All potential values of x are represented by the inequality x≤20.
What is inequality?A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.
An inequality displays the difference between two variables, whereas an equation displays the equivalence of two variables.
So, the inequality that also represents all the possible values of x is:
On Mondays, Kelli walks no more than 25 dogs.
Also, Ms. Lincoln's five dogs are walked by Kelli.
Along with Ms. Lincoln's dogs, the inequality to determine how many additional dogs Kelli walks on Monday is written as:
x+5 ≤ 25
Take 5 away from both sides.
x + 5 - 5 ≤ 25 - 5
x ≤ 20
Therefore, all potential values of x are represented by the inequality x≤20.
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Complete question:
Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?
need help please help me
Using the slope-intercept form, the slope, y-intercept and equation of the graph are -1/7, 5 and y = -1/7x + 5 respectively
Equation of Straight LineThe general equation of straight line is given in slope-intercept form as
y = mx + c.
In the graph given, the function is a straight line with slope and y-intercept.
Taking two points from the graph.
A= (5, 0)B = (-2, 1)The slope of the equation can be calculated using the points
slope (m) = y₂ - y₁ / x₂ - x₁
m = 1 - 0 / -2 - 5
m = 1 / -7
The slope is -1/7
From the graph, we can see the point in which the line passes through the y - axis and it is known as the y - intercept.
The y - intercept on this graph is 5
The slope- intercept form can be written as
y = -1/7x + 5
a) When x = -1, y = ?
y = -1/7x + 5
y = -1/7(-1) + 5
y = 1/7 + 5
y = 36/7
b) When y = 7, x = ?
y = -1/7x + 5
7 = -1/7x + 5
x = -14
c) The y - intercept of the graph is 5
d) The x-intercept of the graph is at -2.2
e) The slope of the line is -1/7
f) The equation of the line is given as y = -1/7x + 5
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[tex]2(3x-4)+10=5(x+4)[/tex]
x = 18
2(3x - 4) + 10 = 5(x + 4) 6x - 8 + 10 = 5x + 206x + 2 = 5x + 20x + 2 = 20Make V the subject
s = 1/2(u+v)t
The subject formula is v= 2s/t- u.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
s = 1/2(u+v)t
Now, we have to work for variable 'v'
2s = ( u+ v)t
2s/ t = u+ v
v= 2s/t- u
Hence, the subject formula is v= 2s/t- u.
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Explain how you can tell if a table of values represen a proportional relationship.
A table of values that represents a proportional relationship must have a constant rate and must pass through the origin
How to identify a table of values of proportional relationshipFrom the question, we have the following parameters that can be used in our computation:
A table that is has proportional relation
A table of values can be represented as
x y
a b
c d
......
.....
For the table of values to be proportional, the following must be true
x y
0 0
a b
c d
......
.....
Also, it must have a constant ratio
i.e. b/a = d/c
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from a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. in how many ways can this be done?
Total ways of required selection is 686, obtained from the sum of the cases of 3, 4 and 5 women in the committee.
What is defined as combination?Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in combinations.
Given that 5 persons are to be selected with a condition of minimum 3 women. Therefore the different possibilities are:
1) 3 women and 2 men
2) 4 women and 1 man
3) 5 women
Final answer will be the sum of the above results.
Total ways to select 3 women from 6 women and 2 men from 8 men,
Total ways = ⁶C₃ * ⁸C₂
Similarly total ways for 4 women and 1 man = ⁶C₄ * ⁸C₁
Total ways for 5 women = ⁶C₅ * ⁸C₀
Add the three results to get the final answer,
Total number of ways = (⁶C₃ * ⁸C₂) + (⁶C₄ * ⁸C₁ ) + (⁶C₅ * ⁸C₀)
Total number of ways = 560 + 120 + 6 = 686
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How do I find the inverse of j(x)=√x - 10 + 4
The inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x
What in mathematics is inverse?
A function that "undoes" another function is known as an inverse in mathematics. To put it another way, if f(x) produces y, then y will produce x when y is fed into f's inverse function. Invertible refers to a function that has an inverse, which is represented by the symbol f1.
Given that:
J(x) = √x - 10 + 4
y = √x - 10 + 4
now replace x with y
x = √y - 10 + 4
now solve for y , x = √y - 10 + 4
x + 4= √y - 10
Squaring both the side
x^2 + 16 + 8x = y - 10
y = x^2 + 26 + 8x
Hence the inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x
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What happens if the insured tenant and the insurance company fail to agree on the amount of loss?.
Appraisal , If the insured and this insurer are unable to reach an understanding regarding the actual cash value or the extent of the loss, then, upon the written demand of either party, each shall choose a qualified and impartial appraiser and notify the other of the appraiser selected within 20 days of the demand.
What does the word "appraisal" mean?
A valuation by an authorized person of a piece of property, such as real estate, a company, a collectible, or an antique, is known as an appraisal.
An accreditation from a regulatory body overseeing the appraiser's area of practice is required for an authorized appraiser.
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2. The table shows the snacks in Melissa's
pantry.
SNACK
Granola Bar
Chips
Fruit Snack
AMOUNT
4
3
5
What is the probability that she chooses a fruit
snack, puts it back, and then chooses a granola
bar?
The probability of choosing a fruit snack replaced and then choosing a granola bar is 5/36.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, Mellisa has options to choose from 3 different snacks,
N(GB) = 4, N(C) = 3, and N(FS) = 5.
So, The sample space N(S) = N(GB) + N(C) + N(FS).
N(S) = 12.
The probability of choosing a fruit snack is,
P(FS)
= N(FS)/N(S).
= 5/12.
Given, She puts it back so replaced and hence the events are independent.
So, The probability of choosing a granola P(GB) = N(GB)/N(S).
= 4/12.
= 1/3.
Therefore The combined probability is (5/12)×(1/3).
= 5/36.
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(
2
5
+
2
2
i)
2
in simplest a+bia+bi form.
The complex number (25 + 22i)² in simplest form a + ib is 141 + 1100i
What is a complex number?A complex number is a number in the form z = x + iy where
x and y are real numbers and i = √(-1)How to find the complex number (25 + 22i)² in the simplest form?To find the complex number (25 + 22i)² in the form a + ib, we proceed as follws.
(25 + 22i)² = (25 + 22i)((25 + 22i)
Expanding the brackets, we have that
(25 + 22i)² = (25 + 22i)((25 + 22i)
(25 + 22i)² = [25 × 25 + 25 × 22i + 25 × 21 + (22i)²]
(25 + 22i)² = [625 + 550i + 550i + 484i²]
(25 + 22i)² = [625 + 550i + 550i + 484 × (-1)] Since i² = -1
(25 + 22i)² = [625 + 550i + 550i - 484]
Collecting like terms, we have that
(25 + 22i)² = [625 - 484 + 550i + 550i]
(25 + 22i)² = 141 + 1100i
So, (25 + 22i)² = 141 + 1100i
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The following loop is intended to print the numbers
2 4 6 8 10
Fill in the blank:
for i in ________:
print (i)
range(2,11,2) because range is a tool for defining a range between two numbers and adding a step value.
How would you describe the range?Range is the difference between the highest and lowest values in a range of numbers. To calculate the range, subtract the smallest number from the largest number in the set.
How do you find range?The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.
range(2,11,2) because range is used to create a range between number and add step value
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1. Jayda drank % of a gallon of water on Monday.
On Tuesday, she drank 1 ½ times as much water
as she did on Monday.
How many gallons of water did Jayda drink in
all?
If Jayda's goal is to drink a gallon by Wednesday,
how many more gallons does she need to drink?
factor the function completely into linear factors y=x^2+4x+11
Answer: y= (x+2)^2 + 7
Step-by-step explanation:
y= (x+2)^2 + 7
y = (x+2) (x+2) +7
y= x^2 + 2x + 2x + 4 +7
y= x^2 + 4x + 11
Larry and Peggy are making decisions about their bank accounts. Larry wants to deposit $350 as a principal amount, with an interest of 4% compounded quarterly. Peggy wants to deposit $350 as the principal amount, with an interest of 6% compounded monthly. Explain which method results in more money after 2 years. Show all work.
Peggy's method will make more money.
What is compound interest?Compound interest is the sum of interest on principal and interest on interest of previous period.
Given, that principal is same in both cases,
Also, Peggy will get total interest = 2×6 = 12%.
Whereas, Larry will get 1 % per quarter compounded quarterly.
Therefore, Larry will get (101/100)⁸%.
Hence, 12 > (101/100)^8 and Simple interest method will make more money.
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What are the values of x and y?
Using linear pairs, [tex]y=102[/tex].
Using the angle sum in [tex]\triangle TRS[/tex], [tex]x=70[/tex].
Two numbers have a sum
of 12. The same two numbers have difference of 4. What are the two numbers?
Answer:
8 and 4
Step-by-step explanation:
Answer: 8 and 4
Step-by-step explanation:
PLease help with this question!
The table shows the dates, times, and high and low tide heights.
Cresap Bay Tide Table
Date
Time
Low/high tide
Thursday, Feb. 7
1:26 a. M.
2. 6 ft (low)
7:26 a. M.
6. 4 ft (high)
2:29 p. M.
–0. 8 ft (low)
9:21 p. M.
4. 8 ft (high)
Friday, Feb. 8
2:24 a. M.
1. 5 ft (low)
8:22 a. M.
6. 5 ft (high)
3:16 p. M.
–1. 6 ft (low)
10:02 p. M.
5. 1 ft (high)
Which list shows the low tides from lowest to highest?
a–1. 6, –0. 8, 1. 5, 2. 6
b–0. 8, –1. 6, 1. 5, 2. 6
c–0. 8, 1. 5, –1. 6, 2. 6
d2. 6, 1. 5, –0. 8, –1. 6
The list that shows the low tides from lowest to highest is -1.6 < -0.8 < 1.58 < 2.6 and this can be determined by using the given data.
The correct option is A).
Given,
In the question:
The table shows the dates, times, and high and low tide heights.
Now, According to the question:
The following steps can be used in order to determine the list that shows the low tides from lowest to highest:
Step 1 - According to the given table, the low tide on Thursday, Feb 7 at 1;26 am is 2.6 ft.
Step 2 - According to the given table, the low tide on Thursday, Feb 7 at 2:29 pm is -0.8 ft.
Step 3 - According to the given table, the low tide on Friday, Feb 8 at 2:24 am is 1.5 ft.
Step 4 - According to the given table, the low tide on Friday, Feb 8 at 3:16 pm is -1.6 ft.
Step 5 - Arrange the data of low tides given in the above steps in increasing order:
-1.6 < -0.8 < 1.58 < 2.6
The correct option is A).
Hence, The list that shows the low tides from lowest to highest is -1.6 < -0.8 < 1.58 < 2.6 and this can be determined by using the given data.
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The perimeter of your rectangular pool is 130ft. Three time the length is equal to 10 times the width. Find the length and width of the pool. Find the area if the pool.
Answer:
Length = 50 ft
Width = 15 ft
Area = 750 ft²
Step-by-step explanation:
Define the variables:
Let W be the width of the rectangle.Let L be the length of the rectangle.Create two equations with the given information.
Given:
Three times the length is equal to 10 times the width.⇒ 3L = 10W
Given:
The perimeter of the rectangle is 130 ft.⇒ 2W + 2L = 130
Rearrange the second equation to make W the subject:
⇒ 2(W + L) = 130
⇒ W + L = 65
⇒ W = 65 - L
Substitute this into the first equation and solve for L:
⇒ 3L = 10(65 - L)
⇒ 3L = 650 - 10L
⇒ 13L = 650
⇒ L = 50
Substitute the found value of L into the second equation and solve for W:
⇒ 2W + 2(50) = 130
⇒ 2W + 100 = 130
⇒ 2W = 30
⇒ W = 15
Therefore:
Length of the rectangular pool = 50 ftWidth of the rectangular pool = 15 ftSubstitute the found values of W and L into the formula for area of a rectangle to find the area of the pool:
⇒ Area = W × L
⇒ Area = 15 × 50
⇒ Area = 750 ft²
Regina made 1,240 pot holders. She wants to sell them in packages of 10. How many
packages will she have? Explain your thinking.
Answer:
124
Step-by-step explanation:
1,240/10 is 124. You divide by 10.
The number of packages of 10 for the 1240 pot holders is 124.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of pot holders = 1240
Number of pot holders in one pack = 10
The number of packages.
= 1240 ÷ 10
= 1240/10
= 124
Thus,
The number of packages of 10 is 124.
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The figure shows the location of three points around a lake. The length of the lake, BC, is also shown.
(The figure is not drawn to scale.)
A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 6 miles. The length BC of the triangle is labeled as 4 miles. This length BC is also the length of an irregular gray shaded shape.
Which of the following choices is closest to the distance (in miles) between points A and B? (5 points)
Question 7 options:
1)
3.16 miles
2)
3.46 miles
3)
4.47 miles
4)
4.90 miles
Answer:
3) 4.47 miles
Step-by-step explanation:
AC is the the hypotenuse
so, 6*6 = 36, and 4*4 = 16
36-16=20
square root of 20 is 4.472135...
so, 4.47
multiplication of matrices
with full workings and explanations
The product of matrices A and B is matrix C
a) [tex]C = (3 )[/tex]
b) [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}4&5\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}2\\ \:-1\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C = \begin{pmatrix}4&5\end{pmatrix}\begin{pmatrix}2\\ -1\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}4\cdot \:2+5\left(-1\right)\end{pmatrix}[/tex]
[tex]C = (3 )[/tex]
Therefore , the value of matrix C is [tex]C = (3 )[/tex]
b)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}2&6\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}-3\\ \:-4\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C = \begin{pmatrix}2&6\end{pmatrix}\begin{pmatrix}-3\\ -4\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}2\left(-3\right)+6\left(-4\right)\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}1&2\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C =\begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}1\cdot \:4+2\cdot \:5&1\cdot \:6+2\cdot \:7\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}0&5\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C =\begin{pmatrix}0&5\end{pmatrix}\begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}0\cdot \:3+5\cdot \:4&0\cdot \:6+5\cdot \:1\end{pmatrix}[/tex]
[tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
Hence ,
The product of matrices A and B is matrix C
a) [tex]C = (3 )[/tex]
b) [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
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For a project in her Geometry class, Aria uses a mirror on the ground to measure t the
height of her school building. She walks a distance of 11.45 meters from the school,
then places a mirror on flaton the ground, marked with an X at the center. She then
steps 1.25 meters to the other side of the mirror, until she can see the top of the
school clearly marked in the X. Her partner measures the distance from her eyes to
the ground to be 1.15 meters. How tall is the school? Round your answer to the
nearest hundredth of a meter.
The height of the tail post is 13.74 m.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that, after travelling 11.45 metres from her school, she lays a flat mirror on the ground in the center, with an x drawn on it. When she can clearly see the top of the goalpost depicted in the x.
She moves 1.25 metres to the other side of the mirror. Her spouse calculates that there are 1.15 metres between her eyes and the earth.
Suppose the height of the tail post is x,
The geometric relation is,
1.5/1.25 = x/11.45
Apply cross multiplication
1.5×11.45=1.25x
17.175=1.25x
Divide both sides by 1.25
x=13.74
Hence, if she moves 1.25 metres to the other side of the mirror. Her spouse calculates that there are 1.25 metres between her eyes and the earth. The height of the tail post is 13.74 m.
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Find f + g if f(x) = 3x-2 and g(x) = 5x + 2.
f(x) +g(x)= (3x-2)+(5x+2)
=3x-2+5x+2 (-2or +2 become cancelled )
=3x+5x
8x
A spring is attached at one end to support B and at the other end to collar A represented in the figure. Collar A slides along the vertical bar between points C and D. In the figure, the angle is the angle created as the collar moves between points Cand D. When the spring is stretched and the distance from point A to point Bis 5.3 feet, what is the value of e to the nearest tenth of a degree? 3 ft B 00000 А
The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°
Given,
A spring is attached at one end to support B and at the other end to collar A.
Part A: Reference angle (θ) = 28°
We have to find out the distance of point A to point B.
Adjacent = 3 ft (given)
Apply the trigonometry function to find AB
cos θ = adj / hypotenuse
Substituting all the values ,
cos 28°= 3/AB
AB = 3/cos 28°
AB = 3.4 ft (nearest tenth of a foot)
Part B:
It is given that Distance from point A to point B is 5.2 feet
We have to calculate the Value of θ
adjacent = 3 ft
hypotenuse = AB = 5.3 ft
To find θ , We will again apply the trigonometry function
cos θ = adjacent/hypotenuse
Substituting all the given values
cos θ = 3/5.3
θ = cos⁻¹ ( 3 / 5.3)
θ = 54.8°
That is,
The length of point A to point B is 3.4 feet
The value of θ is 54.8°
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Diego opened a savings account with $20 to start before he started earning $10 for every hour of babysitting. Is there a proportional relationship between time and amount saved for Diego?
Answer: No, it is not proportional.
Explanation:
We can see that Diego opened an account with $20, meaning that there is going to be a y-intercept of 20 in a graph. Therefore, with a y-intercept of 20 and not zero, we can say that there is not a proportional relationship between and time and amount saved for Diego.
a bank gives interest at a rate of 3.5% each year. If you start an account at the bank with 3500 SWEDISH krona, how much money will you have in the account after a year
Answer:
$3624.48
Step-by-step explanation:
This is a bank interest formula that is -> P(1 +/- r/n)^rt
3500(1 + 0.035/12)^12*1
The answer is 3624.48
Identify this system of equations:
y=4x-4
y=-4x+4
A. Consistent and Independent
B. Consistent and Dependent
C. Inconsistent
And also, this question isn't required, but if the 2 slope-intercept forms are opposite, do they equal each other. (Like the question above, 4x-4+ and -4x+4)
The system is consistent and independent.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have the system of equations:
y = 4x - 4
y = -4x + 4.
Let's take the quotient between both the equations as;
(y/y) = (4x - 4)/(-4x + 4)
1 = (4x - 4)/(-4x + 4)
Solve for x;
1*(-4x + 4) = 4x - 4
-4*x + 4 = 4x - 4
-4x - 4x = -4 - 4
-8*x = -8
x = -8/-8 = 1.
To find the value of y, we can input this value of x in one of the equations:
y = 4 x1 - 4 = 0.
Then we have only one solution, (1, 0).
Therefore, the system is consistent and independent.
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My friend Umpt has no more than 30 mimstoons...........
An inequality that combines two simple inequalities is known as a compound inequality.
What is a compound inequality?It is an inequality when two simple inequalities are combined to form it.The graph that represents the inequality's solution set can be seen in the image below.Combining one or more inequalities results in a compound inequality.The values of x in compound inequality are 1/14 and 2/3. We must determine the compound's value.A compound inequality in mathematics is a clause that joins two claims with the conjunction "and" or "or."Both of the statements in a compound sentence are true simultaneously if the conjunction "and" is used to connect the statements.If "or" is used to connect the statements, the compound phrase is true if at least one of the statements is true.
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Which ordered pair is a solution to the linear inequality below?
x+4y less than 4
A. -3,5
B. 0,4
C. 2,3
D. -8,-2
The solution to the given inequality that is x+4y<4 is (-8,-2) as it only gives the correct result for the equation.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here,
x+4y<4
(-8,-2)
-8+4*-2=-16<4
The provided inequality, x+4y4, has a solution of (-8,-2) because it alone provides the solution to the equation.
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A parabola can be drawn given a focus of (3,9) and a directrix of y = -5.
Write the equation of the parabola in any form.
The equation of the parabola that has a force at (3, 9) and directrix at y = -5 will be x² - 6x + 65 = 28y.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let (x, y) be the locus point. Then the equation is given as,
(x - 3)² + (y - 9)² = (y - 5)²
Simplify the equation, then we have
(x - 3)² + (y - 9)² = (y - 5)²
x² - 6x + 9 + y² - 18y + 81 = y² + 10y + 25
x² - 6x + 65 = 28y
The equation of the parabola will be x² - 6x + 65 = 28y.
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