Answers
Answer:
C
Step-by-step explanation:
For lines AC and EF, line FC is a transversal.
Angles ACF and EFC are same side interior angles.
Since their measures add to 180°, then the lines are parallel.
Answer: Choice C
Related Questions
Which parent function is f(x) = x²?
A. The quadratic parent function
B. The linear parent function
C. An exponential parent function
D. The absolute value parent function
Answers
Answer:
A
Step-by-step explanation:
It is the quadratic parent function
Find the angle between the vectors.
U=< -4,-3>
V = < -1,5>
Answers
Step-by-step explanation:
The formula for the angle between vectors
[tex] \alpha = \cos {}^{ - 1} ( \frac{uv}{ |u| |v| } ) [/tex]
To multiply vectors, multiply the first component and multiply the second component and add them.
(-4*-1) + (-3*5)= 4-15=-11.
To find magnitude of vectors, use the Pythagorean theorem
[tex]u = \sqrt{ { - 4}^{2} + { - 3}^{2} } = 5[/tex]
[tex]v = \sqrt{ - 1 {}^{2} + 5 {}^{2} } = \sqrt{26} [/tex]
so
[tex] |u| |v| = 5 \sqrt{26} [/tex]
Know we have,
[tex] \alpha = \cos {}^{ - 1} ( \frac{7}{5 \sqrt{26} } ) [/tex]
[tex] \alpha = 105.94[/tex]
in degrees,
[tex] \alpha = 1.849[/tex]
in radians
Answer:
115.6° (1 d.p.)
Step-by-step explanation:
To find the angle between two vectors:
Create a triangle with the vectors as two sides and the included angle θ between them.Find the magnitude of each vector (the length of each side of the triangle).Use the cosine rule to find the angle θ.**Please see attached for the triangle diagram**
Given vectors:
[tex]\textbf{u}=-4\textbf{i}-3\textbf{j}[/tex]
[tex]\textbf{v}=-\textbf{i}+5\textbf{j}[/tex]
Use Pythagoras Theorem to find the magnitude of each vector:
[tex]\implies |\textbf{u}|=\sqrt{(-4)^2+(-3)^2}=5[/tex]
[tex]\implies |\textbf{v}|=\sqrt{(-1)^2+5^2}=\sqrt{26}[/tex]
[tex]\overrightarrow{\text{UV}}=\textbf{v}-\textbf{u}=(-\textbf{i}+5\textbf{j})-(-4\textbf{i}-3\textbf{j})=3\textbf{i}+8\textbf{j}[/tex]
[tex]|\overrightarrow{\text{UV}}|=\sqrt{3^2+8^2}=\sqrt{73}[/tex]
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C = anglea and b = sides adjacent the anglec = side opposite the angleFind angle θ using the cosine rule:
[tex]\implies \cos(\theta)=\dfrac{|\textbf{u}|^2+|\textbf{v}|^2-|\overrightarrow{\text{UV}}|^2}{2|\textbf{u}||\textbf{v}|}[/tex]
[tex]\implies \cos(\theta)=\dfrac{5^2+\left(\sqrt{26}\right)^2-\left(\sqrt{73}\right)^2}{2(5)\left(\sqrt{26}\right)}[/tex]
[tex]\implies \cos(\theta)=\dfrac{-22}{10\sqrt{26}}[/tex]
[tex]\implies \theta=\cos^{-1}\left(\dfrac{-22}{10\sqrt{26}}\right)[/tex]
[tex]\implies \theta=115.5599652...^{\circ}[/tex]
Therefore, the angle between the vectors is 115.6° (1 d.p.).
Determine the point where the lines x=4t+1,y=t-9,z=2t+1 and x=5s+1, y= -s, z= 5s -9 intersect.
(Write your answer in the form of a point, (*,*,*). Enter DNE if the lines do not intersect.)
Answers
By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.
How to find the point of intersection between two lines in space
From statement we have two lines in space, whose vector forms are described below:
(x, y, z) = (1, - 9, 1) + t · (4, 1, 2) (1)
(x, y, z) = (1, 0, - 9) + s · (5, - 1, 5) (2)
The point of intersection satisfies the following condition:
(1, - 9, 1) + t · (4, 1, 2) = (1, 0, - 9) + s · (5, - 1, 5)
(1, - 9, 1) - (1, 0, - 9) = s · (5, - 1, 5) + t · (- 4, - 1, - 2)
s · (5, - 1, 5) + t · (- 4, - 1, - 2) = (0, - 9, - 8)
There is a point of intersection if the resulting system of linear equations has at least a solution:
5 · s - 4 · t = 0 (2)
- s - t = - 9 (3)
5 · s - 2 · t = - 8 (4)
By (2):
s = 4 · t/5
(2) in (3):
- 4 · t/5 - t = - 9
- 9 · t/5 = - 9
t/5 = 1
t = 5
(2) in (4):
5 · (4 · t/5) - 2 · t = - 8
4 · t - 2 · t = - 8
2 · t = - 8
t = - 4
By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.
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Any ideas for this graph
Answers
(X+1)(X+3) = 0
X intercepts are at x=1 and x=3
Y intercept is at y=3
It’s neither odd one even function.
Which of the following terms completes the sentence below?
A sign chart helps you record data about a function's values around its
and
asymptotes.
Answers
The terms that completes the sentence are zeros; vertical. Option A
Function of a sign chart
The functions of a sign chart include;
It helps in the record of information about the functions values around its zeros and vertical asymptotesA sign chart indicates the sign of the result any mathematical operation between unknowns.From the mentioned functions, we can se that the terms that completes the sentence are zeros and vertical asymptotes.
Thus, the terms that completes the sentence are zeros; vertical. Option A
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he graphs of y = 3x and y = 3x are shown below.
In general, how does the growth of y = 3x compare to the growth of y = 3x?
The function y = 3x is growing slower than y = 3x.
The function y = 3x is growing faster than y = 3x.
The functions y = 3x and y = 3x are growing at the same rate.
The function y = 3x is growing slower than y = 3x.
Answers
The function which compares the growth of both functions is; The function y = 3x is growing slower than y = 3^x.
Which answer choice correctly compares the growth of the graphs?The graphs in the task content are given as y=3x which is a linear graph, and y=3^x which is the exponential graph.
Hence, it follows that although both graphs are growing, the graph of function y = 3x is growing slower than y = 3^x.
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Which parent function is represented by the graph?
Answers
Answer:
Absolute value parent function
Explanation:
What is an Absolute value function?
It is a function in Algebra in where the variable is inside the absolute value bars (| |)
f(x)=|x|
y=x on the right side and y=-x on the left side of the graph
Hope it helps!
A rental car company charges $20 per day to rent a car and $0.10 for every mile driven. Addison wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $80 to spend.
Answers
Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
This caseA rental car company charges $20 per day to rent a car and $0.10 for every mile driven.
Addison wants to rent a car, knowing that:
She plans to drive 100 miles.She has at most $80 to spend.On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.
Then, the inequality that can be used to determine x is:
20x + 0.1×100≤ 80
So:
20x + 10≤ 80
In summary, the inequality that can be used to determine x is 20x + 10≤ 80
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Question 7 (1 point) The two tables below show the amount of tip, y, included on a bill charging x dollars. A 2-column table with 3 rows titled Restaurant A. Column 1 is labeled x with entries 10, 20, 30. Column 2 is labeled y with entries 1, 2, 3. A 2-column table with 3 rows titled Restaurant B. Column 1 is labeled x with entries 25, 50, 75. Column 2 is labeled y with entries 5, 10, 15. Which compares the slopes of the lines created by the tables?
Answers
The slope of restaurant B is twice that of restaurant A
How to compare the slopes?The tables of values are given as
X(Bill) Y(Tip) X(Bill) Y(Tip)
Rest A 10 1 Rest B 25 5
Rest A 20 2 Rest B 50 10
Rest A 30 3 Rest B 75 15
The slopes are calculated using
Slope = (y2 - y1)/(x2 - x1)
Using the table of values, we have:
Rest A = (2 - 1)/(20 - 10)
Rest A = 0.1
Rest B = (10 - 5)/(50 - 25)
Rest B = 0.2
By comparing the slopes, we have:
Rest B = 2 * Rest A
This implies that the slope of restaurant B is twice that of restaurant A
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An individual is planning a trip to a baseball game for 15 people. Of the people planning to go to the baseball game, 10 can go on Saturday and 12 can go on Sunday, some of them can go on both days. How many people can only go to the game on Sunday?
Answers
The number of people who can go to the game only on Sunday by applying the concept of set theory is equal to 5.
Total number of people for a trip to a baseball game = 15
Number of people planning to go on Saturday = 10
Number of people planning to go Sunday = 12
Let x be the number of people who can go on both Saturday and Sunday.
Then, the number of people who can go only on Saturday is 10 - x.
And the number of people who can go only on Sunday is 12 - x.
Total of 15 people are going to the baseball game.
Using set theory we have,
Number of people going on Saturday only + number of people going on Sunday only + number of people going on both = 15
Substitute the value we have,
⇒(10 - x) + (12 - x) + x = 15
Simplifying the above equation, we get,
⇒22 - x = 15
⇒ x = 7
The number of people who can only go to the game on Sunday is
= 12 - x
= 12 - 7
= 5
Therefore, using set theory number of people can only go to the game on Sunday is equal to 5 .
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a cylinder and a cone have the same radius and height. The volume of the cylinder is 534ft3 . what volume of the cone?
Answers
Answer: 178 ft^3
Step-by-step explanation:
A cylinder has the formula V=pi radius ^2 height
A cone has the formula V= 1/3 pi radius ^2 height
So 1/3 of the volume of the cylinder is the volume of a cone
1/3 of 534 = 178 ft^3
A blimp is flying at a speed of 40mph and going in a direction of 80 degrees. After 3 hours of flying it turns and travels 1 hour in a direction of 350 degrees. How far is the blimp from its starting location and in what direction?
I need a triangle drawing too please.
Answers
Bearing is a topic that can be used to locate the position of an object at a given time. Therefore, the blimp is 80 m far away from its starting point. And in the North-East direction.
The speed of an object relates the distance it covers to the time taken to cover the said distance.
i.e speed = [tex]\frac{distance}{time taken}[/tex]
⇒ distance = speed x time taken
In the given question, the initial distance covered can be determined as;
distance = 40 mph x 3 h
= 120 m
The final distance covered can be determined as;
distance = 40 mph x 1 h
= 40 m
Let the distance from its starting point to its final location be represented by x.
Thus applying the Cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C
[tex]x^{2}[/tex] = [tex]120^{2}[/tex] + [tex]40^{2}[/tex] - 2(120 x 40) Cos 90
= 14400 + 1600 - 9600
[tex]x^{2}[/tex] = 16000 - 9600
= 6400
x = [tex]\sqrt{6400}[/tex]
= 80
x = 80 m
Therefore, the distance of the blimp from its starting point to its final destination is 80 m.
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If x^y = z is there any way to find y if you know x and z?
Answers
We make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
How to solve for y?The expression is given as:
x^y = z
The above expression is an exponential expression.
Start by taking the logarithm of both sides
y log(x) = log(z)
Divide both sides by log(x)
[tex]y = \log_x(z)[/tex]
Hence, we make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
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giving brainliest !!!!!!!!!!!
Answers
The parabola vertex is (1,5), the focus of the parabola is (1,6), and the directrix y = 4.
What is the graph of a parabolic equation?The graph of a parabolic equation is a U-shape curve graph that is established from a quadratic equation.
From the given information:
[tex]\mathbf{y=\dfrac{1}{4}(x-1)^2+5}[/tex]
The vertex of an up-down facing parabolic equation takes the form:
y = ax² + bx + c is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]
Rewriting the given equation:
[tex]\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}[/tex]
[tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]
[tex]\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}[/tex]
[tex]\mathbf{x_v =1}[/tex]
Replacing the value of x into the equation, y becomes:
[tex]\mathbf{y_v = 5}[/tex]
Thus, the parabola vertex is (1,5)
From the vertex, the focus of the parabola is (1,6), and the directrix y = 4.
The graphical representation of the parabola is seen in the image attached below.
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Which histogram represents the data? 1,2,12,14,15,16,18
Answers
Option b) is correct
In statistics, a histogram is a graphical representation of the distribution of data. A histogram is represented by a set of rectangles, adjacent to each other, where each column represents a certain type of data. Statistics is a stream of mathematics that is used in various fields. When figures are repeated in statistical data, this repetition is known as frequency and can be written in the form of a table, called a frequency distribution. Frequency distributions can be displayed graphically using different types of graphs and one of them is a histogram.
A histogram chart is used under certain conditions. They are:
Data should be numeric.
A histogram is used to check the shape of the data distribution.
It is used to check if the process changes from one period to another.
It is used to determine whether the output differs when it involves two or more processes.
It is used to analyze whether the given process meets the customer's requirements.
The data 1,2,12,14,15,16,18 is given
We need to find the histogram which best fits to the given data
Total number that falls between 0-9 is 2
Total Number that falls between 10-19 is 5
Total Number that falls between 20-29 is 1
Total Number that falls between 30-39 is 5
Total Number that falls between 40-49 is 3
Total Number that falls between 50-59 is 1
Hence the histogram is obtained
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Follow the steps to find the
area of the shaded region.
Now use the formula below
to find the area of the
triangle.
Triangle Area = bh
h = 6.2172 cm
Triangle Area = [?] cm²
Round to four decimal places.
129
8 cm
Answers
The area of the triangle will be 14.9835cm².
How fo you find the area of a triangle?Your information is incomplete and the complete question wasn't found. An overview will be given.
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.
Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it.
In this case, let the assumed base be 4.82cm and the height is given as 6.2172cm.
The area will be:
= 1/2 × 4.82 × 6.2172
= 14.9835cm²
In conclusion, the area is 14.9835cm².
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Tom has 7 hamsters. If each hamster weighs 11 pounds, how much weight is there in total?
Answers
Answer:
7
Step-by-step explanation:
7x11=77
Which point lies on the circle represented by the equation x² + (y-12)² = 25²?
A. (20.-3)
B. (-7,24)
c. (0.13)
D. (-25,-13)
Answers
Answer: B
Step-by-step explanation: Trust me bro
PLS HELP OR I WILL FAIL I BEG U HELP
Answers
Answer:
The first one, you cannot factor because the two values do not share any common factors. Hence, the answer would just be:
a. 51x-25
The other one, we can factorise to:
b. 3x(4-x)
Step-by-step explanation:
For the second option:
Common factor between 12x and 3x^2 is 3x.
Take this out to the front, we are left with:
3x(4-x)
A website I recommend you use (math calculator with some instructions) is Symbolab.
https://www.symbolab.com/solver/factor-calculator/factor%2012x-3x%5E%7B2%7D?or=input
40.Find the difference
41&42. Find the product
Answers
Answer:
40. 398nine
41: 432six
42: 14714eight
Step-by-step explanation:
765-367=398
The 'nine' is probably confusing you
3x144=432
The 'six' is there to confuse you.
2x7357=14714
The 'eight' is again here to confuse you.
Ignore the 'six' and 'eight' and 'nine' they are making it harder for no reason
Josie and Pat are filing jointly as a married couple. Their combined taxable income is $142,800. This places them in the 22% tax bracket, owing $9,235 plus 22% of anything over $80,250. How much income tax do they owe?
Answers
The couple are owning income tax of $22,996.
What is tax?
Tax is the obligatory payment payable to the government on earnings.
In this case, the amount of tax to be paid is the sum of $9,235 plus 22% of the excess of the combined taxable income of the couple over $80,250.
Excess over $80,250=$142,800-$80,250
Excess over $80,250=$62,550
Initial tax amount=$9,235
extra tax amount=$62,550*22%
extra tax= 13,761
total tax amount=initial tax amount+ extra tax
total tax amount=$9,235+$13,761
total tax amount=$22,996
In essence, the couple would pay an initial tax of $9,235 plus an extra tax of $13,761 which gives a total tax liability of $22,996
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Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share. Thereafter, dividends are expected to growth at a constant rate of 6% per year. The discount rate for TYK is 10%. How much would you pay for one share in Company TYK?
Answers
14.11 is the price of one share in the company TYK.
How much would you pay for one share in Company TYK?Given:
Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share.Dividends are expected to grow at a constant rate of 6% per year.The discount rate for TYK is 10%.Find:
How much would you pay for one share in Company TYK?Solution:
The dividend is the amount paid to the shareholders for their investment in the company.
Dividend at end of 7th year = $1 per share (given)
dividend expected growth rate = 6% (given)
the dividend will be paid from the end of seven years.
So find the price of the share at the end of the 6th year.
price at the end of the 6th year
= Dividend at the 7th year/discount rate growth rate
= 1/(10%-6%) = 1/4% = 25
price of the share at the end of the 6th year is $25
discount price 10% (given)
current price share = 25/(1+10%)^6
= 25/(1.1)^6
= 25/1.77
= 14.11
The current price of the share is $ 14.11
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Q, Fixed a system of coordinates in the plane, conficer the curve C having equation y = (x-2)^2. The line x + y - 2 = 0 intersects C in:
(A)1 poin
(B) no point
(C) 2 points
(D) infinitely many points
3 points
Answers
Answer:
C
Step-by-step explanation:
y = (x - 2)² = x² - 4x + 4 → (1)
x + y - 2 = 0 → (2)
substitute y = x² - 4x + 4 into (2)
x + x² - 4x + 4 - 2 = 0
x² - 3x + 2 = 0
(x - 1)(x - 2) = 0
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
substitute these values into (2) and solve for y
x = 1 : 1 + y - 2 = 0 ⇒ y - 1 = 0 ⇒ y = 1 ⇒ (1, 1 )
x = 2 : 2 + y - 2 = 0 ⇒ y + 0 = 0 ⇒ y = 0 ⇒ (2, 0 )
the line intersects curve C at 2 points (1, 1 ) and (2, 0 )
????????????????????????????????????????????
Please help
Answers
Answer: (-2,2)
Step-by-step explanation:
The solution to a system of equations represented graphically is the point where the graphs intersect.
A meteorologist found that the rainfall in Vindale during the first half of the month was 1/2 of an inch. At the end of the month, she found that the total rainfall for the month was 2/3 of an inch. How much did it rain in the second half of the month?
Answers
The quantity of rainfall that fell in the second half of the month is; ¹/₆ of an inch.
How to solve fraction word problems?We are given;
Rainfall during first half of the month = 1/2 inch
Total rainfall for the month = 2/3 inch
Now, to find the rainfall for the second half of the month, we just subtract the one for the first half from the one for the month to get;
Rainfall in second half of the month = ²/₃ - ¹/₂ = ¹/₆ inches
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Select all of the following true statements if R = real numbers, N = natural numbers, and S = {10, 11, 12,...}.
A. -15∈N
B. N⊂R
C. S⊂N
D. ∅⊂N
E. N∈S
F. {10.11.12,...}⊆S
Answers
The true statements are:
B. N⊂R
C. S⊂N
D. ∅⊂N
F. {10.11.12,...}⊆S
Subsets and SetsNote that:
All real numbers are numbers that can be found on the real number lineNatural numbers are positive whole numbersAll natural numbers are subsets of real numbersThe null set (∅) is a subset of every setA set is a proper subset of itselfFollowing the points highlighted above, the true statements in the given options re:
B. N⊂R
C. S⊂N
D. ∅⊂N
F. {10.11.12,...}⊆S
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Zaidah plans a raised flower bed 2 ft high by 15 ft wide by 24 ft long. The mulch, soll, and peat mixture used to fill the raised bed costs $12.75 per cubic yard. What is the total cost (in dollars) of the
Ingredients used to fill the raised garden?
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's get started ~
[tex]\qquad \sf \dashrightarrow \: volume = length \sdot width \sdot height[/tex]
[tex]\qquad \sf \dashrightarrow \: v = (24) \sdot(15) \sdot(2)[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 720 \: \: ft {}^{3} [/tex]
now, we know :
[tex]\qquad \sf \dashrightarrow \: 1 \: \: yard {}^{3} = 27 \: \: ft {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: ft {}^{3} = \cfrac{1}{27} \: \: yard {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 720 \: \: ft {}^{3} = \cfrac{1}{27} \times 720 \: \: yard {}^{3} [/tex]
[tex]\qquad \sf \approx\: 26.67 \: \: yard {}^{3} [/tex]
now, total cost of ingredients used is :
[tex]\qquad \sf \dashrightarrow \: 26.67 \times 12.75[/tex]
[tex]\qquad \sf \dashrightarrow \: 340.04[/tex]
so, total cost is $ 340.04
articipation Activity #6
This is similar to Try It #11 in the OpenStax text.
A satellite is rotating around Earth at 0.2 radians per hour at an altitude of 252 km above Earth. If the radius of Earth is 6,378 kilometers, find the linear speed of the satellite in kilometers per hour.
Enter the exact answer.
The linear speed of the satellite is
Number
kilometers per hour.
Answers
The linear speed based on the information is 1326 km/h.
How to calculate the speed?The radius will be:
= 6378 + 252
= 6630 km
The angular speed is 0.2. The linear speed will be:
= 6630 × 0.2
= 1326 km/h.
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What is the answer to this system of equations? 2x - 3y= 21 and -6x + 2y = 7.
Answers
answer:
x = - 9/2
y = -10
Step-by-step explanation:
make both equations look like y =
2x-3y=21 -> -3y= -2x+21 -> y = (-2x+21)/-3 -> y = 2/3x - 7
-6x + 2y = 7 -> 2y = 6x + 7 -> y = 3x + 7/2
now make the equations equal to each other (since they both equal y)
get x
2/3x - 7 = 3x + 7/2
-7 -7/2 = 3x - 2/3x
-14/2 -7/2 = 9/3x - 2/3x
-21/2 = 7/3x
(3/7) -21/2 = x
x = (3/7) -21/2
x = - 63/14
x = - 9/2
put it back in an equation to get y
y = 3x + 7/2
y = 3(-9/2) + 7/2
y = -27/2 + 7/2
y = -20/2
y = - 10
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questions 5 and 6 please!
formula: y = ax + q
Answers
Answer:
5) y = 1x + 2
6) y = -0.5x + 6
Explanation:
5)
Given points are (-3, -1), (2, 4)
[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here, find slope:
[tex]\rightarrow \sf slope \ (a) = \dfrac{4-(-1)}{2-(-3)} = \dfrac{5}{5} = 1[/tex]
Find Equation:
y = ax + q
Here found that a = 1, take (x, y) = (-3, -1)
[tex]\sf -1 = 1(-3) + q[/tex]
[tex]\sf q - 3 = -1[/tex]
[tex]\sf q = -1 + 3[/tex]
[tex]\sf q = 2[/tex]
So, in total equation:
y = 1x + 2
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6)
Given points are (-2, 7), (2, 5)
[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here, find slope:
[tex]\rightarrow \sf slope \ (a) = \dfrac{5-7}{2-(-2)} = -0.5[/tex]
Find Equation:
y = ax + q
Here found that a = -0.5, (x, y) = (-2, 7)
[tex]\sf 7 = -0.5(-2) + q[/tex]
[tex]\sf 7 = 1 + q[/tex]
[tex]\sf q = 7-1[/tex]
[tex]\sf q = 6[/tex]
So, in total equation:
y = -0.5x + 6
Answer:
Since √3√3 is equal to 1 , you simply rearranged the way it was written. The value of the simplified fraction stays the same