By using algebra (5, 4) is not a solution of the inequality.
Boundary does not contain in the given graph this is the error was made when graphed.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
x + 2y ≤ 12
Here the inequality contain ≤ .
Since, if there is ≤ sign then graph must contain boundary line.
The boundary line is solid line need to use in the graph.
But in the given graph the boundary line is dotted.
Boundary does not contain in the graph.
Hence, this is the error was made when graphed.
Also from graph we can see that the point (5, 4) is not contain in the graph.
Hence, (5, 4) is not a solution of the inequality.
Now prove by using algebra.
Plug x = 5, y = 4 in the given inequality
⇒ 5 + 2(4) ≤ 12
5 + 8 ≤ 12
13 ≤ 12
It is not possible that 13 ≤ 12.
Hence, (5, 4) is not a solution of the inequality.
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What effect does a scale factor equal to 1 have on the dimensions of the image being scaled?
The scale factor equal to 1 will have No Effect on the dimensions of the image being scaled .
In the question ,
it is given that ,
the scale factor is = 1.
we have to find the effect of change ;
we know that ,
when the value scale factor is greater than 1 , then dimensions of new image is larger than original .
when the value of scale factor is 1 , then there is no change in the dimensions of the image .
when the value of scale factor is less than 1 , then the dimensions of new image is smaller than the original .
Therefore , if the scale factor is 1 , then there is no change in the dimensions of the image .
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A shelf at a bookstore displays 27 books. Of these 27 books, 9 of the books are nonfiction books. The store owner adds 6 new fiction books to the shelf and wants the ratio of fiction books to nonfiction books to remain the same. What is the total number of nonfiction books that the store should display, after the new fiction books are added?
Right now, the ratio of nonfiction to fiction is 9:18. If this is reduced, it is a ratio of 1:2, so there needs to be twice as many fiction books as nonfiction.
If we add 6 fiction books, we have 24 fiction books. We can now set up this equation:
[tex]1/2=x/24[/tex]
Now we cross multiply
2x=24
We can solve for x by dividing both sides by two, so:
x = 12. There will be 12 nonfiction books.
When is -2x^3-13x^2+8x+52 ≥ 0?
Answer:
x ≤ -13/2 ∨ -2≤ x ≤ 2
Step-by-step explanation:
-x²(2x + 13) + 4(2x+ 13) ≥ 0
(2x+13)(-x²+4) ≥ 0
(2x+13)(2+x)(2-x) ≥ 0
2x + 13 ≥ 0
2x ≥ -13
2/2 x ≥ -13/2
x ≥ -13/2
2+ x ≥ 0
x ≥ -2
2 - x ≥ 0
-x ≥ -2
x ≤ 2
-13/2. -2. 2
- +. +. +
- - +. +
+. +. +. -
+. - +. -
x ≤ -13/2 ∨ -2≤ x ≤ 2
Can an equation have 3 variables?
Answer: I believe yes, as it is simply a multi-variable equation.
Step-by-step explanation: if im wrong, tell me
please help
The price of a home (in thousands of dollars) is associated with the number of square feet in a home. Home prices in Smavile can be modeled using the equation p = 150 + 0.041a where p is the price of the home in thousands of dollars and a is the area of the house in square feet Home prices in Fancyville can be modeled using the equation p = 250 + 0.198a Ngoc saw a real estate advertisement for a 2800 square foot home that was selling for $280,000. Which city should she predict that the home is in?
Answer:
Its most likely in Smavile
Step-by-step explanation:
S - Smavile
F - Fancyville
[tex]p_{s} = 150+ 0.041*2800 \\p_{s} = 150 + 114.8 = 264.8\\\\p_{f} = 250 + 0.198*2800\\p_{f} = 250 + 554.5 = 804.5[/tex]
264.8 * 1000 (its in thousands of dollars) = 264,800
What is the slope of the line that passes through the points (2, -3)(2,−3) and (1, -2)(1,−2)? Write your answer in simplest form.
Answer: 5/7+y is the answear
Step-by-step explanation:
∛
Three packages of chicken and 4 cases of barbecue sauce cost $40 five packages of chicken and 2 cases of barbecue sauce cost $34
Answer: .
Step-by-step explanation: ..
There are 69 students going on a field trip. Each van holds 9 students. How many vans are needed?
Answer:
To find out how many vans are needed for the field trip, we need to divide the number of students by the capacity of each van. In this case, there are 69 students going on the trip, and each van holds 9 students, so we have
69 students / 9 students/van = <<69/9=7>>7 vans
Therefore, 7 vans are needed for the field trip.
Step-by-step explanation:
Answer:You would do 51/8 and you would get 7 vans
Step-by-step explanation:
Find the nth taylor polynomial for the function, centered at c. F(x) = ln(x), n = 4, c = 7.
The nth Taylor polynomial for the function is P₄(x) = ln3 + 1/3 (x-3) - 1/9*2!(x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴
Given:
f(x) = ln(x)
n = 4
c = 3
To find:
nth Taylor polynomial for the function, centered at c
The Taylor series for f(x) = ln x centered at 3 is:
Now
f(3) = ln 3
f'(x) = 1/x ⇒ f'(3) = 1/3
f''(x) = -1/x² ⇒ f''(3) = -1/3² = -1/9
f'''(x) = 2/x³ ⇒ f'''(3) = 2/3³ = 2/27
f (x) = -6/x⁴ ⇒ f (3) = -6/3⁴ = -6/81 = - 2/27
So Taylor polynomial for n=4 is:
P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴
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What is the slope of the line through − 5 − 10 and − 1 5?
Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction. It is typically represented by the m in the equation y = mx + b. Line through points -5, -10, and -1 has a slope of 5.
Slope is calculated by taking the difference in the y-coordinates divided by the difference in the x-coordinates of two points on a line. Since we only have one point, we cannot calculate the slope .The slope of a line is equal to the change in y divided by the change in x. We can calculate the slope by subtracting the y-coordinates and then dividing by the difference of the x-coordinates. In this case, the change in y is (10 - (-5)) = 15 and the change in x is (5 - (-1)) = 6. Therefore, the slope of the line is 15/6 = 5.
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a rectangular poster is to contain square inches of print. the margins at the top and bottom of the poster are to be inches, and the margins on the left and right are to be inch. what should the dimensions of the poster be so that the least amount of poster is used?
The Poster Dimensions of rectangle will be:
W = 18 inches
Y = 36 inches
Area can be defined as the amount of space covered by a plane of a particular shape. It is measured in "number" of square units (square centimeters, square inches, square feet, etc.). The area of a rectangle is the number of unit squares that fit in the rectangle. Examples of rectangles are flat surfaces such as laptop monitors, chalkboards, and painting canvases. You can use the rectangle area formula to find the space occupied by these objects.
Now,
Let's say the printable area of a rectangular poster is 512 square inches
"x". " and "y" - the dimensions of the printed area of the poster
A(p) = printed area of the poster = x × y
512 = x × y ⇒ y = 512/x
Therefore, The total area of the poster is:
A( t) = ( y + 4 ) × ( x + 2 )
⇒ A(t) = yx +2y +4x + 8 and y = 512/x
Total Area of x or Total poster area as x function:
A(x) =( 512/x)*x + 2* (512/x) + 4*x + 8
A(x) = 512 + 1024/x + 4 *x + 8
⇒ A(x) = 520 + 1024/x + 4*x
Differentiating both sides of the equation gives:
A´(x) = - 1024/x² + 4
A´(x) = 0
⇒ - 1024 /x² = -4
⇒ 4*x² = 1024
⇒ x² = 1024/4
⇒ x² = 256
or, x = 16 inches
and y = 512/x
⇒ y = 512/16
⇒ y = 32 inches
So x is found, the y dimension of the print area, Than n is the dimension of the poster:
Therefore,
w = x + 2 ⇒ w = 16 + 2 w = 18 in
And,
Y = y + 4 ⇒ Y = 32 + 4 Y = 36 in
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Are 2 congruent triangles always similar?
Answer: There are only a few similar congruent triangles.
Step-by-step explanation:
How many elements are required to construct a quadrilateral uniquely * 5 Elements 4 Elements 6 Elements 3 elements?
The minimum number of elements required for the construction of a quadrilateral uniquely are 5 elements.
Explanation:
The minimum number of elements required for the construction of a quadrilateral uniquely are as follow:
Total number of elements present in the quadrilateral are ten.Name of the quadrilateral elements are ; four sides, four angles , and two diagonals.If we take two elements it is not possible to construct a quadrilateral.If we consider three elements again we are not able to construct a quadrilateral.If we take any four elements all four vertices will not intersect each other and quadrilateral will not formed.Minimum four sides and one diagonal or four sides one angle that at least 5 elements are required to construct a quadrilateral.Therefore, minimum 5 elements are required to construct a unique quadrilateral.
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Which functions are continuous at x = -4? Select all that apply.
The continuous functions at x = -4 are given as follows:
Second function: -8 at x = -4.Fourth and last function: 0 at x= -4.What makes the function continuous?The function is continuous when it has these two features:
Equal lateral limits.The lateral limits are equal to the numeric value of the function.For the definitions in this problem, we have that:
The lateral limits are calculated with the top definition.The bottom definition gives the numeric value.For the first two functions, the function can be simplified as follows:
(x² - 16)/(x + 4) = [(x - 4)(x + 4)]/(x + 4) = x - 4.
Hence the limit at x = -4 is given as follows:
-4 - 4 = -8.
Meaning that the second function is continuous at x = -4.
For the last two functions, the function can be simplified as follows:
(x² + 8x + 16)/(x + 4) = (x + 4)²/(x + 4) = x + 4.
Hence the limit at x = -4 is given as follows:
-4 + 4 = 4.
Meaning that the fourth and last function is also continuous at x = -4.
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The intersection of B Street and 6th Street is 600 yards east of the intersection of B Street and Ford Street. How many yards north is it?
Answer:
6
Step-by-step explanation:
The intersection of B Street and 6th Street is 600 yards east of the intersection of B Street and Ford Street, so it is 600 yards north of the intersection of B Street and Ford Street.
Who do you solve y= -5/2x-7
Answer:
To solve the equation y = -5/2x - 7, we can first multiply both sides of the equation by 2x + 7, which is the denominator of the fraction on the right-hand side. This gives us the equation 2xy + 7y = -5, which we can rearrange to isolate the variable y on one side of the equation. Dividing both sides of the equation by 2x + 7, we get y = -5 / (2x + 7). This is the solution to the original equation.
Step-by-step explanation:
Simplify each term.
y= −5 x2 −7
Mary used a sample of 68 large u. S. Cities to estimate the relationship between crime (annual property crimes per 100,000 persons) and income (median annual income per capita, in dollars). Her estimated regression equation was crime = 428 + 0. 050 income. If income decreases by 1000, we would expect that crime will:.
The required expected crime when income decreases by 1000 is 50.
What is annual property crimes ?In property crime, a victim's property is taken or obliterated, without the utilization or danger of power against the person in question. Local misdemeanors incorporate thievery and robbery as well as defacing and incendiary.
According to question:We have,
crime = 428 + 0. 050 income
If the income goes down by 1, crime goes down by 0.050.
Similarity, if income goes down by 1000, crime goes sown by 0.050(1000)
⇒ 50
Thus, the expected crime is 50.
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help
Which relation is a function?
Answer:
Top Left
Step-by-step explanation:
For a relation to be a function, every x must have one and only one y
This is only true for the top left, the rest fail this because
Top Right has 2 y values at x = -1
Bottom left has 2 y values at x = 0
Bottom Right has 2 y values at x = -2 AND at x = 2
Write an equation for each line
The equation for each line is 5x-y=6 by using slope and the given points that are passing through the line.
What is a slope?The slope or gradient of the line is a numerical value used to describe a line's steepness and direction in mathematics. It was first used to describe slope in O'Brien's (1844) and Todhunter's (1888) versions of the equation for a straight line, which are both written as "y = mx + b" and "y = mx + c," respectively.
Calculating slope involves comparing the "vertical change" to the "horizontal change" between any two points on a line, or any two points.
The lines are passing through the points (2, 4) and (1, -1)
Slope m =(y₂-y₁)/(x₂-x₁)
m=(-1-4)/(1-2)
m= -5/-1
m=5
The equation of the line with slope m=5 and passes through the point
(2, 4)
y-y₁=m(x-x₁)
y-4=5(x-2)
y-4=5x-10
5x-y=6
The equation of the line with slope m=5 and passes through the point
(1, -1)
y+1=5(x-1)
y+1=5x-5
5x-y=6
Therefore, the equation for each line is 5x-y=6.
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Molly bought 4 pairs of pants for a total of $300. Dress pants cost $100 and jeans cost $50. How many of each type of pants did she buy?
A. 4 dress pants and 3 jeans
B. 5 dress pants and 2 jeans
C. 2 dress pants and 2 jeans
3. 3 dress pants and 3 jeans
Find the probability that a randomly chosen client requested a haircut given they requested a permanent.
Given that the client requested a permanent haircut, there is a 66.66% chance that he would request a haircut.
The following calculation must be performed in order to determine the probability that a randomly selected client requested a haircut given that he has requested a permanent: Given that a salon owner noted what types of services its clients requested last week, the results showed that 5% requested dye only, 30% haircut and dye, 35% requested haircut only, 10% hair cut and permanent, 5% permanent only, and 15% other.
Add all of the options that include a perm, and then use a cross multiplication to figure out how many of those options include a haircut.
10 (permanent and haircut) x 5 (permanent only) = 15 15 = 100 10 = X 10 x 100/15 = 66.66 = X
Thus, the probability that a randomly selected client would have requested a haircut given that he had previously requested a permanent is 66.66%.
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Full Question = a salon owner noted what types of services its clients requested last week. Here are the results. 5% dye only, 30% haircut and dye, 35% haircut only, 10 % haircut and permanent, 5% permanent only, and 15% other. Find the probability that a randomly chosen client requested a haircut given the requested a permanent. P(haircut l permanent).
or
Find the slope of the line that passes through (10, 1) and (3, 2).
Answer: m= -1/7
Step-by-step explanation:
Please HeLp ME IM nOt SMarT !!!!!!
Answer: 420
Step-by-step explanation:
Answer:143.30
Step-by-step explanation:
how is a theory different from a hypothesis? group of answer choices a hypothesis explains observations and cannot be refuted by new evidence. a theory is an explanation that has been carefully examined and tested.
The main difference between Theory and Hypothesis is B) Theory is an explanation that has been carefully examined and tested.
Theory:A theory is a rational way of thinking abstractly about a phenomenon or the consequences of such thinking. Contemplative and rational thought processes are often associated with processes such as observational studies and research. A theory can be scientific, it can belong to a non-scientific field, or it can belong to no field at all. For example, depending on the context, a theory's assertions may include generalized explanations of how nature works. The word has ancient Greek roots, but has taken on several related meanings in modern usage.
In mathematics, the term theory is used differently. Because, inevitably, mathematics itself does not contain an explanation of natural phenomena. However, it can help provide insight into or take inspiration from natural systems. In a general sense, mathematical theory is a branch or topic of mathematics. Individual textbooks for set theory, number theory, group theory, probability theory, game theory, control theory, perturbation theory, etc.
Equivalently, but more precisely, the term theory means a large-scale, structured theory organized in such a way that the proof of each theorem requires only the preceding theorems and axioms (not circular proofs) is a set of theorems. Ideally, the order in which the theorems are presented makes the purpose of the textbook clear in the field of mathematics, but is as easy to understand as possible. they are not written mathematical theories.
Hypothesis:A hypothesis (hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, it must be able to be tested by scientific methods. Scientists generally form scientific hypotheses based on previous observations that cannot be fully explained by available scientific theories. Although the terms "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a tentatively accepted hypothesis proposed for further research in a process that begins with educated guessing or thinking.
Another meaning of the term hypothesis is used in formal logic to denote the antecedent of a proposition. So in the sentence "If P, then Q", P denotes a hypothesis (or premise). Q can be called a sequence. P is a (possibly counterfactual) what-if question assumption.
The adjective hypothesis, meaning "having the nature of a hypothesis" or "supposed as a direct result of a hypothesis", may refer to either of these meanings of the term "hypothesis".
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needs to buy some food. At the nearest store, bags of food cost $. How much would spend on of food?
Function f is a linear function and function g is defined by g(x) = f(x) + k. If the value of k is 7, how does the graph of g compare with the graph of f ?..
The graph of g is the graph of f
translated up 7 units
translated left 7 units
translated right 7 units
translated down 7 units
stretched vertically by a scale factor of 7
stretched horizontally by a scale factor of 7
The graph of g is Transformation up 7 units.
what is Transformation?
A graph transformation is a method for altering an existing graph or graphed equation to create a different version of the graph that follows. The modification of algebraic equations is a typical form of algebraic issue.
solution:
From the question, we have the following parameters that can be used in our computation:
g(x) = f(x) + k
Also, we have the value of k to be
k = 7
From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units
This means that
g(x) = f(x) + k
So, we have
g(x) = f(x) + 7
Hence, the transformation is (a) translated up 7 units
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If g(x) = (x + 1)2, complete each part below.
a. g(5)
b. g(2m + 4)
c. x if g(x) = 9
A) g(5)=(5+1)2
6*2
12
b) (2m+4)2
4m+8
C) (9+1)2
10*2
20
Solve the problem.
The area of a rectangle is 30m2 - 20m - 10. Find the length if the width is 5m - 5.
The length of the rectangle is 6m - 2.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Area = 30m² - 20m - 10
Width = 5m - 5
Now,
Area = Length x Width
30m² - 20m - 10 = Length x (5m - 5)
10(3m² - 2m - 1) = Length x (5m - 5)
10(3m² - (3 - 1)m - 1 = Length x (5m - 5)
10 (3m² - 3m + m - 1) = Length x (5m - 5)
10 (3m(m - 1) + 1(m - 1)) = Length x (5m - 5)
10 (3m + 1)(m - 1) = Length x 5(m - 1)
(m - 1) gets canceled.
10(3m - 1) = Length x 5
2(3m - 1) = Length
Length = 6m - 2
Thus,
6m - 2 is the length of the rectangle.
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Help me please…..My last two questions
By using percentage, it can be calculated that-
13) Option c is correct
15) Option d is correct
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 7% means [tex]\frac{7}{100}[/tex]. Here 7 is expressed as a fraction of 100.
13) Original price of a tablet = $330
Rate of discount = 15%
Discount = [tex]\frac{15}{100}\times 330[/tex] = $49.5
Price after discount = $(330 - 49.5) = $280.5
Amount of money paid by Jeremiah = $302.94
Sales Tax = $(302.94 - 280.5) = $22.44
Rate of sales tax = [tex]\frac{22.44}{280.5} \times 100[/tex] = 8%
Option c is correct
15) Average cost of a bag of popcorn at the movie theatre in 1995 = $3.50
Average cost of a bag of popcorn at the movie theatre in 2015 = $4.75
Increase in cost = $(4.75 - 3.50) = $1.25
Percentage increase in cost = [tex]\frac{1.25}{3.50} \times 100[/tex] = 35.7% increase
Option d is correct
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At the beginning of the year, Skylar had $30 in savings and saved an additional $16 each week thereafter. Faith started the year with $100 and saved $6 every week. Let SS represent the amount of money Skylar has saved tt weeks after the beginning of the year and let FF represent the amount of money Faith has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the amount of money Skylar and Faith have saved in the week that they have the same amount of money saved.
The linear equations for each situation would be: F = 6t + 100 and S = 16t + 30.
The amount of money Skylar and Faith would have saved in the week that they both have the same amount of money saved is: $142.
How to Write a Linear Equation of a Situation?A linear equation that models a situation can be expressed as y = mx + b, where the unit rate or slope value is represented as m, and the y-intercept or initial value (starting value) is the value of b.
Equation that represents the savings made by Skylar:
Unit rate (m) = $16 per week
Starting value/y-intercept (b) = $30
S = y
t = x
The equation for Skylar would be written by substituting m = 16 and b = 30 into S = mt + b:
S = 16t + 30.
Equation that represents the savings made by Faith:
Unit rate (m) = $6 per week
Starting value/y-intercept (b) = $100
F = y
t = x
The equation for Skylar would be written by substituting m = 6 and b = 100 into F = mt + b:
F = 6t + 100.
They will both saved the same amount of money, when F = S. Therefore:
16t + 30 = 6t + 100
Solve for t
16t - 6t = -30 + 100
10t = 70
t = 7
Substitute t = 7 into any of the equations:
6t + 100 = 6(7) + 100
= 142.
Therefore, they would both save $142.
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