Using factoring, we do the following actions to make rational expressions simpler:
As much as you can, factor the numerator and denominator. Any factors that appear in both the numerator and the denominator should be eliminated. Your expression gets simplified as a result. How is an expression factorized:
Step 1 is to identify the expression's prime factors.
Step 2: Find the GCF by enclosing the common factors.
Write each term in the expression as a combination of the GCF and the final factor in step 3.
Step 4: Simplify the equation by applying the distributive property.
Y=12(x-6)(x+2) is an illustration of a quadratic function in factored form. This shape can be examined to determine the vertex as well as the graph's x-intercepts.
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How to solve systems of inequalities
2x + 2y ≤ 20
x + 3y ≤ 21
The solution of the inequalities will be x ≤ 13 and y ≤ 8 / 3.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that the inequalities are 2x + 2y ≤ 20 and x + 3y ≤ 21.
The inequalities will be solved as:-
2x + 2y ≤ 20
x + 3y ≤ 21
Solve the above equation by eliminating variable y as below,
6x + 6y ≤ 60
-2x - 6y ≤ - 41
______________
3x ≤ 39
x ≤ 13
The value of y will be,
x + 3y ≤ 21
13 + 3y ≤ 21
3y ≤ 8
y ≤ 8 / 3
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Find the coordinates of P so that P partitions the segment AB in the ratio 3 to 1 if A(7, -4) and B(-5, 4). Show your work.
Answer: A partition of a line segment is a point that divides the segment into a certain ratio of segments. In this case, point P partitions the segment AB in the ratio 3 to 1.
To find the coordinates of point P, we can use the following method:
Let the point P be (x,y)
The ratio of the segments AP:BP is 3:1, so we can use the proportion: (AP)/(BP) = 3/(1+3) = 3/4
We can use the coordinates of points A and B to find the coordinates of point P. The x-coordinate of P is (3/4) times the difference in x-coordinates of A and B, plus the x-coordinate of A. And the y-coordinate of P is (3/4) times the difference in y-coordinates of A and B, plus the y-coordinate of A.
So, using the coordinates of A and B:
x = (3/4)(-5 - 7) + 7 = -4
y = (3/4)(4 - (-4)) -4 = 3
Therefore, the coordinates of point P are (-4,3)
Step-by-step explanation:
10-2 skills practice simplifying radical expressions
1. √24
2. √108
3. √7 . √14
The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions.
What is meant by algebra?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.Algebra is a common thread that runs through practically all of mathematics. It involves the study of variables and the rules for manipulating them in formulas. Since all mathematical applications involve manipulating variables as though they were numbers, elementary algebra is a prerequisite.The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.Given data :
1. We split it into the following:
[tex]\sqrt{4*6}[/tex]
Now, we use the radical rule which states that,
[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0
So, we get,
[tex]\sqrt{4}[/tex] [tex]\sqrt{6}[/tex]
= 2[tex]\sqrt{6}[/tex]
2. We split it into the following:
[tex]\sqrt{12*9}[/tex]
Now, we use the radical rule which states that,
[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0
So, we get,
[tex]\sqrt{12}[/tex] [tex]\sqrt{9}[/tex]
= 6 [tex]\sqrt{3}[/tex]
3. √7 . √14 =
= √7 . √7 .√2
= 7.√2
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If 92 people attend a concert and ticket for adult cot $3 while ticket for children cot $2. 25 and total receipt for the concert wa $246. 75, how many of each went to the concert?
The people who went to the concert will be 53 Adults and 39 Children respectively.
We will solve this problem with the help of a Binomial equation.
Let the number of adults is X and the number of children is Y.
Our first equation will be =
X + Y = 92
The total cost for adults is $3 and for Children is $2.25.
The total receipt for the concert is $246.75.
Our second equation will be =
3X + 2.25Y = 246.75
From equation 1, we get
X + Y = 92
X = 92-Y
Substitute this in equation second equation, and we get
3(92-Y) + 2.25Y = 246.75
276 - 3Y + 2.25Y = 246.75
-0.75Y = 246.75 - 276
-0.75Y = -29.25
Y = 39
So, our number of Children is 39.
Putting the value of Y in the first equation, we get:
X = 92 - 39 = 53
So, our number of adults is 53.
Therefore 53 Adults and 39 Children went to the concert respectively.
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Use the graphing tool to solve the system.
4x-15=-43
2×-3y=-2
Which ordered pair is the best estimate for the solution to the system?
A (6.5, 5.2)
B (5.5, 4.3)
C (5.1, 4.8)
D (4.8, 5.2)
The solution for the given system of equations is (5.5, 4.333).The correct option is B
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
y - y1 =m (x - x1)
We have the following set of equations -
4x − 15y = −43
2x − 3y = −2
These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graph that the solution is given by coordinate - (5.5, 4.333).
Therefore, the solution for the system of equations is (5.5, 4.333).
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What type of polynomial is the expression 9x² 30x 25?.
The polynomial x° 9x* 3x 5 has a degree of 3.
The highest power of a polynomial's variable is the polynomial's degree. The maximum power of the variable in the polynomial x* 9x* 3x 5 is 3, indicating that the polynomial has a degree of 3.
The highest power of a polynomial's variable is the polynomial's degree. The polynomial x*9x* 3x 5 has a degree of 3 since the largest power of the variable is 3, which is 3. A polynomial's degree is equal to the largest power of the variable it contains. The maximum power of the variable.
The polynomial x* 9x*3x 5 is 3, indicating that the polynomial has a degree of 3. The easiest way to do this is to look at the polynomial's variable's highest exponent. The polynomial's degree reveals its level of complexity and the quantity of its solutions. In order to ascertain a polynomial's type, number of terms, and root values, it is crucial to understand the degree of the polynomial.Understanding a polynomial's degree also aids in predicting the kind of graph it will generate.
Complete question:
What type of polynomial is the expression 9x² 30x25 What degree does the polynomial x3 9x2 3x5 have?What distinguishes the two polynomials?
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The expression 9x² + 30x + 25 is a third degree (or cubic) polynomial.
To determine the degree of a polynomial, we look at the term with the highest degree of x. In this case, the highest degree is x², which has an exponent of 2. Therefore, this polynomial is a third degree polynomial.
Another way to determine the degree is to look at the number of terms in the polynomial, which is three in this case. A polynomial with three terms is typically referred to as a cubic polynomial. In general, the degree of a polynomial with n terms is equal to n - 1.
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ord CB is a diameter and
The Arc AB = (π * r * 38) / 180.
What is central angle?
A central angle is the angle formed when two radii intersect at the center of a circle.
Since chord CB is a diameter of the circle, angle B is a right angle and measures 90 degrees. Arc AB is half the circumference of the circle, so its measure is equal to half the circumference times the ratio of the central angle to the total central angle (360 degrees) of the circle.
Let r be the radius of the circle. Then the circumference is 2 * π * r and the measure of arc AB is:
Arc AB = (1/2) * 2 * π * r * (angle B / 360)
Arc AB = (π * r * angle B) / 180
Arc AB = (π * r * 38) / 180
Therefore, Arc AB would be (π * r * 38) / 180.
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.43333333333 as a fraction
Answer:
13/30
Step-by-step explanation:
In how many ways can four people be selected from this group of seven
Answer:
a group of 4 people can be selected in 35 ways
Which is bigger -1/8 or -2/11
let's put both fractions using the same denominator by multiplying each top and bottom by the other's denominator.
[tex]-\cfrac{1}{8}\cdot \cfrac{11}{11}\implies \boxed{-\cfrac{11}{88}}\hspace{15em}-\cfrac{2}{11}\cdot \cfrac{8}{8}\implies \stackrel{\textit{\LARGE \checkmark}}{\boxed{-\cfrac{16}{88}}}[/tex]
well, let's take a looksie above, on the positive side of the number line, 16/88 is larger than 11/88, however, on the negative side, the closer to "0", the larger, for that matter -1 is a much larger number than -1,000,000.
So, -11/88 is closer to 0 on the negative side, and because of that, is larger than -16/88 that is farther from 0.
Express the following ratio in it's simplest form: 8kg:800g:4000g
Answer:
Step-by-step explanation:
8kg = 8000 grams
New Ratio = 8000:800:4000
Reduced = 20:2:10
Reduced even more = 10:1:5
HOPE THIS HELPED!
y varies directly with x when y=16 then x=4, find what y will be when x is 5.5?
Answer:
30.25
Step-by-step explanation:
This is because y is the square of x
HOPE IT HELPS YOUPLS RATE AS BRAINLIEST ANSWERHow do you translate a log graph?.
Answer:
If h>0 , the graph of the base function shifts to the right. If h<0 , the graph of the base function shifts to the left. The function y=logb(x)+k y = l o g b ( x ) + k is the base function y=logb(x) y = l o g b ( x ) shifted vertically by k .
Step-by-step explanation:
How many types of log functions are there?.
There are mainly two types of logarithmic functions - common logarithm and natural logarithm.
Common logarithm (log): The logarithm function with base 10, it is represented as log10(x) or simply log(x) if the base is not specified.
Natural logarithm (ln): The logarithm function with base e (approx 2.718), it is represented as ln(x)
These two logarithmic functions are the most commonly used and have many applications in mathematics, physics, engineering, and other sciences. They are inverse functions of the exponential functions (10^x and e^x) respectively.
Additionally, there are other types of logarithms, such as logarithms with bases other than 10 or e, for example log2(x) which is logarithm with base 2, it is used in information theory and computer science.
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write a multiplication equation that represents the question How many 2/3's are in 9/8
The equation (2/3)x = 9/8 represents the question "How many 2/3's are in 9/8?" because it shows that the unknown number of 2/3's (represented by x) multiplied by 2/3 equals 9/8.
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.
The following equation represents the question "How many 2/3's are in 9/8?" because it shows that the unknown number of 2/3's (represented by x) multiplied by 2/3 equals 9/8.
(2/3)x = 9/8
To find out how many 2/3's are in 9/8, you would need to solve for x by dividing both sides of the equation by 2/3.
⇒ x = (9/8)/(2/3)
⇒ x = (9/8) × (3/2)
⇒ x = 27/16
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Quadrilateral ABCD has vertices A(3, 8), B(6, -8),
C(-6, -6), and D(-3, 4). Using the origin as the
center of dilation, the quadrilateral is horizontally
stretched by scale factor 4/3 then vertically
compressed by scale factor 1/2
Part A
Graph quadrilateral A"B"C"D".
the dilatation of the quadrilateral ABCD, where the vertices' coordinates are [tex]A (x1,y1), B (x2,y2), C (x3,y3),D(x4,y4){}[/tex] is written as: with scale factor k.
What are the vertices of a quadrilateral ABCD?A(,3,8), B(6,-8), C(-6,-6) and D are the vertices of the quadrilateral ABCD (-3,4) Establish the rhombic shape of ABCD.
A polygon with four sides exactly is referred to as a quadrilateral. The fact that a quadrilateral has exactly four vertices and four angles is also implied by this.
Each diagonal is parallel to the other. It is therefore a rhombus. The diagonals of the parallelogram are a rectangle, rhombus, and square since they are congruent and perpendicular to one another. A rhombus is ABCD.
[tex]A(x1,y1){}[/tex]⇒[tex]A'(kx1,ky1){}[/tex]
[tex]B(x2,y2){}[/tex]⇒[tex]B'(kx2,ky2){}[/tex]
[tex]C(x3,y3){}[/tex]⇒[tex]C'(kx3,ky3){}[/tex]
[tex]D(x4,y4){}[/tex]⇒[tex]D'(kx4,ky4){}[/tex]
Therefore, a dilated quadrilateral A'B'C'D"s vertices would have the coordinates [tex]A'(kx1,ky1), B'(kx2,ky2), C'(kx3,ky3), and D(kx4,ky4){}[/tex]
It should be noted that "k" could have an integer, decimal, or fractional value.
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What is log called?.
The inverse function of the power of two functions is the binary logarithm, sometimes known as log base 2.
Given,
For each real number n, according to the general logarithm, can be expressed as an exponential function.
n = aˣ
The logarithm form is written as follows: Log base 2 is the power to which 2 must be raised to obtain the value of n.
logₐ n = x
Here, "a" is a base that is a positive real integer, and "x" is an exponent. For each real number x, the formulas for log base 2 functions are provided as;
x = log₂ n
That is equivalent to,
2ˣ = n
The base 0 logarithm and negative logarithms are not defined by the real number system.
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What do you call the expression a2 2ab b2?.
Answer:
perfect square trinomials
Step-by-step explanation:
Comes from (a+b) ^2
How do you write 21600000 in standard form?.
To write 21600000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point.
21600000 in standard form would be written as 2.16 x 10^7. Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers. To write a number in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point.
The number of places the decimal point is moved is indicated by a power of 10. In the case of 21600000, the decimal point is moved 7 places to the left, giving us 2.16 x 10^7. This notation makes it easy to compare numbers of different magnitudes, and it simplifies calculations involving large or small numbers. It is commonly used in scientific, engineering and mathematical fields. A standard form is a useful tool for expressing numbers in a clear and concise way.
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(Factoring Algebraic Expressions LC) Rewrite 5x + 25 using a common factor. 5(x + 5) 5(x + 25) 5x(x + 5) 5x(x + 25)
What is an example of no solution?.
The system of equations x + 2y = 3, 2x + 4y = 15 is an example of no solution.
If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution. This sort of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel, and the system of equations has no solution.
Given equations are x + 2y = 3
2x + 4y = 15
a₁ = 1, b₁ = 2, c₁ = -3
a₂ = 2, b₂ = 4, c₂ = -15
a₁/a₂ = 1/2
b₁/b₂ = 1/2
c₁/c₂ = 1/5
a₁/a₂ = b₁/b₂ ≠ c₁/c₂
So, the system of equations has no solution.
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10. The equation 98.4=(12.3)8 shows how much it costs for a company to buy 8 new
uniforms. How much does it cost per uniform?
1
Question 11
1 pts
11. The equation 26.70=k6 shows that buying 6 bags of apples would cost $26.70. How
much would it be for one bag?
10) Using the equation 98.4 = (12.3)8, it costs $12.30 (cost per unit) per uniform.
11) Using the equation 26.70 = k6, the cost of one bag of apples (unit rate) is $4.45.
What is the unit rate?The unit rate is the quotient of the total cost divided by the number of items contained.
The unit rate is the same as the average or mean of a data set.
We describe the unit rate as the slope of a linear equation.
The unit rate shows the constant rate of change in an equation.
The total cost of 8 uniforms = 98.4 = (12.3)8
The cost per uniform = 12.30 (98.4/8)
The total cost of 6 bags of apples = 26.70
The cost per unit = 4.45 (26.70/6)
Thus, the unit rate or cost is also described as the variable unit cost.
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Use cross products to solve for x. Type your answer as a simplified fraction (Ex. 37/4).
5/x+3 = 4/x
X =
Answer:
x=1/3
Step-by-step explanation:
= 5/x - 4/×=3
= 1/x=3/1
= 1=3×
= x=1/3
What is the displacement for the the following changes in position? -4km to 5km
-9km is the displacement for the changes in position from -4km to 5km.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
We have to find the displacement for the the following changes in position
-4km to 5km.
Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude.
-4-5
=-9 km is the displacement.
Hence, -9km is the displacement for the changes in position from -4km to 5km.
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a rectangular garden is 115 * 90 m.it has two roads, each 6 m wide, running in middle of it, one parallel to its length and other parallel to its breadth.find the cost of constructing the roads at $ 100 per m
Step-by-step explanation:
so, the first road is 115 m long, the second is 90 m long.
we should be finished, if we multiply each road length by $100, right ?
well, not quite.
because the 2 roads overlap. for this overlap area we don't need to pay twice.
we have the choice : to which of the 2 roads do we assign the overlap area ?
let's "give" it to the longer road.
so, the cost for the longer road is simply
115 × 100 = $11,500
the cost for the shorter road is then without the overlap area (6 meters : the width of the other road)
(90 - 6)×100 = 84×100 = $8,400
in total the costs are
$11,500 + $8,400 = $19,900
0.4n=4+0.9n i don't know where is the step to solve the problem
Answer:
n = - 8
Step-by-step explanation:
0.4n = 4 + 0.9n ( subtract 0.9 from both sides )
- 0.5n = 4 ( divide both sides by - 0.5 )
n = - 8
2(3b+6) = 78
Algebra
Answer:
b = 11
Step-by-step explanation:
2(3b + 6) = 78 (divide both sides by 2 )
3b + 6 = 39 ( subtract 6 from both sides )
3b = 33 ( divide both sides by 3 )
b = 11
Answer:
2(3b+6) = 78
6b+ 12 = 78
Subtract 12 from both sides
6b+ 12 = 78
6b+12-12=78-12
6b = 66
b = 11
Negative 5X plus 2Y equals 9Y equals 7X solve the system of equations
The solution for the system of equations as given in the task content is; x = 1 and y = 7.
What is the solution of the given system of equations?It follows from the task content that the solution for the given system of equations is to be determined.
On this note, since the given equations can be written as;
-5x + 2y = 9
y = 7x
Therefore, by substitution of y for 7x in the first equation; we have;
-5x + 2 (7x) = 9
-5x + 14x = 9
9x = 9
x = 9/9 = 1
Hence, since y = 7x; y = 7 (1) = 7.
Ultimately, the solution for the system of equations is such that; x = 1 and y = 7.
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"Lake superior has roughly 25 times the volume of Lake Erie. If the volume of Lake
Superior is approximately 1.22x10^10 km^3, what is the approximate volume of Lake
Erie?"
Answer:
[tex]\boxed{\sf{30.5 \times 10^{10}\;km^3}}[/tex]
Step-by-step explanation:
Volume of Lake Erie
[tex]\sf {= 25 \times 1.22 \times 10^{10} \\\\= 30.5\times 10^{10} \;km^3}[/tex]
Determine whether the given coordinate are the vertice of a triangle X(1,-3), Y(6,1), Z(2,2)
Yes, the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.
1. Calculate the distance between the points X and Y using the distance formula:
d = √[(x2 - x1)2 + (y2 - y1)2]
d = √[(6 - 1)2 + (1 - (-3))2]
d = √[52 + 42]
d = √25 + 16
d = √41
d = 6.4
2. Calculate the distance between the points Y and Z using the distance formula:
d = √[(x2 - x1)2 + (y2 - y1)2]
d = √[(2 - 6)2 + (2 - 1)2]
d = √[(-4)2 + 12]
d = √16 + 12
d = √28
d = 5.3
3. Calculate the distance between the points Z and X using the distance formula:
d = √[(x2 - x1)2 + (y2 - y1)2]
d = √[(1 - 2)2 + (-3 - 2)2]
d = √[(-1)2 + (-5)2]
d = √1 + 25
d = √26
d = 5.1
Since each side of a triangle must have a length greater than 0, and the distances calculated above are all greater than 0, then the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.
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