5,3) is not a solution of the pair of equations 3x−2y=4 and 6x−4y=8
The correct option D
Now, According to the question:
Given,
There are two equation are given as:
3x - 2y = 4
6x - 4y = 8
To check the which of the following is not a solution of the pair of equations ?
A) x = 2 and y = 1
=> 3 × 2 - 2 × 1 = 4
6 - 2 = 4
4 =4
=> 6 × 2 - 4 ×1 = 8
12 - 4 = 8
8 = 8
B) x = 4 and y = 4
=> 3 × 4 - 2 × 4 = 4
12 - 8 = 4
4 =4
=> 6 × 4 - 4 × 4 = 8
24 - 16 = 8
8 = 8
C) x = 6 and y =7
=> 3 × 6 - 2 × 7 = 4
18 - 14 = 4
4 = 4
=> 6 × 6 - 4 × 7 = 8
36 - 28 = 8
8 = 8
D) x = 5 and y = 3
=> 3 × 5 - 2 × 3 = 4
15 - 6 = 4
9 ≠ 4
=> 6 × 5 - 4 × 3 = 8
30 - 12 = 8
12 ≠ 8
As the value of x(=5) and y(=3) does not satisfies any of the given equation, hence (5,3) is not a solution of the pair of equations 3x−2y=4 and 6x−4y=8
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The sides of the triangle shown increase in such a way that dz/dt=1, and dx/dt=3 dy/dt At the instant when x = 12 and y= 5, what is the value of dx/dt?
The value of is dx/dt = 0.95, when x = 12 and y =5.
What is Pythagoras theorem?Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
Given:
dz/dt = 1,
dx/dt = 3(dy/dt)
So, dy/dt = 1/3 (dx/dt)
According to the Pythagoras theorem -
z² = x² + y²
Differentiating both sides we get
d/dt (z²) = d/dt (x² + y²)
2z dz/dt = 2x dx/dt + 2y dy/dt
z dz/dt = x dx/dt + y dy/dt
Substituting the value of dy/dt -
z dz/dt = x dx/dt + y/3 (dx/dt)
z dz/dt = dx/dt (x + y/3)
dx/dt = (z dz/dt)/(x + y/3).....(1)
So, when x = 12 and y = 5, the value of z -
z = √[(12)² + (5)²]
z = √(144+25)
z = √169
z = 13
Substituting the value of x, y, z and dz/dt in equation (1), we get
dx/dt = (13 × 1)/(12 + 5/3)
dx/dt = 13 / 41/3
dx/dt = (13 × 3)/41
dx/dt = 39/41
Hence, the value of dx/dt = 0.95.
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5. Comparing Steelers in the modern NFL, teams emphasize the passing game much more than teams in the 1970s
did, which were more run-oriented. This makes it very difficult to compare the performances of quarterbacks
from these eras - even when they both played for the same team. In 1979, Terry Bradshaw threw for a career-
high 3724 yards. In 2014, Ben Roethlisberger threw for a career-high 4952 yards. 36 Whose performance was
better, relatively speaking?
a. In 1979, the top quarterback for each of the 28 teams threw for an average of 2789 yards with a
standard deviation of 752 yards. Calculate and interpret the z-score for Terry Bradshaw's performance in
1979.
b. In 2014, the top quarterback for each of the 32 teams threw for an average of 3447 yards with a standard
deviation of 970 yards. Calculate and interpret the z-score for Ben Roethlisberger's performance in 2014.k
A z-score is used to measure how many standard deviations an individual value is from the mean of a given set of data.
Whose performance was better, relatively speaking?Terry Bradshaw's performance in 1979 had a z-score of 1.21, which means his performance was 1.21 standard deviations above the mean for all quarterbacks in the NFL that year.Ben Roethlisberger's performance in 2014 had a z-score of 1.31, which means his performance was 1.31 standard deviations above the mean for all quarterbacks in the NFL that year.Terry Bradshaw's performance in 1979 had a z-score of 0.98, which indicates that his performance was slightly above average. This indicates that, while his performance was impressive in 1979, it was still slightly below what other quarterbacks in the league were doing at the time. Ben Roethlisberger's performance in 2014 had a z-score of 1.51, which indicates that his performance was significantly above average. This indicates that his performance was significantly better than what other quarterbacks in the league were doing in 2014. This is a testament to the increased emphasis on the passing game in the modern NFL.To calculate the z-score for Terry Bradshaw's performance in 1979, we subtract the mean of 2789 yards from his performance of 3724 yards and divide by the standard deviation of 752 yards. This yields a z-score of 1.95. This means that his performance was 1.95 standard deviations higher than the average of other quarterbacks in the same year. Similarly, to calculate the z-score for Ben Roethlisberger's performance in 2014, we subtract the mean of 3447 yards from his performance of 4952 yards and divide by the standard deviation of 970 yards. This yields a z-score of 1.63. This means that his performance was 1.63 standard deviations higher than the average of other quarterbacks in the same year. Therefore, while both performances were impressive, Roethlisberger's performance was slightly less impressive than Bradshaw's.To learn more about numerical value refer to:
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Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.
k = 4
The coordinates of the points after dilation is S'(-20,10), T'(16,-12), U(-4,-4), and V'(-12,-4).
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given that the scale factor is 4. The coordinates of the points after dilation is,
S(-5,2) = S'(-5 x 4 , 2 x 4) = S'(-20, 8)
T(4,-3) = T'(4 x 4, -3 x 4 ) = T'(16, -12)
U(-1,-1) = U'(-4,-4)
V(-3,-1) = V'( -3 x 4, -1 x 4 ) = V'(-12,-4)
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a. evaluate the integral (9 to 1) x^0.5 dx
The integral of x^0.5 from 9 to 1 is approximately 17.3333
what is integral?An integral is a mathematical concept used to calculate the area under a curve or the total change of a function. It's a fundamental concept of calculus and has many applications in physics, engineering, economics and more.
To evaluate the integral of [tex]\sqrt{x}[/tex] from 9 to 1, we can use the antiderivative method. The antiderivative of [tex]\sqrt{x}[/tex] is (2/3) [tex]x^\frac{3}{2}[/tex], so the definite integral can be evaluated as:
[tex]\int\limits^9_1 {\sqrt{x} } \, dx[/tex] = [tex]\left \{ {{x=9} \atop {x=1}} \right.[/tex] (2/3) [tex]x^\frac{3}{2}[/tex]
On substituting the limits we get
(2/3)[[tex]9^\frac{3}{2}[/tex]- 1]
= (2/3)(27) - (2/3)
= 18 - 2/3
= 17.3333
Therefore, the definite integral of x^0.5 from 9 to 1 is approximately 17.3333
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In this right triangle, what is the length of the hypotenuse?
Answer:
hypotenuse = 55
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse c is equal to the sum of the squares on the other 2 sides, that is
c² = 33² + 44² = 1089 + 1936 = 3025 ( take square root of both sides )
c = [tex]\sqrt{3025}[/tex] = 55
what is the solution of the equation 6-2^(x)=1
Answer:
Step-by-step explanation:
6-2^x=1
-2^x+6=1
-2^x+6-6=1-6
-2^x=1-6
-2^x=-5
x=-5
please find the value of X
Answer:
x ≈ 21.3
Step-by-step explanation:
using the sine ratio in the right triangle
sin80° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{21}{x}[/tex] ( multiply both sides by x )
x × sin80° = 21 ( divide both sides by sin80° )
x = [tex]\frac{21}{sin80}[/tex] ≈ 21.3 ( to 1 decimal place )
What is the smallest possible perimeter of the triangle rounded to the nearest tenth?
The smallest possible perimeter of an acute triangle with the longest side of 30 inches and two congruent sides is 40.96 inches by applying the triangle inequality theorem.
For an acute triangle, the longest side or hypotenuse must be less than the sum of the other two sides, this is known as the triangle inequality theorem.
Given that the longest side of the triangle measures 30 inches, and the two remaining sides are congruent, we can use the triangle inequality theorem to find the smallest possible perimeter of the triangle.
If we call the length of the other two sides x, then we know that x+x>30, so x>15.
The smallest perimeter is then 2x+30.
The smallest possible perimeter of the triangle, rounded to the nearest hundredth is 40.96 inches.
So the answer is 40.96 in.
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The question is -
The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth? 40.96 in. 51.22 in. 72.44 in. 81.22 in.
Solve for y
X=3+(y-5)^2
Answer:
y = 5 + √-3 + x
y = 5 - √-3 + x
Step-by-step explanation:
X=3+(y-5)^2
Let's simplify, and we will get
x = 3 + (y^2 -10y + 25)
x = 3 + y^2 - 10y + 25
x = y^2 - 10y + 28
0 = y^2 - 10y + 28 - x
We use the formula
-b ± √ b^2 -4(ac) / 2a
10 ± √(-10)^2 - 4 · (1 ( 28 - x) ) / 2
The answer will be
y = 5 + √-3 + x
y = 5 - √-3 + x
(-3)^2 without exponent?
Answer: 9
Step-by-step explanation:
A dozen is equal to 12 a case of pens contains 12 dozen. How many pens are in 2 cases
Answer:
24 pens
Step-by-step explanation:
Answer: the answer is actually 288
Step-by-step explanation:
you multiple 12 by 12 to get 144 then you multiply that by 2 to get 288
After driving 54km, Saed found that he ha only covered 18%of ditance. How much did he had to cover?
Therefore , the solution of the given problem of percentage comes out to be 246 kilometers left for distance to covered.
What is percentage ?In mathematics, a percentage is a mathematical ratio that is stated as a portion of 100. Occasionally, the abbreviations "pct.," "percent," and "pt" are also used. However, the percentage symbol "%" is frequently used to represent it. There are no dimensions to the % quantity. Since percentages have a numerator of 100, they are actually fractions. A number must be followed by the cent symbol (%) to denote that it is a percentage. For illustration, you would receive a 75% mark if you answered 75 out of questions on a test correctly.
Here,
Given:
Saed discovered that he had barely traveled 18% of the
distance after driving 54 km.
Therefore, if he traveled 54 kilometers outside of it,
the total distance
=> 100/18 * 54
=> 300 kilometers
Thus , the left distance
=> 300 - 54
=> 246 kilometers
Therefore , the solution of the given problem of percentage comes out to be 246 kilometers left for distance to covered.
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The air pressure, P millibars, at a distance of n kilometres above sea level is given by this formula:
P = 1013 × 0.887
a) What is the air pressure at sea level?
b) By what percentage does the air pressure decrease for each kilometre above sea level?
PLEASEE HELPP BEG!!!!
a) The air pressure at sea level is given by the formula when n = 0, so P = 1013 × 0.887 = 900.71 millibars.
b) To find the percentage decrease in air pressure for each kilometre above sea level, we can use the formula for percentage change:
(New Value - Original Value) / Original Value * 100
What is air pressure?Air pressure, also known as atmospheric pressure, is the force exerted on a surface by the weight of the air above it. Air pressure is typically measured in units such as millibars (mb) or inches of mercury (inHg). It plays an important role in weather patterns and can affect things like airplane flight and altitude sickness.
What is sea level?Sea level refers to the average level of the surface of the ocean. It is used as a reference point for measuring elevation, and for measuring air pressure at a specific location. At sea level, the air pressure is approximately 1013 millibars or 29.92 inches of mercury (inHg). Air pressure decreases as the altitude increases above sea level.
The new value is P = 1013 × 0.887^n and the original value is P = 1013 (at sea level)
So, the percentage decrease in air pressure for each kilometre above sea level is:
(1013 × 0.887^n - 1013) / 1013 * 100 = (-0.113n) * 100 = -11.3n %
So, the air pressure decreases by -11.3 % for each kilometre above sea level.
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Three waiters at a local restaurant earned different amounts of money the past week. Jennifer earned $40 less than twice the amount Tony earned. Chris earned $60 more than Tony. How much did each waiter earn if they earned a total of $900?
Tony earned $220
Step-by-step explanation:
Tony = n
Jenifer = x
Chris = y
x = 2n - 40
y = n + 60
Write an equation for the total the three waiters earned. Solve for Tony's earnings.
n + x + y = $900
n+2n−40+n+60=900
Step 1: Simplify both sides of the equation.
n+2n−40+n+60=900
n+2n+−40+n+60=900
(n+2n+n)+(−40+60)=900(Combine Like Terms)
4n+20=900
4n+20=900
Step 2: Subtract 20 from both sides.
4n+20−20=900−20
4n=880
Step 3: Divide both sides by 4.
4n/4 = 880/4
n=220
Simplify the following expression.
A.23/63x+1/2
B. 23/63x+1/4
C. -5/63x+1/2
D. 3/16x+1/4
Answer:
Step-by-step explanation:
How do I search for a specific value in a table in SQL?
Enter the data value to be searched for in the Search text area. Choose the database to search in from the Database drop-down menu.
what is sequence ?The length of the sequence is the number of ordered elements (which could be infinite). Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of sequences you need to be familiar with. A list of numbers connected by a rule is known as a number sequence. You can determine the subsequent numbers in the sequence if you figure out the rule. The difference in this instance between each number is 6.
given
Enter the data value to be searched for in the Search text area.
Choose the database to search in from the Database drop-down menu.
Select the tables and views you want to search in from the Select objects to search tree, or leave them all checked.
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Along a hike, Jon takes 6 pictures. He takes 1 picture at
equal distances along the 3.72-mile trail. How far did Jon hike
between pictures?
mile(s)
The hike between the pictures will be 22.32 miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that along a hike, Jon takes 6 pictures. He takes 1 picture at equal distances along the 3.72-mile trail.
The hike will be calculated as:-
Hike = 6 x 3.72
Hike = 22.32 miles
Hence, the hike will be 22.32 miles between the pictures.
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f(x)=x^2 Vertical compression, factor of 1/2
The function that represents the vertical compression of function f(x) = x² by a factor of 1/2 is given as follows:
f(x) = x²/2.
How to model the vertical compression of the function?The parent function for this problem is defined as follows:
f(x) = x².
For a vertical compression by a factor of a, the function is multiplied by the constant a with absolute value less than 1, that is:
g(x) = a x f(x), |x| < 1.
The factor of the compression for this problem is of a = 1/2, hence the function that represents the vertical compression of function f(x) = x² by a factor of 1/2 is given as follows:
f(x) = x²/2.
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5. Use the scatter plot to answer the question.
A. What grade would someone with 3 missing assignments
have?
B. After how many missing assignments will a student likely
have a zero for an average?
Average Grade
Number of Hissing Assignments
Therefore ,when the problem of expression is solved, we may state that the necessary inequality statement is 4.50x+1.75y 50.
Expression: What is it?An expression in mathematics consists of a statement, two or more variables or integers, but one or more mathematical functions. Numbers can be multiplied, divided, added, or subtracted using this mathematical operation. The construction of an expression is as follows: Expression: Math operator, variable or number, and math operator.
Here,
Cost per assignment is $4.50.
Therefore, "x" assignment cost equals 4.50x.
Cost per assignment: $1.75
Assignment "Y" cost is therefore 1.75Y.
Consequently, the sum of 4.50x+1.75y must be $50 or less.
Therefore, 4.50x+1.75y ≤ 50 is the necessary inequality statement.
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How do you draw a 1/2 scale?
If the scale factor is a fraction, the shape will be smaller. This is called reduction. Therefore, a 1/2 scaling factor means that the new shape is half of the original shape
What size is a 1/2 scale?Half scale is 1:2. It is helpful to think of this as one unit on the drawing equals two units on the object. A small object can be enlarged on the paper and drawn in 2:1 scale. This means the drawing of the object is twice as large as the object itselfStarting on the upper right portion of your paper, draw five parallel diagonal lines headed downwards to the lower left corner. ...Step 2 – Create a Diagonal Criss-Cross Pattern. ...Step 3 – Fill In the Diamond Spaces With Scales. ...Step 4 – Draw the Scales in the Middle Portion.A full size drawing would be 1:1 (or sometimes 1/1 or 'one to one'). A half size drawing would be 1:2. A tenth size drawing would be 1:10. A double size drawing would be 2:1.
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If the scale factor is a fraction, the shape will be smaller. This is the so-called recovery. So a scale factor of 1/2 means that the new shape is half the original shape.
What size is 1/2 scale?Half scale is 1.
2. It is convenient to imagine that 1 unit on the drawing is equal to 2 units on the object. You can enlarge small objects and draw them on paper 2:
1 scale. This means that the drawing of the object is twice the size of the object itself.
Starting from the top right corner of the paper, draw five parallel diagonal lines towards the bottom left corner.
Step 2 - Create a diagonal cross pattern. ... Step 3 - Put the scales into the diamond shaped box. ...
Step 4 - Draw the scales in the middle part.
A full-size drawing will be 1.
1 (or sometimes 1/1 or "one to one"). A half-sized drawing will be 1.
2. A 10th grade drawing will be 1.
10. A double size drawing will be 2.
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What is the formula to find image?
The formula to find the resolution of an image, also known as its pixel density, is Pixels per Inch (PPI) or Pixels per Centimeter (PPCM). This formula is used to determine the number of pixels in a given area of an image.
The higher the PPI or PPCM, the greater the resolution of the image.
To calculate PPI, you need to know the total number of pixels in the image (width x height) and the physical size of the image (width x height in inches or cm). Once you have this information, you can use the following formula: PPI = (pixels / physical size) x (inches/cm).
For example, if an image has a resolution of 1920 x 1080 pixels and is printed at a size of 8 x 6 inches, the PPI would be (1920 x 1080) / (8 x 6) = 240 PPI.
In conclusion, PPI or PPCM is the formula used to find the resolution of an image, also known as its pixel density. It is calculated by dividing the total number of pixels in the image by its physical size and multiplying it by inches/cm.
The higher the PPI or PPCM, the greater the resolution of the image. It is important to consider the PPI or PPCM when choosing an image to print or display in order to ensure that it will be of high quality and have a high resolution.
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An electrician starts off the day with 600 feet of copper wiring on his truck. During the course of the day he uses pieces 100, 82, 25, and 40 feet long. The next day, he purchases another 400 feet and puts it on his truck and later in the day uses pieces of 41, 39, and 44 feet long. How many feet of wiring are still on the truck at the end of the second day?
The feet of wiring that are still on the truck at the end of the second day is 629 feet.
Arithmetic operations.Arithmetic operations implies solving a given question by addition, subtraction, division or multiplication as required in the question.
From the given question, total feet of copper wire at the start of the first day is 600 feet.
During the first day,
the total length of wire used = 100 + 82 + 25 + 40
= 247
Total length of copper used in the first day is 247 feet.
Length of copper wire remaining at the end of the first day = 600 - 247
= 353 feet
He purchased 400 feet of the wire so that;
total length of wire = 353 + 400
= 753 feet
the total length of wire used the second day = 41 + 39 + 44
= 124 feet
Total length of copper wire left after the second day = 753 - 124
= 629 feet
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The recipe calls for 4 apples to make a pie. If I want to double to recipe to make 2 pies, what would be the percentage change?
The percentage change could be around 50 % as we are doubling the recipe to make 2 pies.
What is percentage ?
percentage can be defined as the product of ratio of given value, total value to the 100.
Given,
The recipe calls for 4 apples to make a pie.
If I want to double to recipe to make 2 pies,
So,
let the percentage could be x ,
x =( change in value / total value ) * 100
x = (8-4/8)*100
x = 50%
Hence , The percentage change could be around 50 % as we are doubling the recipe to make 2 pies.
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10.6 exponential growth and decay
1. y=7500(1+0.3)^x
2. y=(0.85)x
3. y=900(1.27)^x
How do you find the total number of factors of a number?
Total Number of Factors for N = (a+1) (b+1) (c+1) is the formula for how many factors there are in total for a given number.
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
Total Number of Factors for N = (a+1) (b+1) (c+1) is the formula for how many factors there are in total for a given number.
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Solve the system.
6x - 4y = 12
y = 3/2x - 2
This system has no solution because the two equations are not consistent.
What is equation?An equation is a statement that asserts the equality of two expressions. For example, the equation "2x + 3 = 7" asserts that the value of the expression "2x + 3" is equal to the value of the expression "7".
What is system of linear equation?A system of linear equations is a set of two or more linear equations that are to be solved simultaneously. Linear equations are equations in which the highest degree of the variable is 1. For example, the equations "2x + 3y = 7" and "x - 4y = 2" are both linear equations, and solving them together forms a system of linear equations. These systems can be represented graphically by straight lines in a two-dimensional coordinate system, and the solution of a system of linear equations is the point or points of intersection of the lines.
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what are the names of the terms of m/5+4.6
The names of the terms of m/5+4.6 are m/5 and 4/6
How to determine the terms of the expressionFrom the question, we have the following parameters that can be used in our computation:
m/5 + 4.6
Considering an expression a + b
The terms of the expression are a and b
This means that the terms of the expression m/5 + 4.6 are m/5 and 4/6
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someone HELPP me plssss pls
Answer: x=−4
Step-by-step explanation: