Answer:
All real numbers
Step-by-step explanation:
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 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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EVALUATE ₈C₇ and ₁₁P₅
₈C₇=
₁₁P₅=
The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440
How to determine the permutation and combination expressions?From the question, we have
⁸C₇ and ¹¹P₅
The combination expression: ⁸C₇
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 8 and r = 7
Substitute the known values in the above equation
Total = ⁸C₇
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
⁸C₇ = 8!/7!1!
Evaluate
⁸C₇ = 8
(b) The permutation expression: ¹¹P₅
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 11 and r = 5
Substitute the known values in the above equation
Total = ¹¹P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)
So, we have
¹¹P₅ = 11!/6!
Evaluate
¹¹P₅ = 55440
Hence, the values are 8 and 55440
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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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Write an expression to represent: 8 less than the product of 2 and x.
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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Please I need help on both part A and B
Answer:
Step-by-step explanation:
I hope anyone answers
Help
Please
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.
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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please help!! which ones are functions and which aren’t? tyia!
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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How do you know if AB and CD are congruent?
If the length of two segments is equal then the two segments are congruent.
If l(AB) = l(CD) then seg AB ≅ seg CD.
Two line segments to be congruent if and only if they have the same length.
Two shapes are congruent if they are exactly the same shape and exactly the same size. In congruent shapes, all corresponding sides will be the same length and all corresponding angle will be the same measure.
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which number line represents the solution set for the inequality 4x 3 2 2x
The solution to the inequality expression is x ≥ - 5
what is inequality expressions ?
Both equations and inequalities are mathematical phrases created by connecting two expressions. The two expressions are regarded as being equivalent in an equation.
solution:
The given expression - 4(x + 3) ≤ –2 – 2x
- 4x - 12 ≤ -2 - 2x
-4x + 2x ≤ -2 + 12
-2x ≤ 10
-x ≤ 5
Multiply both sides by - 1
Then x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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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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Match each equation with a graph above:
log (x) a. red R
10× b. black K
e× c. green G
ln (x) d. blue B
The equations are matched as below and the graph is plotted and attached
log (x) b. black K 10× d. blue Be× c. green Gln (x) a. red RWhat is logarithm graph?A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.
The exponential graph is the opposite of logarithmic graph
In the given functions
log (x) is logarithmic function
10× is exponential function
Similarly, the natural exponent graph is the opposite of natural logarithm graph
in the given functions
e× is the natural exponential
ln (x) is the natural logarithm
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what 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
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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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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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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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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Why is it important to make ten?
It is important to make a ten in lower grades to make students understand the subtraction.
According to the question,
We have the following information:
Making a ten
Now, we know that in making a ten method we take 1 from the next left digit of the number from which we are subtracting any other number. Now, this number 1 is treated as 10 instead of 1 and then 10 is added to the digit to ease subtraction in lower grades.
Now, the subtraction can be easily performed by subtracting the smaller number from the larger number.
Hence, it is important to make tens in lower grades to make students understand the subtraction.
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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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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
65 less than twice Janelle's savings
Answer:
x = 2y - 65
Step-by-step explanation:
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.
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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Rewrite sin(x-7pi/4) in terms of sin(x) and cos(x)
The expression written in terms of sinx and cosx is
sinx· cos7π/4 - cosx ·sin7π/4
What is an algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is sin(x - 7π/4).
Use the formula for sin(A-B) to rewrite the expression:
sin(x - 7π/4)
= sinx· cos7π/4 - cosx ·sin7π/4
Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4
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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 does it mean when the discriminant is greater than 0?
We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.
An discriminant value definition ?
The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.
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André planted a cedar hedge 15 years ago (currently it's the start of the 16th year). The
hedge is now 3 metres high. The cedars grew an average of 12 cm per year. How tall were
the cedars when he planted them?
The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters
What is an arithmetic progression?An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.
The year André planted the cedar hedge tree = 15 years ago
The present height of the hedge = 3 meters = 300 cm
The average rate at which the cedars grew = 12 cm per year
The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;
The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d
Where;
a₁ = The initial height of the tree
d = The amount the tree grows each year = 12 cm
n = The number of years ago, the tree was planted
When n = 15, we get;
a₁₅ = 3 meters = 300 cm
Therefore;
300 = a₁ + (15 - 1) × 12
a₁ = 300 - (15 - 1) × 12 = 132
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