The factors of substitution are separating a polynomial into its component polynomials.
Factoring polynomials mean separating a polynomial into its constituent polynomials. Sometimes, when polynomials are particularly complicated, it is easiest to substitute a simple term and factor it down.
This is a quick technique to use with complicated polynomials, particularly if subsets of that polynomial repeat.
For example, we need to factorise (x − y)(x − y − 1) − 20
Let S = x − y. Then substituting S in for x − y for ease of computation, we get
(x − y)(x − y − 1) − 20
= (S)(S − 1) − 20
= S² − S − 20
=(S − 5)(S + 4)
=(x − y − 5)(x − y + 4).
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Find the missing values in the radio table. Then write the equivalent ratio
3. 6
4. 24
A ratio remains the same if both antecedent and consequent are multiplied or divided by the same non-zero number.
How to find the missing number?Step by step explanation:
i.e., a/b = pa/pb = q a/q b ,p ,q ≠0
From the given table we can see that:
For the second column
Since, 6*0.5=3
So, multiply 10 by same number
10*0.5=5
For third column:
since 24=10*5
So, multiply 6 by same number
5*6=30
Hence, the missing values are 30,5
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Greatest common factor of 18, 30, 54
Answer: 6
Step-by-step explanation:
1) Ed invests $1,000 into a money market account that earns 8% annual interest compounded quarterly. How much money will
he have earned after 8 years?
The money market account earns 8/4 = 2% interest per quarter.
In one year, there are 4 quarters.
so, the formula to calculate the balance after 8 years is:
A = P (1 + r/n)^(nt)
where A is the final balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested for.
Substituting in the given values,
A = 1000 (1 + .02)^(4*8)
A = 1000 (1.02)^32
A = 1000 (1.8587)
A = 1858.7
So after 8 years, Ed will have earned $1858.7.
How many pizzas in the Venn diagram
have ham as an ingredient?
Has ham
Meat feast
Scorcher
Hawaiian
Capricciosa
Has olives
Napolitana
Veggie
Pepperoni
Margherita
According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.
what is Venn diagram ?The Venn diagram, a frequent style of diagram showing logical connections between sets, was made popular by John Venn in the 1880s. Diagrams are used to teach fundamental set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. The relationships between two or more groups of elements are shown in a Venn diagram by overlapping circles and other shapes. When arranging information graphically, it is frequently advantageous to emphasize the similarities and differences between components. The intersection of two large circles forms the central empty area of a Venn diagram.
given
From the image,
ham is an ingredient in Meat feast, Scorcher, Hawaiian, and Capricciosa.
According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.
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what is the equation of a line with a y-intercerpt of a -3 and a slope of 5
Answer:
Step-by-step explanation:
y = (a-3)x+5
Answer:
y=3x+5
Step-by-step explanation:
Miriam took a survey, asking each family in her neighborhood how many pets they have. She made a graph showing the results: [asy] size(5.5cm); draw((0,30)--(0,0)--(41,0)); for(int i=1; i<7; i+=1) {draw((0.6,5*i)--(-0.6,5*i)); draw((0.6,5*i)--(41,5*i),black+0.5+dashed); }; path a=(3,0)--(3,30)--(9,30)--(9,0)--cycle; path b=(9,0)--(9,15)--(15,15)--(15,0)--cycle; path c=(15,0)--(15,15)--(21,15)--(21,0)--cycle; path d=(21,0)--(21,30)--(27,30)--(27,0)--cycle; path e=(27,0)--(27,5)--(33,5)--(33,0)--cycle; path f=(33,0)--(33,5)--(39,5)--(39,0)--cycle; fill(a,gray); fill(b,gray); fill(c,gray); fill(d,gray); fill(e,gray); fill(f,gray); draw(a); draw(b); draw(c); draw(d); draw(e); draw(f); label(rotate(-45)*scale(0.8)*"0 pets",(5,-1),SE); label(rotate(-45)*scale(0.8)*"1 pet",(11,-1),SE); label(rotate(-45)*scale(0.8)*"2 pets",(17,-1),SE); label(rotate(-45)*scale(0.8)*"3 pets",(23,-1),SE); label(rotate(-45)*scale(0.8)*"4 pets",(29,-1),SE); label(rotate(-45)*scale(0.8)*"5 pets",(35,-1),SE); label(scale(0.8)*"1",(-0.6,5),W); label(scale(0.8)*"2",(-0.6,10),W); label(scale(0.8)*"3",(-0.6,15),W); label(scale(0.8)*"4",(-0.6,20),W); label(scale(0.8)*"5",(-0.6,25),W); label(scale(0.8)*"6",(-0.6,30),W); label(scale(0.8)*rotate(90)*"Number of families",(-3.5,15),W); [/asy]Determine the median number of pets per family.
The median number of pets per family is 2.
What is median number?Median number is the middle value of a set of numbers when they are arranged in numerical order. It is also known as the middle number or the 50th percentile. The median number is used to find the middle value when there is an odd number of values in the set, or to find the average of the two middle values when there is an even number of values in the set.
This can be determined by looking at the graph and counting the number of families in each bar.
The bar with 2 pets has the most families, and is the median number.
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In \triangle GHI,△GHI, \overline{IG}\cong \overline{HI} IG ≅ HI and \text{m}\angle H = 51^{\circ}.m∠H=51 ∘ . Find \text{m}\angle G.m∠G.
The measure of the angle ∠G of the isosceles triangle will be 51°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The two triangular legs and their opposing angles are congruent in an isosceles triangle.
In triangles △GHI, IG ≅ HI, and the measure of the angle ∠H = 51°. Then the measure of the angle ∠G will be given as,
The two sides of the triangle △GHI will be congruent. Then the triangle is known as an isosceles triangle.
If IG ≅ HI, then the measure of the angle ∠G ≅ ∠H.
The measure of the angle ∠G of the isosceles triangle will be 51°.
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What is the greatest common factor of 10 and 4x?
The GCF of 10 and 4x is 2.
The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into each of them. Factoring a number means breaking it down into its prime factors. That is;
10 = 2 * 5 , we can see that 2 and 5 are the prime factors of 10.
4x = 4 * x, we can see that 4 and x are the prime factors of 4x.
Since 2 is the only common factor between 10 and 4x, we can conclude that 2 is the GCF of 10 and 4x.
It means that 2 is the greatest number that divides into both 10 and 4x with a remainder.
Therefore, the GCF of 10 and 4x is 2.
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What is the expression written as a single power?
(−4)8 · (−4) −5. (-4)⁰
O (-4)⁰
O-4
(-4)³
O-43
The expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the expression as -
(−4)⁸(−4)⁻⁵(-4)⁰
The given expression is -
(−4)⁸(−4)⁻⁵(-4)⁰
(- 4)⁸ ⁻ ⁵ ⁺ ⁰
(- 4)³
Therefore, the expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.
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The price of a TV was $900 on Tuesday. On Wednesday, the manager reduced the price by 5%. What was the price in dollars of the TV after the reduction?
help me please . i really need help.
Answer: Congruent figures can slide, flip, or turn.
(Translate, reflect, or rotate)
Corresponding Angles are congruent. (Not always)
Corresponding Sides have a scale factor.
Corresponding Sides are Congruent. (Only if they have the same side and shape)
Corresponding Angles have a scale factor. (I Dont Know about this one)
All transformations (translation, reflection,
rotation, and dilation) result in congruent figures. (It would be similar to the pre-image)
i hope this helps sorry I can't do much but i think it might just be the 3 without the bolded words behind it
Help me please i will make u the brainlyest please help me. I even gave you 50 points.
The solution to the simplification of each of the fractions are;
1) ³/₄ * ¹¹/₅
2) 1 ³/₅ miles
3) 1¹/₈ yards
How to solve fraction problems?
1) We are told that;
Caleb has 2¹/₅ yards of rope
Quantity of rope used by Caleb = ³/₄
Thus;
³/₄ of 2¹/₅ simply means that we will multiply both.
2¹/₅ can also be expressed as 11/5. Thus, we now have;
³/₄ * ¹¹/₅
2) Number of miles mary hiked = 6²/₅ miles = 32/5 miles
He stopped at 1/4 of the way.
Thus;
Number of miles before stopping = 1/4 * 32/5 = 8/5
= 1 ³/₅ miles
3) The area is gotten by;
A = length * width
A = 1¹/₂ * ³/₄
= 3/2 * 3/4
= 9/8
= 1¹/₈ yards
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How do you know if the equation is quadratic or not with example?
You get a quadratic equation when the square of the expression that comes after b plus b times that same expression not squared plus c equals 0.
Any equation in algebra that can be written in standard form as
ax^2+bx+c=0,
where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.
The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.
Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.
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may i get some help with this
The value of x is that will ensure that quadrilateral VWXY is parallelogram is 0.25.
What is Quadrilateral?•A polygon called a quadrilateral has four sides, four angles, and four vertices. Parallelograms, Squares, Rectangles, and Rhombuses are the different types of quadrilaterals. Parallelograms also include squares, rectangles, and rhombi.
• All quadrilaterals have a few characteristics. Parallelograms characteristics are each of them has four vertices, each side has four sides, 360 degrees is the sum of all interior angles and two diagonals are present.
•There are regular and irregular quadrilaterals. An ordinary quadrilateral must have four equal sides, four equal angles, and diagonals that cross one another. Only the square can fulfill each of these requirements of a quadrilateral.
As we know that the opposite angles of a parallelogram are equal
hence 10x + 27 = 2x + 29
8x = 2
x = 0.25
Hence, the angles are 29.5
Let the value of angle v and x be a
Now using angle sum property of a parallelogram
29.5 +29.5 + a + a = 360
2a = 301
a = 150.5
hence angle V is 150.5
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A computer costs $800. It loses 1/4 of its value every year after it is purchased.
Use your equation to find v when t is 5. Show how you substituted
In context of the problem,what does the above value of v mean when t was 5?
The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter.
given
This equation can be used to represent the value of the computer: price of the computer one year ago x (1 - rate of decline)
The computer's current market value 0 = $800
Computer value at time 1 is $800 multiplied by 3/14 by 1 to get $600.
The computer's current market value 2 = $600 x 3/4 = $450
Computer value at time 3: $450 multiplied by 3/4, or $337.50
The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.
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solve the systems. 3r=1-s
7s=4-6r
help quick.
Answer: r= 1/5 and s = 2/5
Step-by-step explanation:
trust me
5. A t-shirt is on sale for 20% off the original price (x). Circle the expressions that would help find the sale price of the t-shirt?
x-.20x
x +.20x
(1-.20)x
.80x
80x
.20x
Therefore , the solution of the given problem of expression comes out to be 0.8x is the required expression.
Expression : what is it?Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.
Here,
Given :
Let x be the original price
To find the expression after 20 % discount :
=> x * 20/100 = 0.2x
So,
New price:
=> x - 0.2x
or
=> 0.8x
Therefore , the solution of the given problem of expression comes out to be 0.8x is the required expression.
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What is the answer ?
Answer:
25x+125< 500 15 fewer seats
Step-by-step explanation
this is number 1
i need this like right now.
Answer:
y = 13
Step-by-step explanation:
given (7, 33 ) is a solution of the top equation, then
x = 7, y = 33 satisfies the equation , that is
33 = 7a + 5 ( subtract 5 from both sides )
28 = 7a ( divide both sides by 4 )
4 = a
then
y = 4x + 5 ← top equation
substitute y = 4x + 5 into the other equation
9x + 2(4x + 5) = 44
9x + 8x + 10 = 44
17x + 10 = 44 ( subtract 10 from both sides )
17x = 34 ( divide both sides by 17 )
x = 2
substitute x = 2 into the top equation for value of y
y = 4x + 5 = 4(2) + 5 = 8 + 5 = 13
linda saves 25 dollar evry month in her saving account she took out 100 dollars
The number of months that it would take for Linda to replenish the amount she took out is 4 months.
How to find the number of months ?The number of months it would take Linda to make back the $ 100 that she took from her savings account will depend on the amount that she saves every month.
This amount is $ 25 per month.
The number of months it would take for Linda to replenish the $ 25 would therefore be:
= Amount taken out of account / Amount saved per month
= 100 / 25
= 4 months
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Rest of the qyestion is:
How many months will it take Linda to replenish the amount she took out of her savings account ?
Hello! I have an inverse function question I don’t understand. Please help!!!
An athlete ran 77 km in 7 days. What is the rate the athlete ran per day?
Answer:11
Step-by-step explanation:
77 divided by 7 is 11.
Find Dy/Dx By Implicit Differentiation. 5x^2-xy-4y^2=0
The Implicit Differentiation of 5x^2-xy-4y^2=0 is Dy/Dx= (5x-y)/(-4y)
Using implicit differentiation, Dy/Dx can be found by taking the derivative of both sides with respect to x.
On the left side, the derivative with respect to x of 5x2 is 10x and the derivative with respect to x of -xy is -y.
On the right side, the derivative of 4y2 with respect to x is 0.
Therefore, the equation becomes 10x - y = 0.
Solving for y gives y = 10x.
Substituting this into the original equation, we get 5x2 - 10x2 - 4(10x)2 = 0, which simplifies to -5x2 - 40x2 = 0.
Finally, we can solve for Dy/Dx:
Dy/Dx= (5x-10x)/(-4(10x))
Dy/Dx= (5x-y)/(-4y)
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Help find the perimeter
Answer:
Step-by-step explanation:
As 9: 16.2
Then 6: EF Lets take EF as side x
9:16.2 as
6:x CROSS MULTIPLY ( 9×x and 16.2×6)
Cross multiplying gives you: 9x and 97.2
Then divide both answers by 9 ( 97.2÷9 and 9x÷9)
This gives you x=10.8 which is side EF
To find side AB ADD 9 and 6 to get 15 and subtract this from 36 and you get 21.
Using the same method to find EF find DE and you will get 37.8
Therefore, perimeter becomes:
16.2 + 37.8 + 10.8 = 64.8
HOPE THIS HELPS
Answer:
P△DEF=64,8
Step-by-step explanation:
P△ABC=36, AC=9, BC=6 → AB=21
AB/DE=BC/EF=AC/DF
AC/DF=9/16,2; AB/DE=21/DE ⇒ DE=(21*16,2)/9=37,8
AC/DF=9/16,2; BC/EF=6/EF ⇒ EF=(6*16,2)/9=10,8
P△DEF=16,2+37,8+10,8=64,8
Question is attached. Show workings
Answer:
First question(unnumbered):
[tex]\mathrm{Choice \; (B) : \;\;\dfrac{1}{2}}[/tex]
Question 48
[tex]\mathrm{Choice \;(C)\;\; (x, y) = \left(-1, \dfrac{3}{2}\right)}[/tex]
Question 49
[tex]\mathrm{Choice \; (D)\;\;-1}[/tex]
Step-by-step explanation:
The imaginary variable i is [tex]\sqrt{-1}[/tex] and [tex]i^2 = -1[/tex]
For the unnumbered first question we have
the equation
[tex]\dfrac{1}{1-i}[/tex]
Multiply numerator and denominator by [tex]i + 1[/tex]
[tex]\rightarrow \dfrac{1\cdot \left(1+i\right)}{\left(1-i\right)\left(1+i\right)}\\\\\\= \dfrac{1 + i}{1 - i^2} \;\;\;\;\;\;\;since \;(a +b)(a-b) = a^2 - b^2\\\\\textrm{Since $i^2 = -1$, the denominator becomes:}\\\\1-i^2 = 1 -(-1) = 2\\\\\\[/tex]
Therefore ,
[tex]\dfrac{1}{1-i} = \dfrac{1 + i}{2}\\\\= \dfrac{1}{2} + \dfrac{i}{2}\\\\[/tex]
The real part is [tex]\dfrac{1}{2}[/tex] and the imaginary part is [tex]\dfrac{i}{2}[/tex]
Answer to first question is: ) [tex]\dfrac{1}{2}[/tex]
-------------------------------------------------------------------------
#48
Solve [tex](x, y)[/tex] for [tex]2y\:+\:xi\:=\:4+x-i[/tex] for [tex]$x,y\in\mathbb{R}$[/tex]
For the equation
[tex]2y\:+\:xi\:=\:4+x-i[/tex]
Move the the x and i terms from the right to left side:
[tex]2y + xi - x + i = 4\\\\2y - x +xi + i =4\\\\[/tex]
Since this works out to a real number, the imaginary part is 0
So
[tex]xi + i = 0\\\\xi = -i\\\\x = \dfrac{-i}{i}\\\\x = -1[/tex]
and the real part
[tex]2y - x = 4[/tex]
Substitute for x = -1 in the above to get
[tex]2y -(-1) = 4\\\\2y + 1 = 4\\\\2y = 4-1\\\\2y = 3\\\\y = \dfrac{3}{2}\\\\[/tex]
[tex](x, y) = \left(-1, \dfrac{3}{2}\right)[/tex]
which is choice (C)
------------------------------------------------------------------------
#49
For [tex]$a,b\in\mathb{R}$[/tex]
[tex]a+ib\:=\:\left(2-i\right)^2 \\\\[/tex]
Expand [tex]x(2-i)^2[/tex]
[tex]= 2^2 - 2.2.i +i^2\\\\[/tex]
Since i² = -1 this works out to:
[tex]4 - 4i -1[/tex]
[tex]3 - 4i[/tex]
Therefore
[tex]a + ib = 3 - 4i\\\\[/tex]
Equation real part on left to the real part on the right :
[tex]a = 3[/tex]
Equation imaginary part on left to the imaginary part on the right :
[tex]ib = 4i[/tex]
[tex]b = -4[/tex]
[tex](a + b) = (3 +(-4))\\\\= 3 - 4 \\\\= -1\\\\[/tex]
This would be option (D)
Select all the correct answers.
Which three pairs of side lengths are possible measurements for the triangle?
30°
0
000
60°
BC=5√2, AC = 10
AB=14, AC = 28
AB= 3, BC = 3√3
AB=
4√3, BC = 4
BC=
19√3, AC = 38√3
BC=16, AC = 32
Find the volume of a pyramid with a square base, where the area of the base is 4. 6\text{ cm}^24. 6 cm 2 and the height of the pyramid is 2. 3\text{ cm}2. 3 cm. Round your answer to the nearest tenth of a cubic centimeter.
The volume of the pyramid is 3.5 cubic centimeters.
The volume of a pyramid can be calculated using the formula:
V = (1/3) * Base area * Height
Where Base area is the area of the base of the pyramid, and Height is the distance from the base to the apex of the pyramid.
Given that the area of the base of the pyramid is 4.6 cm^2 and the height of the pyramid is 2.3 cm, we can substitute these values into the formula and solve for the volume:
V = (1/3) * 4.6 cm^2 * 2.3 cm = 3.53 cm^3
So the volume of the pyramid is 3.53 cubic centimeters. Rounded to the nearest tenth of a cubic centimeter, the volume is 3.5 cm^3.
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What is the additive inverse of [(- 3 )+ (- 6 )]?
The additive inverse of (-3) + (-6) is (3 + 6) which is 9
The additive inverse of a number is its opposite, or the number that when added to the original number results in zero. In other words, it is the number that can "cancel out" the original number and make it disappear.
For example, the additive inverse of 3 is -3, because 3 + (-3) = 0. Similarly, the additive inverse of -6 is 6, because -6 + 6 = 0.
Now, for the given expression, the additive inverse of (-3) + (-6) is the number that can "cancel out" the expression and make it disappear. By adding the additive inverse of each term of the given expression we would get 0. Therefore the additive inverse of (-3) + (-6) is (3 + 6) which is 9.
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1.3) (7²-√81) + √125 a) 5 b) 8 c) 10 d) 4
The value of (7²-√81) + √125) is 45
What are square root and square?Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.Similarly, the square of 4 is 16 and the square root of 16 is 4.
A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system. Therefore 4, 16, 25 are examples of perfect squares
7²-√81) + √125 is calculated as
49- 9+ 5 = 45
Therefore the value of 7²-√81) + √125 = 45
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Solve the equation 0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 for j.
Write your answer as a decimal.
Answer:
j = 1.5
Step-by-step explanation:
You want to solve the equation 0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 for the value of j.
SimplifyIt usually works well to simplify such an equation as the first step. That means eliminating parentheses and combining like terms.
0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 . . . . . . given
0.3j -0.1j +3 +0.1 = 2j +0.2 +0.2 . . . . . . eliminate parentheses
0.2j +3.1 = 2j +0.4 . . . . . . . . . . . . collect terms
Solution2.7 = 1.8j . . . . . . . . . . . subtract (0.2j +0.4)
1.5 = j . . . . . . . . . divide by 1.8
The solution is j = 1.5.
__
Additional comment
You are often taught to solve this kind of 3-step equation by subtracting the unwanted variable term and the unwanted constant term in two steps. (The third step is dividing by the coefficient of the variable.) Here, we show those subtractions being done both at once.
The variable term we choose to subtract is the one with the smallest coefficient. That way, the result of the subtraction (1.8j) leaves the coefficient of the variable as a positive number.
Sometimes the variable term on the right is subtracted, so you end up with a "j = " equation. In that case, the equation you would be solving as the last step is ...
-1.8j = -2.7
which requires arithmetic with negative numbers. Negative numbers tend to be associated with more mistakes, so we choose not to go there.