Fraction of the sensors on the given satellite which have been upgraded is equal to option D. 1/7.
As given in the question,
Total number of modular units = 30
Let 'n' be the total number of upgraded sensors available on the entire satellite
Number of non-upgraded sensors available on one unit = ( 1/5)n
= x/5
Number of non-upgraded sensors available on 30 modular unit
= 30n /5
= 6n
Total number of non- upgraded and upgraded sensors makes one unit
⇒n + 6n = 1
⇒7n = 1
Fraction of upgraded sensors are:
⇒ n = 1/7
Therefore, the fraction of the sensors available on the satellite and are upgraded is equal to option D. 1/7.
The above question is incomplete , the complete question is:
A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
A. 5/6 B. 1/5 C. 1/6 D. 1/7 E. 1/24
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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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It costs chevy $20,000,000 to develop and market a new model of cars. The company sells each car for $25,000. If chevy wants to make a profit of more than $5,000,000, write an inequalty that represents this.(Inequality is this question i need help on)
The inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.
Given that, it costs chevy $20,000,000 to develop and market a new model of cars.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Let the number of cars sold be x.
So, selling price of cars is $25,000x
Profit =Selling price-Cost price
⇒ 25,000x-20,000,000≤5,000,000
Solve the inequality
Add 20,000,000 on both the sides of an inequality, we get
25,000x≤25,000,000
⇒ x≤25,000,000/25,000
⇒ x≤1000
Therefore, the inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.
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Which option below is a different way of writing -5-(-7)?
Answer: I mean- can you found it out yourself by studying. There's your answer.
Step-by-step explanation:
just study not cheat.
theres 4 questions that i need help with asap. #geometry
please help.
After solving the equation we know ABCD is a parallelogram.
What is parallelogram?
A parallelogram is a two-dimensional shape with four straight sides. All of the sides are equal in length and the opposite sides are parallel. Additionally, opposite angles are also equal. The shape is called a parallelogram because parallel lines are present on either side. Parallelograms can come in many different forms, such as rectangles and rhombuses. The properties of a parallelogram include the fact that the diagonal line that divides the parallelogram into two halves bisects the angles. Additionally, the cross product of the two diagonals is equal to the area of the parallelogram. Parallelograms are used in a variety of areas, including architecture, engineering, and mathematics. Depending on the application, parallelograms can be used to construct a variety of shapes, such as circles and ellipses.
Given: A (2,5), B (7,6), C (6,2), D (1,1)
AB ⇒ A (2,5), B (7,6) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(-5+1)^{2}+(-6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(-4)^2+(-8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
CD ⇒ C (6,2), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7-3)^{2}+(6+2)^{2} }[/tex]
⇒ [tex]\sqrt{(4)^2+(8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
BC = B (7,6), C (6,2) ⇒ [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(3+5)^{2}+(-2+6)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
AD ⇒ A (2,5), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7+1)^{2}+(6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
As, AB = CD = BC = AD all sides are equal.
Hence proved, ABCD is a parallelogram.
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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].
41°
x=
(7x)°
5.) solve!!!
Answer: x = 7
Step-by-step explanation:
Sum of the interior angles of a triangle must equal 180.
41 + (7x) + 90 = 180
7x = 180 - 90 - 41
7x = 49
x = 49/7 = 7
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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HELP ASAP!! I will give Brainiest!
Angles X and Y are supplementary. Angle X measures 132.54°, and angle Y measures (m - 15)°. Find mzY
47.46°
62.46
85.08
117.54°
Answer:
47.46
Step-by-step explanation:
Answer: The answer is A. 47.46°.
Step-by-step explanation: Hope this helps.
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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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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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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[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 = 20Question
Which ordered pairs cause this relation NOT to be a function? Why?
{(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)}
Responses
A (0.5, 1), (3, 1); The same y-value has different x-values.(0.5, 1), (3, 1); The same y-value has different x-values.
B (3, 1) and (3, 2); The same x-value has different y-values.(3, 1) and (3, 2); The same x-value has different y-values.
C (3, 1) and (3, 2); The x-value in a function cannot be greater than the y-value.(3, 1) and (3, 2); The x-value in a function cannot be greater than the y-value.
D (0.5, 1) and (0, 0.5); A function cannot contain decimals.
Ordered pair (3, 1) and (3, 2) causes the relation to not be a function; The same x-value has different y-values.
How do you find out if a set of ordered pairs is a function or not?
For a set of ordered pairs to be a function, there must not be any two points that have the same first elements. This means that, the
x-coordinates must not repeat for any two given points.
According to the given question:
Given ordered pairs of a relation are
(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)
Domain set of the relation= {0, 0.5, 1, 3}
Co-Domain set of the relation = {0.5, 1, 2, 6}
Clearly the image of the x-coordinate 3 is not unique.
Hence, (3, 1) and (3, 2); The same x-value has different y-values.
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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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PLease help with this question!
In GHI, h = 820 inches, G=102° ahd H=10°. Find the length of g, to the nearest
inch.
Answer:
4619 inches
Step-by-step explanation:
You want the length of side g in ∆GHI where G=102°, H=10°, and h=820 inches.
Law of sinesThe law of sines tells us ...
g/sin(G) = h/sin(H)
g = h·sin(G)/sin(H) = (820 in)sin(102°)/sin(10°)
g ≈ 4619 in
The length of side g is 4619 inches.
<95141404393>
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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PLS ANSWERRRRRSSSSSSS. I GIVE BRAINLIESTTT
Answer:
x = 5.4
Step-by-step explanation:
[tex]\frac{7.2}{4}[/tex] = [tex]\frac{x}{3}[/tex] Cross multiple and solve for x
4x = (7.2 x3)
4x = 21.6 Divide both sides by 4
x = 5.4
Answer:
x = 5.4
Step-by-step explanation:
[tex]\frac{x}{7.2} =\frac{3}{4}[/tex]
[tex]x=\frac{(7.2)(3)}{4} =\frac{21.6}{4} =5.4[/tex]
Hope this helps
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
Make 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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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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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?
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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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
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
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:
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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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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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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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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