this is technically a 7 page essay, if you put this on 10000000000000x text size, 2+2=4 for bcs thats law of math, 1+1=2 bcs thats law of math.
Count with your fingers,
2 + 2 =4
1+1 = 2
Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible. Which is it?
Hence, yes we can solve the triangle with the help of Law of Cosines.
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given that,
Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible.
Yes, with the help of Law of Cosines we can solve the triangle and the formula for it is
[tex]c^2=a^2+b^2-2abcos(C)[/tex]
where, [tex]a,b,c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle.
Hence, yes we can solve the triangle with the help of Law of Cosines.
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What is an example of linear on a graph?
An example of linear graph is y=2x+1
What is linear graph?A linear equation is graphically represented by a linear graph.
For given real numbers A, B, and C, where A and B are not 0, a linear equation is one that can be expressed as Ax + By = C.It is a straight line graph.
Let's examine the graph.
A straight line is formed on the graph by the equation y=2x+1, which is a linear equation. When the value of x rises, the value of y eventually rises by the sum of the value of x plus two.
1). Determine the two changing quantities.
2).Let x and y be the first and second quantities, respectively.
3).Next, find out three ordered pairs (x, y) which satisfy the given equation.
4).Present these values in a tabular form.
5).Plot the points given in the graph.
6).Join the points.
This way we can form our graph
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please I need help on question 6
The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;
x = 9
DE = 13
EF = 28
DF = 28
What is an isosceles triangle?An isosceles triangle is a triangle that has two angles in the triangle that are congruent and two congruent sides.
The specified parameters are;
∠D is congruent to ∠E in triangle ΔDEF
The length of the segments of ΔDEF are;
DE = x + 4
EF = 4·x - 8
DF = 7·x - 35
The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)
Therefore;
EF = DF (Definition of an isosceles triangle)
4·x - 8 = 7·x - 35
7·x - 4·x = 3·x = 35 - 8 = 27
3·x = 27
x = 27 ÷ 3 = 9
x = 9
DE = x + 4
Therefore;
DE = 9 + 4 = 13
EF = 4·x - 8
Therefore;
EF = 4 × 9 - 8 = 28
DF = 7·x - 35
Therefore;
DF = 7 × 9 - 35 = 28
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The population of a country has been decreasing for several decades. In 1990, the population was about 152 million people. In 2010, the population was about 147 million people. Determine the percent decrease in the country's population during this time period.
During the time period of 20 years the percent decreases in the country's population is 3.28%.
What is Percentage?Percentage is a number or ratio which is a fraction of hundred.
Given,
Population of the country in 1990 = 152 million
Population of the country in 2010 = 147 million
Percent decrease in the population will be ,
= [ (1990's population - 2010's population)/1990's population ]*100
= [ (152 - 147 )/152]*100
= [5/152]*100
= 3.28%
Hence , the decrease in the population will be 3.28%.
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Find the amount Erica owes at the end of 6 years if $5300 is loaned to her at a rate of 8 % compounded monthly. use A=P(1+r÷n)ⁿt
The amount owed is $____.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The compound interest implies that Erica owes $10865 after 5 years
How to determine the amount Erica owes?The given variables can be represented as:
Loan amount P = $5300Rate of interest, R = 8%Time to pay back the loan, t = 6 yearsThe compound interest formula is given as
A = P(1 + r/n)^nt
Also from the question, we have
n = 12
This is so because the loan is compounded 12 times in a year as a result of being compounded monthly
Solving further, we replace the variables with their values in the above equation
A = 5300 * (1 + (8%/12))^(6*12)
Evaluate
A = 10865
Hence, the amount owed is $10865
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please help!! which ones are functions and which aren’t? tyia!
Solve for
x
xx.
Assume the equation has a solution for
x
xx.
19
x
+
r
x
=
−
37
x
+
w
The value of x in the Algebraic expressions is x = w / (56+r).
What is Algebra?
Algebra is a branch of mathematics focused on the study of mathematical symbols and the rules for manipulating those symbols. In algebra, letters and other symbols represent numbers, which can be manipulated and combined to solve equations and other mathematical problems. Algebra is used in a variety of different fields, from engineering to economics, and is essential for anyone studying mathematics. Algebra can be used to solve problems involving linear equations, quadratic equations, polynomials, and more. Algebra also provides an important foundation for more advanced fields of mathematics, such as calculus. By learning the basics of algebra, students can gain an understanding of key mathematical concepts and gain the skills necessary to solve complex problems.
The solution is,
given: 19x + rx = -37x + w
( 19x + 37x) = w - rx
56x + rx = w
x(56+r ) = w
x = w / (56+r)
Therefore the value of x in the algebraic expression is x = w / (56+r).
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3. Represent and Connect Write 2,857 using only hundreds and ones.
By using a linear combination, we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
How to write the number using only hundreds and ones?To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:
2,857 = a*100 + b*1
There are multiple solutions for this, we can use b to cover the ones and the tens, so:
57 = b*1
57 = b
And we can use a to cover the hundreds and thousands, so:
2,800 = a*100
2,800/100 = a
28 = a
Then we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
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What are 6 techniques used by propaganda?
Answer:
Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.
Step-by-step explanation:
What is propaganda ?Information—especially that which is slanted or deceptive—used to advance or publicize a specific political cause or point of view.
Glitzy Generalizations
Use expressions or words that sound appealing and are widely accepted.
Card Arranging
Using only those ideas and facts that support your argument.
Plain people
Tell voters that you are a normal person with same needs and beliefs as theirs.
Testimonial
Persuades people to do something by leveraging their popularity as a celebrity or athlete.
Bandwagon
Encourages a tendency to follow the crowd
Using names
Put a bad name on your opponent.
Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.
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NO LINKS!! Use tests for symmetry to determine which graphs from the list below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply.) Part 1
Answer:
[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]
[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]
Step-by-step explanation:
Part (a)A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.
Linear functions are not symmetric with respect to the y-axis.
Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.
Cubic functions are not symmetric about the y-axis.
Square root functions are not symmetric about the y-axis.
There are two quadratic functions with x² in the given answer options.
Test to see if they are symmetric with respect to the y-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.
Given function:
[tex]y=-6x^2[/tex]
Replace x with (-x):
[tex]\implies y=-6(-x)^2[/tex]
[tex]\implies y=-6x^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Given function:
[tex]y=4x^2-2[/tex]
Replace y with (-y) and x with (-x):
[tex]\implies y=4(-x)^2-2[/tex]
[tex]\implies y=4x^2-2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Part (b)A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.
Linear functions are not symmetric with respect to the x-axis.
Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.
Cubic functions are not symmetric about the x-axis.
Square root functions are not symmetric about the x-axis.
There is one quadratic functions with y² in the given answer options.
Test to see if it is symmetric with respect to the x-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Given function:
[tex]x=\dfrac{1}{4}y^2[/tex]
Replace y with (-y):
[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]
[tex]\implies x=\dfrac{1}{4}y^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.
Determine where the real zeros of f(x)=x^4-2x^3+x-2 are located.a. at -1 & 2 c. at 0 & 1 b. at 1 & 2 d. at -1 & 1
The real zeroes of the given polynomial are located at (1, 2).
What are zeroes of the polynomial?The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
Given that, x⁴-2x³+x-2
Checking the real zeroes,
Considering point (1, 2)
y = 2 and x = 1
Putting the values,
x⁴-2x³+x-2 = 1-2+1-2 = 2
And, y = 2
Therefore, LHS = RHS
Hence, The real zeroes of the given polynomial are located at (1, 2).
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What does it mean for addition to be closed?
For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
Yes, whole numbers are closed under addition
It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
So the set of whole numbers are closed under addition
Addition of the set of positive integers is closed because the sum of any two integers is also an integer.
Consider subtraction. Positive numbers are not closed under subtraction because picking a larger number to subtract from a smaller one results in a negative number result.
Therefore, For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
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Are two triangles with two pairs of congruent angles and one pair of congruent sides congruent?
If two triangles have one pair of congruent sides and two pairs of congruent angles, then the answer is yes.
What in mathematics is a congruence?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
SSS SAS ASA AAS: What is it?
SSS (side-side-side) Congruent on all three of the corresponding sides. SAS (side-angle-side) Congruence exists between two sides and the angle between them. ASA (angle-side-angle)
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2. The two polygons below are congruent.
Which statement is a valid congruence statement?
A. polygon PQRST Ξ polygon XWVZY
B. polygon PQRST Ξ polygon WXYVZ
C. polygon PQRST Ξ polygon XYZVW
D. polygon PQRST Ξ polygon WVZYX
Fill in the boxes with the correct numerator or denominator to make each then ture
Answer:
2. 13
3. 3
4. 5
7. 4
8. 37
9. 5
Step-by-step explanation:
Denominator: same as the denominator of the fraction in the mixed number.
Numerator:
1. Multiplying the denominator of the fraction by the whole number, and
2. Adding that number to the numerator of the fraction
The numerator signifies the total parts taken, and the denominator indicates the entire parts as a whole.
1) 2*3/5 = 13/5
2) 4*2/3 = 14/3
3) 6*4/5 = 34/5
4) 5*3/4 = 23/4
5) 7*2/5 = 37/5
6) 9*1/5 = 46/5
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Write an expression to represent: 8 less than the product of 2 and x.
Use diagram to answer the questions below
a. Angle g is corresponding to angle c.
b. Angle f is alternate to angle d.
c. Angle d is corresponding to angle h.
d. Angle c is vertically opposite to angle a.
e. Angle c is alternate to angle e.
f. Angle f is vertically opposite to angle h.
g. Angle e is corresponding to angle a.
h. Angle e is vertically opposite to angle g.
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Explain why (0,3) is not a solution to y
Answer:
Step-by-step explanation:
3< 0 + 2
3 < 2
the inequality is false because 3 is greater than 2, so the ordered pair (0,3) can’t be a solution of the inequality
Answer:
(0, 3) is not a solution to y < x + 2.
Step-by-step explanation:
Plug the given coordinates in to the inequality:
(0, 3) → x = 0, y = 3
y < x + 2
3 < 0 + 2
3 ≮ 2
(0, 3) is not a solution to y < x + 2.
Find x. Finding an angle measure given extended triangles
Answer:
x = 44°
Step-by-step explanation:
We can take angles as,
→ x = ?
→ y = 52° (opposite angles are equal)
→ z = ?
The value of z will be,
→ z + 96° = 180°
→ z = 180° - 96°
→ [ z = 84° ]
Now the value of x will be,
→ x + y + z = 180°
→ x + 52° + 84° = 180°
→ x + 136° = 180°
→ x = 180° - 136°
→ [ x = 44° ]
Hence, the value of x is 44°.
65 less than twice Janelle's savings
Answer:
x = 2y - 65
Step-by-step explanation:
An exponential function f ( x ) = a b x passes through the points (0, 3) and (3, 81) what are the values of a and b
The values of a and b are;
⇒ a = 3
⇒ b = 3
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
An exponential function is,
⇒ f (x) = a bˣ
And, It passes through the points (0, 3) and (3, 81).
Now,
Since, It passes through the points (0, 3) and (3, 81).
Hence, Substitute x = 0 , f(x) = 3 in the function,
⇒ f (x) = a bˣ
⇒ 3 = a b⁰
⇒ a = 3
And, Substitute x = 3 , f(x) = 81 and a = 3 in the function,
⇒ f (x) = a bˣ
⇒ 81 = 3 b³
⇒ b³ = 27
⇒ b = 3
Thus, The values of a and b are;
⇒ a = 3
⇒ b = 3
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Evaluate the expression.
(6 x 4) + (15÷ 5) =
?
Answer:
27
Step-by-step explanation:
first you multiply 6x4 which is 24 the you divive 15 by 5 you'll get 3 then you add 24 + 3 and your answer is 27
sqrt((x^(2)-1)^(2))=x^(2)-1
The algebraic expression √((x²-1)²) simplifies to x²-1
How to simply an algebraic expression?
An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
Given: sqrt((x^(2)-1)^(2))=x^(2)-1
√((x²-1)²)
The square root will cancel out the square:
Thus, √((x²-1)²) = x²-1
Therefore, √((x²-1)²) simplifies to x²-1
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How do you find the range of a function step by step?
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range.
What is range of a function?
The group of all outputs of a function is called its range. for example: Let's have a look at the function f: A→ B, where f(x) = 2x and A and B each represent a "collection of natural numbers. The domain in this case is A, and the co-domain is B. The range then appears as the function's output. so Set of all even natural numbers is the range.
What do you mean by a function?A relation between a number of set of inputs with only one output corresponding to each of the input is called function.
Example:
Y = 2x
1. First, we have to write the function y=f(x) and then solve the equation for x and taking out equation of form x=g(y).
Suppose we have a function y=x2+1 and we have to find it range so,
we have to solve it for x to get
x=√y-1.
2. Now we have to find the domain of g(y), and this is simply the range of function f(x).
For our example,
y−1≥0, so [1,∞) is the range of f(x)=x2+1.
3. If we can't solve equation for x, then we can try it by drawing the graph of the function and find its range.
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Goran must choose a number between 67 and 113 that is a multiple of 2, 6, and 8. Write all the numbers that he could choose. If there is more than one number, separate them with commas.
The number that Goran can choose, which will be multiples of 2, 6, and 8, between 67 and 113 are 72, 96
What are the multiples of 2, 6, and 8 between 67 and 113?To find out the numbers that Goran can choose, find the multiples of 2, 6, and 8 that are between 67 and 113. Then the common multiples of these numbers within that range, are the numbers to be chosen.
Multiples of 2 between 67 and 113 :
68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112
Multiples of 6 between 67 and 113 :
72, 78, 84, 90, 96, 102, 108,
Multiples of 8 between 67 and 113 :
72, 80, 88, 96, 104, 112
The numbers that are multiples of 2, 6, and 8 are:
72, 96
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Find the number of distinguishable permutations of the letters in each word below.
(a) bigger
(b) Hollywood
(c) possess
The number of distinguishable permutations in the given letters are:
a.) Bigger= 720
b.) Hollywood = 362,880
C.) possess = 5040
What is permutation?Permutation is defined as the arrangement of data set in a definite form which involves multiplication from the given number to 1.
The word 'bigger' contains 6 letters. Therefore the permutation of 6 = 6×5×4×3×2×1 = 720
For the word 'hollywood' contains 9 letters. Therefore the permutation of 9 =9×8×7× 6×5×4×3×2×1= 362,880
For the word 'possess' contains 7 letters. Therefore the permutation of 7 = 7× 6×5×4×3×2×1 = 5040.
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The graph shows the amount of book sales
over several days. Determine if the
relationship is proportional. Find and
interpret the slope. Then find the unit rate
and compare it to the slope.
The two quantities have proportional relationship and it's slope is 333.33
ProportionsProportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
In this case, we have to determine is there's a uniform increase or decrease of the quantity.
The formula of proportionality is often given as
y = kx
k = constant of proportionalityLet's take two points and check if they share the same constant of proportionality
2000 = k(6)
k = 333.33
1000 = k(3)
k = 333.33
The relationship between sales and day is proportional.
The slope of the graph is given as
m = y₂ - y₁ / x₂ - x₁
m = 2000 - 1000 / 6 - 3
m = 333.33
NB: The slope and constant of proportionality in this case are the same quantity.
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if sina + sinb = m and cosa + cosb = n then prove that cos(a-b) = 1/2(m^2 + n^2 -2)
Proved
Used identities
cos (a - b) = cos a cos b + sin a sin b,sin²a + cos²a = 1,(a + b)² = a² + 2ab + b²what is the percent decrease 350 to 200
Answer:
75%
Step-by-step explanation:
First, you subtract 200 from 350 to get the difference, which is 150.
Then, you do 150 divided by 200 since 200 is the starting number and it is increasing by 150.
150/200 = 0.75
To convert the decimal into a fraction multiply by 100.
0.75*100 = 75
Can someone explain the formula I'd use to solve this
The formula for slope-intercept form is: y = mx + b
m = the slope of the line
b = the y-coordinate of the y-intercept, (0,b)
In this case, the slope is 3, since you go up 3 and to the right 1 to get from the point at (1,1) to the point at (2,4). 3/1 = 3
The line crosses the y-axis at (0,-2), so your b-value is -2.
The equation is y = 3x - 2.
In general, lines that increase (go uphill) from left-to-right have a positive slope. Lines that decrease (go downhill) from left-to-right have a negative slope.
